Design and Simulation of a Passive Vertical ...

Journal of Mechanics Engineering and Automation Volume 1, Number 6, November 2011 (Serial Number 6)

David Publishing

David Publishing Company www.davidpublishing.org

Publication Information: Journal of Mechanics Engineering and Automation is published monthly in hard copy (ISSN 2159-5275) and online (ISSN 2159-5283) by David Publishing Company located at 1840 Industrial Drive, Suite 160, Libertyville, Illinois 60048, USA. Aims and Scope: Journal of Mechanics Engineering and Automation, a monthly professional academic journal, particularly emphasizes practical application of up-to-date technology in realm of Mechanics, Automation and other relevant fields. And articles interpreting successful policies, programs or cases are also welcome. Editorial Board Members: Konstantin Samsonovich Ivanov (Kazakhstan) Isak Karabegovic (Bosnia and Herzegovina) Curtu Ioan (Romania) Adel Abdel-Rahman Megahed (Egypt) Zhumadil Baigunchekov (Kazakhstan) Manuscripts and correspondence are invited for publication. You can submit your papers via web submission, or E-mail to [email protected]. Submission guidelines and web submission system are available at http://www.davidpublishing.org. Editorial Office: 1840 Industrial Drive, Suite 160, Libertyville, Illinois 60048 Tel: 1-847-281-9862 Fax: 1-847-281-9855 E-mail: [email protected] Copyright©2011 by David Publishing Company and individual contributors. All rights reserved. David Publishing Company holds the exclusive copyright of all the contents of this journal. In accordance with the international convention, no part of this journal may be reproduced or transmitted by any media or publishing organs (including various websites) without the written permission of the copyright holder. Otherwise, any conduct would be considered as the violation of the copyright. The contents of this journal are available for any citation. However, all the citations should be clearly indicated with the title of this journal, serial number and the name of the author. Abstracted / Indexed in: Database of EBSCO, Massachusetts, USA Chinese Database of CEPS, Airiti Inc. & OCLC CSA Technology Research Database Ulrich’s Periodicals Directory Summon Serials Solutions Subscription Information: Price (per year): Print $450; Online $320; Print and Online $600 David Publishing Company 1840 Industrial Drive, Suite 160, Libertyville, Illinois 60048 Tel: 1-847-281-9862. Fax: 1-847-281-9855 E-mail: [email protected]

D

DAVID PUBLISHING

David Publishing Company www.davidpublishing.org

Journal of Mechanics Engineering and Automation Volume 1, Number 6, November 2011 (Serial Number 6)

Contents Techniques and Methods 413

Characterization of Driving Style and the Influence of Distraction Based on Non-intrusive Driving Parameters Felipe Jiménez, Juan José Sánchez and Óscar Gómez

420

Design and Simulation of a Passive Vertical Suspension System for Spray Boom Structure Roslan Abd Rahman, Mona Tahmasebi and Mohammad Gohari

425

Fuzzy Logic Based Approach in an Enterprise Resource Planning System for Hydraulic Cylinders Assembly Snejana Yordanova, Lubomir Dimitrov, Mila Klochkova and Hristo Bankov

436

Solution of Inverse Problem on Distributed Generation Using Complex-Valued Network Inversion Takehiko Ogawa and Kyosuke Nakamura

Investigation and Analysis 445

Analysis of Potential Failure Modes in an Assembly Line by Fuzzy Expert Systems Mehdi Piltan, Reza Ghodsi, Foad Quarashi and Mehrdad Azizian

450

Calculus of the Railway Vertical Stiffness Depending on the Base Plate Stiffness and the Ballast for High Speed Railways Ramon Miralbes and Luis Castejon

455

Determining of Optimal Dimensions of Compliant Spring Guiding Systems Nenad T. Pavlović, Nenad D. Pavlović and Miloš Milošević

464

Metamodeling Transfer Capability of Manitoba-Ontario Electrical Interconnections Songqing Shan, Wenjie Zhang, Myrna Cavers and G. Gary Wang

473

Stress Analysis of the Sarafix External Fixator Design Elmedin Mešić, Adil Muminović, Nedžad Repčić and Mirsad Čolić

481

Structural Synthesis, Dynamic Modeling and Analysis of a 3-DOF Asymmetric Parallel Mechanism Rynaldo Zanotele Hemerly de Almeida and Tarcisio Antonio Hess-Coelho

491

The Investigation of the Effect of Heaving and Pitching on Wave-Induced Vertical Hull Vibration of a Container Ship in Regular Waves Abdul Hamid

D

Journal of Mechanics Engineering and Automation 1 (2011) 413-419

DAVID

PUBLISHING

Characterization of Driving Style and the Influence of Distraction Based on Non-intrusive Driving Parameters Felipe Jiménez, Juan José Sánchez and Óscar Gómez University Institute for Automobile Research, Technical University of Madrid, Madrid 28031, Spain Received: November 04, 2011 / Accepted: November 18, 2011 / Published: November 25, 2011. Abstract: It is difficult to model human behavior because of the variability in driving styles and driving skills. However, for some driver assistance systems, it is necessary to have knowledge of that behavior to discriminate potentially hazardous situations, such as distraction, fatigue or drowsiness. Many of the systems that look for driver distraction or drowsiness are based on intrusive means (analysis of the electroencephalogram—EEG) or highly sensitive to operating conditions and expensive equipment (eye movements analysis through artificial vision). A solution that seeks to avoid the above drawbacks is the use of driving parameters This article presents the conclusions obtained after a set of driving simulator tests with professional drivers with two main objectives using driving variables such as speed profile, steering wheel angle, transversal position on the lane, safety distance, etc., that are available in a non-intrusive way: (1) To analyze the differences between the driving patterns of individual drivers; and (2) To analyze the effect of distraction and drowsiness on these parameters. Different scenarios have been designed, including sequences with distractions and situations that cause fatigue. The analysis of the results is carried out in time and frequency domains in order to identify situations of loss of attention and to study whether the evolution of the analyzed variables along the time could be considered independent of the driver. Key words: ADAS (advanced driver assistance systems), driver behavior, distraction, driving simulator, professional driver.

1. Introduction Characterize driving styles in professional drivers is a useful tool with which to evaluate several factors that affect driving, such as the effect of new advanced driver assistance systems (ADAS), fatigue and sleepiness, or even to evaluate efficiency of some or other driving styles. This characterization may be estimated by different parameters that give us the sensors installed in vehicles nowadays, such as steering wheel angle, speed, acceleration and braking, or more advanced devices such as radar to detect safety distances between vehicles or on-board cameras with recognition and positioning in lanes However, the characterization of driving styles depends on human behavior, and therefore, on subjective values that can Corresponding author: Felipe Jiménez, Ph.D., research fields: automotive industry, vehicle safety, mechanical design, driver assistance systems and intelligent transport systems. E-mail: [email protected].

vary greatly influenced by the moods or physical state of driver. Human behavior is determined by intentions, which, in turn, are conditioned by attitudes, subjective regulations and perceived control, as well as elements of the immediate surroundings (the road or other users) [1]. It is difficult to model human behavior because of the variability in driving styles and driving skills. Driving style is influenced by motives, attitudes, personality traits and lifestyle and these styles can be recognized by analyzing different driving variables. For example, drivers can be classified based on acceleration, braking and cornering behaviors, because there are clear differences between aggressive or relaxed driving patterns [2-3]. There is a theory that states that drivers are motivated to higher risk behavior to achieve certain benefits but, with experience, their task at the wheel becomes an “automatic” activity in

414

Characterization of Driving Style and the Influence of Distraction Based on Non-intrusive Driving Parameters

which risk control is based on maintaining certain safety margins. It is reasonable to suppose that drivers tend to avoid risky situations if they perceive them, but that the ability to perceive risk can be enhanced [4]. However, at times, poor risk perception can be caused by the road geometry itself. Furthermore, distractions make that drivers do not pay attention to every aspect he should during driving, so crucial information could not be perceived or it could be incorrectly perceived and analyzed. Many of the systems that look for driver distraction or drowsiness are based on intrusive means (analysis of the electroencephalogram―EEG) or highly sensitive to operating conditions and expensive equipment (eye movements analysis through artificial vision). A solution that seeks to avoid the above drawbacks is the use of driving parameters, such as the steering wheel angle, actions on the pedals, safe distance keeping, transverse position in the lane, etc. These variables can be obtained by non-intrusive sensors on board. In particular, some of them are included in the data buses of today’s vehicles, while others are employed in some active safety systems that are being introduced on the market. This article presents the conclusions obtained after a set of driving simulator tests with professional drivers with two main objectives using previous variables that are available in a non-intrusive way:  To analyze the differences between the driving patterns of individual drivers;  To analyze the effect of distraction and drowsiness on these parameters. To this end, different scenarios (urban and rural environments) have been designed, including sequences with distractions and situations that cause fatigue. The analysis of the results was carried out in time and frequency domains in order to identify situations of loss of attention and to study whether the evolution of the analyzed variables along the time could be considered independent of the driver. The paper is organized as follows: Section 2 presents the state of the art of the topic; section 3 introduces the

method; section 4 shows the main results that have been obtained in the experiments; section 5 presents the most relevant conclusions.

2. State of the Art Driver’s alertness can be determined by measures of variables such as steering wheel angular position over time, the vehicle’s position in the lane or maintained speed. It is often found references to the need to employ methods that are not intrusive for the driver, because otherwise they would not be accepted. This is the case noted, for example, in Ref. [5] identifying as measures of driver fatigue, the activity and facial gestures and eye. It also cites the work of other authors which shows that the variability in position on the lane and speed are increased by the accumulated driving time [6]. In the case of changes in the position of the steering wheel, drivers control the position of the vehicle with small and continuous adjustments of the steering wheel position. If the degree of attention and alertness of the driver is not degraded, acting on the wheel is made using precise movements, short and with small amplitude, however if the level of attention or alert is degraded by fatigue or sleepiness, action on the wheel is less precise, sharp and amplitude of the correction is larger. Within this framework, there are various studies, approaches, results and patents covering a broad state of the art on this issue. Patent [7] is an example of the typical design of systems using different vehicle parameters to monitor the alert status, it claims a system that characterizes the driver at the beginning and try to observe changes in the parameters monitored (included the steering wheel position) to determine when a degradation of alertness. In another patent, it is claimed the use of heart rate and the second derivative of the angular position of steering wheel, specifically it comments data processing of the angular position to determine a frequency distribution and therefore a frequency band within which would be normal alertness and also it specifies that the interesting


frequencies are high frequencies [8]. Other patents include systems that somehow measure the steering wheel position [9]. On the other hand, in Ref. [10] a neural network is used to determine the driver’s alertness and the steering wheel angular position is used as input to the neural network. Refs. [11-12] have been found correlations between the activity on the steering wheel evaluated on fixed time intervals and the state of the driver. These variations relate to the position and velocity of these movements. It is relevant the project AWAKE [13]. Part of its results is shown in Ref. [14]. The article shows the influence of fatigue in various physiological and driving parameters in a simulator study. In particular, as measures related to driving, it is selected the lateral position in the lane, the frequency of steering wheel movements and the number of times you set foot on the rail line. The outcome document of the project concludes that there is no fixed rule for the detection of fatigue (mainly by the variability of individuals) and there are precision and sampling limitations in the sensors, etc. There are studies that have determined a clear relationship between the difficulty of maintaining the trajectory and the deterioration in the level of alertness [15]. Thus, it has been observed, mainly in trials on simulator, that prolonged or at night driving associates an increased standard deviation in lane position and speed. This conclusion is corroborated in other studies that illustrate the increase in the mean and standard deviation of the movements on the steering wheel [16-18]. In Ref. [19], the following variables are defined as indicators of control of the vehicle: standard deviation of lateral position of the vehicle, the occurrence of sudden movements of the steering wheel and the minimum time to cross the lane line. There was an increase of sudden movements of the time trial as well as increases in the frequency of low times to step on the lane line. In addition to positioning the lane side,

415

some studies have attempted to analyze the correlation of fatigue with maintained safe distance to the vehicle ahead, and with the ability to react to situations of risk [15]. In conclusion, the variables related to driver behavior and vehicle control are mainly speed (mean and standard deviation as variations), steering wheel turn (position change, speed change), lateral position on the lane (range, time to pass the line, etc.) and safety distance to the vehicle ahead.

3. Method This study focuses on the analysis of patterns of conduct of professional drivers from driving simulator tests. Subsequently, we analyzed the effect that it has on the driving variables take a phone call which involves a high cognitive load for the driver, to study whether it is possible to discriminate a situation of obvious distraction from driving variables. The tests were carried out in the Centre for technical studies and research in Gipuzkoa (CEIT) commercial vehicles driving simulator (Fig. 1). The use of simulators is a preliminary step to assess, in a safe manner, if these new techniques are effective and can be used in a generalized manner. The simulator gives us the data of various drivers in the same road sections and with similar events during the tests, with which different patterns of behavior when driving can be evaluated. Thus, behaviors can be seen in the same driver, and the differences and similarities with other drivers in the same road. In this regard, it should be noted that using driving simulators affects the behavior of drivers at the wheel. However, the simulators have many advantages for this work because it is possible to control many parameters, the environment, there may be different drivers repetitive situations and simulate specific environments of interest for study, etc. Furthermore, although some differences with normal driving in a vehicle are to be expected, there are correlations between behavior in the simulator and in a real environment [14].

416


Henceforth, we denote by A1 and A2 the trials in which there is no distraction and A5 which contains the distraction of the phone call. 4.1 Analysis of Driving Patterns: Driver Behavior without Distractions

Fig. 1 Driving simulator.

In the simulator, there are various scenarios in urban and interurban environment. Specifically, the scenario used is one that includes stretches of highway, single carriageway road and urban area. During the scenario, the driver finds vehicles traveling at an abnormally low speed, platoons of cyclists, etc., and will make choices for overtaking, detention, deviations… So, drivers, after a period of adaptation to the simulator, will make the trip without being distracting, and with distraction of a phone call (phone calls effects have been studied in previous works such as Refs. [20-21]). Parameters are measured continuously. The simulator provides a large amount of data from different variables. In our study, we have focused on the variables of speed, safe distance, revolutions per minute, percentage of accelerator and brake retarder use and special variables as lateral position relative to the rail and wheel steering angle. These variables are representative to study the behavior of drivers and their driving style.

In the highway section (Fig. 2), the incident that occurs is the appearance of abnormally low speed vehicle. Some of the drivers overtake the slow vehicle and others not. Both groups are analyzed. In the single carriageway road section, the incident that occurs is the appearance of abnormally low speed vehicle. In the first sector of this section the driver cannot overtake for being a continuous line section. It also presents a small slope that involves more complications for the driver. In the second sector of this section it is possible to overtake, but some of the drivers decide not to overtake. Also the driver found a group of cyclists that should be overtaken (Fig. 3).

4. Results

Fig. 2 Highway stretch simulator view.

The study is the analysis of the variables acquired from several drivers in the same section of the route. In these particular stretches a specific event occurs the same for all drivers (even though the traffic is random in each test) and it is discussed the effect it has had on driving. There are two case studies: (1) highway and (2) conventional single carriageway road. We distinguish between driver that overtake and drivers that do not overtake. Behaviors were studied to determine patterns of each case, and then contrast the exercises with distractions to determine possible changes produced.

Fig. 3 Group of cyclists in conventional single carriageway road.

417


Tables 1-2 show the values to establish the pattern of behavior that we have of the drivers.

Lateral position 2.5

Table 1 Results on incident section of the highway (O.: overtake; No O.: no overtake). Mean O. Safety distance 108.64 Lateral position 1.82 Steering wheel angle -0.20 St. wheel rotation speed 0.38

No O. 36.03 1.73 -0.10 0.15

Variance O. No O. 50.85 14.69 0.63 0.18

Table 2 Results on incident section of the single carriageway road (O.: overtake; No O.: no overtake). Mean O. Safety distance 18.27 Lateral position 1.50 Steering wheel angle -3.42 St. wheel rotation speed 1.46

No O. 22.52 1.44 -0.81 1.38

Variance O. No O. 8.30 5.74 0.45 0.30

1.5 A1_highway A5_Highway 1

0.5

0 0

100

200

300

400

500

600

700

Distance driven (m)

Fig. 4 Distance from the centre point of the vehicle to the extreme right lane (highway scenario). Lateral position 3.5 3 Lateral position (m)

We establish the comparison between the behavior that has the driver in the same section of the route in an exercise without distraction (exercise A1) and distracting exercise (exercise A5). More specifically, the distraction is the reception of a telephone call. When studying the results in a qualitative way, it can be seen that certain driving variables are significantly affected, as can be seen in Fig. 4 (highway scenario) and Fig. 5 (single carriageway road scenario). In the first case, lateral position is drastically changed and the lane line is crossed by the vehicle. In the second case, the overtaking maneuver of the group of cyclists was made more inefficiently and with less safe distance away from cyclists when the driver is maintaining the conversation. Numerical results are shown in Tables 3-4. As can be seen, although average values do not change significantly, the variance of the variables changes and increases when the driver maintains the telephone conversation. This fact can be explained because the workload is increased so the driver does not pay all his attention to driving tasks so the variables control is not so accurate.

Lateral position (m)

2

4.2 Influence of Distractions on Driver Behavior

2.5 2

A1_Conventional A5_Conventional

1.5 1 0.5 0 0

100

200

300

400

500

600

Distance driven (m)

Fig. 5 Distance from the centre point of the vehicle to the extreme right lane (single carriageway road scenario). Table 3 Comparison of results on highway section with or without the telephone call.

Safety distance Lateral position Steering wheel angle St. wheel rotation speed

Mean A1 73.87 1.80 -0.39 -0.06

A5 75.39 1.33 -0.99 -0.29

Variance A1 A5 43.85 46.79 0.16 0.55

Table 4 Comparison of results on single carriageway road section with or without the telephone call.

Safety distance Lateral position Steering wheel angle St. wheel rotation speed

Mean A1 A5 17.16 17.73 1.46 1.50 30.19 29.54 -0.21 0.24

Variance A1 A5 29.32 30.43 0.47 0.51

4.3 Frequency Domain Analysis Besides analyzing the steering wheel movement in temporal domain, we have studied its frequency components. There are variations in the patterns of driving without overtaking, with overtake and with distraction. As it can be seen, there is a common pattern

418


in frequency components in the tests without overtake and in those with overtake, but there are significant differences between the two situations (Fig. 6). In addition, there are clear differences between the case of distraction and any of the above situations. These differences can be appreciated at high frequency components (Fig. 7).

5. Conclusions

Frequency components of the wheel rotation angle 10000 9000 8000 7000

SujI_A1 (no overtake)

6000

SujIV_A1 (no overtake)

5000

SujII_A1 (overtake)

4000

SujV_A1 (overtake)

3000 2000 1000 0 0

0.5

10000

attention on the driving task and produce worse

8000

system should detect the driver distraction situation

4000

automatically and reliably from measurements that can

2000

etc.). The work presented tries to overcome problems of intrusive systems for evaluating driver behavior in order to try to develop new driver assistance systems that were able to warn the driver in case distraction or drowsiness situations are detected. The solution is based on analyzing the driving variables and infer from them if a state of driver distraction is happening. The results show the great variability among drivers, which makes difficult this identification, worse if we observe different patterns, especially, in the frequency domain, between the cases of having distractions or no distractions. In any case, the more reasonable proposal is to use sensor fusion to obtain a higher degree of reliability in the results and avoid false positives or omit necessary advices. At this point, it is important to note that the identification of reliable thresholds for all drivers to detect distraction or fatigue is a task that has not been finalized and is a field of work for many researchers.

SujI_A1 (no distraction)

5000

SujI_A5 (distraction)

3000 1000 0

be done. To this end, over recent years have been

very sensitive to environmental conditions (lighting,

3

7000 6000

proposed systems, or are intrusive to the driver or are

2.5

9000

behavior at the wheel. However, an automatic alert

variables of driver or machine vision. However, most

2

Frequency components of the wheel rotation angle

in-vehicle devices, external to the vehicle, decreases

ones based on the measurement of physiological

1.5

Fig. 6 Frequency domain steering wheel signal comparison (overtake vs. no overtake).

It is reasonable to consider that attention to the

proposed different systems, the most sophisticated

1

0

0.5

1

1.5

2

2.5

3

Fig. 7 Frequency domain steering wheel signal comparison (without and with distraction).

Therefore is advocated the systems which combine various methods to evaluate driver fatigue in order to determine the best option to characterize potentially hazardous situations due to poor attention or reduced driver faculties [22]. That is, although there are studies that support the relative reliability of some of the measures, we cannot stand a single extreme reliability index, given the great variability of drivers and conditions [5], aspects that sometimes led to conflicting results in the trials.

Acknowledgments This project has been partially supported by Spanish Science and Innovation Ministry (CABINTEC project—PSE37010020072) and FEDER funding from the EU. We would also like to thank the drivers for their enthusiastic willingness to perform the tests with the necessary professionalism.

References [1] [2]

I. Ajzen, From Intentions to Actions: A Theory of Planned Behavior, Springer Verlag, Berlin, 1985. T. Bachmann, The importance of the integration of road, tire and vehicle technologies, in: World Road Congress,

Characterization of Driving Style and the Influence of Distraction Based on Non-intrusive Driving Parameters Montreal, 1995. K.-P. Kuhn, A. Heidinger, On-line driver type classification, International Journal of Vehicle Design 18 (6) (1997) 616-625. [4] H. Summala, Risk control is not risk adjustment: the zero-risk theory of driver behavior and its implications, Ergonomics 31 (4) (1988) 491-506. [5] A. Vincent, I. Noy, A. Laing, Behavioral adaptation to fatigue warning systems, Paper No. 98-S2-P-21, 1998. [6] J.B.J. Riemersma, A.F. Sanders, C. Wildervanck, A.W. Gaillard, Performance decrement during prolonged night driving, in: R.R. Mackie (Ed.), Vigilance Theory, Operational Performance and Physiological Correlates, Plenum Press, New York, 1977, pp. 41-58. [7] Method and apparatus for determining driver fitness in real time, Patent, available online at: http://www.patentstorm.us/patents/5465079.html. [8] Apparatus and method for improving the awareness of vehicle drivers, Patent, available online at: http://www.patentstorm.us/patents/5574641.html. [9] Drowsiness alarm system for a vehicle, Patent, available online at: http://www.freepatentsonline.com/4463347.html, Safety driving system, Patent, available online at: http://www.patentstorm.us/patents/5745031.html. [10] R. Sayed, A. Eskandarian, Unobtrusive drowsiness detection by neural network learning of driver steering, in: Proceedings of the Institution of Mechanical Engineers: Part D, Journal of Automobile Engineering 215 (9) (2001) 969-975. [11] M. Elling, P. Sherman, Evaluation of steering wheel measures for drowsy drivers, in: Proceedings of the 27th International Symposium on Automotive Technology and Automation, October 31-November 4, 1994. [12] J. Fukuda, E. Akutsu, K. Aoki, Estimation of driver’s drowsiness level using interval of steering adjustment for lane keeping, JSAE Rev. 16 (2) (1995) 197-199.

[3]

419

[13] Public Documents of AWAKE Project, available online at: http://www.awake-eu.org/pdf. [14] S. Otmani, T. Pebayle, J. Roge, A. Muzet, Effect of driving duration and partial sleep deprivation on subsequent alertness and performance of car drivers, Physiology and Behavior 84 (5) (2005) 715-724. [15] M.V.D. Hulst, T. Meijman, T. Rothengatter, Maintaining task set under fatigue: A study of time on task effect in simulated driving, Transportation Research: Part F, Traffic Psychology and Behaviour 4 (2001) 103-118. [16] P. Thiffault, J. Bergeron, Monotony of road environment and driver fatigue: A simulator study, Accident Analysis and Prevention 35 (2003) 381-391. [17] J. Skipper, W. Wierwille, Driver drowsiness detection using discriminant analysis, Human Factors 28 (5) (1986) 527-540. [18] D. Chaput, C. Petite, S. Planque, C. Tarriere, Un systeme embarque de detection de l’hypovigilance, in: M. Vallet (Ed.), Le maintien de la vigilance dans les transports, Actes des journees d’Etudes de 1’INRETS Bron (Paradigme), 1991, p. 105. [19] W.B. Verwey, D.M. Zaidel, Preventing drowsiness accidents by an alertness maintenance device, Accident Analysis and Prevention 31 (1999) 199-211. [20] T. Hamada, Experimental analysis of interactions between ‘where’ and ‘what’ aspects of information in listening and driving: A possible cognitive risk of using mobile phones during driving, Transportation Research: Part F, Traffic Psychology and Behaviour 11 (1) (2008) 75-82. [21] M.-P. Bruyas, C. Brusque, S. Debailleux, M. Duraz, I. Aillerie, Does making a conversation asynchronous reduce the negative impact of phone call on driving?, Transportation Research: Part F, Traffic Psychology and Behaviour 12 (1) (2009) 12-20. [22] G.P. Siegmund, D.J. King, D.K. Mumford, Correlation of heavy-truck driver fatigue with vehicle-based control measures, SAE Paper 952594, 1995.

D


DAVID

PUBLISHING

Design and Simulation of a Passive Vertical Suspension System for Spray Boom Structure Roslan Abd Rahman, Mona Tahmasebi and Mohammad Gohari Department of System Dynamics and Control, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, Skudai, Johor 81310, Malaysia

Received: October 05, 2011 / Accepted: October 18, 2011 / Published: November 25, 2011. Abstract: The most usual way of using chemical method to protect crop against weed, insects, and fungi is spraying the mixture of chemicals and water onto crop through the nozzles. Sprayers usually moved on the field by tractor, and tractor induced unwanted vibration to sprayer because of uneven soil or terrain. This oscillation leads to over-doses and under-doses of chemical sprayed on the field. For this reason, many commercial and some theoretical suspension were made to reduce undesirable vibration. Therefore, in this study a finite element based model was established to represent the dynamic behavior of spray boom structure with 8m width. The first tenth natural frequencies were obtained between 9.25 Hz to 1,182.5 Hz. Also, a passive vertical suspension was designed to remove unwanted vibration with 0.5 vibration transmissibility. Finally, the suspension system was simulated to be as certain of its efficiency. The results of simulation have good agreement to the proposed aim. Key words: Spray boom, natural frequency, passive suspension, finite element method.

1. Introduction Nowadays, the population of world is increasing, and agriculture productions are the main resource of nutrition. So, protection of crop against animals, weeds, pests, pathogens, diseases, and insects is necessary. There are many methods to protect crops, but the most popular methods which are applied by farmers are utilisation of chemicals. In this method, dissolved chemicals in water are spread by field sprayer. Use of sprayers in the field decrease the number of labour, and distribution is easy and uniform. Although sometimes under-dose is not absolutely effective, overdoses have environmental effects to human life. Two reasons for the over-doses and under-doses are defects in hydraulic system, and vertical and horizontal vibrations of the Mona Tahmasebi, Ph.D. student, research fields: vibration, control. Mohammad Gohari, Ph.D. student, research fields: vibration, control. Corresponding author: Roslan Abd Rahman, Ph.D., research fields: vibration, structural dynamics. E-mail: [email protected].

spraying system [1]. When the sprayers move on the uneven soil, spray boom and nozzles which are mounted on a horizontal structure, named spray boom, have vertical and horizontal motions. Therefore, one of the crucial factors for optimization of pesticide consumption in the field is the reduction of spray boom vibration by using springs and dampers [2]. The method to evaluate the efficiency of spray application is to do spray distribution test [3]. One of the important effects on the spray distribution is the nozzle motions mostly induced by soil unevenness. The common vibrations on the spray distribution pattern are due to jolting and yawing (two motions in the horizontal plane), and rolling (a motion in the vertical plane) [4]. Vertical vibration, rolling and yawing of spray boom are due to tractor vibration induced by soil unevenness. Mahalinga Iyer and Wills [5] were one of the earliest researchers who studied on the effects of tractor rolling on spray boom distribution pattern, and later many sprayer suspensions are made to reduce the undesired vibrations [6]. Some of

Design and Simulation of a Passive Vertical Suspension System for Spray Boom Structure

simulation models illustrated differences in spray distribution pattern between 20% and 600% for the horizontal vibration and between 0% and 1,000% for the vertical vibration [7]. From 1980s pendulum or twin link suspensions were used to explain dynamic behavior of spray booms until recently when Anthonis et al. introduced horizontal active suspension to neutralize effect of frame yawing and jolting movements on the boom [8]. In brief, spray distribution on the field is very sensitive which can be affected by vertical and horizontal vibration. Also, most of the sprayer suspensions commercially made by manufacturers and without the technical research. So, the main objective of this paper is to design a passive suspension for spray boom to mitigate unwanted vertical vibrations. For this purpose, passive systems are simple in comparison to the active systems, and it is suitable for field operation. The paper is organized as follows: Section 2 discusses the vibration analysis of spray boom structure; section 3 introduces the vertical suspension coefficients of spray boom; section 4 introduces simulation of suspension for evaluation; section 5 describes results and discussions; and section 6 gives conclusions.

2. Vibration Analysis of Spray Boom Structure The design of spray boom structure involves three steps. First step is finding the natural frequencies because it is necessary to avoid the occurrence of resonance in boom structure. The second step is finding the right spring and damper coefficients for the suspension system to ensure that the vibration transmission from chassis to the spray boom is low.

421

The third step is evaluating the performance of system by simulation. This simulation helps to ensure that the system can remove undesirable oscillations. These steps are described below. A physical model of boom structure was modeled in ABAQUS software as illustrate in Fig. 1. The dynamics response of the structure was considered in two dimensions. The 2D ELASTIC beam element was chosen. The material setting was entered as steel (E = 210 × 109 Pa, density = 7,800 kg/m3 and Poisson’s ratio = 0.3). In geometrical view, beam has hallowed rectangular profile with 0.0005 m2 cross-sectional areas and 0.118 × 106 m4 area moment of inertia. Next, whole of structure was meshed, and each link was meshed as ten elements to show better dynamic behavior. At key points number 1 and 8, the structure was fixed by two constraints. These two points are hitch connectors of the spray boom body to the tractor chassis. In addition, the nodes are constrained to vertical motion only in modal analysis. The first 10 natural frequencies were computed as listed in Table 1. The first natural frequency is very low compared to the next frequency. The first third mode shapes is shown in Fig. 2. The first natural frequency shows first bending mode about constrained points 1 and 8. The left and right frames move as one rigid frame. In the second natural frequency, the left and right frame have in-phase first bending mode with points 5 and 12 having minimum motion. The shape then showed out-of-phase motion in the second bending mode and in-phase motion in the forth natural frequency. At the 5th and 6th natural frequency, the motions show third bending mode out-of-phase and in-phase, respectively.

Fig. 1 Sprayer structure was modeled 2-D in ABAQUS software.

422


Table 1 First tenth natural frequencies of spray boom. Mode number 1 2 3 4 5 6 7 8 9 10

Frequency (Hz) 9.252 83.963 192.12 210.44 359.63 377.27 565.84 678.2 1,025.7 1,186.2

3. Vertical Suspension Coefficients of Spray Boom Because most of tractors do not have primary suspension, most vibrations are transmitted to the mounted implements. Tires have little damping and a few vibration can be removed. So, developing a suspension between tractor body and spray boom can remove unwanted vibrations, and it can reduce the vibration transmissibility below unity. The vibration transmissibility function for spring-damper system is represented by

 2  2  t  1  4    s   T 2    2     1    t    4 2   t        s     s 

    2         

0.5

( 1)

where

T  Vibration transmissibility   Damping ratio = C/Cc

(2)

C  Damping coefficient of dashpot ( N

) ms C c  The critical ratio of damping ( N ) , and ms Cc  2 M s t = Sprayer structure natural frequency with damping (rad s)

 s  Natural frequency of spray boom suspension without damping (rad s) In addition,

s 

K M

where

K : Spring coefficient ( N ) and m M : Mass of sprayer (kg )

Fig. 2 First sixth mode shapes of spray boom structure exposed to vertical vibration, respectively.


423

According to Eq. (1), it is known when the transmissibility is less than one, then

t  s is more than

1.41. So, by considering the lowest natural frequency of spray boom structure which was obtained previously as 9.25 Hz (  t  2f  58.117 rad / s ) and transmissibility as 0.5, the damping coefficient can be determined (mass of sprayer and spring constant are 400 kg and 450 kN/m, respectively. It can be shown that the natural frequency of spray boom ( s ) is 33.54 rad/s, damping ratio of 0.4, and damping coefficient as 10,732.8 Ns/m. Hence, the proposed suspension system must have a spring constant of 450 kN/m and damping coefficient of 10.73 kN/m.

Fig. 3 Model of spray boom suspension system in Working Model 2D.

4. Simulation of Suspension for Evaluation To be ensure of the efficiency of system, a field test or making simulation in virtual condition need to be conducted. In this case, the suspension was modeled in 2D Working Model software, and it was subjected to the harmonic excitation. Mass, spring and dampers were constrained to have just vertical motion. An eccentric cam was installed to produce harmonic excitation to the chassis like illustrate in Fig. 3.

5. Results and Discussion Fig. 4 shows the response acceleration of the sprayer mass and tractor body. The vibration transmissibility function was calculated by dividing sprayer acceleration to chassis acceleration in frequency domain as shown in Fig. 5. According to the vibration transmissibility which was obtained from simulation, and it is less than one, here in this simulation, it is near to 0.42. This ratio in low frequency is under 0.5, and the first peak will be made at high frequency near 115 Hz. It means that in low frequency the efficiency of spray boom suspension is at acceptable range. So, this suspension system can satisfy the purposed aim, and it can remove unwanted oscillations. The frequency range were obtained is between 9.25 Hz to 1,186.2 Hz for a spray boom structure with 8 m

Fig. 4 Acceleration of sprayer mass (top) and acceleration of tractor body (bottom).

width. Engelen et al. found out a range between 0.86 Hz to 9.26 Hz for a 24 m width spray boom by finite element method analysis [9]. It seems logical values because by increasing the length of boom, the natural frequency decreases as the mass is more dominant

424


vertical spray boom suspension is applicable in the field, but for more certainly it must evaluate in real condition in farmyard.

Acknowledgment The authors would like to express their gratitude to Universiti Teknologi Malaysia for supporting the research through the Research University Grant (GUP Tier 1 grant No. QJ130000/7124.00H66) and International Doctoral Fellowship (IDF).

References [1] Fig. 5 Vibration transmissibility of spray boom indicating transmissibility at 115 Hz.

compare to stiffness. In addition, Langenakens et al. [1] used experimental modal test for 24 meter width spray boom. Same results were obtained which is between 0.70 Hz to 9.71 Hz. So, the results obtained from FEM are correct, and the result of simulation shows that this suspension can reduce the vibration transmission from tractor to the sprayer.

6. Conclusions A one degree of freedom vertical suspension for sprayer boom with 8m width was optimized and evaluated. This system is able to reduce tractor chassis to spray boom vibration transmissibility lower 0.5. It means, optimized system can remove unwanted vibration and avoid reaching resonance situation in spray boom. This result showed that the aim was obtained by finite element method in modal analysis for spray boom and finding natural frequencies was right because mode shapes and natural frequencies were necessary for calculating suspension system coefficients. Simulation in Working Model software demonstrated and confirmed the results. So, this

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

J.J. Langenakens, L. Clijmans, H. Ramon, J.D. Baerdemaeker, The effects of vertical sprayer boom movements on the uniformity of spray distribution, Journal of Agricultural Engineering Research 74 (1999) 281-291. J. Anthonis, H. Ramon, Design of an active suspension to suppress the horizontal vibrations of a spray boom, Journal of Sound and Vibration 266 (2003) 573-583. H. Gohlich, Deposition and penetration of sprays, BCPC Monogram No. 28, Symposium on Application and Biology, 1985, pp. 172-182. J. Anthonis, J. Audenaert, H. Ramon, Design optimisation for the vertical suspension of a crop sprayer boom, Biosystems Engineering 90 (2) (2005) 153-160. B.M. Iyer, B.M.J. Wills, Factors determining the design of tractor-mounted sprayer booms-sprayer nozzle characteristics, J. Agric. Eng. Res. 23 (1978) 37-43. J.A. O’Sullivan, Verification of passive and active versions of a mathematical model of a pendulum spray boom suspension, J. Agric. Eng. Res. 40 (1988) 89-101. J.J. Langenakens, H. Ramon, J.D. Baerdemaeker, A model for measuring the effect of tire pressure and driving speed on the horizontal sprayer boom movements and spray patterns, Transactions of the ASAE 38 (1) (1995) 65-72. J. Anthonis, H. Ramon, J.D. Baerdemaeker, Implementation of an active horizontal suspension on a spray boom, Transactions of the ASAE 43 (2) (2000) 213-220. K. Engelen, H. Ramon, J. Anthonis, Load spectrum estimation from output-only measurements applied to a spray boom model, in: International Seminar on Modal Analysis (ISMA), Leuven, Belgium, 2006.

D


DAVID

PUBLISHING

Fuzzy Logic Based Approach in an Enterprise Resource Planning System for Hydraulic Cylinders Assembly Snejana Yordanova1, Lubomir Dimitrov2, Mila Klochkova2 and Hristo Bankov2, 3 1. Continuous Processes Control Department, Faculty of Automation, Technical University of Sofia, Sofia 1000, Bulgaria 2. Machine Elements Department, Faculty of Mechanical Engineering, Technical University of Sofia, Sofia 1000, Bulgaria 3. Hydraulic Elements and Systems PLC, Yambol 8600, Bulgaria Received: October 05, 2011 / Accepted: October 18, 2011 / Published: November 25, 2011. Abstract: Trends in modern industry show a tendency towards demassovization of production as a response to the customers’ specific needs for unique and personalized products. This provokes significant changes in the processes of manufacturing, assembly, and testing. The cost of such a type of production can be reduced by employing highly productive reconfigurable equipment with proper software to enable optimization. This paper presents a decision support extension for directing of hydraulic cylinders to assembly-testing lines using fuzzy logic in the Enterprise Resource Planning system of a small size production in a factory in Bulgaria. Different assembly-testing lines are flexibly assigned to the specific cylinder’s parameters by the developed fuzzy system on the basis of the overlapping of parameters in the hydraulic cylinders classification. The final decision on the line assigned in case of alternatives is made through accounting for the minimal cylinder delay time. The effectiveness of the approach is assessed by simulation. It leads to an increase of the efficiency of the assembly-testing flow lines, a reduction of the time needed for hydraulic cylinders assembling and testing and balanced loading of the modules. Key words: Enterprise resource planning, fuzzy decision, hydraulic cylinders assembly, simulations, real time operation.

1. Introduction and State of-the-Art The modern industrial production is characterized by  Demassovization, i.e., decrease of the number of the products produced in series. As a result most of modern industry production can be described as small series;  Reduction of the time needed for commodity production, which is a result of the severe competition on the market and of the need of very fast introduction of the new products;  Reduction of products prime cost: It is important Snejana Yordanova, professor, doctor, research fields: robust, fuzzy logic and neural networks based for control. Mila Klochkova, doctor, M.Sc. Eng., research fields: fuzzy logic, hydraulics, automation of assembly. Hristo Bankov, M.Eng., Ph.D. student, research fields: hydraulics, automation of assembly. Corresponding author: Lubomir Dimitrov, professor, doctor, research fields: design of machines, production automation. E-mail: [email protected].

to reduce the cost in such a way that small series products can compete the mass production. These features lead to problems that can be solved by the use of flexible production systems run by proper software, known in modern industry as Enterprise Resource Planning (ERP) system [1-2]. Such systems are very popular and intrinsic to every small series production plant. Similar systems for real time management of production are described in Refs. [3-5]. A computational model of a flexible manufacturing cell is developed in Ref. [4]. The parts selection for production and the job shop scheduling is organized on the variation of three variables: delay time, number of setups, and number of the tool switches. A group technology (GT) model was presented in Ref. [5]. It is applied to a shop floor area. A real time Manufacturing Resource Planning II system (MRP II) is used in the assembly area. Both works in Refs. [4-5] deal with real

426

Fuzzy Logic Based Approach in an Enterprise Resource Planning System for Hydraulic Cylinders Assembly

time scheduling, the parts flow is strictly constant and no changes are possible in real time production. Liverani and Ceruti [3] employ the GT approach for real time search of similar parts in order to make use of the ERP system advantages. For that purpose they suggest a special code for mechanical components standardization, part similarity and cost evaluation. The developed classification though interesting is difficult to implement because of its complexity. The design of an efficient assembly line is of considerable industrial importance. The work of Zacharia and Nearchou [6] is a good example for the application of fuzzy logic (FL) to assembly. The assembly line balancing problem (ALBP) is a decision problem that arises when an assembly line has to be (re)-configured and consists of optimal partitioning of the assembly work among the workstations in accordance with some objectives. The decision taken to solve ALBPs in modern flow-line production systems affects the final cost of the product manufactured, the product quality and the time-to-market response. The fuzzy job scheduling in Ref. [6] is based on a fuzzy multi-objective ALBP solution. The objectives are fuzzified by introducing fuzzy processing time to describe the real-world uncertain, vague and imprecise data. The line fuzzy cycle time, the fuzzy balance delay time and the fuzzy smoothness index for line workload are optimized using genetic algorithms. The FL approach is efficient in modelling of expert, vague, uncertain and imprecise knowledge and data [7-11]. It has proven to be perspective for improving the ERP systems by modelling tolerances in assembly processes, parameters of planning, market demand forecasting, selection of shift numbers or suppliers [12-13], etc. The aim of this work is to increase the efficiency of hydraulic cylinders assembly-testing process in the production of hydraulic cylinders in Bulgarian factory for “Hydraulic Elements and Systems” (HES) in the town of Yambol, by employing the fuzzy logic approach to decision making in balancing the

assembly-testing flow lines (ATFLs) workload. The main tasks can be defined as  Development of a classification for assigning of hydraulic cylinders to ATFLs accounting for the overlap of groups of parameters, which enables flexible sharing of the assembly lines facilities;  Development of a fuzzy decision support system to balance assembly-testing flow lines workload and to reduce lines idle time and cylinders delay time;  Development of a Simulink model for simulation investigations with real data of optimal assigning of cylinders to assembly-testing flow lines combining fuzzy decision with minimization of delay time;  Assessment of potential ERP improvements with including the fuzzy system. The results of the work are in process of implementation in the HES factory. The boundary conditions that reflect the peculiarities of the production in the factory are  Type of action: single-acting, double-acting;  Type of produced hydraulic cylinders: piston, plunger, telescopic, special;  Diameter: from 25 mm up to 320 mm;  Stroke length: up to 5,000 mm. The requirements to the assembly process are  Reduction of delay time for cylinders to be assembled and tested;  Increase of the ATFL loading coefficient;  Reduction of the time needed for ATFL reconfiguration. The rest of the paper is organized as follows: A classification of hydraulic cylinders for assembly-testing flow lines is developed in section 2; section 3 explains the design of a Sugeno Fuzzy Decision Support System; simulation investigations and system assessment are shown in section 4 and section 5; section 6 is conclusion.

2. Classification of Hydraulic Cylinders for Assembly-Testing Flow Lines The equipment needed for assembly and testing has


been unified on the basis of analysis of the production list of hydraulic cylinders produced in the HES factory. All hydraulic cylinders have been classified in assembly groups according to their specific parameters. The analyses are based on the “object orientated approach” [14-15]. The classification divides produced cylinders to assembly groups depending on their  Functional parameters: type of action (single or double acting) and type of cylinder (piston, plunger, telescopic, special);  Structural parameters: diameter and stroke length. The ATFLs are designed to assemble and test all cylinders in the corresponding group considering also the overlapping of assembly groups [16]. A classification structure with possible solutions for hydraulic cylinders assembly and testing, presented in Fig. 1, is developed on the basis of the observations on the produced hydraulic cylinders over the last year at the HES factory. The classification enables to reduce ATFL reconfiguration effort (time and costs needed) and to ensure flexibility by the increased ATFL

427

functionality—possibility via slight adjustment to assemble cylinders from adjacent assembly groups. The ATFLs operate in a stream regime and each one consists of different zones connected by a transport system. The main zones are the following:  Warehouse production zone—all parts needed for production of a certain cylinder are delivered here;  Washing zone—all hydraulic cylinders’ elements are washed before assembly in a specific solution;  Pre-assembly zone—it is equipped with stands, on which cylinder and gasket are assembled;  Assembly zone—the piston group is assembled with the cylinder group;  Testing zone—a quality control for assembled cylinders is carried out. The inner and outer leakage, deaeration and force parameters, given by customer’s order, are measured and controlled. The ATFL infrastructure is of extreme importance for the proper functioning of the whole system. It provides supply of oil with different pressure, water, electricity, air under pressure, etc. in a proper moment with desired quality and quantity.

Fig. 1 Hydraulic cylinders classification and proposed options for assembly and testing.

428


Hydraulic cylinders in each assembly group are subdivided in basic groups according to the similar technologies for assembly and testing and according to the similarly used equipment and tools [16]. In each basic group a representative hydraulic cylinder is selected and the complete technology for its assembly and testing is designed. The representative technology can by applied to each member in the basic group by some insignificant changes in equipment, tools, and infrastructure. This approach is a type of group technology [17-18], applied to the process of assembly and testing of hydraulic cylinders. Thus the introduced flexibility via the developed classification makes appropriate the application of the fuzzy logic approach to finding alternative solutions for balancing of the ATFLs workload.

3. Sugeno Fuzzy Decision Support System Considering the predetermined specific fixed and shared—to a certain extent—functionality of each ATFL from the classification in Fig. 1, a Sugeno fuzzy model is suggested as a decision support supplement to the existing ERP system. It is developed via Fuzzy Logic Toolbox of MATLAB [19]. The role of the model is to establish the degree of fitness of the ATFLs to process hydraulic cylinders, specified by Diameter (D), Stroke Length (L) and Type (T). The Sugeno model has 3 inputs: D, L, T, and 10 outputs: the assembly-testing flow lines—Line k, k = 110. The MAX and the MIN operators are employed for ‘OR’ and ‘AND’, respectively, and weighted average is selected as a defuzzification method. The membership functions (MFs) for the inputs “Diameter” and “Stroke length” are shown in Fig. 2. By D1-D6 are denoted the terms for the cylinder diameter, by L1-L6—the terms for the cylinder stroke length (or shortly length). The five terms for the type of cylinder Т1 for type 1—single-acting piston and single-acting plunger cylinders, T2 for type 2—single-acting telescopic, Т3 for type 3—double-acting piston, Т4 for type 4—double-acting

Fig. 2 Membership functions for the terms of the two inputs.

telescopic and Т5 for type 5—double-acting special are described by singletons at [1,2,3,4,5] correspondingly. The MFs for the ten outputs are singletons—for each output k, Line k = [Line k1], where Line k1 = 1 and k = 110. The model fuzzy rule base, presented in Fig. 3, describes the relationships in Fig. 1. It consists of 17 rules and is not complete due to the restrictions on the possible parameters of the cylinders. The model input-output surfaces, valid for L < 2.5 m, for type 3 are given in Fig. 4. They show correct classification, i.e., ATFL selection. The fuzzy model follows the data from Fig. 1 and puts together two independent fuzzy units (FUs):  One for type 1 and type 2 with rules 18 and outputs Line1Line3 and Line10, and type 4 and type 5 with rules 1517 and outputs Line9 and Line10;  Another for type 3 with rules 914 and outputs Line4Line8 (Line5 and Line6 are identical). The rule activation for selecting the most proper ATFL for an input cylinder with parameters D = 45 mm, L = 1.38 m and T = 3 is seen in Fig. 5. The rules are enumerated from 1 to 17. The first three columns correspond to the inputs and describe the MFs in each rule. The rest of the columns are the ten lines (outputs),

429

Fuzzy Logic Based Approach in an Enterprise Resource Planning System for Hydraulic Cylinders Assembly 1. IF (Diameter is D1) AND (Length is L1) AND (Type is T1) THEN (Line1 is Line11) 2. IF (Diameter is D1) AND (Length is L2) AND (Type is T1) THEN (Line3 is Line31) 3. IF (Diameter is D2) AND (Length is L1) AND (Type is T1) THEN (Line2 is Line21)

Line 4

Line 5 and Line 6

Line 7

Line 8

4. IF (Diameter is D2) AND (Length is L2) AND (Type is T1) THEN (Line3 is Line31) 5. IF (Diameter is D3) AND (Length is L1) AND (Type is T1) THEN (Line2 is Line21) 6. IF (Diameter is D3) AND (Length is L2) AND (Type is T1) THEN (Line3 is Line31) 7. IF (Diameter is D4) AND (Length is L3) AND (Type is T2) THEN (Line3 is Line31) 8. IF (Diameter is D4) AND (Length is L4) AND (Type is T2) THEN (Line10 is Line101) 9. IF (Diameter is D1) AND (Length is L1) AND (Type is T3) THEN (Line4 is Line41) AND (Line7 is Line71) 10. IF (Diameter is D1) AND (Length is L2) AND (Type is T3) THEN (Line8 is Line81) 11. IF (Diameter is D5) AND (Length is L1) AND (Type is T3) THEN (Line5 is Line51) AND (Line6 is Line61) AND (Line7 is Line71) 12. IF (Diameter is D5) AND (Length is L2) AND (Type is T3) THEN (Line8 is Line81) 13. IF (Diameter is D6) AND (Length is L1) AND (Type is T3) THEN (Line5 is Line51) AND (Line6 is Line61) AND (Line7 is Line71) 14. IF (Diameter is D6) AND (Length is L2) AND (Type is T3) THEN (Line8 is Line81) 15. IF (Diameter is D4) AND (Length is L5) AND (Type is T4) THEN (Line9 is Line91) 16. IF (Diameter is D4) AND (Length is L6) AND (Type is T4) THEN (Line10 is Line101) 17. IF (Type is T5) THEN (Line10 is Line101)

Fig. 3 Model fuzzy rule base.

which are depicted as singletons according to the rules in Fig. 3. The degree of certainty, with which each line is selected as proper for the input cylinder, appears numerically on the top and graphically with thin line at the bottom. For the specific cylinder rules 9 and 10 are

Lines 1, 2, 3, 9 and 10 (not applicable) Fig. 4 Model input-output surfaces for hydraulic cylinders of type 3.

activated. They show selection of Line4 and Line7 with equal degrees of certainty 0.167 and Line8 with degree of certainty 0.833. These three lines are suitable for the assembly of the cylinder but to a different extent.

4. Simulation Investigations The simulation investigations aim at proving the efficiency of the fuzzy decision support system in reducing of the delay time by properly assigning ATFLs to each cylinder. They are carried out using collected data from the plant operation for two days and a specially developed Simulink model. The sample of 197 batches, containing 2,935 cylinders, used for the assessment of the potential improvements that the fuzzy decision support system can offer, is analysed in Fig. 6 with respect to: the type of the cylinders produced (Fig. 6a) and the line adjustment and testing (or processing) time required for each batch (Fig. 6b). The longest processing time is 605 min for batch 134 of 30 cylinders. Further Line8 processes this batch. A Simulink model is developed to

430


Fig. 5 Rules activation for given input cylinder parameters.

Batch Processing and Adjustment Time

700

600

500

400

300

200

100

0

0

20

(a) Type of produced cylinders at HES

40

60

80

100 Number of Batch

120

140

160

180

200

(b) Processing time required for each batch

Fig. 6 Characteristics of the cylinders in the sample.

assign cylinders to ATFLs using the fuzzy model for cylinder classification and in case of alternatives to take final decision for a line from the requirement for least cylinder delay time. In the development of the Simulink model, the following assumptions are accounted for: (1) There is a continuous flow of cylinders so that every minute a cylinder arrives at the fuzzy system to be classified and directed towards the specified line; (2) The cylinders move in batches, a batch contains one or more

cylinders of identical parameters; (3) A batch of cylinders is inseparable and cylinders are processed one after another by the same line with single adjustment; (4) Parameters of the cylinders are D, L, T; (5) The line adjustment takes 5 minutes regardless of the type of the line or the cylinder and is included as a part of the batch processing time; (6) The fuzzy selection may result in several alternatives, from which only one final line is selected—the one that ensures a minimal delay time; (7) From several lines with equal


minimal delay times, the first (the line with the lower number) is selected; (8) The loading of the ATFL follows the fixed scenario, suggested in Fig. 1, and is objectively and automatically determined. The Simulink model has the block diagram, given in Fig. 7. The algorithm performed corresponds to a mixed continuous and discrete event queuing systems deterministic simulation—the time between arrivals and the servicing time is given and fixed [20]. The computation of the servicing (or processing) start-time to, the servicing end-time tf as well as the cylinder delay and the line idle times tw and twL of the batches is based on the following relations:

t on  max(t an , t fn 1 ), t fn  t on  t pn , t wn  t on  t an , for t on  t an t wLn  t an  t on , for t on  t an where the times ta, tp, to and tf as explained in Fig. 7 are the batch arrival, processing, start-of-servicing and end-of-servicing times, respectively. The number of the batch is identified by n, n = 1197. The fuzzy line selection computes the degree of selection (fitness) [0-1] of the lines for processing of the current batch of cylinders. The selected lines with nonzero degree are considered equivalent alternatives

Fig. 7 Block diagram of Simulink model.

431

after the conversion of the degree of selection into 1. The final selection is based on the line that ensures minimal batch delay time. In case several lines ensure one and the same minimal batch delay time, the first in order is selected. Thus a selection pattern is constructed, presented by a matrix of n rows, corresponding to the number of the batches that have passed, and 10 columns, corresponding to the ten ATFLs, with elements ‘1’ for a selected line and ‘0’ otherwise. In each row appears only one ‘1’, which corresponds to the only one selected line for the batch. Input data to the Simulink model are the parameters of the cylinders in the 197 batches, the sizes of the batches, the processing and the arrival time of each batch. Output data is the selection pattern, the pattern distribution of the total number of the processed cylinders, the batches delay time and the lines idle time, and the processing time along lines and batches. The simulation results are further statistically processed and graphically represented to make easy the analysis, discussion and recommendations and to conclude on the efficiency of the fuzzy decision support system in improving the existing ERP system. Fig. 8 shows a comparison of the loading of the lines in the HES system and in the simulated new fuzzy system. In the HES system lines 4 and 7 as well as 5

432

Fuzzy Logic Based Approach in an Enterprise Resource Planning System for Hydraulic Cylinders Assembly 6000

900 Fuzzy System

HES

800 5000 Total Processing Time, min

Total Number of Cylinders

700 600 500 400 300

4000

3000

2000

1000

200 100 0

0

1

2

3

4

5 6 7 Line Number

8

9

10

6

Decision

Support

System

The simulation results, obtained for the fixed scenario of 10 lines, tuned according to Fig. 1, allow the following assessment analysis of the fuzzy developed decision support system. (1) In the fuzzy support system lines 3 and then 8 process the greatest number of cylinders. Lines 9, 2 and 10 process only few cylinders and have very small loading in total processing time. In the real HES system the heaviest loaded lines are 4, followed by 5 and 3.

3

4

5 6 7 Line Number

8

9

10

x 10

4

5 4 Cy linders 3 2 1 0

Lines 1

2

3

4

5 6 7 Line Num ber

8

9

10

3

4

5 6 7 Line Num ber

8

9

10

9

10

Maximal Delay/Idle Time, min

3500 3000 2500

Cy linders

2000 1500

Lines

1000 500 0

1

2

(a) Batches’ delay times 1000 Lines Idle Tim e 900 Average Cylinders Delay and Line Idle Times, min

5. Fuzzy Assessment

Total Delay/Idle Time, min

and 6 are identical and not distinguished, so the processed cylinders are counted for Line4 and Line5, lines 1 and 2 are united as Line1 and Line9 was temporally not used. The distribution of the processing time along lines in the fuzzy system is given in Fig. 9. Fig. 10 facilitates the comparison of the batches

Fig. 11 gives the distribution along batches of the delay/idle time for the most loaded lines and for the lines with the longest cylinders delay time Line3 and Line8 and for one normally loaded line—Line5.

2

Fig. 9 Processing time of each line.

Fig. 8 Processed cylinders by each line.

delay time (total, average, and maximal)—Fig. 10a, taken at batch’s arrival at the corresponding line, and lines idle time—Fig. 10b. The batches delay time after the batch arrival decreases with time till the next arrival of a batch at the same line upon selection. So, delay and idle times in Fig. 10 are at the time the line is selected.

1

800 700 600 500 400 300 200 Cylinders Delay Tim e

100 0

1

2

3

4

5 6 7 Line Num ber

8

(b) Lines’ idle times Fig. 10 Total, maximal and average batches’ delay times and lines’ idle times.


Cylinders Delay Time, min

4000

3000

Line 3

Line 8 2000 Line 5

1000

0

0

20

40

60

80 100 120 Number of Batch

140

160

180

200

2000 Lines Idle Time, min

Line 3 1500 Line 5 1000 Line 8 500

0

433

ensures more uniform loading for line 8 till batch 152 as seen also from the line selection, while line 5 is loaded in the range between batches 55 and 160 and line 3—for the batches after 165. (10) The heavy loading of line 8 is predetermined by the flow of cylinders with given parameters [D, L, T] since line 8 has processed 31 batches of cylinders with no alternative line and only 1 batch where there were alternative lines. This means that the industrial demand for cylinders that can be assembled and tested by this line is great and adding a new line can reduce the cylinders delay time. (11) The relatively great batches delay time is due to

0

20

40

60

80 100 120 Number of Batch

140

160

180

200

Fig. 11 Distribution of batches’ delay time and lines’ idle time for lines 3, 5 and 8 along batches.

Lines 2, 6, 7 and 9 are not shown as loaded in Fig. 8. Line 2 is missing while line 9 has not been used. The workload of the rest is included in the workload of lines 4 and 5, respectively, since lines 4 and 7 and 5 and 6 are indistinguishable in HES. The fuzzy system ensures more uniform distribution of cylinders over the 10 lines. (2) The longest processing time have lines 8 and 3, while lines 9, 2 and 10 have the shortest. (3) Total line idle time is by times shorter, compared to the cylinders delay time. (4) Cylinders’ total and maximal delay time is longest for line 8, followed by 3. (5) The average delay time for cylinders and idle time for lines is minimized using the fuzzy decision support model, except for line 9 idle time. (6) The line idle time is more evenly distributed over the ten lines than the cylinders delay time, which is concentrated mainly on lines 3 and 8. The addition of new lines there can release the load of these lines. (7) Line 3 has the greatest line idle time for the batches about 95, then line 5 for the batches about 55. (8) The longest delay time have the cylinders from batches 135-155, processed mainly by line 8, and batches 175-197, processed by line 3. (9) The sample of cylinders from the 197 batches

the restriction that a batch is inseparable. The total processing time for all the lines is 17,376 min, approximately 5.92 min per cylinder. The total batches delay time for all lines is 114,150 min or 3.89 min per cylinder per line. The total line idle time for all lines is 13,175 min, which makes about 11.5% of total batches delay time for all lines and also about 75.8% of the total processing time. Table 1 shows the coincidence of the decision on selection of proper processing line made subjectively in HES and objectively and automatically in the fuzzy system. The percentage of batches, for which there is no alternative to the selected line, is 36% for the fuzzy system against 45% for HES. Table 1 Coinciding decisions on processing line in HES and in the fuzzy system. Number of Line batches number (cylinders) 1/2 4 (45) 3 27 (721)

1 2

4&7

25 (333)

3

5&6

47 (501)

3

8 10

16 (112) 3 2 (10) 2 121 (1722) or 61% (59%)

Total

Cylinder Comments type

For 3 batches (151 cylinders) out of 25, the fuzzy system offers one alternative more than HES. For all the 47 batches the fuzzy system offers one or two alternatives more than HES.

50 batches with alternatives at the system than at HES.

more fuzzy

434


The fuzzy model can be used as a part of a real ERP system, implemented in HES factory in Yambol. The fuzzy decision support system can add to the ERP flexibility with reduction of decisions without alternative with 9%. The decisions taken using the fuzzy system are different from those taken in HES for 41% of the total number of cylinders as shown on Table 1, which can lead to potential improvement. Besides, cylinders average delay time is smaller and the cylinder distribution over ATFLs is more even.

6. Conclusions The main contribution of our investigation could be summed up as follows: (1) A classification for linking hydraulic cylinders to assembly-testing flow lines is suggested. It takes into account assembled elements functional and structural specifics and the overlapping of lines facilities, which introduces flexibility and new options. (2) A fuzzy logic decision support system for ATFL assignment to cylinders has been developed. It helps to optimize the loading of assembly-testing flow lines offering alternative lines and thus enabling the reduction of the cylinders delay time in the lines. (3) A Simulink model has been constructed to study by simulation the facilities of the fuzzy decision support system and to assess the potential improvements it can cause to the existing ERP in HES prior to its implementation. (4) The simulation investigations prove that the developed fuzzy system allows to plan and to carry out in real time assembly and testing of every single hydraulic cylinder and group of cylinders as well. (5) The use of the fuzzy decision support system in an ERP system for assembly-testing process leads to  A reduction of the time needed for ATFL reconfiguration;  A reduction of delay time;  An increase of the ATFL loading coefficient.

project KSIKHEl № NIF-02-59/28.12.2007 in the HES factory in Yambol, financed by the Bulgarian National Innovation Fund. The authors express their gratitude to the management and staff of HES for their help and support in the preparation of this paper.

References [1] [2]

[3]

[4]

[5]

[6]

[7]

[8]

[9] [10] [11]

[12]

[13]

Acknowledgments This paper is based on the work done under the

[14]

E.F. Monk, B.J. Wagner, Concepts in Enterprise Resource Planning, 3rd ed., Course Technology, Boston, 2009. D.E. O’Leary, Enterprise Resource Planning Systems: Systems, Life Cycle, Electronic Commerce, and Risk, Cambridge University Press, UK, 2000. A. Liverani, A. Ceruti, Interactive GT code management for mechanical part similarity search and cost prediction, Computer-Aided Design & Applications 7 (1) (2010) 1-15. A.G. Rodrigues, A.T. Gómez, Production times minimization in the job shop scheduling problem, Scientia—Interdisciplinary Studies in Computer Science 18 (2) (2007) 110-118. O. Torkul, I. Calli, An integrated real time MRP and group technology system: Intelligent manufacturing systems: Vision for the future, Journal of Intelligent Manufacturing 15 (4) (2004) 561-567(7). P.Th. Zacharia, A.C. Nearchou, Multi-objective fuzzy assembly line balancing using genetic algorithms, Journal of Intelligent Manufacturing, 2010, doi: 10.1007/s10845-010-0400-9. J.-S.R. Jang, C.-T. Sun, E. Mizutani, Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, Prentice-Hall, NJ, 1997. T. Neshkov, S. Yordanova, I. Topalova, Process control and production automation, Technical University of Sofia, Sofia, 2007. T.J. Ross, Fuzzy Logic with Engineering Applications, McGraw-Hill, NY, 1995. R.R. Yagеr, D.P. Filev, Essentials of Fuzzy Modeling and Control, John Wiley & Sons, NY, 1994. S. Yordanova, R. Petrova, N. Noykova, P. Tzvetkov, Neuro-fuzzy modelling in anaerobic wastewater treatment for prediction and control, International Scientific Journal of Computing 5 (1) (2006) 51-56. M.R. Adali, M.F. Taşkin, H. Taşkin, Selecting the optimal shift numbers using fuzzy control model: A paint factory’s facility application, Journal of Intelligent Manufacturing 20 (2) (2009) 267-272. H.-Y. Kang, A.H.I. Lee, C.-Y. Yang, A fuzzy ANP model for supplier selection as applied to IC packaging, Journal of Intelligent Manufacturing, 2010, doi: 10.1007/s10845-010-0448-6. T. Budd, An introduction to Object-Oriented

Fuzzy Logic Based Approach in an Enterprise Resource Planning System for Hydraulic Cylinders Assembly Programming, 3rd ed., Addison-Wesley, NY, 2002. [15] P. Coad, J. Nicola, Object-Oriented Programming, Prentice Hall, NJ, 1993. [16] L. Dimitrov, R. Shikov, H. Bankov, M. Klochkova, Automated assembly of hydraulic cylinders in small and medium size production, in: Proceedings of the 32nd Congress with Int. Participation, HIPNEF 2009, Serbia, 2009, pp. 25-33. [17] C.C. Gallagher, W.A. Knight, Group Technology

435

Production Methods in Manufacture, Ellis Horwood, England, 1986. [18] C.S. Snead, Group Technology: Foundation for Competitive Manufacturing, Van Nostrand Reinhold, NY, 1989. [19] J.-S.R. Jang, N. Gulley, The Fuzzy Logic Toolbox for Use with MATLAB, The MathWorks, MA, 1995. [20] S.J. Bose, An Introduction to Queueing Systems, Kluwer/Plenum Publishers, NY, 2002.

D


DAVID

PUBLISHING

Solution of Inverse Problem on Distributed Generation Using Complex-Valued Network Inversion Takehiko Ogawa1 and Kyosuke Nakamura2 1. Faculty of Engineering, Takushoku University, Tokyo 193-0985, Japan 2. Graduate School of Engineering, Takushoku University, Tokyo 193-0985, Japan

Received: October 06, 2011 / Accepted: November 02, 2011 / Published: November 25, 2011. Abstract: Solutions of inverse problems are required in various fields of science and engineering. The concept of network inversion has been studied as a neural-network-based solution to inverse problems. In general, inverse problems are not limited to a real-valued area. Recently, complex-valued neural networks have been actively studied in the field of neural networks. As an extension of network inversion to complex numbers, a complex-valued network inversion has been proposed. Moreover, inverse problems for estimating the parameters of distributed generation systems such as distributed energy plants or smart grids from observed electric circuit data have been studied in the field of natural energy. These emphasize the need to handle complex numbers in an alternating current (AC) circuit. In this paper, the authors propose an application of the complex-valued network inversion to the inverse estimation of a distributed generation. Further, the authors confirm the effectiveness of the complex-valued network inversion on the basis of simulation results. Key words: Neural networks, network inversion, complex numbers, inverse problems, distributed generation.

1. Introduction It is necessary to solve inverse problems for estimating causes from observed results in various fields of science and engineering, such as tomography [1], astronomy [2], and inverse kinematics [3]. Thus far, an inverse problem has been solved mainly by a numerical method [4]. The concept of network inversion has been studied as a neural-network-based solution to inverse problems [5]. Further, network inversion has been applied to image restoration [6] and the inverse kinematics of robot arms [7]. While the original network inversion has been applied to a typical multilayer neural network with real-valued inputs and outputs, the inverse problem is not limited to the real-number area. Recently, complex-valued neural networks have been actively studied in the field of Kyosuke Nakamura, B.E., research field: artificial neural networks. Corresponding author: Takehiko Ogawa, Dr.Eng., research fields: artificial neural networks, computational intelligence. E-mail: [email protected].

artificial neural networks [8-10], and a complex-valued network inversion method has been proposed to solve inverse problems with complex numbers [11-12]. Recently, distributed generation systems, including natural power sources or fuel cells, have attracted significant research attention. A distributed generation system is an electric power network that connects a number of small-scale power supplies; this technology has been considerably effective in terms of the utilization of natural energy and the efficiency of electric transmission [13]. In general, a small-scale power supply is unstable because of the characteristics of natural energy and the required cost reduction. A stable operation of the electric power network is important. Hence, it is necessary to control a small-scale power supply for the stabilization of the electric power, and, in the worst case, to separate the unstable power supply from the network. To realize such a control and ensure synchronized operation of power supplies in the distributed generation system, we need to estimate the parameters of a number of power supplies [14-15]. The

Solution of Inverse Problem on Distributed Generation Using Complex-Valued Network Inversion

problem that estimates these parameters from a considerable amount of observed data is an inverse problem extended to complex numbers [16]. In this paper, we propose an application of the complex-valued network inversion to the inverse estimation of the distributed generation. In particular, we consider the problem that estimates the voltage of a power supply from the observed output voltage of a circuit with two power supplies. We examine the complex-valued network inversion to estimate the parameters of the power supplies because this problem is an estimation problem of the inverse mapping in the complex space. In this paper, we present the obtained results in the form of a vector diagram to illustrate the procedure of the estimation of the inverse mapping by a complex-valued network inversion. In addition, the effect of the complex-valued network inversion is shown as the distribution of the estimated input. The paper is organized as follows: Section 2 discusses the inverse problems and network inversion; section 3 introduces the complex-valued neural networks; section 4 is the inverse estimation of distributed generation; section 5 presents the simulation; section 6 gives the conclusion.

2. Inverse Problems and Network Inversion An inverse problem is used for deciding the cause of a phenomenon on the basis of the observed phenomenon. The cause is estimated from the fixed model and the given result in the inverse problem. For the relation Kx = y, where K is a mathematical model, we consider the forward problem, which determines the result y from the cause x. In this forward problem, generally, the definition of the operator K is fixed and its mapping is supposed to be continuous. For this forward problem, we can define an inverse problem that determines the cause x from the operator K and the result y or one that estimates the operator K from the cause x and the result y [1]. It is necessary to solve inverse problems for estimating causes from observed results in various

437

fields of science and engineering. For instance, in a tomography problem, an internal image of the object is composed of an object scan carried out using radiation. In underground exploration, the distribution of underground resources is obtained from the reflected ultrasound wave. In the inverse kinematics of a robotic arm, the joint angles required to realize the coordinates of the given end effector are estimated. As a solution to inverse problems, a neural-network-based method has been proposed, while other methods such as the numerical method have also been studied. The direct method and the repetition method are known as the numerical methods of the linear equation system. Moreover, a solution to an inverse problem that uses a typical neural network is proposed; this solution has been used for estimating the inverse model of plants and for solving the problem of inverse kinematics. 2.1 Network Inversion A typical multilayer neural network is used for solving the forward problem. In the usual multilayer network whose training has been completed, the input–output relation is given by y = f(w, x), where x, y, and f are the input vector, the output vector, and the function defined by the interlayer weights w of the network, respectively. Using the input vector x, the network calculates the output vector y. Linden and Kindermann proposed a method of network inversion [5]. In this method, one can apply the observed output data y with a fixed value of f, after finding the forward relation f by training. The input x can be updated according to the calculated input correction signal on the basis of the duality of the weights and the input. In fact, the input is estimated from the output by an iterative update of the input; this iterative update is based on the output error, as shown in Fig. 1. Thus, the inverse problem for estimating the input x from the output y is solved with a multilayer neural network by using a forward relation inversely.

438


Tutorial output Y’ Error E

T raining phase

Output Y

tra in in g in p u t

output layer

weights

fo rw a rd le a rn in g

tra in in g o u tp u t

fixed weights

E stimation phase

b y m u ltila ye r N N

hidden layer

weights

fixed weights

input layer

Input X

Fig. 1 Iterative update of input from provided output in inverse estimation phase of network inversion.

The network is used in two phases—forward training and inverse estimation—to solve an inverse problem by network inversion. This phased procedure is shown in Fig. 2. In the training phase, we provide the training input x and the training output y and calculate the output error E. Then, the weight w is updated as follows: E wn  1  wn    t (1) w where t represents the training gain; the output error is due to the maladjustments of the weights. By repeating this update procedure, we can obtain a forward relation. This procedure is based on the typical back-propagation method. In the inverse estimation phase, we fix the relation obtained in the training phase, obtain the random input x and the test output y, and calculate the output error E. Then, the input x is updated as follows: E x n  1  x n    e (2) x where e indicates the input update gain; the output error is due to the input error. By repeating this update procedure, we can estimate the input from the output. In the inverse estimation phase of network inversion, an iterative update based on the steepest descent method is carried out along with the training phase. Therefore, there seems to be a disadvantage in that the calculation time of the inverse estimation is large. However, the iterative update in the inverse

e stim a te d in p u t

in ve rse e stim a tin g

te st o u tp u t

Fig. 2 Two-step estimation procedure for solving an inverse problem using network inversion.

estimation is carried out only for one given observation output as opposed to the repetitive updates in the training phase. Therefore, the computing time for inverse estimation is inconsiderable for a typical network.

3. Complex-Valued Neural Networks Recently, complex-valued neural networks have been studied to learn and recognize the data in the complex region directly. These networks learn the complex input–output relation using complex weights and complex neurons. Various models such as the multilayer-type neural network [8-9], the self-organizing map [17], and associative memory [18] have been proposed for representing these networks, and a number of applications of these networks have been studied. The complex-valued neural networks are effective for processing data in a coordinate system where the phase rotates or for learning the relation in the frequency domain. Some of the applications of complex-valued neural networks are the adaptive designing of patch antennas [19], radar image processing [20], and traffic-dependent optimal control of traffic signals [21]. In this study, we consider a multilayer neural network based on the error back-propagation learning method. This model learns the complex input–output relation using complex weights and complex neurons. Complex-valued neural networks are classified on the basis of their architecture and the type of neurons that


comprise these networks. For instance, one type of complex-valued neural networks is based on the transfer function of the neuron, and another consists of the real-type neurons. Here, we consider a neuron that independently applies the sigmoid function to the real and imaginary parts of the weighted sum of inputs. This neuron applies a complex sigmoid function to each real part and imaginary part independently and can be defined as

1  e u f C s   f s R   if s I , f u   (3) 1  e u where i and s = sR + isI indicate the imaginary unit and the weighted sum of the neuron input, respectively. In this network, the complex-valued neurons are used for the hidden layer and the output layer. When processed with the complex weights between each layer, the complex input becomes the complex output. 3.1 Complex-Valued Network Inversion The original network inversion solves an inverse problem by using a typical multilayer neural network that handles the relation between the real-valued input and the output. However, a solution based on the complex-valued neural networks is considered to solve the inverse problem that extends to the complex domain. Hence, complex-valued network inversion has been proposed to solve a general inverse problem whose cause and result extend to the complex domain [11]. The complex-valued network inversion uses a multilayer neural network that includes complex weights and complex neurons. In this method, the complex-valued neural network estimates the complex input from the complex output by using a trained network. This neural network is an extension of the input correction principle of a typical network inversion to the complex domain. In fact, the complex input is estimated from the complex output by giving the

random

input

to

the

trained

network,

back-propagating the output error to the input, and repeating the input. In the training phase, we provide the complex

439

training input x = xR + ixI and the complex training output y = yR + iyI and calculate the complex output error E = ER + iEI. Then, the complex weight w = wR + iwI is updated by

 E E I w R n  1  w R n    t  R   w R w R  E E  w I n  1  w I n    t  I  R   w I w I 

   (4)

where t represents the training gain; the output error is due to the maladjustments of the weights. By repeating this update procedure, we obtain the forward relation. This procedure is based on the typical complex back-propagation method. In the inverse estimation phase, we fix the relation obtained in the training phase, provide the complex random input x = xR + ixI and the random test output y = yR + iyI, and calculate the complex output error E = ER + iEI. Then, the complex input is updated by

 E E  xR n  1  xR n    e  R  I   xR xR   E E  xI n  1  xI n    e  I  R   xI xI 

(5)

where e indicates the input update gain; the output error is due to the input error. By repeating this update procedure, we estimate the complex input from the output. When the target error is attained, the input correction is terminated and the obtained complex input becomes a solution. Thus, the complex input can be inversely estimated from the complex output by using the complex weight distribution obtained by training. This is similar to the iterative correction of the weights or the input during the training phase and the inverse estimation. However, the inverse estimation is the iterative correction for a provided pattern, which differs from the training carried out by the repeated correction for plural patterns. Here, we consider a neural network with three layers: the input, hidden, and output layers. It is sufficient to realize any function by using these three layers of a multilayer-type neural network. However,

440


we do not discount the possible use of a network with a different architecture in future research.

4. Inverse Generation

Estimation

of

Distributed

Recently, distributed generation systems, including natural power sources or fuel cells, have been studied. The small-scale power supplies allocated near the consumer are an example of distributed generation. The introduction of a distributed generation system has led to the expectation of a reduction in the environment load and the cost of power. However, a small-scale power supply is often unstable because of the characteristics of natural energy and the required cost reduction. The maintenance of the quality of the electric power and prompt incident detection become difficult when there is an increase in the number of distributed generation systems. Hence, it is necessary to control a small-scale power supply for the stabilization of electric power. To realize such a control and ensure synchronized operation of power supplies in the distributed generation system, we need to estimate the parameters of a number of power supplies. The problem that estimates the parameters of the distributed power supplies from a considerable amount of observed data is an inverse problem that is extended to complex numbers, such as an inverse problem to estimate the voltage data of the sources from the output voltage or the current data. In this study, we consider an alternating current (AC) electric circuit model with distributed generation. In this circuit, we assume that the impedance element is driven by a number of AC power sources. We use two power sources with complex impedances and an output complex impedance, as shown in Fig. 3. We aim to estimate the parameters of the input power sources from the observed parameters of the output complex impedance. The value of each impedance is Z1 = Z2 = Z3 = 1 + i [], where i represents an imaginary unit. We change

Fig. 3

Distributed generation circuit model for simulation.

the parameters of the power source VG1 to obtain the training data for the neural network. Further, we obtain the test data by changing the output of the complex impedance. The parameter of the power source VG2 is set to 100 [V]. The parameters of the power source VG1 are changed to create three cases: in case 1, the amplitude is varied from 0 to 200 [V]; in case 2, the phase is changed from -180° to 180°; and in cases 3, both the amplitude and the phase are varied within the abovementioned ranges.

5. Simulation We carry out the inverse estimation of the power supply parameters of the distributed generation circuit shown in Fig. 3. We use the complex-valued neural network with two input neurons and an output neuron, which correspond to the complex voltage of two sources and the measured complex voltage, respectively. These values are normalized by each maximum and minimum value and are used as the input and the output values of the network. The network architecture and network parameters are shown in Fig. 4 and Table 1. In the simulation of the neural network, aspects such as the parameter setting of the number of hidden-layer neurons and the learning coefficient always give rise to problems. In this study, we do not use any decision techniques and simply decide on the parameter setting by trial and error. This is because the purpose of this study is to show the basic inverse-estimation ability of the complex-valued network inversion in the distributed generation estimation problem.

Solution of Inverse Problem on Distributed Generation Using Complex-Valued Network Inversion Training Complex training input pattern x

Complex training output pattern y Complex test output pattern y

Complex initial random input pattern x

Inverse estimation

Fig. 4 Table 1

Network architecture for simulation.

441

value to one test data. The mean error is the average of the input error obtained in the five trials. The correction of the estimated result is shown in the input distribution chart by the inverse estimation. Then, we evaluate the mapping ability in the inverse direction of the learned network by using the vector distribution chart from the output to the input. Further, we show the estimation accuracy by using the mean error of the ideal input and the inversely estimated input.

Network parameters for simulation.

Parameter Number of input neurons Number of hidden neurons Number of output neurons Training rate t Input correcting rate e Maximum number of training epochs Maximum number of estimation epochs

Value 2 10 1 0.0001 0.001 20,000 5,000

We perform three experiments by changing the parameters of a voltage source: one with a variation in the amplitude, another with a variation in the phase, and the third with variations in both the amplitude and the phase of the input data. First, we use the input data with a variation in the amplitude and the corresponding output. The network learns the input/output relation using these data. We inversely estimate the corresponding input to the provided output by using the trained network. Next, we use the input data with a variation in phase and carry out the simulation. We aim to confirm the basic ability of the complex-valued network inversion for the inverse estimation of the distributed generation by these simulations. In addition, we simulate the inverse estimation of the input by changing both the amplitude and the phase of the input data. We aim to show the applicability of the complex-valued network inversion to the inverse estimation problem of distributed generation by this simulation. The results of each simulation are shown by using three methods: a plot chart of the inverse-estimated input, a vector distribution chart from the output to the input, and the mean error of the estimated input. A plot chart is a result of five trials which changed the initial input

5.1 Case 1: Variation in Amplitude First, we attempt to obtain the parameters of the power source VG1 from the output voltage when the amplitude of VG1 is changed. In this case, the input values corresponding to VG1 become real values. In other words, the real input values need to be estimated from the complex output values in this problem. The learning of the network is completed in the set maximum training epochs and confirms the convergence of learning. The inversely estimated inputs are shown in Fig. 5a. This is a result of five trials which changed the initial input value to one test data. The values on the horizontal and vertical axes in the graph are the voltage values converted from the inversely estimated values as network inputs. The complex voltage is estimated almost correctly on the real axis of the graph. According to this result, we find that the input is estimated almost correctly. The vector distribution chart from the output to the input is shown in Fig. 6a. The horizontal axis and the vertical axis represent the real and the imaginary parts of the provided output, respectively; these are the values of the normalized complex voltage of VZ3. From the obtained result, we find that the transforming vector from the output to the input is almost precisely estimated on the complex plane. Moreover, the mean squared error and the standard deviation of the inversely estimated input become 7.975 [V] and 2.845 [V], respectively. From these results, we find that the values of VG1 are estimated almost accurately by the complex-valued network inversion.


442

1

250 200 150

V1est

Im(VZ3)

VI [V]

0.5

V1

100 50

0

-0.5

0 -50

0

50

100

‐50

150

200

-1 -1

-0.5

VR [V]

0 Re(VZ3)

0.5

1

0.5

1

0.5

1

(a)

(a) 1

150

VI [V] V1est

100

0.5

V1

0 -150

-100

-50

0

50

100

‐50

150

Im(VZ3)

50

VR [V]

0

-0.5

‐100

-1 -1

‐150

-0.5

(b) VI [V]

0 Re(VZ3)

(b)

150

1

100

0.5

0 -150

-100

-50

0 ‐50 ‐100

50

100

150

VR [V]

Im(VZ3)

50

0

-0.5

V1est V1

‐150

(c) Fig. 5 Simulation results of inversely estimated inputs of voltage source: variation in (a) amplitude, (b) phase, and (c) both amplitude and phase.

5.2 Case 2: Variation in Phase Next, we attempt to obtain the parameters of the power source VG1 from the given output voltage when the phase of VG1 is changed. In general, the complex-valued neural networks are efficient at processing of data where the phase rotates. The training is completed in the expected number of epochs.

-1 -1

-0.5

0 Re(VZ3)

(c) Fig. 6 Simulation result of vector distribution chart from outputs to inputs of voltage source: variation in (a) amplitude, (b) phase, and (c) both amplitude and phase.

First, the results of the inversely estimated inputs are shown in Fig. 5b. This is a result of five trials which changed the initial input value to one test data. The estimated points are distributed on a circle at an equal distance from the origin. The complex voltage of the source is estimated but includes some errors. The voltage is mostly estimated at an equal distance from the origin of the graph. Next, the vector


distribution chart from the output to the input is shown in Fig. 6b. A spiral movement vector that centers on the origin is seen in this result. This shows the difference in the phases between the input and the output. Moreover, the mean squared error and the standard deviation of the inversely estimated input become 9.101 [V] and 3.521 [V], respectively. We have confirmed that the voltage source VG1 whose phase is changed can be estimated by the complex-valued network inversion sufficiently correctly. 5.3 Case 3: Variation in Both Amplitude and Phase Finally, we examine the estimation of the parameters of the power source VG1 from the output voltage when both the phase and the amplitude of VG1 are changed. The aim of the simulation of data in which both phases and amplitudes change is to confirm the applicability of the complex-valued network inversion to an actual distributed generation estimation problem. The training of the network is completed within the maximum number of epochs as in the case of the previous simulations. First, the results of the inversely estimated inputs are shown in Fig. 5c. This is a result of five trials which changed the initial input value to one test data. The distribution of the input is almost correctly estimated, although there is a small estimated error in the case of the large-amplitude data. Next, the vector distribution chart from the output to the input is shown in Fig. 6c. A spiral movement vector that centers on the origin is seen in this figure. The difference in the phase between the input and the output is considered to be correctly learned by the network. Moreover, the mean squared error and the standard deviation of the inversely estimated input becomes 9.594 [V] and 4.425 [V] respectively, which is approximately as small as that in the previous simulations. The complex voltage of the source is estimated. It is found that the error of the estimated input is not small. However, we confirm that the parameters of the

443

voltage source distributed on the complex plane can be estimated by a complex-valued network inversion. We confirm the effectiveness of the inverse estimation of the distributed generation by the complex-valued network inversion from these results. That is, complex-valued network inversion is applicable to the actual inverse estimation problem of the distributed generation.

6. Conclusions In this study, we proposed an application of the complex-valued network inversion to the inverse estimation problem of distributed generation. Moreover, we simulated the inverse estimation of the voltage source by a simple distributed generation model. We demonstrated that the inverse estimation of the voltage source was possible when either the amplitude or the phase was changed or when both the amplitude and the phase were changed. From these results, we confirmed the inverse estimation by complex-valued network inversion and the applicability to the inverse estimation problem in an actual distributed generation. In this study, we charted the proposal and performed simulations as the first step to the inverse estimation of distributed generation by a complex-valued network inversion. Therefore, we modeled and set the problem with some assumptions. One of the assumptions was the number of dispersed power sources. It is necessary to estimate the actual number of distributed power sources. The other assumption was that of the well-posedness for the unique solution. The method of regularization [22] is required to distinguish the distributed power supplies because there is no distinction between them. Regularization has already been researched from the perspective of a neural network [23]. Moreover, we proposed the introduction of regularization to simple network inversion [24] and complex-valued network inversion [25]. Hence, it is necessary to consider the estimation of the actual number of distributed power

444


sources and the ill-posedness of inverse problems as future problems. Moreover, a thorough examination of the estimated error and estimation accuracy is required.

Acknowledgment This work was partly supported by a Grant-in-Aid for Scientific Research (#21700260) from the Japan Society for the Promotion of Science.

References C.W. Groetsch, Inverse Problems in the Mathematical Sciences, Informatica International, Inc., CA, 1993. [2] I.J.D. Craig, J.C. Brown, Inverse Problems in Astronomy, Adam Hilger, 1986. [3] J.J. Craig, Introduction to Robotics Mechanics and Control, Addison-Wesley, 1989. [4] J. Kaipio, E. Somersalo, Statistical and Computational Inverse Problems, Springer, 2005. [5] A. Linden, J. Kindermann, Inversion of multilayer nets, in: Proc. IJCNN, 1989, pp. 425-430. [6] I. Valova, K. Kameyama, Y. Kosugi, Image decomposition by answer-in-weights neural network, IEICE Trans. on Information and Systems 78-D (1995) 1221-1224. [7] B-L. Lu, K. Ito, Regularization of inverse kinematics for redundant manipulators using neural network inversion, in: Proc. IEEE Int. Conf. on Neural Networks, 1999, pp. 2726-2731. [8] N. Benvenuto, F. Piazza, On the complex backpropagation algorithm, IEEE Trans. on Signal Processing 40 (1992) 967-969. [9] T. Nitta, An extension of the backpropagation algorithm to complex numbers, Neural Networks 10 (8) (1997) 1392-1415. [10] A. Hirose, Complex-Valued Neural Networks, Springer, 2005. [11] T. Ogawa, H. Kanada, Network inversion for complex-valued neural networks, in: Proc. of ISSPIT 2005, pp. 850-855. [12] T. Ogawa, Complex-valued neural network and inverse

[13] [14]

[15]

[16]

[1]

[17]

[18] [19]

[20]

[21]

[22] [23]

[24]

[25]

problems, in: T. Nitta (Ed.), Complex-Valued Neural Networks: Utilizing High-Dimensional Parameters, IGI-Global, 2009, pp. 27-55. G.T. Heydt, The next generation of power distribution systems, IEEE Trans. on Smart Grid 1 (3) (2010) 225-235. J.D.L. Ree, V. Centeno, J.S. Thorp, A.G. Phadke, Synchronized phasor measurement applications in power systems, IEEE Trans. on Smart Grid 1 (1) (2010) 20-27. J. Kodama, H. Shinji, T. Tanabe, T. Hamagami, H. Hirata, Cooperative control for distributed generation by using multiagent learning (in Japanese), IEEJ Trans. EIS 126 (2) (2006) 194-195. N.V. Korovkin, V.L. Chechurin, M. Hayakawa, Inverse Problems in Electric Circuits and Electromagnetics, Springer, 2007. A. Hirose, T. Hara, Complex-valued self-organizing map dealing with multi-frequency interferometeric data for radar imaging systems, in: Proc. of WSOM 2003, pp. 255-260. I. Nemoto, M. Kubono, Complex associative memory, Neural Networks 9 (1996) 253-261. K.L. Du, A.K.Y. Lai, K.K.M. Cheng, M.N.S. Swamy, Neural methods for antenna array signal processing: A review, Signal Processing 82 (2002) 547-561. T. Hara, A. Hirose, Plastic mine detecting radar system using complex-valued self-organizing map that deal with multiple-frequency interferometric images, Neural Networks 17 (8-9) (2004) 1201-1210. I. Nishikawa, Y. Kuroe, Dynamics of complex-valued neural networks and its relation to a phase oscillator system, in: Proc. of ICONIP 2004, pp. 122-129. A.N. Tikhonov, V.Y. Arsenin, Solutions of Ill-Posed Problems, Winstion and Sons, 1977. T. Poggio, F. Girosi, Regularization algorithms for learning that are equivalent to multilayer networks, Science 247 (1990) 978-982. T. Ogawa, H. Kanada, Solution for ill-posed inverse kinematics of robot arm by network inversion, Journal of Robotics 2010 (2010). T. Ogawa, S. Fukami, H. Kanada, Regularization for complex-valued network inversion, in: Proc. of SICE 2008, pp. 1237-1242.

D


DAVID

PUBLISHING

Analysis of Potential Failure Modes in an Assembly Line by Fuzzy Expert Systems Mehdi Piltan1, Reza Ghodsi1, Foad Quarashi1 and Mehrdad Azizian2 1. Department of Industrial Engineering, University College of Engineering, University of Tehran, Tehran 14399-55961, Iran 2. School of Industrial Engineering and Management, Shahrood University of Technology, Shahrood 36199-95161, Iran

Received: August 22, 2011 / Accepted: September 02, 2011 / Published: November 25, 2011. Abstract: The failure modes and effects analysis (FMEA) is widely applied in manufacturing industries in various phases of the product life cycle to evaluate the system, its design and processes for failures that can occur. The FMEA team often demonstrates different opinions and these different types of opinions are very difficult to incorporate into the FMEA by the traditional risk priority number model. In this paper, for each of the Occurrence, Severity and Detectivity parameters a fuzzy set is defined and the opinion of each FMEA team members is considered. These opinions are considered simultaneously with weights that are given to each individual based on their skills and experience levels. In addition, the opinion of the costumer is considered for each of the FMEA parameters. Then, the Risk Priority Numbers (RPN) is calculated using a Multi Input Single Output (MISO) fuzzy expert system. The proposed model is applied for prioritizing the failures of Peugeot 206 Engine assembly line in IKCo (Iran Khodro Company). Key words: FMEA (failure modes and effects analysis), fuzzy expert systems, engine assembly line.

1. Introduction The finding most important potential errors in a production line is one of the most important part of production cost reduction. In this research we have developed a model to prioritize the potential error in Iran Khodro Company (IKCo) [1]. The failure mode and effect analysis (FMEA) is an engineering technique used to define, identify and eliminate known and/or potential failures, problems, errors and so on from the system, design, process and/or service before they reached the customer [2]. When it is used for a criticality analysis, it is also referred to as failure mode, effects and criticality analysis (FMECA). FMEA has gained wide acceptance and applications in a wide range of industries such as aerospace, nuclear, chemical and manufacturing. A good FMEA can help analysts identify known and potential failure modes Corresponding author: Reza Ghodsi, assistant professor, Ph.D., research fields: artificial intelligence, production engineering and control, operation research, discrete-event simulation. E-mail: [email protected].

and their causes and effects, help them prioritize the identified failure modes and can also help them work out the corrective actions for the failure modes. FMEA is a very helpful tool for identifying weak points in the design stage of a plant as well [3]. This is also related to safety issues and also to redundancy allocation, cost optimization, etc. FMEA should be implemented as early as the design conception stage, so that weak points are identified as soon as possible [4]. FMEA is also used for operating plants to direct maintenance tasks, to identify more efficient operational methods, and to explore the points with higher potential of damage. Here, design changes tend to be avoided on the grounds of the higher costs incurred. For these reasons, FMEA is very important in the context of probabilistic safety assessments (PSA). In the traditional PSA failure modes describe the component failures [5]. In order to rank actions to be taken in design, it is necessary to establish a ranking order among the critical points that have been identified by means of the potential failure modes. Once these latter

446

Analysis of Potential Failure Modes in an Assembly Line by Fuzzy Expert Systems

are gathered, risk attributes may be assigned to them. The main objective of FMEA is to allow the analysts to identify and prevent known and potential problems from reaching the customer. Traditionally, when performing an FMEA, three indices have been used for ranking the failure modes. They are related to their occurrence probability, to the severity of the associated effects to each failure mode, and also to the potential for detecting them. The risks of each identified failure mode need to be evaluated and prioritized so that appropriate corrective actions can be taken for different failure modes. The priority of a failure mode is determined through the risk priority number (RPN), which is defined as the product of the occurrence (O), severity (S) and detection (D) of the failure [6]. RPN = O × S × D The three factors O, S and D are all evaluated using the ratings (also called rankings or scores) from 1 to 10, where the higher the number, the more unfavorable the effect. The occurrence index is related to the occurrence probability of the failure mode at hand. The severity index is directly related to the potential effects associated to the occurrence of a failure mode (health or environmental effects, death risk, economic losses, law infringement, etc.). The detection index is related to the power of identifying the occurrence of a potential cause of a failure mode. It represents the ability of the process for identifying a failure before the system is put to work, by means of inspection, periodic testing, or the like. The failures with higher RPNs are assumed to be more important and should be given higher priorities. It is a group decision function and cannot be done on an individual basis. The FMEA team often demonstrates different opinions and knowledge from one team member to another and produces different types of assessment information such as complete and incomplete, precise and imprecise and known and unknown. In traditional approach crisp data are used to determine O, S and D parameters in FMEA table. This

approach is not very suitable here, because these parameters are determined by group opinions in which this has vague concept. Because the FMEA team generally suggests different opinions and knowledge from one team member to another produces different types of assessment information due to its cross-functional and multidisciplinary nature. These different types of information are very difficult to incorporate into the FMEA by the traditional risk priority number model. Garcia et al. present a data envelopment analysis approach for determining ranking indices among failure modes in which the typical FMEA parameters are modeled as fuzzy sets [7]. Chin et al. present an FMEA using the evidential reasoning (ER) approach, a newly developed methodology for multiple attribute decision analysis, and the proposed FMEA is then illustrated with an application to a fishing vessel [8]. When performing failure mode and effects analysis for quality assurance and reliability improvement, the interdependencies among several results may be questionable. To address this issue, Xu et al. present a fuzzy-logic-based method for FMEA and integrated a platform for a fuzzy expert assessment with the proposed system to overcome the potential difficulty in sharing information among experts from various disciplines [9]. Chen and Ko propose fuzzy linear programming models to determine the fulfillment levels of PCs under the requirement to achieve the determined contribution levels of design risks for customer satisfaction [10]. Considering the design risk, their work incorporates failure modes and effect analysis into QFD processes, which is treated as the constraint in the models. To cope with the vague nature of product development processes, fuzzy approaches are used for both FMEA and QFD. Although in recent years, to improve the performance of the traditional FMEA model, fuzzy numbers have been used in the FMEA structure as an appropriate approach to handle this uncertainty and fuzziness, but it is not sufficient and appropriate to consider each opinion


of FMEA individual group in the FMEA table. In this study a fuzzy FMEA for determining ranking indices among failure modes is presented in which the typical FMEA parameters are modeled as fuzzy sets. And by using these sets each opinion of FMEA individual member is included. Each opinions considered in the fuzzy sets simultaneously with a membership degree in which it’s equal to weight that given to each individual due to their skill and experience (weights vary between 0 and 1, where more experienced and expert person has a weight closer to 1). And if just a number is suggested from two people, the suggested number with bigger membership degree (weight) will be considered. Therefore, all opinions of FMEA team are considered in FMEA table. Another advantage of this approach in comparison to previous studies is that it considers the opinion of costumer like as in QFD. The opinion of costumer is taken into account as a member of those three fuzzy sets with a membership degree. In other words, costumer is considered as a member of FMEA team. By collecting these fuzzy sets we will consider all opinions including opinions of each members of FMEA group and opinions of costumers. And then by using a MISO fuzzy expert system for each failure mode we will find RPN index as a fuzzy set. This fuzzy expert system has three inputs (O, S and D) and one output (RPN). The weighted average method is used to defuzzify the results. This new fuzzy FMEA method has been implemented in Peugeot 206 engine assembly line in IKCo. The rest of this paper is organized as follows: Section 2 discusses about the methodology which is divided into five subsections including fuzzy inference system, fuzzy expert system, difuzzification and validation; and finally, the conclusions are summarized in section 3.

2. Methodology 2.1 Description of the Fuzzy Inference System A pure fuzzy logic system is made up by a set of inference rules of the kind IF...THEN so as to perform the mapping of the input universe V  R n onto the

447

output universe V  R. The sets of fuzzy rules are presented in the following way: R(1): IF X1 is Fi and ... Xn is Fn THEN y is G(1) Where F and G are fuzzy sets and x = (Xl,...,Xn) Ԗ U and y Ԗ V are the linguistic variables which belong to the input and output universes, respectively. With those rules, one can take into account expert opinions in a mathematical model. The aim is to enhance the discriminating power of the failure mode ranking mechanism and at the same time to associate the uncertainties related to the linguistic variables to the degree of criticality. These latter are: L (low), M (medium) and H (high). 2.2 Fuzzy Expert System In this section, a fuzzy expert system is presented for finding RPN index in FMEA table. This fuzzy expert system is a MISO system in which the inputs are O, S and D indices. To calculate these inputs we use a FMEA team with 9 members (here n = 9). Every one of FMEA members suggests a number among 1 to 10 for each one of O, S and D indices of each failure. We also want some people who have already used the product sufficiently to select a number among 1 to 10, considering the rate of the importance of that failure. Then a membership degree is considered to each number according to each person’s rate of experience and skill (The weight of more expert and experienced person is close to 1). For opinions from costumers, the average of suggested numbers is considered and finally it is taken into account with the membership degree of 0.5. Thus, if a number is suggested from two persons, the suggested number with bigger membership degree (weight) will be considered. Reference set to determine the membership degree for Detectivity, Severity and Occurrence is as follows:

X  {1,2,3,4,5,6,7,8,9,10} Reference set for RPN number:

Y  {1,2,3,...,1000} Divide membership degrees for O, S and D indexes to high, medium and low sets as shown in Fig. 1.


448

Hence, if we have Al = (Al1, Al2, Al3) as sets of membership degrees for failure mode l as input for fuzzy expert system, and by Mamdani mechanism with FITA approach the output of this fuzzy expert system (RPN) for that failure mode is as follows: RPN  A oR  A o( (X  X  X  Y ))   ( A  A  A  ( ( X  X  X  Y ))) (1)   ( ( A  A  A  X  X  X  Y )) 27

l

l

l

i1

i 1

i2

i3

i

27

l1

Fig. 1 Membership functions for high, medium and low.

i 1

X 1  X high

0 0.2 0.4 0.6 0.8 1 { , , , , , } 5 6 7 8 9 10

X 2  X medium  0 0.2 0.4 0.6 0.8 1 0.8 0.6 0.4 0.2 0 { , , , , , , , , , , } 0 1 2 3 4 5 6 7 8 9 10 1 0.8 0.6 0.4 0.2 0 X 3  X low  { , , , , , } 0 1 2 3 4 5

Divide RPN numbers to high, medium and low sets as shown in Fig. 2. 0 0.2 0.4 0.6 0.8 1 Y1  Yhigh  { , , , , , } 500 600 700 800 900 1000 Y2  Ymedium 0 0.2 0.4 0.6 0.8 1 0.8 0.6 0.4 0.2 0 , , , , , , , , } { , , 0 100 200 300 400 500 600 700 800 900 1000 1 0.8 0.6 0.4 0.2 0 Y3  Ylow  { , , , , , } 0 100 200 300 400 500

The structure of this fuzzy expert system is Ri: If S is Xi1 and O is Xi2 and D is Xi3 then RPN is Yi For example, three rules in this expert system are as follows: R1: If S is high and O is high and D is high then RPN is high; R2: If S is high and O is high and D is medium then RPN is high; R3: If S is high and O is high and D is low then RPN is medium.

l2

l3

i1

i 1

i2

i3

i

27

l1

l2

l3

i1

i2

i3

i

27

 i 1 ( ( Al1  Al 2  Al 3  X i1  X i 2  X i 3 ) Yi )

That obtained from this relation: R 



27

Ri 



27

( X i1  X i 2  X i 3  Y i )

(2) Here, RPNl (l = 1 to 10) are the fuzzy risk priority number of failure mode l, Al1 (l = 1 to 10) are sets of membership degree of failure mode l for Severity index, Al2 (l = 1 to 10) are sets of membership degree of failure mode l for Occurrence index, Al3 (l = 1 to 10) are sets of membership degree of failure mode l for Detectivity index and Xij (i = 1 to 10, j = 1 to 3) are high (j = 1), medium (j = 2) and low (j = 3) sets for dividing membership degree for O, S and D indexes of rule i. i 1

i 1

2.3 Difuzzification To difuzzify the outputs of the fuzzy expert system, the weighted average method is used with the following equation: Yl  *

 y F(y )  F(y ) j

j

j

j

(3)

j

That Yl* is the difuzzfied risk priority number of failure mode l, yj (j = 1 to 1000) are members of Y set, and F(yj) are membership degree of yj as from the result of Eq. (1). 2.4 Validation

Fig. 2 Output membership functions.

In this section for validating the purposed method to find RPN in FMEA table, failure modes of the engine assembly line in IKCo are analyzed. Here, 10 failure modes are concerned. They are (1) Oil sump leakage; (2) Holder plate seal leakage; (3) Linear seal leakage;


(4) Dip stick leakage; (5) Cylinder head seal leakage; (6) Crankshaft seal leakage; (7) Exhaust manifold leakage; (8) Intake manifold leakage; (9) Camshaft; (10) Water inlet box (WIB). And here for the opinion of costumer, the membership degree is 0.5. For example, fuzzy sets inputs for O, S and D indexes of failure mode 1 means Oil sump leakage and is given below: 0.5 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 1 O1  { , , , , , , , , , } 6 3 4 5 2 3 4 3 2 4 0.5 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 1 S1  { , , , , , , , , , } 5 2 3 3 4 2 3 3 3 2 0.5 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 1 D1  { , , , , , , , , , } 3 3 4 2 3 2 4 3 4 3

After removing equal opinions with smaller membership degrees we have these following sets as inputs of fuzzy expert system. 0.9 0.8 1 0.5 , , , } 2 3 4 6 1 0.9 0.4 0.5 S1  { , , , } 2 3 4 5 0.6 1 0.9 D1  { , , } 2 3 4

O1  {

For other failure modes we do similarly by using (1) as the amounts of RPN for each failure modes. After difuzzifying the inputs by relation (3) the priority of the failure modes is as shown in Table 1.

3. Conclusions The use of linguistic variables allows for the experts to assign more significant values for the indices to be considered, besides taking into account the uncertainties associated with them. Considering the fact that FMEA is a group decision function and cannot be done on an individual basis and different FMEA team members may provide different assessment information, we proposed in this paper an FMEA using a MISO fuzzy expert system. The fuzzy FMEA for determining ranking indices among failure modes is presented in which the typical FMEA parameters are modeled as fuzzy sets. And by using these sets we will

449

Table 1 Priority of the failure modes. Priority 1 2 3 4 5 6 7 8 9 10

Failure mode Linear seal leakage Dipstick leakage Crankshaft seal leakage Cylinder head seal leakage Camshaft Intake manifold leakage Oil sump leakage Holder plate seal leakage Exhaust manifold leakage Water inlet box (WIB)

RPN 677.777 643.478 630.555 578.571 575.439 419.444 403.703 382.353 370 281.81

get each opinion of FMEA individual group. Therefore all opinions of FMEA team are considered in FMEA table. Another advantage of this approach in comparison to previous studies is the consideration of customer’s opinion. We considered costumer as a member of the FMEA team.

References [1] [2]

Available online at: http://www.ikco.com. J.D. Linton, Facing the challenges of service automation: an enabler for ecommerce and productivity gain in traditional services, IEEE Transactions on Engineering Management 50 (4) (2003) 478-484. [3] D.H. Stamatis, Failure Mode and Effect Analysis: FMEA from Theory to Execution, ASQC Quality Press, Milwaukee, Wisconsin, 1995. [4] H.J.W. Vliegen, H.H.V. Mal, Rational decision making: structuring of design meetings, IEEE Transactions on Engineering Management 37 (3) (1990) 185-191. [5] P. Palady, Failure Modes and Effects Analysis, PT Publication, USA, 1995. [6] D.H. Stamatis, Failure Modes and Effect Analysis, FMEA from Theory to Execution, ASQ Quality Press, USA, 1995. [7] P.A.A. Garcia, R. Schirru, P.F. Frutuoso, E. Melo, A fuzzy data envelopment analysis approach for FMEA, Progress in Nuclear Energy 46 (3-4) (2005) 359-373. [8] K.-S. Chin, Y.-M. Wang, G.K.K. Poon, J.-B. Yang, Failure mode and effects analysis using a group-based evidential reasoning approach, Computers & Operations Research 36 (2009) 1768-1779. [9] K. Xu, L.C. Tang, M. Xie, S.L. Ho, M.L. Zhu, Fuzzy assessment of FMEA for engine systems, Reliability Engineering System Safety 75 (2002) 17-29. [10] L.-H. Chen, W.-C. Ko, Fuzzy linear programming models for new product design using QFD with FMEA, Applied Mathematical Modelling 33 (2009) 633-647.

D


DAVID

PUBLISHING

Calculus of the Railway Vertical Stiffness Depending on the Base Plate Stiffness and the Ballast for High Speed Railways Ramon Miralbes1 and Luis Castejon2 1. Design and Manufacturing Department, University of Zaragoza, Zaragoza 50017, Spain 2. Mechanical Engineering Department, University of Zaragoza, Zaragoza 50017, Spain

Received: March 10, 2011 / Accepted: May 25, 2011 / Published: November 25, 2011. Abstract: The study aims to determine a mathematical formula that correlates the vertical stiffness of the principal elements of a high speed railway. To do this, beginning on the traditional formulations, a new mathematical model has been proposed, and has been verified and confirmed with the real information of high speed railways. Finally, there has been obtained a simple expression that correlates simply the vertical stiffness of the railway with the vertical stiffness of the elements that compound it, essentially with the base plate and the ballast system set. On the other hand, also the accuracy of the model has been verified to select the stiffness of the base plate and the ballast system depending on one of this stiffness and the total vertical stiffness that it is wanted. With this simplified formula, it is possible to optimize the vertical stiffness of the railway to obtain the best behavior in each zone and to reduce the final cost of the use of the via, taking in consideration the energy needed to move the trains, the maintenance cost, the useful life, etc.. The process to optimize the railway stiffness in each point depends on the vertical stiffness of the ballast and the sub-ballast, and it is possible to use different plate bases with different stiffness to obtain the optimal stiffness that has been previously obtained with a cost and maintenance analysis. Key words: Railway, way, stiffness, ballast, platform, base plate.

1. Introduction The development of the railroads lines, especially high speed ones, puts of manifest the necessity to establish a vertical ideal stiffness in the tracing, to obtain a system that, along its useful life, has the lowest global cost. These costs depends so much on the maintenance of the way, the construction and the rubbing energy cost, which are highly related to the vertical stiffness of the way. Diverse authors have tried to settle the mentioned problem introducing diverse theories and formulations, of which, nowadays one of the most developed is P.F. Luis Castejon, doctor, industrial engineer, research field: structural design. Corresponding author: Ramon Miralbes, doctor, industrial engineer, research fields: structural design, aerodynamic design. E-mail: [email protected].

Teixeira’s studies [1-2]. These theories try to obtain a vertical ideal stiffness of the rail way that minimizes the global costs of it; nevertheless, they do not present the way to obtain the vertical stiffness of the way depending on the elements that compose it, except using experimental or numerical (F.E.M.) procedures and data bases, like the studies of P. Lv [3] and C. González-Nicieza [4]. It is for it this, that along this work, a mathematical direct correlation, that relates the vertical stiffness of the route, the stiffness of the base plate and the stiffness of the rest of the elements, is tried to be obtained, in order to be able to select rapidly from the formulations previously mentioned, a base plate that provides the vertical ideal stiffness of the rail way depending on the theories established by other authors, and especially in

Calculus of the Railway Vertical Stiffness Depending on the Base Plate Stiffness and the Ballast for High Speed Railways

451

case of high speed railways, sector nowadays in wide development.

2. High Speed Description

Railway

Geometry

Before the formulation of the new method, it is necessary to observe the elements that compose the railway.

Fig. 1

Transversal section of a high speed way.

Fig. 2

Splice bar, rail and base plate.

Analyzing the infrastructure of any high speed railway, we can advise that structurally, it is constituted by the following sets (Figs. 1-2): platform, sub-ballast, ballast, plate base, splice bar and rail. Of these elements, the vertical stiffness of the platform, the sub-ballast and the ballast depends on the properties of the elements of these sets, the properties of the caps and the thickness of these, factors determined frequently by the terrain and the applicable regulation. Besides, the relation between the stiffness of the elements is difficult to state and difficult to change because there is a great inter-relation among them. In relation to the splice bars in high speed, pre or post strained mono-block-concrete has been chosen with a length of 2.6-2.8 m and a weigh of 300-400 kg, which usually have the stiffness higher than the rest of the elements. About the rails it is necessary to emphasize that there has been generalized the employment of the rail UIC60 in high speed, so the stiffness of this element always is the same except if it is used a different material different; then the elastic modulus would change. It is necessary to emphasize again that the stiffness of this element in relation to the rest is high. About the base plate, it is necessary to emphasize that there exists great variety of constructive solutions for this element, of which its vertical stiffness is known perfectly depending on the adopted solution. So it is observed that, to modify the vertical stiffness of the way and to adapt to the vertical ideal stiffness, only the element that it is possible to modify and that contributes to the global stiffness is the base plate.

3. Theory of the Rigidity Coefficients of the Support Along the history there have appeared diverse formulations and theories, which purpose was the evaluation of the vertical stiffness of a railway. Of these theories, the Ballast’s coefficient, the Timoschanko-Saller-Henkel, the Module of way and that of Coefficient of Stiffness of Support are the most important. Of these theories, it is necessary to distinguish the “Theory of the Rigidity Coefficient of the Support” that stable a model in whom the global stiffness is related to the partial stiffness of each one of the elements, like details in Ref. [5], supposing as elastic elements, which are alike a set of four springs arranged in parallel. It is for it that establishes that 1 1 1 1 1 (1) = + + + Keq Kb Kpa Kpb Ksb where Keq: Equivalent stiffness of the rail; Kb: Vertical stiffness of the ballast; Kpa: Vertical stiffness of the platform; Kpb: Vertical stiffness of the plate base; Ksb: Vertical stiffness of the ballast splice bar. Besides, it is observed that the stiffness of the rail and the platform is higher than the rest of elements one,

452


so contribution of the stiffness of the rest is despicable. On the other hand, appears the problem of finding separately the stiffness of the ballast and of the platform. Then the previous formula is modified and is simplified like this: 1 1 1 = + K eq K bp K pa

(2)

Kbp: Vertical stiffness of the ballast-platform se. Nevertheless, the obtained results experimentally present very different values (Fig. 3).

4. Experimental Dates For the study, the experimental information of high speed lines with UIC60 rails and naughty like previously established has been used. In this

Fig. 3 Vertical Stiffness of a high speed line depending on the stiffness of the ballast-platform system with a 60 kN/mm base plate.

information what has been done is to obtain experimentally the global vertical stiffness, changing the vertical stiffness of the ballast- platform system and the vertical stiffness of the base plate (Fig. 4).

5. Mathematical Approach for the Vertical Stiffness of the Way To obtain the formula that relations the vertical stiffness of the way depending on the vertical stiffness of the rest of the elements, it has been begun with the theory of the ballast coefficient, but in this paper it has been proposed this type of formula: 1 A B = + +C K eq K bp K pa

(3)

With it is claimed, beginning with the previous theory and supposing this type of relation, on the one hand, to add some weight (A and B) to each of the partial stiffness and on the other hand, to praise with the constant “C” the stiffness of the rest of elements that they can contribute. So, Keq has been cleared out in order to obtain with a iterative process an expression that can approximate highly the experimental results. The formula used is K eq =

1 A B + +C K bp K pa

(4)

Fig. 4 Vertical experimental stiffness of the way depending on the vertical stiffness of the platform-ballast system and of the vertical stiffness of the base plate.

Then, using iterative approach methods the final expression is 1 0.32732 0.31472 = + + 0.00153 K eq K bp K pa

(5)

The experimental results and the result obtained with the formula 5 are compared in Fig. 5. After the analysis of the dates obtained with the previous formula (5), it can be observed that the approximation presents a R2 of 0.99, so it is an acceptable value for the mentioned formula and comparing them with the real values we obtain a


453

present for Eq. (6), for a Kbp equal or higher than 40 kN/mm, a low deviation (< 5.3% for any value of the rest of parameters), and for Eq. (7), the deviation is also lower than 5.3% for a range of Kpa values equal or higher than 60 kN/mm. Figs. 6-7 show these deviations.

7. Conclusions

Fig. 5

Experimental results vs. formula results.

maximum deviation of 16% and a average mistake of 2.8%, so the previous formula can be a very trustworthy approximation to obtain the vertical stiffness of the way depending on that of the rest of the elements.

The principal conclusions obtained after analyzing the obtained equation is that, this equation presents low and acceptable deviation values and very good correlation among values, for a Kbp range equal or higher than 40 kN/mm and for Kpa equal or higher than 60 kN/mm. On the other hand, Eq. (5) is a very good correlation for any range of values of the rest of parameters.

6. Results and Discussions The principal problem that presents the previous model is that, when the stiffness of the ballast-platform system or the stiffness of the plate base is clear out, and depends on the stiffness of another element. Then, Keq =

1 0.31472 ⇒ Kbp = A B 1 0.32732 + +C − − 0.00153(6) Kbp K pa Keq K pa K eq =

=

1 ⇒ K pa A B + +C K bp K pa

Fig. 6 Approach of the ballast-platform system compared with real dates.

(7)

0 .32732 1 0 .31472 − − 0 .0015 K eq K bp

In this study, the deviation that takes place is highly when the values of the diverse variables are small. For Kbp wants to be obtained depending on the ideal stiffness and Kpa, the obtained values present a high deviation for low Kbp values and the same occurs for Kpa; this is impossible to correct because of the characteristics of the equation. It is for it that the equations previously exposed,

Fig. 7 Approach for the plate base stiffness compared with real dates.


454

So, the proposed mathematical model is good enough to estimate of the vertical stiffness of a way depending on the partial stiffness of the platform-ballast system and the base plate one; then it can be used in future implementations when it is necessary to obtain the vertical stiffness of the way depending on its components. Eqs. (6) and (7) can be used if an optimal stiffness of the way (to optimize the design of the way) is required, and it can be modified the plate base or the ballast-platform system stiffness, because now there is no experience to do it and it is very useful to design the way and reduce the cost of the way during its useful life, as appeared in D. Uzarski and S. McNeil’s studies [6].

References [1]

A.L.-Pita, P.F. Teixeira, C. Casas, L. Ubalde, F. Robusté, Evolution of track geometric quality in high-speed lines:

[2]

[3]

[4]

[5]

[6]

Ten years experience of the Madrid-Seville line, in: Proceedings of the Institution of Mechanical Engineers: Part F, Journal of Rail and Rapid Transit 221 (2) (2007) 147-155. P.F. Texeira, A.L.-Pita, Nuevos Criterios para Reducir los Costes de Mantenimiento de Líneas de Alta Velocidad, Congreso de Ingeniería del Transporte, Santander, 2002. P. Lv, W. Pang, L.J. Meng, L.Q. Gao, Numercial analysis of geogrid and plastic drainage plate used in existed railway alteration project, Geosynthetics in Civil and Environmental Engineering: Part 9, 2009, pp. 673-676. C. González-Nicieza, A. Álvarez-Fernández, A. Menéndez-Díaz, Failure analysis of concrete sleepers in heavy haul railway tracks, Engineering Failure Analysis 15 (2008) 90-117. E.T. Selig, D. Li, Track modulus: Its meaning and factors influencing it, Transportation Research Recorder 1470 (1994) 47-54. D. Uzarski, S. McNeil, Technologies for planning railroad track maintenance and renewal, Journal of Transportation Engineering 120 (1994) 807-820.

D


DAVID

PUBLISHING

Determining of Optimal Dimensions of Compliant Spring Guiding Systems Nenad T. Pavlović, Nenad D. Pavlović and Miloš Milošević Faculty of Mechanical Engineering, Univesrity of Niš, Niš 18000, Serbia Received: October 31, 2011 / Accepted: November 10, 2011 / Published: November 25, 2011. Abstract: Compliant mechanisms transfer an input force or displacement to another point through elastic body deformation. The field of compliant mechanisms is expected to continue to grow as materials with superior properties are developed. The paper takes into consideration some typical spring guiding systems, being able to realize translating planar displacement of the link. Some types of compound spring guiding systems, such as S-shaped guiding spring system, U-shaped guiding spring system and four spring guiding system with additional rigid-body link have been considered and analyzed as compliant structures. The mobility as well as guiding accuracy of the developed compliant mechanisms, that is, their capability to realize translating planar displacement of the link, have been researched, and the optimal dimensions of the mechanism have been determined in order to provide minimal guiding inaccuracy. Key words: Compliant mechanisms, spring guiding systems, guiding accuracy, mobility.

1. Introduction Compliant mechanisms gain at least some of their mobility from the deflection of flexible members rather than movable joints only [1]. The structure of compliant mechanisms consists of relatively rigid sections as well as relatively elastic sections (compliant joints). Compliant mechanisms can provide many benefits in the solution of design problems. These are usually monolithic (single-piece) or jointless structures with certain advantages over the rigid-body mechanisms. They are desirable because they have less wear, weight, noise and backlash than their rigid-body counterparts. Although there are many advantages, the inclusion of compliance provides several challenges in mechanism analysis and design. The mechanisms with compliant joints can realize relatively small displacements, that is, their mobility is limited. Another limitation to their use is fatigue failure at the elastic joints. Corresponding author: Nenad T. Pavlović, associate professor, research field: compliant mechanisms. E-mail: [email protected]; [email protected].

There are many papers considering the structure and function of the compliant joints and compliant mechanisms. Ref. [2] established basic nomenclature and classification for the components of compliant mechanisms. Ref. [3] introduced a method to aid in the design of a class of compliant mechanisms wherein the flexible sections (flexural pivots) are small in length compared to the relatively rigid sections. Ref. [4] presented a formal structural optimization technique called the homogenization method in order to design flexible structures (compliant mechanisms). Ref. [5] presented two approaches being usually used for compliant mechanisms synthesis: converting a known rigid-body mechanism into compliant mechanisms and optimal synthesis with continuum models. Ref. [6] introduced new ideas of technically realizable joints from nature and their integration into elastically movable structures for motion tasks in positioning and manipulating engineering. Some papers have analyzed the influence of the geometry, as well as the material type of the compliant joints on the guiding accuracy of the compliant

456

Determining of Optimal Dimensions of Compliant Spring Guiding Systems

mechanisms [7-8]. Ref. [9] introduced a method for determining the limit positions of compliant mechanisms for which an appropriate pseudo-rigid-body model may be created. Ref. [10] deals with the influence of the geometry, as well as the material type of the compliant joints on a mobility of the single compliant joint and entire compliant mechanisms. Refs. [11-12] introduced some new designs of compliant mechanisms being able to realize translating

been fixed to the frame at the points A0 and B0 respectively (Fig. 2), whilst the other end has been connected to the movable “coupler” at the points A and B. The force F acting at the coupler point A causes parallel guiding of the coupler AB. The horizontal displacement Δx of the coupler AB and vertical deviation Δy (the difference between realized and straight line link translation) can be calculated using the equations:

planar displacement of the link.

x 

This paper takes into consideration some typical spring guiding systems with translating planar

y 

displacement of the link, being analyzed as compliant structures. The aim of the paper is to suggest optimal dimensions of the compliant spring guiding systems being able to realize translating planar displacement of the link as well as to compare their mobility and guiding accuracy. The paper is organized as follows: Section 2 discusses the rigid-link parallel-guiding mechanisms and

introduces

the

compliant

spring

guiding

mechanisms as the counterparts of the rigid-link parallel-guiding

four-bar

linkage;

sections

Fl 3 24 EI z

3x  5l

(1)

2

(2)

where: E—Young’s modulus, Iz—area moment of inertia of the elastic links. On the basis of Eqs. (1)-(2), it can be concluded that the horizontal displacement of the “coupler” AB (Δx) and vertical deviation (Δy) do not depend on the “coupler” length AB . This guiding system could be also analyzed as a compliant mechanism with distributed compliance.

3-5

introduce a S-shaped spring guiding system, an U-shaped spring guiding system and a four spring guiding system respectively, as the examples of the compound spring guiding systems being able to be analyzed as the compliant mechanisms with distributed compliance; section 6 deals with the limits of mobility of the presented compliant spring guiding systems; section 7 gives conclusions. Fig. 1

Rigid-link parallel-guiding four-bar linkage.

2. Compliant Parallel-Guiding Mechanisms Fig. 1 shows a rigid-link parallel-guiding mechanism. The mechanism is a simple four-bar linkage in which the opposing links have the same length, thus forming a parallelogram being able to realize translating planar displacement of the coupler. A spring guiding system based on the rigid-link parallel-guiding four-bar linkage has been shown in the Fig. 2 [13]. The bottom end of the springs 1 and 3 has

Fig. 2 Spring guiding system based on the rigid-link parallel-guiding four-bar linkage [13].


Figs. 3-4 show a designed compliant mechanism with the beam joints, that is, with the film joints, as the counterparts of the rigid-link parallel-guiding four-bar linkage [12]. Fig. 5 shows a parallel-guiding plate-spring mechanism [1] as an example of practical use of compliant spring guiding mechanism. This mechanism is used in various fields of application for force-displacement measurement systems, accurate and reproducible motion in optical systems (Fig. 6), and guiding parts over small displacement while subject to and without disturbance from dynamic loading forces.

Fig. 5

457

Plate-spring mechanism [1].

3. S-Shaped Spring Guiding System Fig. 7 shows an S-shaped spring guiding system [13] as an example of the compound spring guiding systems, that has been designed in order to provide greater horizontal displacement of the “coupler”.

Fig. 3 A compliant mechanism with the beam joints as a counterpart of the rigid-link parallel-guiding four-bar linkage.

Fig. 4 A compliant mechanism with the film joints as a counterpart of the rigid-link parallel-guiding four-bar linkage.

Fig. 6 Optical lens focusing mechanism used in a compact disc player [1].

Fig. 7

S-shaped spring guiding system [13].

The S-shaped spring guiding system can be analyzed as a compliant mechanism with distributed compliance (Fig. 8). We have performed the calculation of the “coupler” horizontal displacement and vertical deviation (Δy) for this compliant mechanism by using of ANSYS Software. Two-dimensional Elastic Beam (Fig. 9) has been used as a characteristic ANSYS element type in the calculation procedure. The element has three degrees of freedom at each node (I, J): translations in the nodal x- and y-directions and rotation about the nodal z-axis.

458


(a)

Fig. 8 S-shaped spring guiding system as a compliant mechanism.

Fig. 10 Fig. 9

(b) Cross sectional area of the links.

Two-dimensional elastic beam.

The link lengths of the mechanism have been: a = 40 mm, c = d = 80 mm, e = f = 20 mm. Cross sectional area is assumed to be rectangular (Fig. 10), defined by the width b = 5 mm and height h = 0.5 mm (for the links A0A and B0B), that is, width B = 16 mm and height H = 8 mm (for the link AB). The results for different values of curve radius r have been shown in Fig. 11. The best guiding accuracy (minimal deviation Δymax) has been provided by the S-shaped spring guiding system with the smallest value of curve radius (r = 2.5 mm). Further, we have analyzed the influence of the eccentricity value e = f on the guiding accuracy. The results have been shown in Fig. 12. The best guiding accuracy has been provided by the S-shaped spring guiding system with the eccentricity value e = f = 22 mm (Table 1).

Fig. 11 The horizontal displacement (Δx) and maximal vertical deviation (Δymax) of the S-shaped spring guiding system (a = 40 mm, c = d = 80 mm, e = f = 20 mm).

4. U-Shaped Spring Guiding System Fig. 13 shows a U-shaped spring guiding system [13] as an example of the compound spring guiding systems that has been designed in order to provide greater horizontal displacement of the “coupler” with greater

Fig. 12 The horizontal displacement (Δx) and maximal vertical deviation (Δymax) of the S-shaped spring guiding system (a = 40 mm, c = d = 80 mm, r = 2.5 mm).


459

Table 1 The horizontal displacement (Δx) and maximal vertical deviation (Δymax) of the S-shaped spring system (a = 40 mm, c = d = 80 mm).

Δx [mm] 2.5 5 10

e = f = 22 mm r = 2.5 mm Δymax [mm] 0.033 0.082 0.383

Fig. 14 U-shaped spring guiding system as a compliant mechanism.

Fig. 13

U-shaped spring guiding system [13].

stability in transversal direction, that is, direction being orthogonal to the motion direction. The U-shaped spring guiding system can be also analyzed as a compliant mechanism with distributed compliance (Fig. 14). We have performed the calculation of the “coupler” horizontal displacement and vertical deviation (Δy) for this compliant mechanism by using of ANSYS Software. We would like to compare the guiding accuracy of U-shaped spring guiding system with S-shaped spring guiding system, and therefore the link lengths of the mechanism have been: a = 40 mm, c = 80 mm, r = 2.5 mm. Cross sectional area is assumed to be rectangular (Fig. 10), defined by the width b = 5 mm and height h = 0.5 mm (for the links A0AA0' and B0BB0'), that is, width B = 16 mm and height H = 8 mm (for the link AB). The results for different values of the eccentricity e have been shown in Fig. 15. The best guiding accuracy has been provided by the U-shaped spring guiding system with the smallest value of eccentricity e = 5 mm. Further, we have analyzed the influence of the value of curve radius r on the guiding accuracy. The results have been shown in Fig. 16.

Fig. 15 The horizontal displacement (Δx) and maximal vertical deviation (Δymax) of the U-shaped spring guiding system (a = 40 mm, c = 80 mm, r = 2.5 mm).

Fig. 16 The horizontal displacement (Δx) and maximal vertical deviation (Δymax) of the U-shaped spring guiding system (a = 40 mm, c = 80 mm, e = 5 mm).

The best guiding accuracy has been provided by the U-shaped spring guiding system with the value of curve radius r = 7.5 mm (Table 2). We have also analyzed the U-shaped spring guiding system with smaller length of the coupler (c = 35 mm).

460


Table 2 The horizontal displacement (Δx) and maximal vertical deviation (Δymax) of the U-shaped spring system (a = 40 mm, c = 80 mm).

Table 3 The horizontal displacement (Δx) and maximal vertical deviation (Δymax) of the U-shaped spring system (a = 40 mm, c = 35 mm).

e = 5 mm r = 7.5 mm Δx [mm] 2.5 5 10

Δymax [mm] 1.9 × 10-9 4.2 × 10-9 10.1 × 10-9

Δx [mm] 2.5 5 10

e = 5 mm r = 7.5 mm Δymax [mm] 1.2 × 10-9 2.6 × 10-9 6.2 × 10-9

This structure is more compact from a constructive point of view, and it provides even greater guiding accuracy (Table 3) than the one with the length of the coupler c = 80 mm.

5. Four Spring Guiding System Fig. 17 shows a four spring guiding system with additional rigid-body link (1) as an example of the compound spring guiding systems that has been designed in order to provide better system stability [13]. The four spring guiding system with additional rigid-body link can be also analyzed as a compliant mechanism with distributed compliance (Fig. 18).

Fig. 17 Four spring guiding system with additional rigid-body link [13].

We have performed the calculation of the “coupler” horizontal displacement and vertical deviation (Δy) for this compliant mechanism by using of ANSYS Software. The link lengths of the mechanism have been: a = 40 mm, c = A 0 B0 = 80 mm, r = 5 mm, g = 5 mm.

Fig. 18 Four spring guiding system as a compliant mechanism.

Cross sectional area is assumed to be rectangular (Fig. 7), defined by the width b = 5 mm and height h = 0.5 mm (for the links A0A1A, A1A''' as well as B0B1B, B1B'''), that is, width B = 16 mm and height H = 8 mm (for the links AA'A''B''B'B and A'''B'''). The results for different values of eccentricity e have been shown in Fig. 19. The best guiding accuracy has been provided by the four spring guiding system with the value of eccentricity e = 10 mm. Further, we have analyzed the influence of the value of curve radius r on the guiding accuracy. The results have been shown in Fig. 20. The best guiding accuracy has been provided by the four spring guiding system with the smallest value of curve radius r = 2.5 mm.

Fig. 19 The horizontal displacement (Δx) and maximal vertical deviation (Δymax) of the four spring guiding system (a = 40 mm, c = 80 mm, r = 5 mm, g = 5 mm).

Further, we have analyzed the influence of the coupler eccentricity g on the guiding accuracy. The results have been shown in Fig. 21.

461


The results have been shown in Table 5. Maximal realizable displacement of the guiding “coupler” AB has been denoted with Δxmax. Maximal acting force causing appearing of maximal permissible bending stress has been denoted with Fmax. The mobility and guiding accuracy of the compliant spring guiding systems have been compared in Fig. 22. The mobility of the U-shaped compliant spring guiding system (Fig. 14) has been denoted with Δx1max, the mobility of the four spring guiding system with rigid Fig. 20 The horizontal displacement (Δx) and maximal vertical deviation (Δymax) of the four spring guiding system (a = 40 mm, c = 80 mm, e = 10 mm, g = 5 mm).

link (Fig. 18) has been denoted with Δx2max, and the mobility of the S-shaped spring guiding system (Fig. 8) has been denoted with Δx3max. Table 4 The horizontal displacement (Δx) and maximal vertical deviation (Δymax) of the four spring guiding system (a = 40 mm, c = 80 mm). e = 10 mm r = 2.5 mm g = 2.5 mm Δx [mm] 2.5

Fig. 21 The horizontal displacement (Δx) and maximal vertical deviation (Δymax) of the four spring guiding system (a = 40 mm, c = 80 mm, e = 10 mm, r = 2.5 mm).

The best guiding accuracy has been provided by the four spring guiding system with the value of coupler eccentricity g = 2.5 mm (Table 4).

Δymax [mm] 9.1 × 10-3

5

17.8 × 10-3

10

36.1 × 10-3

Table 5 The mobility of the compliant spring guiding systems. Compliant spring guiding system S-shaped

Fmax [N] 10.5

U-shaped

49.4

Four spring with rigid link 22.85

Δxmax [mm] 18.84 4.097 6.632

Δymax [mm] 1.53 3.3 × 10-9 23 × 10-3

6. Mobility of the Compliant Spring Guiding System The compliant spring guiding systems are moveable due to flexibility of their elastic segments. However, their mobility is limited. We have researched the limits of their mobility by using of ANSYS Software. The links are assumed to be made of spring steel (Young’s modulus E = 210,000 N/mm2, bending strength σbs = 900 N/mm2). Maximal permissible bending stress σmax< σbs determines constraint positions of the links, that is, the limits of their displacement (mobility) and maximal permissible acting force.

Fig. 22 The mobility and guiding accuracy of the compliant spring guiding systems.

462


7. Conclusions In this paper three types of the compliant spring guiding systems being able to realize translating planar displacement of the link have been analyzed: S-shaped spring guiding system, U-shaped spring guiding system and four spring guiding system with additional rigid-body link. Firstly, we have analyzed a S-shaped spring guiding system as a compliant mechanism and determined its optimal dimensions in order to obtain the best guiding accuracy. For the mechanism made of the spring steel, with the dimensions a = 40 mm, c = d = 80 mm, r = 2.5 mm, e = f = 22 mm, the maximal deviation (the difference between realized and straight line link translation) Δymax = 82 μm has been obtained on the planar displacement of Δx = 5 mm. Further, we have analyzed a U-shaped spring guiding system as a compliant mechanism and determined its optimal dimensions in order to obtain the best guiding accuracy. For the mechanism made of the spring steel, with the dimensions a = 40 mm, c = 80 mm, r = 2.5 mm, g = 5 mm, the maximal deviation Δymax = 4.2 × 10-9 mm has been obtained on the planar displacement of Δx = 5 mm. This spring guiding system with smaller length of the “coupler” (c) provides even better guiding accuracy as well as it seems to be more compact from a constructive point of view, in comparison with the one with the greater length of the “coupler”. Finally, we have analyzed a four spring guiding system with additional rigid-body link as a compliant mechanism and determined its optimal dimensions in order to obtain the best guiding accuracy. For the mechanism made of the spring steel, with the dimensions a = 40 mm, c = 80 mm, r = 2.5 mm, g = 10 mm, e = 10 mm, the maximal deviation Δymax = 17.8 μm has been obtained on the planar displacement of Δx = 5 mm. The guiding accuracy of the U-shaped spring guiding system is extremely better than the accuracy of the other above mentioned compliant spring guiding systems.

Also, we have analyzed the mobility of all above mentioned compliant spring guiding systems, that is, the limit positions of the translating link determined by permissible maximal bending stress. The S-shaped spring guiding system provides considerably greater mobility and the acting force providing this mobility is smaller in comparison with the acting force of others compliant spring guiding systems. If it is necessary to realize maximal displacement with no strong demands regarding guiding accuracy, then S-shaped spring guiding system should be used. If it is necessary to realize maximal guiding accuracy with no strong demands regarding the value of horizontal displacement, then U-shaped spring guiding system should be used. The mobility limits of the U-shaped spring guiding system can be increased by increasing of the value of curve radius r (Fig. 11). Increasing of the value of curve radius r causes, however, the decreasing of guiding accuracy. Nevertheless, this guiding inaccuracy is still considerably smaller in comparison with the guiding inaccuracy of the others compliant spring guiding systems.

References [1] [2]

[3]

[4]

[5]

[6]

L.L. Howell, Compliant Mechanisms, John Wiley &Sons, Inc., New York, 2001. A. Midha, T.W. Norton, L.L. Howell, On the nomenclature, classification and abstractions of compliant mechanisms, ASME Journal of Mechanical Design 116 (1) (1994) 270-279. L.L. Howell, A. Midha, A method for the design of compliant mechanisms with small-length flexural pivots, ASME Journal of Mechanical Design 116 (1) (1994) 280-290. G.K. Ananthasuresh, S. Kota, Designing compliant mechanisms, Mechanical Engineering 117 (11) (1995) 93-96. N.D. Pavlović, D. Petković, N.T. Pavlović, Optimal selection of the compliant mechanism synthesis method, in: Proceedings of the International Conference Mechanical Engineering in XXI Century, Niš, 2010, pp. 247-250. F. Böttcher, G. Christen, H. Pfefferkorn, Structure and function of joints and compliant mechanism, Motion Systems 2001, Collected Short Papers of the Innovationskolleg “Bewegungssysteme”


[7]

[8]

[9]

Friedrich-Schiller Universität Jena, Technische Universität Jena, Technische Universität Ilmenau, Shaker Verlag, Aachen, 2001, pp. 30-35. N.T. Pavlović, N.D. Pavlović, Rectilinear guiding accuracy of roberts-чебышев compliant four-bar linkage with silicone joints, Механика на машините XII (4) (2004) 53-56. N.T. Pavlović, N.D. Pavlović, Stress analysis and guiding accuracy of the compliant four-bar linkages for rectilinear guiding: 47. Internationales Wissentschaftliches Kolloquium, Tagungsband, TU Ilmenau, 2002, pp. 345-346. A. Midha, L.L. Howell, W. Norton, Limit positions of compliant mechanism using the pseudo-rigid-body model

[10]

[11]

[12]

[13]

463

concept, Mechanism and Machine Theory 35 (1) (2000) 99-115. N.T. Pavlović, N.D. Pavlović, Mobility of the compliant joints and compliant mechanisms, Theoretical and Applied Mechanics 32 (4) (2005) 341-357. N.T. Pavlović, N.D. Pavlović, Compliant mechanism design for realizing of axial link translation, Mechanism and Machine Theory 44 (2009) 1082-1091. N.T. Pavlović, N.D. Pavlović, Design of compliant spring guiding mechanism: 53. Internationales wissenschaftliches Kolloquium TU Ilmenau, Tagungsband (DVD), Ilmenau, 2008, pp. 39-40. S. Hildebrandt, Feinmechanische Bauelemente, VEB Verlag, Berlin, 1988.

D


DAVID

PUBLISHING

Metamodeling Transfer Capability of Manitoba-Ontario Electrical Interconnections Songqing Shan1, Wenjie Zhang2, Myrna Cavers2 and G. Gary Wang3 1. Dept. of Mech. & Manu., Falculty of Engineering, University of Manitoba, Winnipeg, MB R3T 5V6, Canada 2. System Performance Department, Manitoba Hydro, Winnipeg, MB R3C 2P4, Canada 3. Mechatronic Systems Engineering, School of Engineering Science, Simon Fraser University, Surrey, BC V3T 0A3, Canada

Received: August 25, 2011 / Accepted: September 09, 2011 / Published: November 25, 2011. Abstract: The electric power transfer capability on the Manitoba-Ontario interconnection depends on various system operating conditions such as area generation patterns and ambient temperatures. This work models the power network as a black-box function, which is evaluated with the system reliability analysis techniques to determine the maximum transfer capability under a given operating condition. A metamodel or an approximation model of the maximized power transfer capability is built based on the sampled system responses and optimized with respect to the corresponding operating conditions. An optimal metamodel is implemented as a prototype software tool, PTCanalyzer, and applied to Manitoba-Ontario interconnection power transfer calculations. This optimized metamodel technique provides an in-depth understanding of the dependency of the power transfer capability on system operating conditions and proves to be an effective tool in optimizing the operation planning of the interconnection for a given power system configuration. The PTCanalyzer has the potential to be used for optimization of other power network interconnections. Key words: Power transfer, black-box function, metamodel, optimization.

1. Introduction The power transfer capability on the Manitoba-Ontario interconnection (OMT) is limited by respecting the operating criteria of the Manitoba Hydro Winnipeg River 115 kV systems, subject to contingency disturbances. The current operating guides are derived from a pre-determined generation pattern of the six hydraulic generating plants on the Winnipeg River and the thermal generating plant at Selkirk, a suburb of Winnipeg. Extensive simulation studies are required to determine the interface transfer capabilities for pre-determined operating conditions. The problem with the existing operational planning procedure is that for any deviation of the generation pattern or the temperature from the pre-determined values, additional studies are required or the conservative power transfer Corresponding author: G. Gary Wang, professor, research field: design, optimization, electric vehicles, fuel cells, advanced manufacturing. E-mail: [email protected].

limits are applied. It is expected to find a solution to effectively maximize the power transfer capability of the interconnection under forecast system operating conditions. The power transfer capability will be determined as a TLAP (Tie-line Limit Advisory Program) compatible function of the area generation patterns. This work provides a continuous mathematical model to capture the relation between the power transfer capability on OMT and the output of the related generating plants. This continuous mathematical model maximizes the power transfer capability on OMT while optimizing the generation resource on the Winnipeg River system. This work develops a general methodology and the corresponding tool that can be used to maximize the electric power transfer capability of interconnected power grid. The work is organized as follows: Section 2 introduces the proposed methodology; section 3 presents the case study; and section 4 gives the conclusion.

Metamodeling Transfer Capability of Manitoba-Ontario Electrical Interconnections

2. Proposed Methodology

a xb otherwise

(1)

X

The corresponding uniform Cumulative Density Function (CDF) is xa 0  x  a F ( x)   a xb (2) b  a 1 bx In this project, it is assumed that the generation patterns are of the uniform distribution. 2.1.2 Mathematical Model There are a number of widely used metamodels such as polynomials, Radial Basis Functions (RBF), Artificial Neural Network (ANN), and Kriging model. Among these models, the polynomial model is robust, simple-to-implement, and easy to interpret and understand. This project therefore adopts the polynomial metamodel, which is in the form of Ref. [1]. β ε  (3) where is an n  1 matrix and represents sampled is an n  p matrix, representing n number responses;

f

The transfer capability over a power network is determined by computer simulations, the process of which is considered in the study as a so-called black-box function. For optimization of black-box problems, a widely-used approach is using sampling and modeling techniques to build a metamodel, on which optimization is performed [1]. This section introduces related sampling, optimization, and

 1 f ( x)   b  a 0

X

2.1 Related Theories

metamodeling theories. 2.1.1 Sampling In this work, we use the term “sampling” to refer to the computer experimental design, which is widely used to build surrogate models or metamodels. Wang and Shan [2] reviewed the techniques of the computer experimental design. This work uses uniformly distributed random sampling to sample the inputs. The uniform distribution has a constant Probability Density Function (PDF) between its two bounded parameters (a, b) as follows [3]:

f

This study proposes the use of metamodeling to build a mathematical model of the maximized transfer capability of interconnected power grid. The metamodeling approach literally means the “model of model”. It starts with systematically planned samples, or “experiments”. Each sample is an assumed combination of all the related factors. These factors will be used as inputs to the system model, on which various analyses are performed. The output will be the feasibility of the sample point and the values of the interested factors. For example, if the transfer capability is of interest, generation patterns may become the input factors. Given a set of values of these input factors, system models are called to test feasibility of such a combination. If it is feasible, the analysis should determine the maximum possible value for the transfer capability. Once all the samples have been evaluated, a metamodel can be built for the transfer capability as a function of the input factors. After validation, the metamodel can be used to schedule and plan the interchange across the interconnections depending on the real time values of the input factors. Generally speaking, this project applies sampling, optimization, and metamodeling techniques to build a mathematical model of the transfer capability, which will be implemented as a TLAP compatible function. This model provides a solution to effectively maximize the transfer capability of the interconnection under forecast system operating conditions.

465

of sample points of p predictor variables. The predictor variables include input variables, quadratic terms of the variables, or combinations of variables;β is a p  1

ε matrix of regression coefficients; and

is an

n  1 matrix and represents random disturbances.

The performance and response of a power network can be modeled and evaluated by the PSS/ETM power system simulation program coded by IPLAN language [4]. Given a system operating condition such as a


466

. The residuals are the

difference between the sampled value predicted value ˆ .   ˆ(  )

and the

f H

I

bl  x l

is called the hat matrix

f

because it puts the “hat” on

(6)

The residuals are useful for detecting failures in the model assumptions since they correspond to the ε in the model Eq. (3). By assumption, these errors ε have independent normal distributions with errors zero mean value and a constant variance. The residuals, however, are correlated and have variances that depend on the locations of the data points. It is a common practice to scale the residuals so they all have the same variance. By scaling the residuals, a confidence interval for the means of each error can be obtained as

where K  0.618 and I  bu  bl . (3) Perform black-box function analysis and decide on the next interval for further search. Evaluate xu If xu meets operating criteria, set b l  x u Else Evaluate xl If xl meets operating criteria, set

T

f

x1  bu  KI xu  bl  KI

X

function is to be performed.

f H

and define the two points, at which the black-box



f f r

(2) Break up the searching range into three intervals

T

X

tolerance  (for example   10 MW).



(5)

1

f

Section method are as follows: (1) Specify bl and bu and set K  0.618 and



where



X X

trial values of f, which will be evaluated against contingency conditions to ensure such a value is achievable and feasible. Then a new trial value of f is generated until the maximum f max is obtained. The steps for searching f max based on the 1-D Golden

b X

f

dimensional search process. In specific, given a search range for f max in [bl，bu ] , the process starts from

ˆ

H

generation pattern, the maximum power transfer capability, f max can be determined through a one

ci  ri  t 1  ,i ˆ i  1  hi

(7)

2

where ci is the confidence interval for the means of the i-th error; ri is the raw residual for the i-th data point; t i is the scaled residual for the i-th data point; ˆ (i ) is the estimate of the variance of the errors

H

excluding the i-th data point from the calculation, and hi is the i-th diagonal element of .

bu  xu

Else bu  xl

(4) Check whether a satisfactory level of tolerance is

fX

reached. If bu  bl   , return to Step 2. (5) Maximum transfer is obtained as f max  bu .

b

is the vector of For the problem in Eq. (3), f max ' s for each given input vector . The solution to

,b p

, where    

, p

as

T ]

, pb p

 b b

. . . ,2 ,1 T ] [

at the data points

. . . ,2 ,1 [

the predicted values

f

back into the model formula to get

2

(4)

. . . ,2

1

T

re-write  b  b ,1



f X

T

X

b

Substituting



X

b

β  ˆ 

1

[

solution is

confidence intervals help to identify outlier observations for a given model. 2.1.3 Metamodel Optimization A good metamodel should objectively reflect the black-box function, being both accurate and simple. In order to get such an optimal metamodel, the metamodel is optimized to best fit the data points. We T b ]

the problem is the vector, , which estimates the unknown vector of parameterβ . The least square

Confidence intervals that do not include zero are equivalent to rejecting the hypothesis that the residual mean is zero at a significance probability of  . Such

with γi = 0 or 1. By various combination of the components of  , the predictor variable terms of the


467

X

f



︶

n /

︶︵*

(8)

b X



f

(  ˆ) T * (  ˆ) / n T

︵

* /n

f



b r f X

rmse 

f f T r

metamodel or the column of can be selected and the metamodel optimized. According to Eq. (6), the root mean squared errors (RMSE) are given as

and the optimal metamodel can be obtained by solving the following combinatorial integer optimization problem. min rmse (9) s.t. γi ( 0 or 1 )

X

We simplify this optimization by the following steps: (1) Transform the components of data points (the partial components of ) into a common range [-1, 1]. (2) Build a metamodel and find . (3) Set the small value components of as zero

b

b

b

and build a new metamodel. In this work, we set the to be zero if the value of components of component’s value is less than one. (4) Observe the new value of rmse. If the new rmse value is acceptable, the optimal metamodel is obtained. Otherwise, a metamodel with a smaller rmse value is selected.

metamodel optimization is for model building and the optimal model selection. The procedures as illustrated in Fig. 1 are explained here in some detail. Step 1: Initial sampling In this project, the sampling function “RAND” in MatlabTM is used to sample the generation patterns and ambient temperatures. The number of sampling data points is n  (nv  1) * (nv  2) / 2 , where nv represents the number of the generation plants plus one ambient temperature variable. By assuming the uniform distribution of the generation patterns and temperature, the proposed method and associated tool, PTCanalyzer, automatically samples the multiple generation patterns and temperature within the given lower and upper limits of each variable. This sampled data is sequentially fed into PSS/ETM for power network simulations coded by IPLAN language [4]. Step 2: Black-box function evaluation This step includes the power network system simulation to determine the transfer limits. PTCanalyzer automatically starts the PSS/ETM and loads Start Initial sampling Black-box function evaluation

2.2 Implementation and Convergence Criteria

Based on the above black-box function realization and related theories, this section describes the implementation procedures and metamodeling convergence criteria. 2.2.1 Implementation Procedures The implementation procedure for the entire metamodeling process includes three main components, sampling, black-box function evaluation, and metamodeling/optimization. The purpose of sampling simulates the inputs, i.e., the generation patterns and ambient temperature. The black-box function evaluation simulates the power network responses and determines its maximum transfer capability for the given generation pattern. Metamodeling and

Metamodeling

Model Validation

N

Converged? Y Metamodel optimization

Output

Stop Fig. 1 Optimal metamodeling flowchart.

468


in an initial base case representing a specified operating condition. For each combination of generation patterns and temperature, PSS/ETM performs the contingency analysis and the results are automatically sorted and searched for criteria violations and a maximum transfer level is found. Step 3: Metamodeling Once the transfer limits for the sampled generation patterns and temperatures are obtained, the remaining task is metamodeling. In the previous section, a general mathematical model Eq. (3) is introduced and it can have different types such as linear, pure quadratic, and so on. In this project, a full quadratic model is proposed based on the fact that a full quadratic model suits better

It can be optimized to become a model most suitable to a specific application by removing terms from the full quadratic model. Step 4: Model validation Model validation includes re-sampling nv data points as in Step 1, performing black-box function

the black-box function and metamodel prediction at test points. The comparison result is checked against

new

the metamodel. The true response values,

new

, are

w e

fn

w e

fn

w e

fn

obtained by calling the black-box function. The relative errors are calculated by (  ˆ )/ (10)

er

The maximum absolute relative error is ermax  max

er

one of the two convergence criteria as discussed below. Step 5: Convergence check This step checks whether convergence criteria are met. If the convergence criteria are not met, the new nv sampling data points from Step 4 are added to the previous modeling data set and the process goes back to Step 3. Step 6: Metamodel optimization A full quadratic model is a fixed model, and is to be optimized into a more succinct and accurate model by using the methodology as described in the previous section. Step 7: Result output The result output includes two categories. One is the

f

predicted values at test points, and comparing values of

The metamodel is called to predict values of the black-box function on the new sample point set. In the model validation step (Step 4), after sampling a new data set, the predicted values, ˆ , are obtained from

f

analysis as in Step 2, evaluating metamodel to give

b

linear, pure quadratic, and two-factor interaction terms.

b

degree of flexibility. A full quadratic model covers all

b

for the application. It is simple and offers a certain

parameter output. The other is the graphic output. The parameter output includes the optimal metamodel, root mean squared error, number of black-box function evaluations, and number of iterations. The graphic output includes a prediction plot of the metamodel, the metamodel coefficients and their 95% confidence intervals, a plot of residual vs. predicted values, as well as residuals and their 95% confidence intervals. 2.2.2 Convergence Criteria This work applies two convergence criteria. The first criterion is the change of the metamodel coefficients. As the coefficients define a polynomial metamodel, if the change of the coefficients between iterations is small, it means that the metamodel is stable. For example, the convergence criteria for the metamodeling coefficient may be specified as max i  i 1  0.1 in two consecutive iterations. This criterion tests the metamodel at all evaluated sample points. The second criterion is applied for new sample points, and the number of new sample points is set to be the same as the number of initial sample points n  (nv  1) * (nv  2) / 2 .

(11)

This work sets e rmax  0.05 (a preset value). The new sample data set will be added to existing evaluated data set, which is used to update the metamodel. Besides the above two criteria, the maximum number of iterations is also applied. If convergence criteria are met or the number of iterations reaches the maximum number, the metamodeling process terminates.

3. Case Study The proposed methodology in section 2 has been


implemented as a prototype software tool, PTCanalyzer. PTCanalyzer provides users with both graphical and numerical outputs and has been applied for modeling and calculating power transfer capability on the Manitoba-Ontario interconnected systems. Seven cases representing different operating conditions are used to test the proposed methodology with two to be described in detail in this work.

469

Pine Falls

Selkirk

Great Falls

PDB

Slave Falls MCA

Rosser

Seven Sisters

3.1 Case Description OMT St. Vital

Fig. 2 shows a single line diagram of Winnipeg River

area

system

and

Manitoba-Ontario

interconnections. The 115 kV transmission system interconnects the generating plants of the Winnipeg River,

the

Selkirk

generating

station,

the

Manitoba-Ontario interface, and the major 230 kV transmission grid surrounding the City of Winnipeg. There are six hydraulic generating plants on the Winnipeg River. Four plants, Seven Sisters, Great Falls, McArthur Falls, and Pine Falls, are connected through the 115 kV transmission system. The other two plants, Pointe du Bois and Slave Falls, feed radially into the City of Winnipeg 66 kV system. Selkirk generating station is a gas fired thermal plant located near the City of Winnipeg and connected to the 115 kV transmission system. The OMT consists of two 230 kV tie lines from

Fig. 2 Winnipeg River area system and OMT. Table 1 Winnipeg River generation output ranges. Generation levels High Low

G1

G2

G3

G4

G5

84-168

69-115

0-23

28-56

45-90

28-84

23-69

0-23

7-28

15- 45

low scenarios. The G2 and G3 are generating units at Great Falls station, which are modeled separately. Temperature is assumed at a constant 40 °C. Seven cases of different generation levels have been tested. But due to the page limitation, only two cases for high generation levels are presented in the paper. 3.2 Case 1—Import

Manitoba to northwestern Ontario. The interface is

The import is for power transfer west from Ontario

controlled by the 115 kV phase shifting and 115/230

to Manitoba. The total generation on the four Winnipeg

kV voltage regulating transformers at Whiteshell

River plants varies between 333 MW and 558 MW,

station near the Manitoba-Ontario border. Generation

which falls into the high level generation range as listed

levels of the hydraulic plants on the Winnipeg River

in Table 1. For this case, the Selkirk generating units

are a function of river system management and

are off line. The simulation runs 30 iterations with 651 times of black-box evaluations. The rmse for this case is 3.5 and the maximum absolute residual is 23.8. Fig. 3 shows the modeling interface of PTCanalyzer. The horizontal coordinate denotes the various generating plants and their corresponding generation level ranges, respectively. The vertical coordinate denotes the transfer capability on the OMT. The “Export” button is used to select specific terms to build a simplified

economic operation of the plants. The total generation levels can vary significantly from a maximum of 590 MW to minimum of 137 MW depending on the river flow. Selkirk Generating station is operated when required for system reliability. The case studies in the paper are for 2007 summer peak load with all the transmission lines in service. The Winnipeg River generation levels are listed in Table 1 where the generation levels are organized into high and

470


Table 2 Metamodeling data for Case 1. Coefficients Model terms

Fig. 3 Case 1 modeling output interface.

metamodel. The users can use the pop-up menu, “user specified”, to interactively change the model between “linear”, “pure quadratic”, “interaction”, “full quadratic” and the optimal model. There is a family of curves, each showing the sensitivity of a generating plant output to the transfer capability on Manitoba Ontario interconnection. The two red dash curves show 95% global confidence intervals for the predictions. Fig. 3 visualizes the relationship between the power transfer capability on the OMT and the generation patterns of Winnipeg River generating plants. Users can drag the horizontal dashed blue reference line and watch the predicted values update simultaneously. Alternatively, users can get a specific prediction by typing the values of the generation pattern into an editable text field. For example, users can input a generation pattern, G1 = 120, G2 = 92, G3 = 11, G4 = 41, and G5 = 67, to predict the transfer capability to be 127.9138  1.2995. Other metamodeling related data are listed in Table 2, where the first column shows the model coefficients; the second column shows the terms in the optimized model, and the third column gives the 95% coefficients’ intervals for the coefficients. For this example, the value of the root mean square errors is 3.5423 and the maximum absolute residual is 23.7687. In the output model, each term has not only its physical meaning, but also some uncertainty. Fig. 4 shows the 95% confidence interval of the coefficients by the term of the coefficients on the horizontal axis.

-345.2390 0.9763 0.3888 0.5094 0.6801 0.3232 0.0052 -0.0040 -0.0067 0.0018 0.0040

Constant G1 G2 G3 G4 G5 G2 * G3 G2 * G5 G3 * G5 (G2)2 (G5)2

95% Confidence Interval -365.2464 0.9651 0.0457 0.1296 0.6458 0.0399 0.0019 -0.0056 -0.0100 0.0001 0.0022

-325.2316 0.9875 0.7320 0.8892 0.7145 0.6065 0.0084 -0.0024 -0.0033 0.0035 0.0059

Fig. 4 Case 1 95% coefficient confidence intervals.

Only the constant term has a bigger interval. A big interval under a fixed confidence level indicates more uncertainty. The constant term is related to the power network conditions and status. In this case, the big interval of the constant terms indicates that the big uncertainty comes from the power network, and the power transfer capability depends on the power network conditions and status. Fig. 5 displays the residuals vs. the predicted values. The general impression is that the residuals symmetrically scatter along zero with a few points scattering out, which approaches the assumption that the errors have independent normal distributions with mean zero and a constant variance. Fig. 6 plots the residuals and 95% confidence intervals for all the function evaluations. The 95% confidence intervals about these residuals are plotted as error bars. There are

4  100%  0.61% outliers since 651

their errors bar do not cross the zero reference line.


471

Table 3 Case 1 transfer capabilities comparison. G1 168 84

Generation pattern G2 G3 G4 G5 115 23 56 90 46 23 28 45

Meta model -42.2 -125.4

Black box -47 -127

Difference 4.8 1.6

Table 4 Case 1 metamodel comparison. Pure quadratic -42 ± 5.2 -42 ± 2.5 -40 ± 4.8 -5 -5 -7 -125 ± 3.4 -124 ± 1.7 -123 ± 3.2 -2 -3 -4

Optimal

Fig. 5 Case 1 residuals vs. predicted values.

Linear

Interactions -45 ± 8.8 -2 -125 ± 3.8 -2

Full quadratic -42 ± 10.6 -5 -124 ± 5.1 -3

3.3 Case 2—Export

The second case study is for export, which is power transfer east from Manitoba to Ontario. Generation on the Winnipeg River plants varies between 333 MW and 558 MW, which falls into the high level generation range as shown in Table 1. For this case, the Selkirk generation is at 65 MW. The simulation runs 24 iterations with 525 times of black-box evaluations. The rmse for this case is 2.9 and the maximum absolute residual is 30.6. The modeling output interface is shown in Fig. 7. As can be seen, the Fig. 6 Case 1 95% Residuals confidence intervals.

non-linear relationship between the input factors and

Table 3 compares the power transfer capabilities determined by the optimal model from the PTCanalyzer and the conventional method, respectively, for two generation patterns and their differences. It can be seen that the derived model can accurately predict the power transfer capability. In the modeling process, users can select five different models, optimal model or specified model, linear model, pure quadratic model, interactions model and full quadratic model. Table 4 lists the various models’ results and their differences for the two generation patterns listed in Table 3. It can be seen that each model can accurately predict the power transfer capability on OMT. Among all, the optimal model yields better-than-average performance from the perspectives of both the difference between the predicted value and the actual value, as well as the variance.

the output is apparent, which is in contrast to Case 1 whose relationship is mostly linear. Other metamodeling related data are listed in Table 5, in a format similar to Table 2. Table 6 lists the power transfer capabilities determined by the metamodel and the conventional method, respectively, for two generation patterns and their difference. It can be seen that the proposed model can accurately predict the power transfer capability even for non-linear relationships. Table 7 lists the various models’ results and their differences for the two generation patterns in Table 6. From the test results it is found that the optimized metamodel technique provides an in-depth understanding of the dependency of the power transfer capability on system operating conditions and proves to be an effective tool in optimizing the operation


472

planning of the interconnection for a given power system configuration.

G1 168 112

4. Conclusions This work investigates the power transfer capability on the Manitoba-Ontario Interconnection for various operating conditions by applying the metamodeling techniques. This work can enhance the understanding of the performance of Manitoba-Ontario interconnected

Fig. 7

Case 2 modeling output interface.

Table 5 Case 2 metamodel data. Coefficients

Model terms

290.2372 0.0078 0.2068 0.0026 0.0014 0.0019 -0.0025 -0.0035 -0.0014 -0.0015

Constant G1 G2 G1 * G2 G1 * G4 G1 * G5 G2 * G4 G2 * G5 (G1)2 (G2)2

Table 6 Case 2 transfer capabilities comparison.

95% Confidence Interval 280.0010 300.4734 - 0.1247 0.1402 0.0609 0.3526 0.0021 0.0032 0.0006 0.0022 0.0014 0.0024 -0.0038 -0.0013 -0.0043 -0.0027 -0.0019 -0.0009 -0.0022 -0.0007

Generation pattern G2 G3 G4 G5 115 23 56 90 93 22 42 75

Table 7

Meta model 297.4 296.2

Black box 300 300

Difference -2.6 -3.8

Case 2 metamodel comparison.

Pure Optimal Linear 297 ± 3.7 297 ± 2.5 294 ± 4.7 -3 -3 -6 296 ± 1.2 296 ± 1.4 297 ± 2.5 -4 -4 -3

Interactions Full 301 ± 7.3 299 ± 8.6 1 -1 295 ± 2.1 297 ± 3.0 -5 -3

power grid. A modeling tool, PTCanalyzer, is developed and used for power transfer capability metamodeling under varying system conditions. The optimized metamodel indicates the effects of generation stations on the transfer capability and maximizes the use of the Manitoba-Ontario Interconnections. The method and the tool are proved to be useful in operational planning of the interconnected power grid.

References [1] [2]

[3] [4]

R.H. Mayers, D.C. Montgomery, Response Surface Methodology, John Wiley & Sons, 1995. G.G. Wang, S. Shan, Review of Metamodeling Techniques in Support of Engineering Design, Transaction of ASME, Journal of Mechanical Design 129 (4) (2007) 370-380. R. Johnson, G. Bhattacharyya, Statistics, Principles and Methods, John Wiley & Sons, 1986. Power Technologies, Inc., IPLAN Program Manual, December, 2000.

D


DAVID

PUBLISHING

Stress Analysis of the Sarafix External Fixator Design Elmedin Mešić, Adil Muminović, Nedžad Repčić and Mirsad Čolić Department of Mechanical Design, Faculty of Mechanical Engineering Sarajevo, Sarajevo 71000, Bosnia and Herzegovina Received: September 16, 2011 / Accepted: October 11, 2011 / Published: November 25, 2011. Abstract: A stress analysis of the Sarafix external fixator design was performed using finite element analysis (FEA) and experimental tensometric measurements. The study was conducted at one of the Sarafix fixator configurations that have a clinical application in the treatment of tibia fractures. The intensity of principal and von Mises stresses generated at two measuring points (MP) on the fixator connecting rod were monitored and analyzed during the testing on axial compression on the fixator design and its finite element model (FEM). The 3D geometrical and FEM model of the fixator was formed using the computer aided design/computer aided engineering (CAD/CAE) software system CATIA. Verification of the results for the dominant principal stresses obtained from FEA was carried out through tensometric measurements. The measuring chain consisted of strain gauges connected into two Wheatstone half-bridges, digital measuring amplifier system and a computer with software for acquisition and monitoring of measurement results. A quite good agreement was observed between the results obtained on the basis of FEA and results of experimental tensometric analysis. Key words: Finite element analysis, tensometric measurements, principal stresses, von Mises stress, Sarafix external fixator.

1. Introduction After J.F. Malgaigne invented the external fixator in 1840, their selection and application was generally carried out on empirical grounds and accumulated experience in clinical orthopedics and traumatology. In order to promote and carry out necessary research to improve fixation, a development of a theoretical analysis of problems fixation based on the principles of structural mechanics is pursued. With the aim of determining mechanical characteristics of external fixators, various sensors and transducers are set up on their designs [1]. During the past few years, except for performing the experimental testing, there has been an increased use of 3D modeling and FEA, in order to more fully describe the behavior of the fixator and its components during the loading [2]. The external fixator is a medical device for the immobilization of fractures or serious damage to the structure of extremities. External fixation is a method Corresponding author: Elmedin Mešić, M.Sc., M.Eng., research fields: mechanical design, medical engineering, CAD/CAE, FEA, experimental stress analysis, biomechanics. E-mail: [email protected].

of fracture immobilization achieved by the application of pins or wires into or through a bone and their binding to the outer frame. The above basic concept of the method has not changed since its origin, but progress is reflected through the development of new design solutions and materials used. The most complicated aspect of bone fractures, both in terms of complexity of treatment and structural stresses of external fixator, is an open fracture. In the case of open fractures, in the initial phase of treatment, the full load is transferred through the fixator. This paper presents the results of a stress analysis of the unilateral uniplanar configuration of the Sarafix external fixator (Fig. 1) in the case of load under axial compression. Otherwise, the most significant load of the external fixator during the postoperative treatment of patients is the axial compression itself. An open fracture at the middle of tibia with the fracture gap of 50 mm was examined. The analyzed configuration of the Sarafix fixator contains four half-pins in the proximal and distal segment of a bone placed in one plane.

474

Stress Analysis of the Sarafix External Fixator Design

Fig. 1 The Sarafix external fixator.

The paper is organized as follows: Section 2 presents used methods of work; section 3 is finite element analysis of the fixator design; section 4 introduces experimental tensometric analysis; section 5 presents results; section 6 gives conclusions and future work.

2. Objective and Methods Complete mechanical research of the fixator, besides the examination of its rigidity to the loads to which it was exposed after the application, includes the analysis of stresses (von Mises and principal stresses) on the characteristic location of fixator designs. Mechanical testing of Sarafix fixator was not performed before its clinical application, because of the war-time circumstances in which it originated. Extensive studies of the mechanical research of the Sarafix fixator were carried out within the master’s thesis [3]. Geometrical modeling of the Sarafix fixator and FEA were carried out at the Laboratory for Computer aided design—CADlab of the Faculty of Mechanical Engineering Sarajevo. The first step consisted of forming a 3D geometrical model of the analyzed Sarafix fixator configuration, whereupon the FEA was performed on the model using CAD/CAE software system CATIA. During the structural FEA, values of von Mises stresses were observed at two control points

in the middle of the fixator connecting rod. The intensity and direction of principal stresses were monitored and analyzed at the same points. Experimental testing was conducted at the Laboratory for materials testing and Laboratory for machine elements. At the Laboratory for materials testing, the examination of the analyzed configuration of the Sarafix fixator on the axial compression was performed, using a universal material testing machine (Zwick GmbH & Co., Ulm, Germany, model 143501). During the testing, the intensity of the load on the model of proximal segment of the tibia was controlled, using the force transducer. A wooden model of the proximal and distal bone segments are supported on the ball joint supports. Tensometric measurement equipment (Laboratory for machine elements) was used to control and monitor the value of the dominant principal stress on the two measurement points at the middle of the fixator connecting rod. The following equipment from the HBM (Hottinger Baldwin Messtechnik GmbH, Darmstadt, Germany) manufacturer was used:  Digital measuring amplifier system—digitales messverstarker-system (DMC) 9012A;  Computer with software for acquisition, monitoring and processing of measurement results—Catman; and  Four strain gauges (type 3/120LY11) connected in two Wheatstone half-bridges. The strain gauges were placed on the opposite sides of the Sarafix fixator connecting rod at the same locations where intensities of maximum and minimum principal stresses were monitored during the FEA. Thereafter, the strain gauges were connected with the DMC system and computer through two separate channels. In this way, the maximum and minimum principal strains on the measuring points were measured independently. This measurement method was applied because the connecting rod was subjected to a compound strain, which consisted of bending strain and axial compressive strain.

475


3. FEA of the Fixator Design Understanding the physical behavior of the model is a basic prerequisite for successful process of modeling real systems. Before that, it is necessary to make numerous assumptions related to modeling: structure, joints between the components, boundary conditions, loads, materials, etc. During the processes of the linear FEA, the material of wooden bone models was defined as orthotropic, while materials of the fixator design were modeled as isotropic. The FEM model consisted of solid finite elements of a linear (TE4) and parabolic tetrahedron (TE10) type (Fig. 2). Join elements of the spider type were used for modeling the joints between the components of the Sarafix fixator [3]. The following joints were used: Fastened connection, Contact connection and Bolt tightening connection. The modeling of the influence of supports was performed using a Smooth virtual part. Fig. 3 shows the CAD and FEM model of the analyzed Sarafix fixator configuration after preprocessing. At the end of the proximal bone segment, the axial load in the form of surface force (Force density) was applied in the direction of the z axis of the Cartesian coordinate system. A displacement constraint of the Sarafix FEM model was derived by using the Ball join restraint on the model of distal bone segment. Likewise, a displacement constraint at the model of proximal bone segment was performed by using the User-defined restraint, which prevented the two translations in direction of x and y axis of the Cartesian coordinate system (Fig. 3). The principal stresses of the stress tensor are the distinctive values of the stress tensor, while their direction vectors are the principal directions or eigenvectors [4]. When the coordinate system is chosen to coincide with the eigenvectors of the stress tensor, the stress tensor is represented by a diagonal matrix: 0  1 0  (1) σ   0  2 0   0 0  3 

TE4

Fig. 2

TE10

Finite elements of tetrahedron TE4 and TE10 type. User-defined

Force

Restraint

Connecting rod

One-half

Ball

pin

join

Fig. 3 3D CAD and FEM model of the analyzed Sarafix fixator configuration.

where σ1, σ2 and σ3 are the principal stresses. The values of the principal and von Mises stress were controlled on two locations at the middle of the fixator connecting rod during the FEA. The measuring point closer to the model of the bone segment was marked with MP- and the point on the opposite side of the connecting rod was marked with MP+ (Fig. 4). Compressive stresses, which were recorded at the measuring point MP- have a higher intensity compared to the tensile stress at the MP+. This is a direct consequence of the appearance of an eccentric compression that exposed fixator connecting rod.

476


Detail A MP+, σ1

MP-, σ3

B

A View B MP+, σ1

MP-, σ3

Fig. 4 Plot of the principal stresses.

The direction of the maximum principal stress (σ1) on the measuring point MP+ coincides with the direction of z axis, i.e., the axis of symmetry of the connecting rod. Likewise, the direction of the minimum principal stress (σ3) on the MP- coincides with the axis of symmetry of the connecting rod. The minimum principal stress compared to the other two principal stresses at the MP- is dominant. Within Fig. 4 a view B is given where directions and intensities of the principal stresses on the measuring points are presented. Note that at the MP+ the maximum principal stress is in fact the tensile stress, while at the MP- the minimum principal stress is actually the compressive stress. Also, it can be seen that the dominant principal stresses (σ1 and σ3) are in the bending plane of the fixator which is not parallel with the plane of the one-half pins. For this reason, the vectors of the dominant principal stresses do not match either (Fig. 4, View B). A quantity called the equivalent stress or von Mises stress is commonly used in solid mechanics to predict

yielding of materials under multiaxial loading conditions using the results from simple uniaxial tensile tests. The equivalent stress is defined as  e   vm  3 J 2 





1  1   2 2   2   3 2   3   1 2 (2) 2

where J2 is the second deviatoric stress invariant. The von Mises stress is equivalent to the maximum distortion strain energy and it is a good indicator of the yielding of materials. By analyzing the distribution of von Mises stress fields shown in Fig. 5, it can be concluded that the highest stresses on the fixator design did not occur at the measuring point. The maximum value of von Mises stress at the measuring points was σvm = 355 MPa. Generally, the highest von Mises stress on the Sarafix fixator design occurred in the contacts between the connecting rod and the clamping ring (σvm = 550 MPa) (Fig. 5). The element stresses at Gauss points may be expressed as (3)   D


477

4. Experimental Tensometric Analysis

Fig. 5 Von Mises stress contour plot on the model of the Sarafix fixator.

where: D—elasticity matrix or comportment law; ε—strains computed according to the displacement. The node stresses are extrapolations of the element stresses. The method consists of defining a continuous stress field within the element:   N n (4) where: N—a matrix of the finite element shape functions; σn—the nodal stresses. The nodal stresses values are obtained using the least square minimization method: (5)   M in     ˆ n 

T    ˆ  d  



where:

ˆ —the stresses computed with the FEM from the nodal displacement; Ω—domain.

The analyzed configuration of the Sarafix fixator was attached to proximal and distal tibia bone segments modeled with cylindrical wooden bars with known physical properties. Intensities of the loads were determined based on in-vivo testing on patients [1]. During the axial compression testing (Fig. 6), the tibia bone models were supported on ball joints and, using the force transducer, the axial load was controlled in the range of 0 to 600 N at the rate of 5 N/s. The connecting rod, due to the axial compression at the proximal segment of the bone model, is exposed to the combined loading (eccentric pressure), which consists of a combination of bending and axial compression. This form of the strain is manifested by the unequal distribution of tensile and compression stresses along the longitudinal section of a connecting rod, i.e., neutral line does not coincide with the axis of symmetry of the fixator connecting rod. Therefore, the two separate Wheatstone half-bridges were formed and connected with the DMC system via two measurement channels. Wheatstone half-bridges consist of active strain gauge SG1 and compensation (inactive) strain gauge SG2 (Figs. 6-7). The compensating strain gauges were placed near the active strain gauges on a plate tied to a connecting rod (Fig. 6). The plate and connecting rod are made of the same material. The strain, registered by Wheatstone half-bridge with one active and one compensation strain gauge, is given by the relation [5]: 4 U (6)   A k UE where: k—gauge factor; UA—bridge output voltage; UE—excitation voltage (bridge input). Compensating strain gauges are used to compensate the effect of temperature on the measurement and they are of the same type as the active ones. In this way, it is possible to determine the intensity of the dominant principal stresses at the measuring points. Previously

478


Active strain gauge, SG1+

Compesation strain gauge, SG2 Fig. 6 Set-up for experimental tensometric testing.

SG1

R4



UE

UA c SG2

R3

Fig. 7 Wheatstone half-bridge.

performed FEA determined the direction and intensity of the principal stresses. Also, it was noted that the intensities of the other two principal stresses at the measuring points were negligible compared to the maximum (σ1 on MP+) and minimum (σ3 on MP-) principal stress (Table 1). Active strain gauges are placed on the opposite sides of the connecting rod at the nearest and farthest point from the model of the bone, so that their longitudinal axis coincides with the directions of dominant principal strains (ε1 and ε3) at the measuring points. Simultaneous measuring of the largest positive and negative principal strains on the opposite sides of the fixator connecting rod was carried out independently at two measurement points (Fig. 8). In the following analysis, the strain gauge placed on the side of the

connecting rod closer to the bone model will be referred to as SG-, while a strain gauge placed on the opposite side will have a label SG+. This way of setting up strain gauges enables the measurement of the greatest positive principal strain (ε1) at the measuring point MP+, on the basis of which the intensity of the maximum principal stress (σ1) is determined. Analogously, on the measuring point MP-, the greatest negative principal strain (ε3) was measured, on the basis of which the intensity of the minimum principal stress (σ3) is determined. The minimum principal stress compared to the other two principal stresses at the point MP- is dominant. Independently

measured

total

strains

at

the

measuring point consisted of the compressive and bending strain [6-8]. The total (principal) strains are defined by the principle of superposition, as follows:

F M  AE EZ F M  3   p   s    AE EZ

 1   p   s  

(7)

where: εp—the strain component caused by the axial compressive force; εs—the strain component caused by the bending moment;

479


Mf

F

3

1

s 1 p

p

SG -

SG +

SG2

s 3

SG2

Mf

F

Fig. 8 Arrangement of strain gauges and distribution of loads and strains in the longitudinal section of the connecting rod.

F —the axial compressive force; A—the area cross-section of the fixator connecting rod; E—modulus of elasticity; M—bending moment; Z—section modulus of the fixator connecting rod. In this case of load, the bending strain was significantly higher than the compression strain

(εs εp ) Distribution of the strains in the longitudinal section of the fixator connecting rod is shown schematically in Fig. 8. The dominant principal stresses at the measuring points (MP+ and MP-) are determined through the relations:

 1  1 E  3  3E

(8)

Acquisition, display and processing of measurement results are performed using the HBM Catman software.

5. Results In order to achieve a direct comparison of results of the FEA and tensometric analysis, all parameters of geometry, materials, loads, restrains on the FEM model are set according to experimental settings. Tables 1-2 show the intensities of main and von Mises stresses generated at the measuring points in the

Table 1 Maximum values of principal and von Mises stresses at the measuring point MP+. Method σ1 (MPa) FEA 330 Experiment 334

σ2 (MPa) 0.2 -

σ3 (MPa) σvm (MPa) 0.001 330 -

Table 2 Maximum values of principal and von Mises stresses at the measuring point MP-. Method FEA Experiment

σ1 (MPa) -0.003 -

σ2 (MPa) -0.4 -

σ3 (MPa) -355 -368

σvm (MPa) 355 -

case of maximum axial compression force. The value of the maximum principal stress (σ1) at the MP+ was significantly higher than the other two principal stresses (σ2 and σ3). On this basis, and bearing in mind the relationship by which the value of von Mises stress are calculated (relation 2), it follows that at the MP+ the von Mises stress (σvm) has the same value as the maximum principal stress (σ1). Likewise, the value of the minimum principal stress (σ3) at the MP- was significantly higher than the other two principal stresses (σ1 and σ2). Analogously as in the previous case, it follows that the von Mises stress (σvm) is equal to the minimum principal stress (σ3) at the MP(Table 2). The maximum deviations of the results obtained by FEA in relation to the results obtained by experimental testing are range: the principal stress σ1 to 1.2%, and


the principal stress σ3 to 3.6% (Fig. 9). Principal stresses with the negative sign represent compressive stress. It is noted that at the MP+ all principal stresses are with positive signs (Table 1), while at the MP- all principal stresses are with negative signs (Table 2). The maximum values of von Mises and maximum principal stress at the control points is respectively σvm = 355 MPa and σ3 = 368 MPa and they are lower than the yield strength of the material of the fixator connecting rod (σV = 650 MPa).

6. Conclusions The conducted research has shown that there is a linear dependence between the loads and stresses generated on the fixator connecting rod, as a result of the absence of large displacement and plastic deformation of the fixator components. Comparing the results of FEA and tensometric analysis of the principal stresses at the measuring points reveals their good agreement and argues that the solutions obtained by FEA were verified. The CATIA software system can be successfully used in the development of CAD models, FEA and computer simulations of the process from different areas of technics and medical engineering. Using the developed CAD/FEM model of the Sarafix fixator, it is possible to control displacement and stresses generated at any point of the bone-fixator system and then make possible corrections on the fixator design. Due to extreme flexibility of the formed 3D geometrical model, rapid changes were enabled not only to the geometry and position of components and fixator, but also to the materials applied in the external fixation (medical stainless steel, composite materials, titanium alloys). In this way, conditions for design optimization of the external fixator are created, which would significantly shorten time and reduce costs of development of medical devices for external fixation of bones. In addition, the application of such models greatly reduces the volume of conventional preclinical experimental testing of fixators.

500 400 300

P rin cip al stresses, M P a

480

200 100

Axial load, N

0

-100

0

100

200

300

400

500

600

-200

MP+, Exp.

-300 -400

MP-, Exp. MP+, FEA MP-, FEA

-500

Fig. 9 Comparative diagram of the principal stresses (σ1 on MP+) and (σ3 on MP-).

References [1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

D. Jasinska-Choromanska, I. Sadzynski, Monitoring technique of bone fracture healing using external fixators, in: 39th International Conference on Experimental Stress Analysis, 2001, pp. 35-40. H. Radke, D.N. Aron, A. Applewhite, G. Zhang, Biomechanical analysis of unilateral external skeletal fixators combined with IM-pin and without IM-pin using finite-element method, Veterinary Surgery 35 (2006) 15-23. E. Mesic, Research of mechanical stability of the Sarafix external fixation system, Post-Graduation Master Thesis, Faculty of Mechanical Engineering, University of Sarajevo, Sarajevo, 2008. O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 6th ed., Butterworth-Heinemann, Oxford, 2005. H. Basic, Mechanical Engineering Measurements, Faculty of Mechanical Engineering, University of Sarajevo, Sarajevo, 2008. E. Mesic, A. Muminovic, N. Repcic, Structural analysis and experimental testing of external fixator system under axial compression, in: 13th International Research/Expert Conference—Trends in the Development of Machinery and Associated Technology (TMT 2009), Hammamet, Tunisia, 2009, pp. 497-500. E. Mesic, A. Muminovic, N. Repcic, M. Colic, Stiffness analysis of the Sarafix external fracture fixation system, Journal of Society for Development of Teaching and Business Processes, Technics Technologies Education Management—TTEM 5 (1) (2010) 60-66. A. Muminovic, E. Mesic, N. Repcic, Structural Analysis of Mechanical Characteristics of External Fixation Systems, in: 6th International Scientific Conference on Production Engineering (RIM 2007), Bihać, 2007, pp. 111-116.

D


DAVID

PUBLISHING

Structural Synthesis, Dynamic Modeling and Analysis of a 3-DOF Asymmetric Parallel Mechanism Rynaldo Zanotele Hemerly de Almeida and Tarcisio Antonio Hess-Coelho Department of Mechatronics and Mechanical System, Escola Politecnica, University of Sao Paulo, Sao Paulo 05508-030, Brazil

Received: September 13, 2011 / Accepted: October 11, 2011 / Published: November 25, 2011. Abstract: Most research papers about parallel kinematic chain mechanisms investigate symmetric robot manipulators, in which all the limbs connecting the end-effector to the fixed based are composed by the same sequence of links and joints. Contrarily, in some manipulation tasks the velocity and stiffness requirements are anisotropic. In such cases, the asymmetric parallel kinematic chain mechanisms may offer advantages. This work objective is to present the synthesis, dynamic modeling and analysis of a 3-dof asymmetric parallel chain mechanism, conceived as a robot manipulator for pick-and-place operations. First, a structural synthesis, resulting in a three translations end-effector, and a kinematic modeling are carried out. Then, the inverse dynamic modeling is developed by employing the virtual work principle. Based on the model equations and on the saturation of the mechanism actuators, a maximum acceleration analysis is performed and shows that although the mechanism has a parallel architecture its actuators influences on the 3-dof are quite decoupled. Key words: Parallel, asymmetric, synthesis, dynamic, modeling.

1. Introduction The advantages of parallel kinematic chain mechanisms over serial kinematic chain ones are well known: high rigidity, lightness, fast dynamic response, high precision and high load capacity [1-2]. In some tasks, as pick and place operations, these advantages overcome the reduced workspace and the complexity of kinematic and dynamic modeling. Some architectures, as those analyzed in Refs. [3-5], have reduced modeling complexity since their kinematic equations are linear and fully decoupled. However, due to the fact that these robots are overconstrained mechanisms, they require a very special care on manufacturing and assembly of their parts. Such requirements often demand more tight dimensional and Tarcisio Antonio Hess-Coelho, professor, research fields: synthesis and optimization of mechanisms and machinery, robotics and bioengineering. Corresponding author: Rynaldo Zanotele Hemerly de Almeida, Ph.D. student, research fields: dynamic modeling, simulation and control of mechanical systems. E-mail: [email protected].

geometrical tolerances, increasing their costs. Most of the proposed parallel robot architectures present symmetric kinematic chains, while there are only few works dealing with asymmetric architectures [6-7]. This fact reflects the preference of researchers for a modular structure showing a behavior as close as possible to the isotropic. However, there are some applications in which the speed and rigidity requirements do not need to be the same in all the directions. For instance, the loading-unloading of goods in conveyor belts usually demand higher manipulator speeds in the transversal direction of transportation than in its main direction. As a result of this observation, a project concerning an asymmetric parallel manipulator robot for pick-and-place operations has been developed at the Department of Mechatronics and Mechanical Systems of the Escola Politécnica of the University of São Paulo, Brazil [8]. As shown in Fig. 1, the kinematic structure of the proposed parallel mechanism is composed by three active limbs, connecting the moving platform with the

482

Structural Synthesis, Dynamic Modeling and Analysis of a 3-DOF Asymmetric Parallel Mechanism

model is developed and validated for both lumped and distributed mass parameters. In section 4, the results of the performed simulations are presented. Finally, in section 5, the conclusions are enumerated.

2. Structural Synthesis, Kinematic Modeling and Analysis 2.1 Structural Synthesis

(a)

(b) Fig. 1 Asymmetric parallel mechanism: (a) CAD model (b) graph representation.

fixed base. Two among them are Revolute-Spherical-Spherical (RSS) type, while the other is Prismatic-Parallelogram subchain-Prismatic (PPaP), that is located in the central region of the mechanism. The underlined letter means an active joint. The proposed kinematic structure 2 RSS + PPaP was conceived by applying an alternative type synthesis [9-10] procedure outlined in section 2. The central limb PPaP was chosen in such a way that the moving platform only performs three translations. This asymmetric and parallel architecture also presents an important feature: The kinematic equations are partially decoupled. Such feature is possible due to the fact that one of end-effector coordinates coincides with the displacement provided by the linear actuator coupled to the central limb. The main goal of this paper is to carry out a dynamic analysis of the 3-degrees of freedom (3-dof) asymmetric parallel chain mechanism using the optimized links lengths found in Ref. [8]. Initially, in section 2, the structural synthesis and the kinematic modeling are derived. Then, in section 3, the dynamic

In order to generate a parallel mechanism, able to position the tool in the 3D-space, in such a way that it performs only three independent translations, an alternative type synthesis procedure, proposed by Hess-Coelho [9] and cited in Ref. [11], is employed. Basically, the procedure has three steps: structural synthesis of the mechanism by the method of addition of passive limb; then, the elimination of one among the other active limbs; finally, setting active the constraining passive limb. According to the first step, to constrain the tool motions, we choose the kinematic chain PPaP as the passive limb. The axis of the first prismatic joint (P) and the axes of the four revolute joints, that belong to the parallelogram (Pa), are parallel to the horizontal axis . In addition, the second prismatic joint axis is parallel to the vertical axis . Let the kinematic bond [12] between the base and the end-effector , associated to the passive limb I, is labeled as , . In accordance with the Lie´s theory of continuous groups [13], the limb I is a generator of the translation displacement group , along the axes , and , respectively, , (1) In order to control the motion of the end-effector, by employing the topology of a parallel architecture, we need to add to the original kinematic structure three active peripheral limbs, named as II, III and IV. They correspond to generators of the general six-dimensional group of rigid-body displacements , , , , (2) A feasible choice for each peripheral limb is the utilization of a RSS chain, which stands for a sequence of three connected joints, the revolute and two


spherical joints. The underlined letter means an active joint. Then, one possible mechanism for the task is the 3 RSS + PPaP. By applying the second step, we eliminate one active RSS limb. Finally, in the third step, we set active the constraining limb by coupling an actuator to drive the prismatic joint closest to the base. Fig. 2 indicates the synthesized parallel mechanism, the 2 RSS + PPaP. One can notice that the set of displacements common to the three groups mentioned above, , , , coincides with the group generated by the limb I. , , , (3) Therefore, the dimension of the resultant group of displacement is three, which equals to the connectivity between the base and the end-effector, enabling the tool to perform three independent translations, , , , 3 dim (4)

483

The mathematical relations between the active joints coordinates and the end-effector coordinates are obtained from the property that the bar lengths CE and DF are constants. From the partial decoupling feature, the end-effector position along the direction coincides with the active prismatic joint coordinate. So, it can be stated that 0 0 0

(5) Differentiating Eq. (5) with respect to time yields to Eq. (6), a velocity equation written in a matrix form, (6) where 1

0

0 0

0 0

2.2 Kinematic Modeling

0 0

0 1

The kinematic modeling of the parallel mechanism 2 RSS + PPaP is briefly derived here and a more detailed description can be found in Ref. [8]. The coordinates correspond to the displacements provided by the actuators and the coordinates define the position of the end-effector, and are as it can be observed in Fig. 2, where the link lengths and masses and M is the load mass.

2.3 Kinematic Analysis The conditions for occurrence of singularities can be investigated by the inspection of the determinants of and [14]. Fig. 3 shows two Jacobian matrices, examples of singular configurations, where the PPaP limb was removed for clarity. When det( ) is null, the

Fig. 2

Mechanism kinematic diagram.

mechanism reaches the boundary of its workspace (Fig. 3a). On the other hand, when det( ) equals zero, the mechanism might become uncontrollable. In Fig. 3b one can notice such configuration: The actuators at A and B cannot withstand vertical forces acting upon the end-effector. Fortunately, this condition will occur only if the parameter is larger than . The mechanism workspace was determined in Ref. [8] by a discretization method and its shape can be observed in Fig. 4. As expected, the workspace does not have a regular shape but it may be improved by using adequate bar length ratio in each limb.

484


approach, the input forces and torques appear as isolated terms from other variables in the derived equations. Moreover, the consideration of other effects such as joint friction, may be directly included in the model proposed here. Consequently, the dynamic model may be incrementally refined. 3.1 Lumped Mass Modeling (a)

(b) Fig. 3 Singularities: (a) workspace boundary (b) uncontrollable position.

In this first case, we assume that the bars masses are lumped in their respective centers-of-mass. Hence, the mechanism itself is subject to the action of the inertia wrenches. In addition, the external forces and torques are due to the gravitational field and the actuators. Before applying the virtual work principle, it is important to realize that the virtual displacement and the center of mass acceleration of a rigid bar may be calculated from the virtual displacements and accelerations of its end points. Considering the homogeneous CE bar, for example, Eqs. (7a)-(7b) may be used. (7a) (7b)

Fig. 4

Workspace shape.

3. Dynamic Modeling The mechanism dynamic modeling was carried out in a previous paper [15] and is repeated here for clarity reasons. Two different cases were considered: lumped and distributed masses. In both cases, the bars are assumed to be rigid and the joints ideal (rigid, no friction and no clearance). The virtual work principle is applied for the dynamic modeling due to the great easiness to build the equations, mainly because our focus is the inverse dynamic model of the mechanism, as it can be perceived in Refs. [16-18]. With this formulation

and are the center-of-mass virtual where displacement and acceleration of the CE bar. These relations are very useful in the mechanism modeling because the virtual displacements and accelerations of points E and F equal to the virtual displacements and accelerations of the end-effector, respectively. On the other hand, the virtual displacements and accelerations of points C and D may be easily calculated from the movement of the active joints q2 and q3. Then, there is no need to find one jacobian matrix for each part of each mechanism limb. Therefore, the following sum of the virtual works of the actuators force and moments, inertia forces and gravitational forces must equals zero:


2

0

(8)

where are the actuators force and 2 moments and 0 0 9.81 m/s is the gravity acceleration vector. From the kinematics conditions, one can write Eqs. (9a)-(9f). (9a) 0 0 0

0

(9b) (9c) (9d) (9e) (9f)

Substituting Eqs. (9a)-(9f) into Eq. (8), we obtain Eq. (10), in which only the actuated joints virtual displacements , and and their correspondent coefficients are present. , , , , , , 0 (10) Once the actuated joints virtual displacements in Eq. (10) are independent, the algebraic expressions of force and the torques and can be obtained. 3.2 Distributed Mass Modeling We intend here to extend the previous model by assuming the hypothesis of distributed mass along the links. In this case, it is sufficient to include the torques due to bars rotational inertia. The following terms must be added to the sum of virtual works for the bars with constant orientation rotation axis: For bar AC, ; For bar BD, ; For the parallelogram bars,

485

where IACx1, IBDx1 and IHIx1 are the AC, BD and parallelogram bars moments of inertia with respect to their principal axes that are parallel to the x1 direction and is the angle between the parallelogram bars and the horizontal direction, defined in the same way as q2. For the CE and DF bars, of which the angular velocity vector has time varying orientation, it is necessary to include the following virtual work terms: For bar CE, Θ For bar DF, Θ where ICE and IDF are the CE and DF bars inertia matrices with respect to the global frame and , , Θ and Θ are the angular velocities and virtual displacements of the same bars. The inertia matrices ICE and IDF may be calculated from Eqs. (11)-(12) [14]. (11) (12) and

where and

and

are the principal inertia matrices are the rotation matrices of the

moving frames (body-fixed) with respect to the global frame. For each bar, either CE or DF, the angular velocity vector and its time derivative can be calculated from the velocities and accelerations vectors of the their end-points and from assuming that the angular velocity vector is always orthogonal to the longitudinal direction of the bar. In other words, there is no rotation along the longitudinal direction of the bar. For the CE bar, for example, its angular velocity is obtained by

(13) Simplifying and rearranging Eq. (9), it may be written as follows: (14) where 0 0 0

0 0 0

(15)

486


. 0 0 0

(16)

Thus, (17) ΘCE Using Eq. (17), the torque due to bar CE rotational inertia equals to (18) that may be rearranged in the following form: (19) The same strategy can be applied to the bar DF. Finally, it is necessary to collect the terms dependent of , and and include them in Eq. (10) to complete the dynamic model.

Fig. 5 Distributed masses simulation: torque τ2.

3.3 Dynamic Model Validation The validation of the lumped and distributed mass models was carried out by the comparison of motion simulation results of two different computing environments: Scilab [19] software subroutines implemented in accordance with the previous sections equations and ADAMS [20] software, a commercial package for multi-body analysis. In order to make the end-effector reach the assorted positions, velocities and accelerations, we prescribed the input motions for the actuated joints, defined by sinusoidal functions with varied amplitudes and frequencies, as shown in Eqs. (20)-(22). sin k t (20) /4 sin k t (21) /4 sin k t (22) Part of the results obtained in Ref. [15] is shown in Figs. 5-6. They are representative of the calculated input torques over the joints q2 and q3 related to the required motion described in Eqs. (20)-(22) according to the distributed mass model. One can notice that the discrepancies between the results of the two simulation environments are small. The greatest relative error was smaller than 2% and the results of the lumped mass models were even better.

Fig. 6 Distributed masses simulation: torque τ3.

4. Dynamic Analysis Once the models are validated, the model equations may be used for dynamic analysis of the mechanism. Here, we are interested in determine the maximum acceleration that can be reached by the end-effector, limited by the maximum force and torques available by the mechanism actuators. The end-effector is assumed to have velocity zero and will start a movement in a pre-defined direction over a section of the workspace at x3 = 0.6 m. In the following simulations the optimized link lengths fond in Ref. [8] were employed. The mechanism’s parameters are listed in Table 1. The accelerations in x1, x2, and x3 positive directions obtained by the distributed mass model considering an

Structural Synthesis, Dynamic Modeling and Analysis of a 3-DOF Asymmetric Parallel Mechanism Table 1

Simulations parameters.

Bars lengths (mm) a1 = 267 a2 = 533 l = 180 a4 = 100 a5 = 364 a6 = 100 L = 180 -

Bars and load masses (kg) m1 = 0.27 m2 = 0.53 m3 = 0.45 m4 = 0.1 m5 = 0.72 m6 = 0.1 M = 0 (no load)

487

maximum acceleration in x3 was not qualitatively different and was omitted. But it can be observed in Fig. 13 the influence of the two peripheral limbs over the maximum acceleration in the positive x1 direction the

input saturation force [N] and torque [Nm] vector 20 20 20 may be observed in Figs. 7-9. In Fig. 7 it may be observed the great influence of the gravity force in the motion of the mechanism. It is easier to approximate of the x1 = 0 position than to move away from it. This suggests that it is desirable to add springs or counter-weights to the mechanism for gravity compensation. For the same directions and input saturation vector it were calculated the maximum accelerations using the lumped mass model. The results are shown in Figs. 10-12. Confirming the results of Ref. [9], the lumped mass model is a reasonable approximation of the more general distributed mass model. As the lumped mass model is less computationally demanding, it was used in the next simulations. In order to simulate the dynamic characteristics of the mechanism in gravity compensated hypothesis the gravity was imposed to be zero. The result of the

Fig. 9 Distributed masses simulation.


Fig. 10 Lumped masses simulation.


488




Fig. 14 Lumped masses simulation, no gravity.

symmetric, what was not obtained in the previous simulation (Fig. 11). Changing the input saturation vector to 40 20 20 and considering again the existence of gravity the results presented in Figs. 15-17 were obtained. It can be perceived that despite the influence of the two peripheral limbs over the maximum acceleration in the x1 direction, a double higher saturation force in the prismatic joint lead to a double higher maximum acceleration in that direction. At the same time, almost no difference is observed over the other directions. This shows that although the mechanism has a parallel architecture its actuators influences are quite decoupled. Thus one can choose the actuators capacity according to the required acceleration performance in each movement direction.

5. Conclusions

Fig. 13 Lumped masses simulation, no gravity.

farther the end-effector is from x1 = 0. This was expected from the mechanism configuration (alignment of links at x1 = 0). Fig. 14 shows that without gravity the acceleration map becomes perfectly

Due to the fact that some industrial tasks have distinct motion requirements in each direction, asymmetric parallel mechanisms have a great potential to be more efficient and adequate for such applications. We developed the dynamic model of the proposed asymmetric mechanism, which was successfully obtained for both the lumped mass and distributed mass assumptions. The simulation results showed that although the mechanism has a parallel architecture its actuators


489

gravity compensation. And the lumped mass model presented again a reasonable, less computationally demanding, approximation of the more general distributed mass model.

References [1]

[2] [3] Fig. 15 Lumped masses, double input force saturation. [4]

[5]

[6]

Fig. 16 Lumped masses, double input force saturation.

[7]

[8]

[9]

[10]

Fig. 17 Lumped masses, double input force saturation.

[11]

influences are quite decoupled, according to its particular asymmetric configuration. The great dependence of gravity force suggests that it is desirable to add springs or counter-weights to the mechanism for

[12] [13]

J.P. Merlet, Still a long way to go on the road for parallel mechanisms, in: ASME DETC Confer., Montreal, Canada, 2002. M. Ceccarelli, Fundamentals of Mechanics of Robotic Manipulation, Kluwer, Dordrecht, 2004. H.S. Kim, L.-W. Tsai, Design optimization of a cartesian parallel manipulator, in: ASME DETC Confer., Montreal, Canada, 2002. C.M. Gosselin, X. Kong, S. Foucault, I.A. Bonev, A fully-decoupled 3-dof translational parallel mechanism, in: Proceedings of the 4th Chemnitz Parallel Kinematics Seminar (PKS2004), Verlag Wissenschaftliche Scripten, 2004, Vol. 24, pp. 595-610. D. Gregorio, V.P.-Castelli, Design of 3-dof parallel manipulators based on dynamic performances, in: Proceedings of the 4th Chemnitz Parallel Kinematics Seminar (PKS2004), Verlag Wissenschaftliche Scripten, 2004, Vol. 24, pp. 385-397. Q. Li, Z. Huang, Type synthesis of 5-DOF parallel manipulators, in: Proc. of the 2003 IEEE Int. Conf. on Robotics and Aut., Taipei, Sep 14-19, 2003, pp. 1203-1208. T. Huang, M. Li, X.M. Zhao, J.P. Mei, D.G. Chetwynd, S.J. Hu, Conceptual design and dimensional synthesis for a 3-DOF module of the TriVariant—A novel 5-DOF reconfigurable hybrid robot, IEEE Transactions on Robotics 21(3) (2005) 449-456. V.D. Kumazawa, T.A. Hess-Coelho, D. Rinaudi, G. Carbone, M. Ceccarelli, Kinematic analysis and operation feasibility of a 3-DOF asymmetric parallel mechanism, in: 20th Brazilian Congress of Mechanical Engineering COBEM2009, Gramado, RS, Brazil, Nov 15-20, 2009. T.A. Hess-Coelho, An alternative procedure for type synthesis of parallel mechanisms, in: 12th IFToMM World Congress, Besançon, 2007. V.D. Kumazawa, Development of a parallel robot, Final Report, Escola Politecnica, Universidade de Sao Paulo, 2008 (available in portuguese). G. Gogu, Structural Synthesis of Parallel Robots: Parts 1 and 2, Kluwer, Dordrecht, 2009. J. Angeles, Qualitative synthesis of parallel manipulators, Journal of Mechanical Design 126 (2004) 617-624. J.M. Hervé, The Lie group of rigid body displacements, a fundamental tool for mechanism design, Mechanism and Machine Theory 34 (1999) 719-730.

490


[14] L.W. Tsai, Robot Analysis—The Mechanics of Serial and Parallel Manipulators, John Wiley & Sons, New York, 1999. [15] R.Z.H. Almeida, T.A. Hess-Coelho, Dynamic modeling of a 3-dof asymmetric parallel mechanism, Open Mechanical Engineering Journal, Special Issue on Kinematic Design of Manipulators (2010). [16] Y. Li, Q. Xu, Dynamic modeling and robust control of a 3-PRC translational parallel kinematic machine, Robotics and Computer-Integrated Manufacturing 25 (2009) 630-640. [17] S. Staicu, Dynamics analysis of the Star parallel

manipulator, Robotics and Autonomous Systems 57 (11) (2009) 1057-1064. [18] J. Gallardo-Alvarado, C. Aguilar-Najera, L. Casique-Rosas, J. Rico-Martinez, M. Nazrul Islam, Kinematics and dynamics of 2(3-RPS) manipulators by means of screw theory and the principle of virtual work, Mechanism and Machine Theory 43 (10) (2008) 1281-1294. [19] Scilab Consortium, Scilab Manual, available online at: http://www.scilab.org, accessed: June 9, 2010. [20] MSC Software Corporation, MD Adams Basic Full Simulation, ADM 701 Course Notes, 2007.

D


DAVID

PUBLISHING

The Investigation of the Effect of Heaving and Pitching on Wave-Induced Vertical Hull Vibration of a Container Ship in Regular Waves Abdul Hamid Faculty Engineering, University of Mercu Buana, Jakarta 11650, Indonesia

Received: September 07, 2011 / Accepted: September 29, 2011 / Published: November 25, 2011. Abstract: The aim of this paper is to investigate the effect of heaving and pitching of ship motion due to springing bending moment. The investigation was conducted both experimentally and validated theoretically. Series of experiment were carried out using a container model-ship of which length was 3 meter, and the possibility of the so-called nth resonant springing vibration is tested by taking n from n = 2 to n = 4. The bending moment due- to vibration is also measured. The following conclusions were obtained: (1) Occurance of the higher order resonant vibration between 2nd-4th is recognized experimentally; (2) The results indicated that heaving and pitching of ship motion influenced the springing bending moment accurately. Key words: n-th resonant springing order, buoyancy force, virtual added mass force, heaving and pitching motion, springing bending moment.

Nomenclature B Cb D El F Gm h H Hm L mm(x)

Breadth molded of ship Block coefficient of ship Depth of ship Bending rigidity Dissipation function Coefficient of polynomial Wave elevation Wave height Coefficient of polynomial Length of ship Normal function of bending moment of m-th mode vibration MS Amplitude of springing bending moments amidships n Springing order N Damping coefficient T Kinetic energy Um(x) Normal function V Potential energy Vs Ship speed W Work done by external force ρA Mass per unit length including virtual added mass of water θ Pitching ζ Heaving φmn(t) Normal coordinate of m-th mode vibration. ωe Circular frequency of wave encounter Corresponding author: Abdul Hamid, M.Eng., research field: ship hull vibration. E-mail: [email protected].

ωV2

Circular frequency of two node vertical ship hull vibration

1. Introduction When sailing, a ship at certain type sometimes experiences violent and steadily-frequent vibrations even in the comparatively calm seas. This vibration is due to the resonance of the natural frequencies of the two-node ship hull vibration and the wave exciting force. This vibration is called springing vibration. Since the frequency of the wave exciting force depends on the characteristics of ocean waves, the ship speed and the shape of the ship hull, the so-called n-th resonant springing vibration must also be considered. That’s being said, springing vibration occurs on both full and slender ship, especially on fast, long container ships with a sharply flared bow and no parallel body. In general, the springing vibration may affect life-time of the structure. Furthermore, this vibration gives her crew uncomfortable feeling and sometimes fears.

492

The Investigation of the Effect of Heaving and Pitching on Wave-Induced Vertical Hull Vibration of a Container Ship in Regular Waves

Many investigations on this problem have been published until now. Full-scale measurements were carried out by Kumai [1] on a tanker of the length 230 meter by taking measurement of springing order n = 4 to n = 9. Kumai and Tasai [2] measured the bow pressure variation on board of a 76,000 dwt tanker. Bell and Taylor [3] investigated the springing stress of the main hull at the bow on board of a 47,000 dwt tanker. Model experiments were carried out by Hoffman and Van Hoof [4] in short regular waves, i.e., L/λ = 8-16, and investigated the springing in model experiments on a 2.116 meter of Great Lakes Carrier. J.S. Wu [5] continued Goodman’s method and evaluated the hull girder response to wave excitation. Hashimoto et al. [6] studied the springing vibration based on the second-order theory. The model used in this study is one-body model of hard rubber of 3.80 meter length. Kagawa et al. [7-8] studied the springing vibration based on their experimental results and derived the coefficients for calculating the first and the second order exciting forces. They investigated the springing in model experiments on a 7-meter tanker. Kawakami [9-10] introduced the non-linear theory to evaluate the cause of the springing vibration and took into account the effect of ship speeds and wave elevations. He also carried out the model experiments, in which he tried to verify the occurrence of the so-called higher-order resonant springing vibrations. Recently, the linear and nonlinear springing effects on the hull girder are evaluated by Chang Doo Jang et al. [11] using Timoshenko’s beam model. In this report, the author followed Kawakami’s proposal, however the author considered the effect of heaving and pitching of the ship motion, as well as wave heights and ship speeds.

2.1 Ship Model This model is for a ship with high-speed and long-size length. Typical dimensions of the ship are L × B × D = 3.00 m × 0.432 m × 0.262 m, Cb = 0.575. The model ship of FRP (Fiberglass Reinforced Plastic) is separated in six blocks and connected at five transverse section by elastic plates, strain gauges, accelerometers and an encounter wave height recorder are used for measurement. 2.2 Procedure of Experiments As stated previously, springing vibration of a ship may occur when (1) V 2  ne where ωe, the circular frequency of wave encounter, is expressed by

e  2 (Vs  1.25  ) / 

(2)

From these formulae, there is a combination of Vs, ωe, and ωV2 which causes the springing vibration. The measured ωV2 of the model ship was 28.0 rad/sec. Test conditions of the model experiment are shown in Fig. 1.

2. Model Experiments In order to make clear the characteristic of springing vibration, model experiment in regular waves are carried out.

Fig. 1 Springing resonance chart of ship model in regular head waves.


Simultaneous observations of bending moments, wave heights encountered, pitching, heaving motions and their accelerations have been carried during the towing experiments. The measured bending moments are compared with theoretical calculations and will be shown later. In spite of the existence of limitation in the combinations of Vs, ωe, and ωV2, the so-called resonant springing of 2nd, 3rd and 4th order were measured by these experiments.

493

When (n + 1 ) is an even numbers, then nl k , Cl  1 for l = k, C = 2 for elsewhere 2

When ( n +1) is an odd number, n k  , C l  2 for all 2 As shown in Eq. (7), the sectional buoyancy force is composed of integer multiple components of the encounter wave circular frequency. 3.2 Sectional Virtual Added Mass Force

3. Wave Exciting Force It is considered that the wave exciting force induced by the wave ship motions consist of the buoyancy, virtual added mass and damping forces is expressed as follows:

dF dFb dFa dFd    dx dx dx dx

(3)

It is also mentioned that the higher order damping force is negligibly small comparing with the other forces. Then, the higher order damping force is neglected in this study. The wave exciting force is generated by the variation of relative position of the ship’s sectional form and water level. To calculate the wave exciting force, the ship’s sectional form is expressed by polynomial and the relative vertical displacement between the ship and the wave elevation at x is expressed by the following equations respectively: (4) b / 2  B / 2 Gm x m . H n z n m0

n 0

zr    x  h  z0 cos( e   e )

(5)

3.1 Sectional Buoyancy Force The sectional buoyancy force can be expressed as z

z

r r dFb  2  g  ( b / 2 )dz  2  B  Gm x m   H n z n dx m 0 0 0 n0

(6)

If the integral is executed and the binominal theorem is applied, then Eq. (6) is transformed to be dFb H  z nlk n 1  2BGm xm  n  0 Cl   cos( n 1 2l )( e  e ) dx n m0 n0 1  2  l 0  l 

(7)

In this equation, k and Cl, vary in the following way according to the property of (n+1).

The sectional virtual added mass force is expressed by dFa dm 2 dm dz   (8) z  V z  V m r   mz  dx



r

dz

r

S

dx

r

S

dx 

The above equation is based on the momentum theory, and is used in this study. The added mass of water is obtained by using Landweber’s method and is defined by c  b (9) m ( ) 2 2 The correction factor for the three-dimensional effect is neglected. One can obtain the virtual added mass force by substituting Eqs. (4) and (5) into Eq. (8). The sectional virtual added mass force is also composed of integer multiple components of encounter wave circular frequency.

4. Springing Response The springing vibration induced by the wave exciting force which varies along the ship’s length can be calculated by the Lagrange’s equation of motion, which is given by d T T V F W (10) ( )( )( )( )( )  dt  mn

 mn

 mn

  mn

 mn

Here assume the response of the system in the following series: (11) y( x,t )   mn ( t )U m ( x )

 m

The following equation can be obtained from Eq. (10): L (12) 1 dF 2    mn ( t )  2 m  mn ( t )  m  mn ( t ) 

m

 dx u 0

m

( x )dx


494

In this equation, following notations are introduced: L

 m   Aum2 ( x)dx

figures: One is the new model (Hamid’s method) , and the old model is Kawakami’s method.

0

2 m 

1

m

75.0

d um ( x) 2 ) ]dx dx 2 2

L

 Nu

2 m

50.0

Ms(N.cm)

m   [ EI (

( x)dx

25.0

0

Using the method judicious guessing, one can find the solution of Eq. (12) in the form:  mn ( t ) 

2 2 [ pmns  pmnc ]1 / 2 cos( net   mn ) n n  m  2 m [{ 1  ( e )2 }2  ( 2 m e )2 ]1 / 2

m

(13)

0.0 1.15

1.25

Third Order Resonance

5.0

exp.

Ms(N.cm)

0.0 0.30

The springing bending moment can be expressed as follows: (14) M( x,t )  mm ( x )mn ( t ) Above mentioned procedure is the general treatment of forced vibration, but in this study only the two node vibration is considered. The comparisons between experimental and calculated results of springing bending moment at midship from 2nd to 4th order resonance are made in Figs. 2-11. Two calculated results are presented in these exp.

exp.

10.0

0.0 0.40

0.30

0.50

Vs (m/sec.)

0.60

Fig. 5 Third order resonance for λ = 1.17 m, H = 5.00 cm. exp.



: H=3.3. cm =1.17 m : Without heaving and pitching : With estimated heaving and pitching

10.0




20.0




5.0

Ms(N.cm)

Ms(N.cm)

0.60

Fig. 4 Third order resonance for λ = 1.17 m, H = 3.30 cm.

pmnc (2 m ne )  pmns {2m  (ne ) 2 } pmns {2m  (ne ) 2 }  pmnc (2 m ne )

20.0

0.50

0.40

Vs (m/sec.)

Ms(N.cm)

 mn  tan 1




2.5

L

dF   sn u m ( x)dx dx 0

1.45

Fig. 3 Second order resonance for λ = 1.17 m, H = 5.00 cm.

m

dF dF dFcn  cos net  sn sin net dx dx dx L dF p mnc   cn u m ( x)dx dx 0

1.35

Vs (m/sec.)

Here,

p mns




exp.

0

L

2.5

0.0

0.0 1.15

1.25 Vs (m/sec.)

1.35

Fig. 2 Second order resonance for λ = 1.17 m, H = 3.30 cm.

0.60

0.70

0.80

0.90

Vs (m/sec.)

Fig. 6 Third order resonance for λ = 1.53 m, H = 3.30 cm.

The Investigation of the Effect of Heaving and Pitching on Wave-Induced Vertical Hull Vibration of a Container Ship in Regular Waves Fourth Order Resonance

: H=5.00. cm  =1.53 m : Without heaving and pitching : With estimated heaving and pitching

exp.

495

exp. 7.5


Ms(N.cm)

Ms(N.cm)

40.0

20.0

5.0

2.5

0.0 0.35

0.0 0.70

0.60

0.80

0.90

Vs (m/sec.)



Ms(N.cm)

7.5 5.0 2.5 0.0 1.30

1.20

1.10

1.40

Vs (m/sec.)


: H=5.00. cm =2.08 m : Without heaving and pitching : With estimated heaving and pitching

Ms (N.cm)

50.0

25.0

0.0 1.20

1.10

1.30

1.40

0.55

0.45

0.65

Vs (m/sec.)

Fig. 11 Fourth order resonance for λ = 2.08 m, H = 5.00 cm.

Now, the Hamid’s method considers heaving and pitching terms, which are ζ and xθ, respectively. This can be found on Eq. (5), while Kawakami’s method considered wave elevation, h only. The results by Hamid’s method show a good agreement with the experiment in quantity and quality. From the comparison between the Hamid’s method and Kawakami’s method, it may be said that the ship motion plays an important role and must be taken into consideration. As the order of resonant vibration increases, the springing bending moment decreases. This reason is that the wave exciting force becomes small as the resonance order increases. Then, it may be not necessary to take the higher order springing resonance into consideration for the longitudinal ship strength; however this conclusion must be verified by the measurements of actual ships.

Vs (m/sec.)

Fig. 9 Third order resonance for λ = 2.08 m, H = 5.00 cm. exp. 2.5


Ms(N.cm)

2.0

1.0

0.0 0.35

0.45

0.55

0.65

Vs (m/sec.)

Fig. 10

Fourth order resonance for λ = 2.08 m, H = 3.30 cm.

5. Result and Discussions The following discussions of the study could be written as follows: (1) The result of experiment shows that the amplitude values of springing bending moment are increasingly smaller according to an order resonance. t means that the higher the value of its resonant order, the smaller the amplitude value of springing bending moment (MS); (2) According to experimental result, every resonance with the same wave length (λ), it has shown

496


evidence that the higher the wave height (H), the higher amplitude (MS).  In the order of resonance n = 2 and n = 3, the amplitude value of springing bending moment (MS) for wave height H = 5 cm, reaches between 5 and 6 times more than to wave height H = 3.30 cm.  In the order of resonance n = 4 ,the amplitude value (MS) for the same wave height H = 5 cm, reaches only 2 times (twice) more than to wave height H = 3.30 cm. (3) According to order of resonance n = 3, the amplitude value (MS) of Figs. 6-7 is almost twice bigger than amplitude value (MS) of Figs. 4-5 which influenced by wave length (λ). (4) Therefore, Hamid’s method has given strong indicator that heaving (ζ) and pitching (xθ) must also be considered.

6. Conclusions Experimental and theoretical studies on the springing vibration of a ship have been carried out. Occurrence of the so-called higher order resonant springing vibration of 2nd to 4th was recognized experimentally. A “close fit wave surface method” of calculation for the higher order buoyancy and virtual added mass force taking into account of ship motion was obtained. By the use of this method some of the characteristics of wave exciting force were made clear. And this method was applied to calculate the springing vibration of the model ship. Comparisons between the experiments and the analytical calculations were made on the springing bending moments amidships (MS) and resulted in a good agreement.

Acknowledgments This paper has been a long time growing, and many more persons than the author have given and

volunteered their time, energy and suggestions during its completion. Among the persons to whom the author wishes to express their special appreciation for guidance on this paper is Prof. DR. Ir. Darwin Sebayang of Universiti Tun Hussein Onn Malaysia (UTHM) for the reading of the manuscript and for his valuable comments and encouragement. At the last the guidance of the late Prof. Dr. M. Kawakami of Hiroshima University is gratefully acknowledged.

References [1]

T. Kumai, F. Tasai, On the wave exciting force and response of whipping of ships, European Shipbuilding 19 (1970) 42-47. [2] T. Kumai, F. Tasai, On the wave exciting force and response of whipping of ships, European Shipbuilding 19 (1970) 42-47. [3] A.O. Bell, K.W. Taylor, Wave-excited hull vibration, measurement on a 47.000 dwt tanker, Shipping World and Shipbuilder, Feb. 1968. [4] I. Hoffman, F.W.V. Hoof, Experimental and Theoretical Evaluation of Springing on a Great Lakes Bulk Carrier, I.S.P., 1976. [5] J.S. Wu, On the Wave Excited Ship Vibrations in Regular Waves and in Confused Seas, I.S.P., 1980. [6] H. Kunifumi, F. Masataka, M. Seizo, On the wave-induced ship-hull vibration: Springing caused by higher-order exciting force [in Japanese], Journal of the Society of Naval Architects of Japan, 1978. [7] K. Kagawa, K. Ohtaka, M. Onoue, A study of wave-induced vibrations (1st Report), JSNA Japan, 1975. [8] K. Kagawa, K. Ohtaka, M. Onoue, A study of wave-induced vibrations (2nd Report), JSNA Japan, 1976. [9] M. Kawakami, et al., On the wave induced ship hull vibration, The West Japan of Naval Architects, No. 51, March 1976. [10] M. Kawakami, T. Kiso, On the wave induced ship hull vibration, The West Japan of Naval Architects, No. 51, March 1976. [11] C.D. Jang, J.J. Jung, A.A. Korobkin, An approach to estimating the hull girder response of a ship due to springing, Journal of Marine Science and Technology 12 (2) (2008) 95-101.

Design and Simulation of a Passive Vertical ...

Design and Simulation of a Passive Vertical ...

Suggest Documents

design and simulation of vertical handover algorithm

A validated design simulation tool for passive solar space heating ...

Design and characterization of a passive flow

Design and fabrication of a passive droplet

Integrated Design of Simulation Models for Passive Houses

Theoretical and Experimental Simulation of Passive ...

Design of Vertical Curves

Monitoring and simulation of a passive house with ...

A simulation study of the Cosmic Ray Inspection and Passive ...

Numerical simulation on a straight-bladed vertical

Passive treatment of Fe and Mn using vertical flow ...

Design and Sensitivity Analysis Simulation of a

Design and Simulation of a Bluetooth Communication

Simulation Model Design and Validation of a

Dynamics, Design and Simulation of a Novel

DESIGN AND SIMULATION OF A BUILDING ... - CiteSeerX

Design and Parametric Simulation of a Miniaturized

Simulation of a passive house coupled with a heat ...

Nuclear Engineering and Design Scaling of passive

Design and Testing of Superconducting Microwave Passive

Design, Fabrication and Characterization of Passive ...

Design and Motion Planning of a Semi-Passive Mobile Platform

Design of a Continuous Passive and Active Motion ...

Design and Implementation of a Compact Practical Passive Beam