RSM Based Modeling for Surface Roughness Prediction ... - CiteSeerX

International Journal of Engineering & Technology IJET-IJENS Vol: 10 No: 04

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RSM Based Modeling for Surface Roughness Prediction in Laser Machining Sivarao, T.J.S.Anand, Ammar, Shukor

Abstract—Statistics is a branch of mathematics used extensively in natural science and also in the engineering field as well as in social science, physics and computing. The machining process selected for this study is laser cutting process of mild steel. Response surface methodology will be used as a technique for the statistical study. The influence of cutting speed, frequency and duty cycle on surface roughness will be a main portion of this study. For statistical approach, a mathematical based model has been developed through regression analysis to study the response prediction. It is found that for the surface roughness, cutting speed plays an important role. Only a high cutting speed can produce good surface roughness coupled with high duty cycle regardless of frequency. Index Terms—RSM, cutting speed, frequency, duty cycle, surface roughness.

I. INTRODUCTION

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n the field where the customers control the demand and market pattern, the quality of the manufacturing industry has become a critical criteria where a slightest error in manufacturing and processing can cause tremendous lost in terms of financial value of the industry or worse still, lost of customers trust on the product all together. Once the customers do not trust the quality of a company’s products, it will be very hard to convince them other vice. The primary focus of this study will be on predicting the responses of a process by statistical means. Statistical approach here refers to an empirical method of describing the relationship between the input factors (parameters) as to how far their

Manuscript received June 23, 2010. This work was supported in part by the University Teknikal Malaysia Melaka (UTeM) towards working on UTeM funded modeling of laser machining project. Project number: S149. Ir. Sivarao, T.J.S.Anand, Shukor & Ammar are the academic members of Faculty of Manufacturing Engineering, Universiti Teknikal Malaysia Melaka (UTEM), Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia who are currently working on modeling of machining processes. The correspondence author can be contacted via e-mail: [email protected] or [email protected]).

influence ranges on the output (responses). It is a mathematical evaluation of signifying the relationship of the parameters to the responses. A part of statistical branch revolves around deriving information about the properties of random processes from sets of observed samples [1]. A general objective for a statistical study is to investigate causality especially to correlate the effect of changes in the parametric values to the responses. It is most helpful to construct a model which provides a mathematical representation of the given situation for most of the statistical based investigation [2]. The model should provide an adequate description of the given data in order to enable prediction and other inferences to be made. In general, the statistical approach can be divided into three categories: 1) Statistical model 2) Empirical model 3) Mathematical model A. Statistical Model A statistical model normally contains one or more systematic components as well as a random (or stochastic) element [2]. The random element is sometimes referred to as noise. This element arises for various reasons and it is sometimes helpful to differentiate between: 1) Measurement error 2) Natural random variability The natural random variability occurs due to the difference between experimental units and from changes in experimental circumstances that cannot be controlled. As for the systematic components, it is sometimes refers to as signal. In the engineering point of view, statistical analysis can be regarded as extracting information about the signal in the presence of noise. B. Mathematical Model A mathematical model can be described as a theoretical model that uses mathematical language to explain the behavior of a system. Among the forms of a mathematical model are game theory model, differential equation and dynamic system.


However, mathematical model are not just limited to these alone. Mathematical model is able to overlap with other models involving an array of abstract structure. In a mathematical model, there are six basic groups of variables: 1) 2) 3) 4) 5) 6)

Decision variables Input variables State variables Exogenous variables Random variables Output variables

C. Empirical Model An empirical model can also be referred to as a regression or ANOVA model. This model aims to capture some sort of smooth average behavior in the long run [2]. The advantage of this model (or in some cases seen as the disadvantage) is that it is not based on highly specific subject-matter consideration. In general, empirical model can be summarized as building a model then using experimentation data to test the model. A scientist’s empirical model is simply his current best guest as the underlying mechanism at hand [3]. In other, an empirical model is developed to understand the factors that contribute to a process and how they affect each other as well as the output. An empirical model can be built to explain the existing situation by using the existing data related to it. The empirical model consists of a function that fits the data. A matter to note here is that empirical model cannot be used to explain the system. It can only be used to predict and estimate behavior where data does not exist. D. Objectives There are several matters that are subjected to investigation in this study. The objectives of this study are: 1) Develop an empirical model for kerf width and surface roughness by adjusting the design parameters. 2) Integrate more than one response into the empirical model for prediction. 3) Check the consistency between the mathematical models with actual experimentation data. 4) To be able to predict the output of the responses based on the parametric values. E. Surface Roughness In this study, the affects between cutting speed, frequency and duty cycle on surface roughness in laser cutting of mild steel. Surface roughness is a clear factor affecting reflectivity. Rough surface

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will tend to open up opportunity to the surface to absorb more laser beam by creating multiple reflections. This as a result reduces the reflectivity and absorption is increased. The general aim is to get the lowest value of surface roughness to obtain a clear and smooth surface. It is also sometimes termed as cut edge surface roughness. The roughness on the cut surface happens when the laser beam is cutting the material. During the process, hot liquid and vaporized metal particles are washed out by the assist gas. This flow is then freely dispersed in the open – ended upstream part of kerf width. At the side and the front wall of the kerf, the flow interacts with the laser beam which in some conduct partially wave guided. The flow then re–solidifies where the rate depends on cutting speed and the material’s properties. This results in a striated cut edge due to interaction with laser beam before solidification as shown in Fig. 1. Thus, the surface roughness connected to the striation formation during the re–solidification.

Fig. 1. Surface roughness pattern on a thick – plate’s laser cut edge

II. LITERATURE REVIEW The central composite design (CCD) technique is the most commonly used experimental design technique in mathematical modeling for laser machining process optimization [4]. In addition, they also stated that the most common research done in laser machining is experimental studies, modeling and optimization studies. In this case, the latter is used where statistical design experiment is used to show the relationship between input parameters and responses by using mathematical equation. There are more experiments with relation to laser machining uses a single response as objective for optimization [4]. This paper shall carry out multi–objective optimization where there are two responses being investigated. In order to optimize the process and achieve the best kerf width, kerf deviation and kerf taper, a set of parameters used in an experiment as shown in Fig. 2 were assisting gas pressure, pulse width, pulse frequency and cutting speed [4]. The RSM technique used in this statistical design experiment is Taguchi method. In their study, they discovered that pulse width and cutting speed play a


significant role in affecting the kerf width and keft deviation respectively. In addition, they integrated two different method i.e. Taguchi method and principle component analysis to obtain the optimum values for the parameters. They concluded that the gas pressure of 2kg/cm2, pulse width 0.6ms, pulse frequency value 23Hz and cutting speed value of 20 mm/min for optimum value control. The optimum level for the kerf width, kerf deviation and kerf taper are 0.246mm, 0.01mm and 0.2728º [5].

Fig. 2. The percentage of contribution of each parameter on the responses [4]

RSM CCD technique was used in laser micro– drilling process to achieve optimum responses of hole tapper and the circularity of the hole formed. The parameters investigated here were Lamp current, pulse frequency, air pressure and thickness of the material. The study shows that the lamp current and the thickness of the material have significant effect on the responses. The pulse frequency affects the hole tapper more while air pressure is the dominant parameter for the hole circularity. It is noted here that a lower lamp current value, lower air pressure, higher pulse frequency and a higher material thickness will give an optimum hole tapper value. A moderate value for air pressure and pulse frequency coupled with low lamp current value and a high material thickness will give an optimum hole circularity [6]. An experimental study on laser welding process was done using Design Expert software to apply the RSM Box – Behnken technique for process optimization to attain desirable weld bead quality and also to increase production rate. The parameters controlled were laser power, welding speed and focused position. It was observed that a full depth penetration has a negative influence on the bead parameters due to the high laser power and low welding speed. For a half-depth penetration, the welding has to be double-sided

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butt-welding to attain excellent welded joints. To achieve the best half-depth penetration, the optimal setting for the parameters are in the range of 1.2 and 1.24 kW for the power, welding speed between 69.77 and 70 cm/min and a focused positioning ranging from -1.71 to -2.03. A higher welding speed will reduce the cost and at the same time increase the process productivity [7]. Another experimental design study on laser texturing by combining RSM CCD technique and Taguchi method was aimed to identify the key parameters that contribute to productivity and surface quality. The results of their study show that frequency and energy of the pulse have the most influence in the laser texturing process. MRR is linearly proportional to pulse energy and frequency while the surface roughness is inversely affected by them. The increase in the pulse energy and frequency leads to an increase in surface roughness and a decrease in material removal rate (MRR). The optimal setting for the pulse frequency and energy are 12.5 kHz and 5 mJ respectively. It is predicted that the model can function with a 95% confident level [8]. In a laser micro-drilling modeling and analysis to study the effects of the laser machining parameters on the HAZ thickness and tapering of the micro-holes, the chosen parameters as variables were lamp frequency, pulse frequency, assisted air pressure and pulse width. The experimental designs were done using response surface methodology with CCD technique where the model was then use to optimize the process performance. The results showed that to attain the minimum HAZ width at 0.00675 mm, the optimal setting for the parameters should be 17 A, 2 kHz, 2 kg/cm2 and 2% of the duty cycle respectively. Meanwhile, minimum taper was yielding at 0.0319 at the parameter settings 17 A, 2 kHz, 0.6 kg/cm2 and 2% duty cycle respectively [9]. A study on surface roughness by Nd:YAG laser cutting of 1mm thick sheet of nickel based superalloy shows that surface roughness value reduces as the cutting speed and frequency were increased and laser power and gas pressure were decreased. It was also observed that nitrogen results in better surface finish compared to oxygen. In a study of high power CO2 laser cutting, the value of surface roughness reduces as the nitrogen and argon gas pressure were increased but when the gas pressure of air was above 6 Bar, the surface result was poor [3]. It was also noted that a higher cutting speed produces better surface finish [3]. There was a design of experiment study that investigates the effects of laser cutting inputs on polymeric materials. The effects of the laser power, cutting speed and compressed air pressure against


the HAZ, surface roughness and dimensional accuracy for three different polymer materials (PP, PC, PMMA) was the main objective of this study. Using RSM CCD technique, predictive model have been developed to analysis how the parameters were related to the responses. The results of the experiment showed that the HAZ is directly proportional to the laser power and inversely proportional to cutting speed and compressed air pressure. It was observed that the quality of cut of PMMA is much better than PC and PP. Surface roughness is found to be inversely proportional to all the parameters with cutting speed and compressed air has more influence on it than laser power. The dimensional deviations for in all measured dimensions were around 0.07 mm [10]. In another study on laser turned micro–grooving. This study uses RSM CCD technique to get the experimental data and ANN technique for process optimization. In this process, the optimal setting for the process parameters were concluded as lamp current at 19 A, pulse frequency at 3.2 kHz, pulse width of 6% duty cycle, cutting speed at 22 rpm and assist air pressure of 0.13 N/mm2. The predicted responses were minimum deviation of upper width by 0.0101 mm, lower width 0.0098 mm and depth at 0.0069 mm. The percentage error between the ANN predicted output and the data from the experiment are found to be within the acceptable range [11]. III. EXPERIMENTATION A. Design of Experiment For this project, response surface methodology (RSM) is used to develop the mathematical model to study the effect of the parameters selected on the responses i.e. surface roughness and kerf width. From RSM itself, central composite design (CCD) method will be used to develop the matrix for modeling. CCD is one the primary design techniques in RSM. This technique is used to build a second order model (quadratic model) and commonly used for process optimization. The parameters that are chosen as factors will be executed at one of the five level that later allows a quadratic model to be fit in. This technique uses a two-level design where by a center point and star configuration is added to allow the experiment to explore outside the two level designs. For this experimental study, MINITAB 14 software was used to conduct the RSM. Before proceeding with the experiment, we must first identify the high and low value of the parameters that are selected to be used for this experimental study. The high and low value for the experiment depends on the material used. For this

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experiment, the material used for the cutting process is mild steel. The initial dimensions of the material were length of 6 m, width of 0.15 m and thickness of 6 mm. To make it easier to measure work piece, shearing machine was used to cut the material into 1000 mm x 150 mm size work piece. The three parameters under investigation here are cutting speed, frequency and duty cycle. Table I below shows the parameters and the also the high and low values. TABLE I HIGH AND LOW VALUES OF THE DESIGN PARAMETERS Low Value

Parameters

High Value

Duty Cycle (%)

60

75

Frequency (Hz)

1000.0

1800.0

Cutting Speed (mm/min)

800.0

1200.0

The other parameters as shown in Table II were kept at a constant value throughout the entire experimentation. TABLE II PARAMETER SETTINGS FOR CONSTANT PARAMETERS Parameters S.O.D (mm) F.D (mm) Beam diameter (mm) Gas Jet Selection Gas Selection Lens Pre-flow time Nozzle Diameter (mm) Nozzle Type Gas Pressure (bar) Power (W)

Low Value 1 0.5 0.5 O2 1 (O2) 7.5 0 1.5mm Cylindrical 7 2100

B. Preparation of Doe Matrix Once the responses, factors and levels have been selected, the next step is to design the experimental runs. After the parameters and the values input into the software (MINITAB 14), a DOE model will be automatically generated with specific number of runs coupled with specific parametric settings. In this case, 20 runs were generated as shown in Table III. TABLE III EXPERIMENTAL LAYOUT FOR RESPONSE SURFACE Run

Cutting Speed

Frequency

Duty Cycle

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0 1 0 0 1 0 0 1 0 0 0 -1 -1 0 -1.68 0 -1 1.68 -1 1

0 1 0 0 -1 1.68 0 1 -1.68 0 0 -1 1 0 0 0 1 0 -1 1

0 -1 0 0 1 0 0 -1 0 -1.68 0 -1 -1 1.68 0 0 1 0 1 1


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Based on the runs given with the specific parametric values, the experiment is carried out and the corresponding surface roughness values taken were re-entered into the matrix. IV. RESULTS AND DISCUSSION Once the surface roughness values were entered, a complete analysis can be executed using RSM. A. Surface Roughness Analysis

Fig. 4. Contour analysis at 1000 Hz

Fig. 3. Analysis for surface roughness

Fig. 3 above shows the analysis for surface roughness (Ra) done using the response surface regression. The important factor to note here is the p – value whereby it denoted the importance of the parameter with any parameter having less than 0.05 is deemed important. Out of the three parameters, it can be observed from the estimated regression coefficients for Ra that the cutting speed and duty cycle has the lowest p – value of 0.002 and 0.000 respectively. This indicates that both of these parameters have considerable effect on the surface roughness of the cut since the p – value of these are less than 0.05. Another point to take here is that the p – value for “cutting speed*duty cycle” is also less than 0.05, with the value of 0.012. This shows that the interaction between cutting speed and duty cycle could bring about an effect on the surface roughness. The R – Sq is given as 92.1% while the lack–of– it is 0.625. This shows that the model is fit and the defect in this model is not too significant. As it can be noted from the analysis of variance section, linear regression has the smallest p – value with 0.000. This means that the empirical model is going to be a linear model.

Fig. 4 shows a contour based interaction analysis between the duty cycle and cutting speed. The frequency for this analysis was set at a constant 1000. From this plot, we can observe that the best value for the surface roughness can be obtained at high cutting speed value and low duty cycle value. It can be observed that the lowest surface roughness is at cutting speed between 1100 and 1300 and at duty cycle below 60 to 55. Therefore, we can predict that the best surface roughness can be obtained by using the cutting speed and duty cycle within these values. A further analysis was done by holding the frequency at 1800 Hz. From Fig. 5, the best surface roughness is still maintained at high cutting speed and low duty cycle. As compared to the earlier contour plot, this one suggests that a cutting speed between 1100 and 1300 and at duty cycle below 60 to 55 could yield surface roughness between 0 to 6μm. Although the 0 m is practically impossible, the Ra value can still be below 6 m. This shows that in both cases, the frequency is not a major factor in influencing the outcome of the surface roughness.

Fig. 5. Contour analysis at 1800 Hz


It can be summarized that to obtain a good surface roughness, it is best to use a high cutting speed value coupled with a low duty cycle regardless of the frequency. By furthering the investigation, the regression analysis below gives the equation for the surface roughness as: Ra = 2.74 – 0.0110 * cutting speed + 0.00117 * frequency + 0.261 * duty cycle

(1)

Hz for frequency and 60 % duty cycle. The response for this value is 3.794 m for surface roughness. C. Validation Validation is the final step in the experimental investigation. This session verified the analysis and the regression model through actual machining process. These not only test the predictability of the model, it also provides deviation error for the model. The model obtained from the response surface methodology analysis is:

The R – Sq value for this model as shown in Fig. 6 is 77.6% suggesting that the model is considered fit.

Fig. 6. Regression analysis

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Ra = 2.74 – 0.0110 cutting speed + 0.00117 frequency + 0.261 duty cycle

(2)

From the validation experimentation, the data obtained through calculation using (2) are as in the Table IV. The parametric setting from this table is then used to conduct an actual experimentation and surface roughness values were observed. These values can be summarized in Table V. By comparing the computed results with the actual results, the deviation error between these two can be obtained. This error shows how far the predictability of the model is in terms of how many percent it varies from the actual results. A comparison is made in Table VI for a better understanding for surface roughness.

B. Response Optimization Fig. 7 shows the suggested values for the parameters to obtain an optimal surface roughness. The values in red represent the optimal parametric settings suggested by the machine to achieve good responses. The graph below shows individual factor in each column affect the response with the other factors kept constant. At the upper left corner, D represents the composite desirability while d is the individual desirability.

TABLE IV PREDICTED SURFACE ROUGHNESS FROM DEVELOPED MODEL No

Cutting Speed (Mm/Min)

Frequency (Hz)

Duty Cycle (%)

Ra (μm)

1 2 3 4 5

1800 1000 1200 1200 800

1800 1800 1580 1800 1010

60 60 60 75 60

3.094 5.294 3.3514 7.009 7.7514

TABLE V OBSERVED SURFACE ROUGHNESS Cutting Speed (Mm/Min)

Frequency (Hz)

Duty Cycle (%)

Ra (μm)

1 2 3 4 5

1800 1000 1200 1200 800

1800 1800 1580 1800 1010

60 60 60 75 60

3.63 4.60 3.89 7.73 7.25

TABLE VI COMPARISON OF OBSERVED AND PREDICTED Ra

Fig. 7. Suggested Input Variables

Several response optimization graphs can be generated. The most important things that need consideration for selecting optimal setting are the D and d values. The highest possible values for D and d are 1.000. In, the suggested optimal parametric settings are 1200 mm/min for cutting speed, 1580

No

No

1 2 3 4 5

Input variables Cutting Freq. D. Cycle Speed. (Hz) (%) (mm/min)

1200 1000 1200 1200 1000

1800 1800 1580 1800 1010

60 60 60 75 60

Surface Roughness Predicted (μm)

Observed (μm)

3.094 5.294 3.351 7.009 7.751

3.63 4.60 3.89 7.73 7.25

Error %

14.76 12.82 13.85 9.33 6.90


For the surface roughness, it can be observed that the first three error values are rather close to each other than the last two. Although the error values differ, the deviation can be said to be close to each data suggesting persistency in the data. The average error can be calculated as: Average = (14.76 + 12.82 + 13.85 + 9.33 + 6.90) / 5 = 11.5%

statistical representation of the parameter to the responses. From this experimental study, an empirical model was developed from the statistical study through the regression analysis to correlate the parameters to the response. The model is: Ra = 2.74 – 0.0110 cutting speed + 0.00117 frequency + 0.261 duty cycle

(4)

(3)

Fig. 8 shows the comparison of the data between the calculated and observed for surface roughness. As noticeable, the values do not deter much from each other. Overall, the deviation error between the predicted and the observed are not more than 15% indicting that the mathematical model obtained for surface roughness is rather reliable.

Fig. 8. Comparison of Regression Model to the Validation of Surface Roughness

By adding in the error occurrence into the regression model, the mathematical model can be remodeled as: Ra = 2.74 – 0.0110 cutting speed – 0.00117 frequency + 0.261 duty cycle + ε Where, ε = 11.5%

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(4)

The ε here represent the error occurrence in the data. V. CONCLUSION In this study, response surface methodology is used to investigate the relationship between laser machining parameter with the responses. The parameters studied here are cutting speed, frequency and duty cycle. The effects of these parameters on the surface roughness are one of the important aspects of the study as well as finding a

This model takes into accounts the influence of three different parameters to the response. As observed the model produced is a linear empirical model for the surface roughness. The model can predict possible response values based on the given parameters values with some degree of error. The surface roughness model shows a low error not more than 20%. The results of this study show that surface roughness is highly affected by the cutting speed and duty cycle. Even when it comes to interaction between the three parameters i.e. cutting speed, frequency and duty cycle, only cutting speed and duty cycle have prominent effect on the surface roughness value. The statistical analysis shows that a best surface roughness is obtained by setting a high cutting speed with a low duty cycle regardless of the frequency used. Therefore, it is wise to use a low duty cycle and high cutting speed setting in situations where the surface roughness matters most. VI. RECOMMENDATION There are few recommendations can be given for the next experimental study to be taken under this topic. They are: 1) Repeat the same experiment (same level with same parameters and responses) with different software such as Design Expert to see the variation in the model predictability. 2) Use material with different thickness. 3) Use material of different types. 4) Further the study by including other parameters; stand–off distance, assist gas pressure, focal distance and etc.


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ACKNOWLEDGEMENT The authors would like to extend their sincere thanks to the top level management of manufacturing engineering faculty, the lab coordinator and lab technicians for their continuous help and support throughout the experimental and research period of this work.

REFERENCES [1] [2] [3]

[4]

[5]

[6]

[7]

Arce R. G. (2005). “Nonlinear signal processing: a statistical approach.” John Wiley & Sons. Chatfield C. (1995). “Problem solving: a statistician’s guide, 2nd edition.” Chapman & Hall/CRC. Thawari, G. et al. (2005). “Influence of process parameters during pulsed Nd:YAG laser cutting of nickel-base superalloys.” Journal of Materials Processing Technology. vol 170. pg 229– 239. Avanish, K. D. and Vinod, Y. (2007). “Laser Beam Machining – A Review.” International Journal of Machine Tools & Manufacture. vol. 48, no. 2008, pp 609 – 628. Avanish, K. D. and Vinod, Y. (2007). “Multi-Objective Optimization of Nd:YAG Laser Cutting of Nickel-Based Superalloy Sheet Using Orthogonal Array With Principal Component Analysis.” Optics and Lasers in Engineering. vol. 46, no. 2008, pp 124 – 132. Biswas R. et al. (2009). “A Parametric Study of Pulsed Nd:YAG Laser Micro-Drilling of Gamma-Titanium Aliminide.” Optics & Laser Technology. vol. 42, no. 2010, pp 23 – 31. Benyounis K. Y. et al. (2005). “Optimizing the Laser-Welded Butt Joints of Medium Carbon Steel Using RSM.” Journals of Materials Processing Technology. vol. 164 – 165, no. 2005, pp 986 – 989.

[8]

Soveja A. et al. (2008). “Optimization of TA6V Alloy Surface Laser Texturing Using an Experimental Design Approach.” Optics and Lasers in Engineering. vol. 46, no. 2008, pp 671 – 678. [9] Kuar A. S. et al. (2005). “Modeling and Analysis of Pulsed Nd:YAG Laser Machining Characteristics During MicroDrilling of Zirconia (ZrO2).” International Journal of Machine Tools & Manufacture. vol. 46, no. 2006, pp 1301– 1310. [10] Choudhury, I. A. and S. Shirley. (2009). “Laser Cutting of Polymeric Materials: An Experimental Investigation.” Optics & Laser Technology. vol. (NA), no. (NA), pp (NA). [11] Dhupal D. et al. (2009). “Modeling and Optimization on Nd:YAG Laser Turned Micro–Grooving of Cylindrical Ceramic Material.” Optics and Lasers in Engineering. vol. 47, no. 2009, pp 917 – 925. [12] Beal V. E. et al. (2005). “Optimisation of Processing Parameters in Laser Fused H13/Cu Materials Using Response Surface Method (RSM).” Journals of Materials Processing Technology. vol. 174, no. 2006, pp 145 – 154. [13] Caristan C. L., (2004). “Laser Cutting Guide For Manufacturing.” Society of Manufacturing Engineers. USA. pp 17 – 23. [14] Hibbert D. B., (2007). “Quality assurance for the analytical chemistry laboratory.” Oxford University Press Inc. pp23 – 25. [15] Ion J. C., (2005). “Laser Processing of Engineering Materials; Principles, procedures and industrial application.” Elsevier Butterworth – Heinemann. pp 355 – 363. [16] Myers R. H., Montgomery D. C., Christine M. Anderson-Cook (2009). “Response Surface Methodology: Process and Product Optimization Using Designed Experiments 3rd Edition.” John Wiley & Sons Inc. pp 74 – 76 [17] Thompson J.R. (1989). “Empirical model building.” John Wiley & Sons.