Influence of the Main Technological Variables of

Journal of Mechanics Engineering and Automation Volume 6, Number 1, January 2016 (Serial Number 55)

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Journal of Mechanics Engineering and Automation Volume 6, Number 1, January 2016 (Serial Number 55)

Contents Techniques and Methods 1

Influence of the Main Technological Variables of Cyclical Mechanic-Thermal Processing on the Strain Hardening of Steel Parts Eleno Alfonso Brindis, Sanjeevkoemar Bissesar, Faizel Abdoel Wahid and Francisco Tchiquendja Eleno

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A Study on Preconditions Setting of Long-Term Contract between Manufacturer and Component Supplier Sidi Wu and Hisashi Onari

19

Latest Development and Application of High Strength and Heavy Gauge Pipeline Steel in China Zhang Yongqing, Guo Aimin, Shang Chengjia, Liu Qingyou, J. Malcolm Gray and Frank Barbaro

25

Critical Buckling of Drill Strings in Cylindrical Cavities of Inclined Bore-Holes Nabil Musa, Valery Gulyayev, Nataliya Shlyun and Hasan Aldabas

Investigation and Analysis 39

Long Distance GIL PD Fault Localization Method Based on Amplitude Difference and Time Difference Calculation of UHF Coupling Signal Zhang Hui, Hu Po and Tao Ke

47

Analysis of Percolation of the Stabilized Suspensions of TiO2 and SiO2 Nanoparticles in Soil Columns Simulating Landfill Layers Elizabeth Mendes de Oliveira, Daniele Aparecida Nogueira, Luis CarlosRolim Lopes, José Flávio Silveira Feiteira and Jose Adilson de Castro

53

Fractal Interpretation of Ultrasonic Crystallization of Solutions Valery Katz and Slava Katz

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Journal of Mechanics Engineering and Automation 6 (2016) 1-8 doi: 10.17265/2159-5275/2016.01.001

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Influence of the Main Technological Variables of Cyclical Mechanic-Thermal Processing on the Strain Hardening of Steel Parts Eleno Alfonso Brindis1, Sanjeevkoemar Bissesar1, Faizel Abdoel Wahid1 and Francisco Tchiquendja Eleno2 1. Department of Mechanical Engineering, Faculty of Science Technology, Anton de Kom University of Suriname, Paramaribo 9212, Suriname 2. Department of Mechanical Engineering, Faculty of Engineering, University of Matanzas, Matanzas 44740, Cuba Abstract: The main objective of the present work was to determine the influence of the most important technological variables of CMTP (cyclical mechanic-thermal processing) on the strain hardening in the surface layers of steel parts. For this, it was designed a full factorial plan at two levels of five independent variables that include the whole processing in two and three cycles, the cold-forming degree and force during the plastic deformation (burnishing), and the temperature and time at the given temperature during the aging. Each cycle is composed of plastic deformation at room temperature plus aging. As dependent variables, the degree and penetration depth of strain hardening were evaluated. Based on the appropriately used set of experimental data, it had been fitted an exponential model for each dependent variables and also a two-degree polynomial fitting of in-depth evolution of microhardness profile was obtained. The amount of cycles and the cold-forming degree are the technological variables of CMTP that influence the most on strain hardening, although other variables also are significant. The microhardness profile highlights that during the CMTP, the strain hardening decreases from the outer bound to the transition zone of the surface layers, where it disappears. Key words: Mechanic-thermal processing, strain hardening, surface layers, microhardness.

1. Introduction The CMTP (cyclical mechanic-thermal processing), according Gordienko’s definition [1], is a kind of substructural hardening that consists of submitting the parts to several combined cycles of cold plastic deformation and aging in order to obtain a set of high physic-mechanic indicators of quality in their surface layers. This means that, as results of the treatment in the surface layers of parts, a high level of strain hardening with a dislocation cell nanostructure is achieved, which keeps its stability until temperatures are close to the recrystallization temperature of given alloy. At applying the CMTP, an improvement of the mechanical properties and the performance takes place in the metals and their alloys, particularly in those with a BCC (body-centered cubic crystal) structure, as the Corresponding author: Eleno Alfonso Brindis, Ph.D., professor, research field: materials science and engineering.

AISI 1045 plain mid-carbon steel, used in the present research work. The strain hardening is the effect of cold plastic deformation process within the surface layers of the metals and alloys, and it is associated with the presence, movement and interaction of dislocations, involving the dislocation density growth. The average distance between dislocations decreases and dislocations start blocking the motion of each other, and these phenomena become the metal harder and stronger. Panwar et al. [2] also explained the role of the combination of cold work and subsequent aging through analysis of a microalloyed Cu-bearing HSLA (high-strength low alloy) steel; the mechanical properties had been studied at various stages of aging with and without prior cold work at different percent. M’Guil et al. [3] explained the strain hardening through models of observed true stress-true strain curves in the

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Influence of the Main Technological Variables of Cyclical Mechanic-Thermal Processing on the Strain Hardening of Steel Parts

work hardening region after tensile tests; they modeled the large plastic deformation behavior and anisotropy evolution in cold rolled BCC steel. Before testing, the specimens are almost always prepared under different cold-forming degrees by means of: (a) Rolling [4, 5], these studies report the mechanical property and microstructure of cold rolled low and high carbon steel and its work-hardening behavior during the deformation process; (b) Burnishing process [6], the obtained results achieved by then show the enhancement in the surface roughness and magnification in surface hardness were achieved, because of application of roller burnishing in mild steel specimens; (c) High-pressure torsion at room temperature for up to 5 turns, were applied to low-carbon triple-alloyed steel specimens by Marulanda et al. [7]. Microhardness, scanning electron microscopy and X-ray diffraction were used to investigate the hardness and microstructural evolution of the steel. The results show a gradual evolution in both the hardness and the microstructure with increasing numbers of turns. There are many ways to model strain hardening, each one of them has its own advantages and disadvantages. The strain hardening can be obtained through statistical dislocation density models, dislocation dynamics model and empirical models, as was showed by Prassad [8] in his Master’s thesis. That is precisely why in this work are proposed two new empirical models for establishing the influence of the technological rate of CMTP on strain hardening of steel parts.

2. Experimental Materials and Procedures 2.1 The Material under Study and Its Properties in Supply State According to Standard Specification ASTM A 29/A 29M-04 [9], several grades of plain and low-alloy mid-carbon steels were evaluated, and AISI 1045 steel was chosen, since it is the most economic grade, that

allows to fulfill the objective of the present work. From the employed bar to prepare the specimens, the chemical composition of studied steel was obtained, in %: C = 0.47, Mn = 0.70, Si = 0.21, P = 0.04, S = 0.03, Cr = 0.15 and Ni = 0.09. Moreover, in supply state the following mechanical properties of the tested steel were determined: average hardness, HBS 185 (ASTM E 10-01a) [10]; yield strength, σy = 338 MPa; and the tensile (ultimate) strength, σu = 620 MPa. The tensile specimens were prepared, following the Standard Test Method for Tension Testing of Metallic Materials [Metric] ASTM E 8M-04 [11]. The specimens for the CMTP application, and later on the microhardness test, were machined to little thick-walled cylinders of 30 mm outer diameter, 20 mm inner diameter and 15 mm wideness. 2.2 Machines, Devices, Tools and Instruments The macrohardness measuring of supply state material was done using the HB-3000B Manual Digital Display Brinell Hardness Tester/Metal Brinell Durometer. The surface roughness was evaluated using the comparison method by means of the ZUZI model 173/2. Mounted specimens for the microhardness measurement were ground in STRUERS Labopol-21 Machine, and lastly they were polished in the STRUERS Labopol-5 Machine. The microhardness measurement had been developed in the metallographic microscope model SCHENK TREBEL, with a Vickers diamond pyramid indenter and its own devices for fixing the specimens. A cutting disk for the STRUERS Labopol-5 Machine was used. Both single point-brazed cutting tools P10 and P20 (ISO R513-1975E) [12] for the preliminary specimens sizing had been used. For the drilling operation ware employed a 60 degree center drilling bit, M2 drill rods (10 and 18 mm

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diameter); and a M2 reamer (20 H8 diameter). The burnishing operation was made using a Yamasa Sx8-1.2 single roll type roller burnishing tool. A set of carborundum (SiC) emery paper (240, 320 and 600, according to ASTM E 3-01 [13]) was employed for the specimens grinding, while for the polishing operations one used both diamond paste in sizes 6 μm and 1 μm. 2.3 Design and Run of Experiments CMTP experiments were carried out on external surfaces of little thick-walled cylinders. In the experiments, the work pieces were burnished after turning on lathe, in the same set-up. While burnishing, the roller burnishing tool is fixed in its own coupled-dynamometer. That dynamometer is capable of measuring three force components. The zcomponent was taken as the burnishing force. After each stage of burnishing, the specimens have been subjected to the aging for completing each cycle, that is, it is in order to organize the dislocation, forming sub-grains and sub-borders in all grains by means of cell fragmentation (Gordienko [1]). Independently of the applied variables’ combination, the surface roughness were improved till Ra = 0.32… 0.16 micrometers after burnishing process and remains at the same level after aging stage. It was not formed any oxide husk over the surface layer, inasmuch as the temperature never rose higher than 200 °C. In order to reveal a clear picture of CMTP, a series of experiments were conducted on prepared specimens from selected AISI 1045 plain carbon steel. A full factorial orthogonal array had been chosen, for five factors at two-level, that required 32 (25) experiments (Table 1).

3. Results and Discussion During the cold processing of ductile alloys (as AISI 1045 steel in supply state), the strain hardening behavior, the degree and depth of strain hardening are reported mainly as result of plastic deformation, using

Table 1 Factors and levels chosen for experimentation (common for both degree and depth of strain hardening experiments). Factors Amount of cycles (A) Cold-forming degree (), % Force (F), kN Temperature (t), ºC Time (), h

Low level (-1) 2 4 0.8 100 1.0

High level (1) 3 7 1.5 200 1.5

different models and theories for its foundation, thus González et al. [14] established a connection between the coefficient of strain hardening, mechanical strength and admissible thickness tolerances in steel sheets, that it is an important contribution for materials testing. The empirical models are quite a bit used, and they describe the flow stress in terms of power laws as a function of strain with many empirical constants. One of the simplest approaches is the Hollomon equation which describes the flow stress as a simple power law in strain, it is applied in several recent works [15]; even in these works the true stress-strain curve and its polynomial fit curve of a cold rolled low-carbon steel had been compared. The Hollomon equation is given as σ = Kε nH (1) where, σ is the true stress, K is the coefficient of deformation strengthening, ε is the true strain and nH is the index of strain hardening. The results of above mentioned research works and other with more complicated models depend of tensile test and they do not show any explicit physic-mechanic indicator of quality in the surface layers of tested material. In the present work, an empirical model had been used, that evaluates the strain hardening, as the main physical-mechanical quality indicator in the surface layers of the AISI 1045 plain mid-carbon steel. Here both degree and penetration depth dependencies of the strain hardening on the main cold plastic deformation and aging variables were analyzed, after specimen were submitted to CMTP. Table 2 shows the experimental matrix and results, for both features of strain hardening: degree (N), and depth (h).

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Table 2 Experimental matrix and results for degree and penetration depth of strain hardening. Nº exp. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

A 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2

 (%) 7 7 4 4 7 7 4 4 7 7 4 4 7 7 4 4 7 7 4 4 7 7 4 4 7 7 4 4 7 7 4 4

Factors F (kN) 1.5 1.5 1.5 1.5 0.8 0.8 0.8 0.8 1.5 1.5 1.5 1.5 0.8 0.8 0.8 0.8 1.5 1.5 1.5 1.5 0.8 0.8 0.8 0.8 1.5 1.5 1.5 1.5 0.8 0.8 0.8 0.8

t (ºC) 200 200 200 200 200 200 200 200 100 100 100 100 100 100 100 100 200 200 200 200 200 200 200 200 100 100 100 100 100 100 100 100

The values of “N” and “h” were obtained after measuring the microhardness across the surface layers of specimens during each experiment and then using the following classic dependencies: N = [(Hmax - Ho)/Ho]*100% (2) DepthSH = h = f(Hmax, Ho) (3) where, Hmax characterizes the achieved level of strain hardening that is the maximum value of microhardness in the outer edge of surface layer at its deformation zone, Ho corresponds to the microhardness value at the transition zone of surface layer, and it is taken when

 (h) 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

Experimental N (%) 48.000 70.000 34.000 53.000 44.000 65.000 33.000 52.000 55.000 72.000 39.000 58.500 46.000 67.000 36.000 58.000 52.000 75.000 36.500 55.000 47.000 68.000 33.000 56.000 53.500 78.000 44.500 59.000 52.000 75.000 40.000 52.500

Results h (mm) 0.850 0.500 0.750 0.450 0.800 0.450 0.700 0.400 0.800 0.500 0.650 0.400 0.750 0.400 0.600 0.350 0.850 0.500 0.650 0.400 0.700 0.400 0.600 0.350 0.750 0.450 0.600 0.400 0.700 0.450 0.550 0.300

the value of measured microhardness remains almost constant, independently from the increasing distance of indentation towards the specimen core (Fig. 1). As results of this study two empirical relationships among the input- main technological variables of the processing rate and output- two of the major physic-mechanic features of the strain hardening were fitted. Once established the final fitted models, the influences of input (independent variables) on output (dependent variables) were analyzed.

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3.1 Degree of Strain Hardening N = 99.335A-0.9500.488F0.112t -0.120 -0.135 (4) The joint assessment of Tables 2 and 3, as well as Eq. (4), one can explain that: The greatest influence on the magnitude “N” is exhibited by the amount of cycles (A). In Table 2, experimentally it is showed that at the low level (2 cycles) correspond the highest values of “N”, this situation is consistent with the statistics depicted in Table 3, where the estimated coefficient for variable “A” has a negative value, as well as in the Student distribution, whose absolute value is the highest (this means the most significant variable). In this sense, another significant detail is that its pValue is the lowest. From the metallographycal point of view, this phenomenon is because of the difference between the added by the cycle maximal microhardness “Hc” and the microhardness in the transition zone “H0” of the surface layers, consecutively decreases after each cycle due to the strengthening of material by dislocation mechanism. The influence in the magnitude “N” of the cold-forming degree () and the force (F), one can explain as: the greater “” and “F” values, the greater the magnitude “N”. An increase of the cold-forming degree and proportionally of the force during the plastic deformation process (burnishing), involves major amount of dislocation in the surface layers. According to the results of Xue et al. [16], at the beginning of deformation, plastic deformation caused by applied force prompts out pouring dislocation movement along gliding plane and lead to the dislocation multiplication. It further makes the dislocation density bigger and bigger, the main and second slip system of the parallel dislocation interaction blocks the dislocation further moving, and so it produces remarkable strain hardening. Gordienko [1] showed that after aging, the blocked into grains dislocations and other defects clump together to form thousands sub-grains in each grain. These sub-grains achieve a cellular dislocation

structure that raises the performance of machine parts during the CMTP. The aging temperature “t” strongly influences on the magnitude “N”, while greater is the value of temperature, lesser is the magnitude “N”, as it is showed in Table 2. At the same time, this statement can be corroborated in Table 3, where the estimated coefficient for variable “t” has sign “-” and correspondingly the value of tStat exhibits the same sign; moreover, the pValue of variable “t” is the third lowest of the whole model. The aging time “” is the variable that less influences in the magnitude “N”. Although in lesser degree, the aging time experimentally and statistically follows the behavior of aging temperature, with regard to dependent variable “N”. The greater values of aging temperature and time benefit the recovery process inside the surface layers which, in turn, mean that the degree of strain hardening decreases by lowering the levels of microhardness in the surface layers. 3.2 Penetration Depth of Strain Hardening h = 0.053A1.2910.339F0.192t0.1100.191 (5) At analyzing the outcomes from Tables 2 and 4, as well as Eq. (5), it is possible to realize that the greater values of every independent variables generate the greater values of dependent variable “h”. Here, as in the case mentioned above, the amount of cycles (here with sign “+”) and the cold-deformation degree have Table 3 The fitting results of degree of strain hardening.

Intercept

Estimate Coef. 3.82780

A

-0.9504



0.48794

0.028728

16.985

1.3603e-15

F

0.11157

0.025575

4.3625

0.00018073

Variable

SE

tStat

pValue

0.22116

17.308

8.6602e-16

0.03965

-23.97

2.9705e-19

t

-0.12030

0.023194

-5.1866

2.0548e-05



-0.13506

0.039650

-3.4062

0.0021509

Number of observations: 32, Error degrees of freedom: 26. Root mean squared error: 0.0455. R-squared: 0.973, Adjusted R-Squared 0.967. F-statistic vs. constant model: 184, p-value = 1.97e-19.

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Table 4 The fitting results of penetration depth of strain hardening. Variable Intercept

Estimate coef. -2.94330

SE

tStat

pValue

0.146320

-20.116

2.2596e-17

A

1.29150

0.044656

28.921

2.6709e-21



0.33907

0.032355

10.479

7.9243e-11

F

0.19175

0.028804

6.6571

4.6208e-07

t

0.11050

0.026122

4.2300

0.00025604



0.19148

0.044656

4.2878

0.00021998

Number of observations: 32, Error degrees of freedom: 26. Root mean squared error: 0.0512. R-squared: 0.975, Adjusted R-Squared 0.971. F-statistic vs. constant model: 205, p-value = 4.96e-20.

the greatest influence on the dependent variable “h”; but in this case, it is different the ranking for the other variables, since in descending hierarchical order go on the force, the time and the temperature. Note that between the time and temperature just a slight difference of values. In the case of penetration depth of strain hardening, at increasing the amount of cycles also are increased the progressive effect of cold-forming degree and of applied force after each cycle [17]; this leads to greater enlargement of the deformation zone of the surface layers towards the specimen core. The greater values of aging time and temperature, in spite of benefiting the recorvery process, moreover, they enhance the diffusion and self-diffusion processes inside the surface layers, therfore, they also contribute to increase the penetration depth of strain hardening.

3.3 In-depth Evolution of Microhardness Profile It is usual, in many research works within the fields of materials science and engineering, to establish several dependencies that involve the microhardness as the starting point for the studies of strain hardening through its level, degree and penetration depth. These studies cover the most varied materials and treatments applied during the manufacturing processes of machine parts: Alfonso [18], for quenched and tempered steel; Nobre et al [19] proposed methodology for estimating the local yield stress in work-hardened surface layers; Marulanda et al. showed that full homogeneity of the microstructure across the tested steel disks, and therefore of the microhardness requires to apply pressures higher than 6.0 GPa. In-depth evolution of microhardness profile is presented in those works. Fig. 1 depicts the in-depth evolution of microhardness profile along the processed surface layers, from their outer bound of deformation zone to the transition zone, with prediction bounds (Pred bnds) of 95%. The value of microhardness, decreases continuously from the outer surface, where its maximum value “Hmax” is found, to the interior of material to its basic value “Ho”, further this value remains practically constant, which means that transition zone is not affected by the strain hardening. In Fig. 1, the microhardness is given in Megapascal (MPa), and the depth of strain hardening (DepthSH) is given in millimeters (mm).

Fig. 1 Microhardness profile of AISI 1045 plain carbon steel after three cycles of mechanic-thermal processing.


4. Conclusions Once finished this research, it was possible to reach the following conclusions: (1) The CMTP increases, strengthens and stabilizes the strain hardening in the surface layers of steel parts at raising their main physic-mechanic indicators of quality. (2) Both obtained models for degree and penetration depth of strain hardening allow to predict these two physic-mechanic quality indicator of the surface layers through the applied technologycal rate of CMTP. (3) There are many empirical models for steel machining, cold and heat forming, but the CMTP of steel are not sufficiently investigated through empirical models. (4) Empirical models can be used in order to have a sense of how CMTP parameters influence on the main characteristics of the strain hardening, saving time and resources during the research works. (5) The microhardness profile highlights that during the CMTP the strain hardening decreases from the outer bound to the transition zone of the surface layers, where it disappears.

Acknowledgment This work was supported by the Department of Mechanical Engineering of Anton de Kom University of Suriname.

[4]

[5]

[6]

[7]

[8]

[9]

[10] [11] [12] [13] [14]

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Gordienko, L. K. 1973. “Substructural Hardening of Metals and Alloys.” Nauka Issue, Moscow: 224. (in Russian) Panwar, S., Goel, D. B., and Pandey, O. P. 2007. “Effect of Cold Work and Aging on Mechanical Properties of Copper Bearing Microalloyed HSLA-100 (GPT) Steel.” Bulletin of Material Science 30 (2): 73-9. M’Guil, S., Wen, W., Ahzi, S., and Gracio, J. J. 2011. “Modeling of Large Plastic Deformation Behavior and Anisotropy Evolution in Cold Rolled BCC Steels Using the Viscoplastic -Model-Based Grain-Interaction.” Mater. Sci. Eng. A 528 (18): 5840-53.

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Zemčík, O., Chladil, J., Otoupalík, J., and Sedlák, J. 2013. “Changes in the Surface Layer of Rolled Bearing Steel.” Journal Proceedings in Manufacturing Systems 8 (2): 99-104. Wang, S. F., Peng, Y., and Li, Z. J. 2013. “Work Hardening and Deformation Mechanism of Cold Rolled Low Carbon Steel.” Research Journal of Applied Sciences, Engineering and Technology 5 (3): 823-8. Malleswara, R. J. N., Chenna K. R. A., and Rama R. P. V. 2011. “The Effect of Roller Burnishing on Surface Hardness and Surface Roughness on Mild Steel Specimens.” International Journal of Applied Engineering Research 1 (4): 777-85. Marulanda, D. M., Wongsa-Ngam, J., and Langdon T. G. 2014. “Microstructural Evolution and Microhardness in Low Carbon Steel Processed by High-Pressure Torsion.” Journal of Materials Research and Technology 3 (4): 344-8. Prassad, G. V. S. S. 2007. “An Improved Dislocation Density Based Work Hardening Model for Al-alloys.” M.Sc. Thesis, Rheinisch-Westfälischen Technischen Hochschule. ASTM A 29/A 29M-04. 2004. “Standard Specification for Steel Bars, Carbon and Alloy, Hot-Wrought, General Requirements.” ASTM E 10-01a. 2001. “Standard Test Method for Brinell Hardness of Metallic Materials.” ASTM E 8M-04. 2004. “Standard Test Method for Tension Testing of Metallic Materials [Metric].” ISO R513-[1975 (E)] System “Application of Carbides for Machining by Chip Removal.” ASTM E 3-01. 2001. “Standard Guide for Preparation of Metallographic Specimens.” González, R., García, J. O., Barbés, M. A., Quintana, M. J., Verdeja, L. F., and Verdeja, J. I. 2010. “Ultrafine Grained HSLA Steels for Cold Forming.” Journal of Iron and Steel Research International 17 (10): 50-6. Chen, L., and Deng, M. 2011. “Study on Algorithm of Statistics for Bolts Information of Steel Bridge and Iron Tower Based on Assembly Feature.” Advances in Information Sciences and Service Sciences 3 (10): 1-11. Xue, Z. Y., Zhou, S., and Wei, X. C. 2010. “Influence of Pre-transformed Marten Site on Work-Hardening Behavior of SUS 304 Metastable Austenitic Stainless Steel.” J. Iron Steel Res. Int. 17 (3): 51-5. Delgado, S. Y. 2014. “Sub-microcrystalline Structural State Formation of Low Carbon Steel and Steel

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Composites, during Their Thermomechanical Processing.” Ph.D. Thesis, Ural Institute of Metal Physics. (in Russian) [18] Brindis, E. A. 1990. “Microstructure and Properties Formation in the Surface Layers of Quenched and Tempered Steel, after Its Finish Turning.” Ph.D. Thesis,

Moscow Institute of Chemical Machinery-Construction. (in Russian) [19] Nobre, J. P., Dias, A. M., and Kornmeier, M. 2004. “An Empirical Methodology to Estimate a Local Yield Stress in Work-hardened Surface Layers.” Society for Experimental Mechanics 44 (1): 76-84.

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A Study on Preconditions Setting of Long-Term Contract between Manufacturer and Component Supplier Sidi Wu and Hisashi Onari Dept. of Industrial & Management Systems Engineering, Faculty of Science & Engineering, Waseda University, Tokyo 169-8555, Japan Abstract: To provide a risk-sharing mechanism that encourages a component supplier and a manufacturer to expand their production capacity of components and products, many researches on SCM suggested that it is better for the SC players to connect a long-term contract with flexible preconditions before doing the decision-making of production capacity. With considering of the uncertainty of demand and integrity problems between SC players, it is difficult to set reasonable preconditions. As a result, under-investment problems still occur frequently. In this paper, after we had discussed the decision-making of production capacity with the preconditions by analyzing the character of the players, we verified the under-investment problem of the supply chain. In order to clarify the optimum preconditions to alleviate the under-investment problem, we also analyzed the relations between preconditions and supply capacity of the whole supply chain. In the last part of this paper, we proposed a method of preconditions setting in such uncertain situations. Key words: Supply chain management, production capacity, contract, under investment.

1. Introduction In this paper, we focus on the under-investment problem in a supply chain that consists of an assembly manufacturer and his subcontract component supplier. The manufacturer and the component supplier are planning their production capacity of new products and new components for next term. The component is a key part of the new product, such as the liquid crystal display panel, automotive motor and so on. It only can be purchased from limited suppliers, and product production cannot be in progress without this component. During the decision making of investment planning, high investment cost of production capacity makes the component supplier think about profit acquisition more than risk hedging. Especially, in this kind of supply chain, the under-investment problem of component production capacity occurs frequently. Corresponding author: Sidi Wu, research associate, research fields: collaborative decision making, supply chain management, and information sharing.

With considering of the under-investment problem, the assembly manufacturer tends to set a lower production capacity of product to hedge the risk of product over-investment. As a result, supply capacity of products of the whole supply chain becomes lower than the expected level. So, it is difficult for the manufacturer to get the expected share rate in the product market. In order to solve this problem, a long-term sale contract with preconditions such as the minimum trading volume and option trading price has been proposed in many researches before. With considering of expected profit and expected loss, the manufacturer sets the preconditions of the long-term contract and gives them to the component supplier. Under these preconditions, the supplier and the manufacturer set their production capacity themselves with considering of investment behavior of the opponent player. But it is difficult for the manufacturer to do appropriate decision of preconditions under demand uncertainty. Without the exact demand information and the appropriate

10

A Study on Preconditions Setting of Long-Term Contract between Manufacturer and Component Supplier

preconditions from manufacturer, the supplier may consider risk hedging seriously. The less-supply problem of the supply chain cannot be solved effectively. In this paper, after finished modeling the decision-making of production capacity of the component supplier and the manufacturer, we analyzed the under-investment problem quantitatively. Furthermore, with using the decision-making models, a method of preconditions setting for the manufacturer was proposed. The effectiveness of the proposal was proved by comparing with the supply chain total supply capacity and the production capacity difference between the supply and the manufacturer.

2. Literature Review In this section, we will discuss the studies about long-term sales contracts for decision-making of production capacity setting and preconditions of contracts between supply chain players. With considering of the uncertainty of trading price in spot market, the decision-making model for each collaboration level of the supplier and the buyer was proposed with using a long term capacity reservation contract and a short term sales contract simultaneously [13]. Effectiveness of the proposal was proved with comparing with the supply chain total profit. In high-tech industry, it is difficult for component suppliers to expand their production capacities with constraints of investment capital. As a result, opportunity loss of whole supply chains occur due to buyers cannot get enough volume of components to meet the needs of product demand. In this kind of situation, a contract called deductible reservation was proposed. Decision-making models of players with the contract were created. Deductible reservation contract was compared with take-or-pay contract by supply chain total profit and profit of each player, the proposed deductible reservation contract was proved as the effectiveness one [3]. The two studies discussed uncertainty of market demand and effectiveness of

long term contract while doing decision-making of production capacity setting. The effectiveness of preconditions was also discussed to hedge risks of demand uncertainty in many studies. Pay-to-delay contract set the trading volume and price to three levels, players will set their production capacity with considering of the preconditions about the level of volume and price [2]. Preconditions make the sales contract more flexible, and supplier and buyer can decide a fixed price of components by negotiation in the first step, trading volume can be adjusted in a decided range in the second step [4]. Many studies proposed a lot of new contract methods and preconditions of contract to hedge supply chain risks, but few studies concerned the way of contract connection and preconditions setting. In this paper, we discussed the process of preconditions setting and production capacity setting. We also proposed the method to get the optimum production of the sales contract.

3. The Contract 3.1 Contract Contents The component supplier and the manufacturer are planning the production capacity for next new components and products. In order to hedge risks of demand uncertainty, it is better to decide the trading volume at an early time before production capacity planning. It is also necessary to decide a reference trading price for trading volume in such kind of negotiation. 3.2 Preconditions In this paper, we set the preconditions as Fig. 1. It is a simple structure of option contract in many studies to do risk hedging. The effectiveness has also been proved before. : Minimum trading quantity (volume) : Price per unit of : Price per unit of trading quantity over

11


P

Demand probability distribution to a price

Q

Q Qc Fig. 1

Average product price

Contract preconditions. Probability

The supplier and manufacturer should decide their production capacity with considering of the three parameters which were set by the manufacturer. In the next section, we will discuss the method of preconditions setting.

P

Opportunity Loss Risk Excess Risk

4. Preconditions Setting Actual Production Actual Demand Capacity Demand

4.1 Demand Uncertainty The demand of new products in the product market in next several years is uncertain. In this paper, we defined the demand uncertainty as the product demand fluctuations with a product price. The demand is not the whole demand of product market, just the product demand to the manufacturer. We considered the product demand follows a probability distribution. It will fluctuate within a certain range by the intermediate value. To describe the demand uncertainty, PQ curve were used to show the relation between demand and market price. It is a long-term capacity investment, so the trading period was set to about 5 years. Fig. 2a shows the demand uncertainty and Fig. 2b shows the definition of risks. Excess investment risk and opportunity loss risk are taken into consideration when the production capacity was decided. 4.2 Preconditions Evaluation The purpose of preconditions setting of manufacturer is to improve investment incentives of supplier. It is necessary for manufacturer to set preconditions with considering of investment behavior and the characteristics of supplier. Value of expected profit

Fig. 2

(a) Demand uncertainty; and (b) risk definition.

and expected loss were calculated with one production capacity by the manufacturer. The manufacturer should know the supplier’s attitude (evaluation result) to the expected profit and expected loss in order to set proper preconditions of contract. We use the value function of prospect theory to describe the evaluation value of supplier. Formula 1 shows the value function. V(X)

⇒

0,

0 (1)

α, β, λ are the characteristic parameters of players. With using of value function, the uncertainty of the other player’s investment behavior can be quantified. 4.3 Minimum Trading Quantity

Setting

setting of manufacturer is to The purpose of hedge the risks of components supply shortage in the future and the price rising. After finished demand forecast, the manufacturer will do the calculation of expected profit and expected loss to decide . The biggest total value of expected profit and expected loss can be calculated by the production capacity of . Setting procedure of :

12


Step1. Forecast the market demand of the new product with considering of the market demand information of existing products; Step2. Create the PQ curve and demand distribution of average price; Step3. Calculate the expected profit and expected loss of each demand value from demand distribution. The following two cases are taken into consideration. ′ Case 1: ) Expected Profit＝

′

′

(2)

′

′

Expected Loss＝

(3)

′

Case 2: (

′

′

) Expected Profit＝ (4) ′

Expected Loss＝ ′

(5)

q: Actual demand; I: Investment Cost; : Average price of product; C: Production Cost; Step4. Use value function to do the calculation of total value about the expected profit and the expected loss. Step5. Find out the ′ with the max total value of the expected profit and the expected loss, set this ′ as . ′ ′ (6) It is necessary to decide and after finished setting of . From step 5, we will show the decision-making process of and . Step6. Manufacturer should set the desired profit by himself which is a part of the gross profit of supply chain. We set the desired profit rate as K. SC gross profit= (7)

Desired profit= (8) K will not get changed though the manufacturer faces the worst situation. The worst situation to the manufacturer is that he can only get component volume from the supplier. Desired profit = (9) = If the actual demand was the average demand of product market, profit of supplier could be expected by manufacturer with next formula. Expected profit of supplier = 1 = Step7. Calculate (10).

(10) by formula (9) and

and 1

/

(11)

1 2 / (12) : Investment cost of supplier; : Investment cost of manufacturer; : Average demand to average price in the product market; : Production cost of supplier; : Production cost of manufacturer The manufacturer will pass the preconditions to the supplier. The manufacturer will also decide his production capacity with the preconditions himself. We will discuss the production capacity of supplier and manufacturer in next section.

5. Decision-Making of Production Capacity Setting 5.1 Decision-Making of Production Capacity Setting by Manufacturer The manufacturer will set his production capacity for new products with considering of the preconditions of contract. He will choose capacity which can reach the max value of total amount of expected profit and expected loss, and set it as his max


13

production capacity. Eq. (13) shows the objective function of the manufacturer. Sub to: (13) As shown in Fig. 2b, the following two cases of the actual demand are taken into consideration by the manufacturer. Case 1: ) Expected Profit＝

(14) Expected Loss＝ (15) Case 2: ) Expected Profit＝ (16) Expected Loss＝ (17) q: Actual demand; : Candidate max production capacity of manufacturer. 5.2 Decision-Making of Production Capacity Setting by Supplier After getting the preconditions from manufacturer, the component supplier will set his new component production capacity without the latest demand information of product market. Because component suppliers are far from the product market, information asymmetry occurs easily without supply chain collaboration. As the same as the manufacturer, the component supplier will choose capacity which can reach the max value of total amount of expected profit and expected loss from the demand distribution forecasted by himself, and set it as his max production capacity. Eq. (18) shows the objective function of the supplier. Sub to:

(18)

Fig. 3

(a) Range of

; and (b) Actual demand and

.

As shown in Fig. 3b, the following three cases of the actual demand are taken into consideration by the manufacturer. Comparing with Fig. 2b, without the exact demand information, the component supplier may consider the case of . Case 1: ) Expected Profit＝ (19) Expected Loss＝ (20) Case 2: Expected Profit＝

)

(21) Expected Loss＝ (22) Case 3: ) Expected Profit＝ (23)

14


manufacturer, so he may evaluate loss more serious than the manufacturer. We set the parameters of value function as following table. 6.1 Experiment Plan Firstly, we compare the supply capacity setting with preconditions and without preconditions to confirm the effectiveness of the preconditions. Secondly, we do the analysis about the relation between the desired profit rate K of manufacturer and the whole supply capacity of this supply chain. Thirdly, we analyze the relation between the desired profit rate K and the preconditions. At last, we discuss the difference between production capacity of supplier and manufacturer with the desired profit rate K. 6.2 The Results

Fig. 4

(a) Range of

; and (b) Actual demand and

.

Expected Loss＝

q: Actual demand; capacity of supplier.

(24) : Candidate max production

6. The Experiment In this section, we will discuss the experiment of this paper. Before the experiment, it is necessary to reveal two things. First one is optimum supply capacity, and the second one is player characteristics setting. We consider the optimum supply capacity of supply chain as the production capacity of components and products that set by one player, the manufacturer. In other words, the supply chain is integrated. In this situation setting, there is no need to consider the opponent player’s investment behavior. We have discussed the supply chain players before. The component supplier is a subcontractor of the

In the following section, we analyze the result of simulation based on simulator which was developed by VBA. Fig. 4 shows the production capacity of supplier and manufacturer with preconditions and without preconditions comparing with the optimum supply capacity. We confirmed the effectiveness of preconditions of contract while doing the decision-making of production capacity. We also found the difference between production capacity of the component supplier and the assembly manufacturer is less with using of preconditions. Fig. 5 shows the relation between desired profit rate and SC supply capacity. The higher expected profit rate setting of manufacturer, the probability of achieving the optimal production capacity is also higher. We found that it is not better to cede the profit to the supplier during the decision-making of preconditions setting. While the manufacturer planning to propose preconditions of contract to the supplier before the Table 1 α β λ

Supplier 0.3 0.4 2.5

Manufacturer 0.4 0.2 1.5


15

Percentage of the optimum supply capacity

100.0%

最適生産能力の割合

90.0% 81.6% 80.0% 73.3%

70.9%

70.0% 60.8% 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0%

With preconditions オプション条件あり

Without preconditions オプション条件なし

Production capacity of manufacturer Production capacity of supplier バイヤの生産能力サプライヤの生産能力

Fig. 5

Production capacity setting of supplier and manufacturer with preconditions and without preconditions.

Probability of achieving 95% of the optimum production capacity

0.8

9 5 % の最適生産能力を達成した確率

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.6 0.62 0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 係数Kの設定 Parameter(Desired profit rate) K

Fig. 6

Relation between K and supply capacity.

production capacity setting, just to set a higher profit rate himself, and it may make the component supplier do investment positively. As a result, it can help the supply chain to reach a higher supply capacity so as to achieve more profit for both players. As shown in Fig. 6, we discuss the desired profit rate and the precondition and . The larger

difference between and , the SC supply capacity is higher. The reason is that large difference between and may improve the investment incentive of component supplier. During the decision-making of preconditions setting, it is better for the manufacturer to set a higher value of K to make the difference of and large. The manufacturer may get a little

16


3000 2500 2000

Amount

設定 1500 値 1000

Pc Pe

500 0 0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

係数Kの設定 Parameter(Desired profit rate) K

Fig. 7

Relation between K and preconditions of

.

Difference of production capacity between supplier and manufacturer

250 生産能 200 力の 150 差の平 100 均と範 50 囲 0 0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

係数Kの設定 Parameter(Desired profit rate) K

Fig. 8

Relation between K and production capacity difference.

loss with his profit achieving, however it can help the manufacturer to hedge risks. Fig. 7 shows the relation between K and the production capacity of supplier and manufacturer. We analyzed the average value, range and standard deviation of the difference of production capacity between supplier and manufacturer with different value of K. From Fig. 8, we found that higher expected profit rate may make the difference of production capacity large. But there is no significant relation between the standard deviation of production capacity difference and the expected profit rate K.

7. Conclusions In this paper, we designed the manufacturer’s

decision-making model of preconditions setting of the long-term sales contract during the decision-making of production capacity setting of the two supply chain players. We set the preconditions as minimum trading quantity, price of minimum trading quantity and price of trading quantity over minimum trading quantity. We also designed decision-making model of production capacity setting of the supplier and the manufacturer with considering of the preconditions. We proved the effectiveness of under-investment improvement with using of the preconditions quantitatively. Supply chain over-investment problem (production capacity difference between supplier and manufacturer) could also be improved by the preconditions. We found that the larger difference between and , component supplier’s


investment incentive becomes higher. It can improve the SC under-investment problem. From the simulation result, we found that the setting of the price of trading quantity over minimum trading quantity is more important than the price of minimum trading quantity. Because of the price which may affect the SC supply capacity more sensitive. From this paper, during decision-making of preconditions setting, it is an incorrect way to reduce the expected profit rate to make more SC supply capacity in such situation. It seems a better way to share the supply chain total profit. But a lower expected profit rate may make the supplier’s investment incentive lower. In this paper, we used the value function to show the characteristics of supply chain players. But we did not show how to set the characteristics parameters with considering of investment behavior of the opponent. We will finish the model of uncertainty of opponent’s investment behavior in the near future to improve this paper.

[8]

[9]

[10]

[11]

[12]

[13]

[14]

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[22] Ojala, M., and Hallikas, J. 2006. “Investment Decision-Making in Supplier Networks: Managment of Risk.” International Journal of Production Economics 104: 201-13. [23] Callen, J. L., and Sarath, B. 1995. “Risk Aversion, Generalized Correlation and Investment in Manufacturing Capacities.” Journal of Operations Management 12: 225-37.

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Latest Development and Application of High Strength and Heavy Gauge Pipeline Steel in China Zhang Yongqing1, Guo Aimin1, Shang Chengjia2, Liu Qingyou3, J. Malcolm Gray4 and Frank Barbaro5 1. CITIC Metal Co., Ltd, Capital Mansion, Chaoyang district, Beijing, China 2. University of Science and Technology Beijing, Beijing 100083, China 3. Central Iron & Steel Research Institute, Beijing 100081, China 4. Microalloyed Steel Institute 5100 Westheimer, Suite 540, Houston, TX 77056, USA 5. CBMM Technology Suisse, 14, Rue du Rhone, Geneve 1204, Switzerland Abstract: Over the past twenty years, significant advances have been made in the field of microalloying and associated applications, among which one of the most successful application cases is HTP practice for heavy gauge, high strength pipeline steels. Combined the strengthening effects of TMCP and retardation effects of austenite recrystallization with increasing Nb in austenite region, HTP conception with low carbon and high niobium alloy design has been successfully applied to develop X80 coil with a thickness of 18.4 mm used for China’s Second West-East pipeline. During this process, big efforts were made to further develop and enrich the application of microalloying technology, and at the same time the strengthening effects of Nb have been completely unfolded and fully utilized with improved metallurgical quality and quantitative analysis of microstructure. In this paper, the existing status and strengthening effect of Nb during reheating, rolling and cooling have been analyzed and characterized based on mass production samples and laboratory analysis. As confirmed, grain refinement remains the most basic strengthening measure to reduce the microstructure gradient along the thickness, which in turn enlarges the processing window to improve upon low temperature toughness, and finally make it possible to develop heavy gauge, high strength pipeline steels with more challenging fracture toughness requirements. As stated by a good saying that practice makes perfect. Based on application practice and theoretical analysis, HTP has been extended to develop heavy gauge and high strength pipeline steels with increasing requirements, including X80 SSAW pipe with a thickness of 22.0 mm and above, X80 LSAW pipe combining heavy gauge and large diameter, heavy gauge X80 LSAW pipe with low temperature requirements, as well as X90 steels. In this paper, alloy design, production processing, as well as mechanical properties and microstructure used for these products would be illustrated. Key words: HTP, high strength pipeline steel, low carbon bainitic microstructure.

1. Introduction As described by Greek mythology, Prometheus’ theft of fire from Olympus for the benefit of humanity, and then human civilization started to develop. Anyway, energy has become an indispensable part for modern civilization and daily life, even the induced factor of international conflict. Coincidentally, niobium also got its name from Greek mythology: Niobe, daughter of Tantalus. As said by Mr. Mirror Cohen in his paper of Microalloying ’75: “For the foreseeable future, the technology of microalloyed Corresponding author: Zhang Yonqing, senior engineer, research fields: microalloying technology and pipeline steel.

steels will be greatly influenced by mankind’s ever-growing demands for energy. In fact, there is an inseparable reciprocity between energy and materials in general, with each mirroring the other”. Among all application fields of microalloyed steels, large diameter pipeline steels was firstly studied and spread to other structural sector. What is more, niobium played a significant role for its pronounced effect on retardation recrystallization and grain refinement coupled with thermo-mechanical processing (controlled rolling and controlled cooling) and currently used HTP (high temperature processing). Just as concluded by Mr. Kozasu, a worldwide well-known

20

Latest Development and Application of High Strength and Heavy Gauge Pipeline Steel in China

expert, niobium is footstone of chemical design and metallurgy in high strength pipeline steel. Here I am honored to present the metallurgical design of X80 strip used for the China’s Second West-East pipeline based on production practice, and at the same time to validate the expectation and conclusion of early predecessors. One of the most important features for the Second’s West-East pipeline is the Class one area with 0.72 design parameter employed Φ1,219 × 18.4 mm spiral welded pipe, rather than widely used longitudinal welded pipe made from X80 plate. Table 1 shows the basic requirements of mechanical properties, of which 30° tensile direction is the most weak. With the technical support from CBMM’s technical experts, HTP technology with low carbon and high niobium alloy design had been introduced, and laid the foundation for early production practice, but it is equally important that low coiling temperature up to 300 °C played a significant role for successful development.

2. Metallurgical Design and Production Processing It is well known that a low carbon bainitic microstructure (acicular ferrite) offers the optimum combination of strength and toughness, especially when formed from nonrecrystallised austenite, namely TMCP (typical thermo-mechanical processing). Compared with traditional ferrite plus pearlite, this new kind of bainitic microstructure is composed of a mixture of bainitic ferrite with high dislocation density and carbon enriched martensite regions, mainly existing as discrete islands, named MA islands. In order to achieve low carbon bainitic microstructure (acicular ferrite), grain refinement and transformation

strengthening are the two pronounced characteristics besides traditional solution strengthening and precipitation strengthening. Fig. 1 gives the typical three controlled rolling processes, namely conventional controlled rolling (TMCP), RCR (recrystallization controlled rolling) and HTP (hot temperature processing). With powerful rolling mills put into operation, RCR ultimately came to an end because of strength limitation of ferrite-pearlite structure, whereas HTP ushered in its time for X80 pipeline steels with demanding toughness requirements, in particular in China. Considering the tensile direction of 30° to the rolling, the actual equivalent strength level is close to X90 or X100 of steel plate. So the metallurgical design of X100 firstly proposed by Europipe was referred for D design process of X80 strip, as shown from Fig. 2. Based on HTP practice, a steel with maximum 0.06%C, 1.85%Mn, 0.25%Mo, 0.10%Nb, 0.25%Cu and 0.25%Ni was preferred in the beginning stage. As presented by early trial results, the yield strength levels remained unstable. For this case, coiling temperature was firstly lowered to 300 °C based on CCT diagram of recommended chemical compositions, as shown from Fig. 3. In the past, the designed coiling temperature is higher than 500 °C according to equipmentability. As presented by recent HIPERC project undertaken by European steel mills and research institutes, the set cooling stop temperature for X80 hot-coiled plate are higher than 500 °C. So, it is first time for China’s steel mills to carry out coiling temperature up to 300 °C, which later regarded as the key reason for the successful development. In addition, Mr. Volker Schwinn and co-author gave their analysis results on relationship between mechanical properties and

Table 1 Requirements of mechanical properties of X80 hot rolled coil. Properties YS (Rt0.5) TS (Rm) Y/T (Rt0.5/Rm) Charpy Impact Energy at -20 °C Shear area of DWTT at -15 °C

Specified value 555-690 MPa 625-825 MPa 0.94 (max) 180/240J (single/average) 70/85% (single/average)

Test direction

30° to the rolling direction


Fig. 1 Schematic illustration of different controlled rolling.

Fig. 2 Metallurgical design of X80 strip.

Fig. 3 CCT diagram of X80 strip.

21

22


finishing cooling temperature in the paper “Recent Developments and Applications of TMCP Steel Plates” in 2011.

3. Mass Production Mechanical Properties

and

Analysis

of

Figs. 4 and 5 show the statistical results in 30° to rolling direction based on above given chemical compositions and production processing. The mean yield strength and ultimate tensile strength are 594 MPa and 713 MPa, respectively. What is more exciting, the test result of DWTT is all 100%, and the average Charpy energy at minus 20 °C is 342 J.

Fig. 6 shows the analysis results of microstructure of X80 strip by metalloscope, SEM and TEM, as shown, the microstructure are composed fine, uniform acicular ferrite, dispersed MA constituents and bainitic lath.

4. Existing State and Strengthening Effects of Niobium in Different Stage In order to confirm the existing state of high Nb addition and their effects, chemical extraction techniques had been performed to get the precipitated particle of Nb(CN). The chemical compositions of three test steels are shown in Table 2. Table 3 shows the analysis results of second phase of

Fig. 4 Test results of tensile test for X80 coil with a thickness of 18.4 mm.

Fig. 5 Charpy impact energy and DWTT test results, 30° to the rolling.

(a) Metalloscope image Fig. 6

Microstructure of X80 strip.

(b) SEM image

(c) TEM image


23

Table 2 The chemical composition of test steels. No. 1 2 3 4 5

state As-rolled As-rolled Austeniting As-rolled Heat treatment

C 0.04 0.04 0.04 0.04 0.04

N 0.0040 0.0040

Mn 1.85 1.85

Mo 0.15 0.26

Nb 0.09 0.06

Ti 0.015 0.015

V 0.025 0.025

0.0040

1.85

0.26

0.096

0.015

0.025

Table 3 Existing state of Nb different stage with different alloy design. Sampled No. 1 2 3 4 5

Nb 0.0391 0.0229 0.0099 0.0483 0.0875

Mass fraction of each element among the MC、MN、M(C,N)、M2C, wt/% Ti Mo V C* N 0.0115 0.0019 0.0004 0.0050 0.0038 0.0120 0.0025 0.0003 0.0034 0.0035 0.0102 0.0016 0.0002 0.0007 0.0040 0.0111 0.0024 0.0003 0.0058 0.0039 0.0135 0.0286 0.0052 0.0164 0.0036

MC、MN、M(C,N) 、M2C. As shown from measured results of sample three, 0.0099%Nb exists in precipitate of Nb(CN), namely 0.086%Nb is in solution when the slabs are reheated to 1,180 °C. The measured result is consistent with calculated results of Irvine’s solubility product equation. The measured results of sample four demonstrated that about half of niobium addition precipitated for as-rolled X80 strip, but there is possible that very fine particle cannot be extracted. The measured results of sample five show that carbide, nitride and carbonitride of Nb precipitated when sample was reheated to 550 °C, and holding 30 minutes. The measured results of sample one show high Mo contents promote precipitation of Nb during hot rolling process. For test steel with 0.06%Nb, only 0.0229% precipitated during hot rolling process. In addition, as seen from analysis results, almost all nitrogen are fixed by Ti, Nb or/and V, and V contents exist in solution state. It is clear about retardation recrystallization of high Nb addition, but the effects of Nb in solution after rolling need to clarify further, which can be reflected by the relationship between coiling temperature and strength level, as well as aging strain. Fig. 7 gives the analysis results between tensile strength and coiling temperature. As we know, higher coiling temperature is corresponding to high yield strength and low tensile strength, which can be explained solution Nb still

Σ 0.0617 0.0446 0.0266 0.0698 0.1548

precipitated, but suppressed with decreasing coiling temperature. As coiling temperatures lower, the volume fraction of MA will increase, which is regarded as the reason for high tensile strength at lower coiling temperature. In addition, too lower coiling temperature will lead to aging strain during pipe-making and coating process, which can be balanced by coiling temperature and carbon contents to the interests of steel steels. During this process, Nb in solution still plays a positive role in improving yield strength.

Fig. 7 Effect of coiling temperature on yield and tensile strength.

5. Latest Application of HTP in Heavy Gauge and Large-Diameter Pipe Since successful application of HTP for X80 strip, low carbon and high niobium alloy design coupled with HTP has become the fundamental metallurgical conception for high strength pipeline steels. Together with research institutes, steel mills and pipe makers,

24


CITIC-CBMM

established

three

R&D

projects

focusing on Φ1,422 × 21.4 mm2 and 22.0 mm X80 strip and spiral welded pipe, Φ1,422 × 25.4 mm2, 27.7 mm X80 plate and longitudinal welded pipe, as well as recent X90 and weldability research. As validated, HTP manifested its positive to enlarge processing window through higher nonrecrystallized temperature range and flexible adjustment of pass reduction. Up to now, Φ1,422 × 21.4 mm2 and 22.0 mm X80 strip and spiral welded pipe had been successfully developed and also passed the assessment and approval by TGRI, the unique institute of CNPC in charge of pipe research. Φ1,422 × 25.4 mm2, 27.7 mm X80 plate and longitudinal welded pipe had been produced for export order.

References [1]

[2]

[3]

[4]

[5]

6. Conclusions With the contributions of forerunner and predecessor, microalloying has developed to be a complete unity of metallurgy and steel material, and will continue to achieve itself with social need and economic benefits.

[6]

Gray, J. M. 2014. “Application of High Strength Linepipe Steels Worldwide: Historical Perspective, Development, Specification and Application.” Presented at the 2014 China Oil & Gas Forum, China. Korchynsky, M. 1995. “Twenty Years since Microalloying ’75.” Presented at the Conference Microalloying ’95, Pittsburgh, PA. DeArdo, A. J. 1995. “Modern Thermomechanical Processing of Microalloyed Steel: A Physical Metallurgy Perspective.” Presented at the Conference Microalloying ’95, Pittsburgh, PA. Graf, M., Schroder, J., Schwinn, V., and Hulka, K. 2002. “Production of Large Diameter Grade X70 with High Toughness Using Acicular Ferrite Microstructure.” Presented at the International Conference on Application and Evaluation of High Grade Linepipes in Hostile Environments, Yokohama, Japan. Pizzimeni, N., DeVito, A., Bufalini, P., and Pontremoli, M. 1981. “Production and Properties on Pipeline Steels with Non-Polygonal Ferrite Microstructure.” Presented at the International Symposium Niobium ’81, San Francisco, California. Webster, S., and Drewett, L. 2010. “The EU Project HIPERC-Performance, Economic Steel Concept for Linepipe and General Structural Use.” Niobium Bearing Structural Steels.

D


DAVID

PUBLISHING

Critical Buckling of Drill Strings in Cylindrical Cavities of Inclined Bore-Holes Nabil Musa1, Valery Gulyayev2, Nataliya Shlyun2 and Hasan Aldabas1 1. Department of Mechanical Engineering, Philadelphia University, Amman, Jordan 2. Department of Mathematics, National Transport University, Suvorov str. 1, Kiev 01010, Ukraine Abstract: Notwithstanding the fact that the problem of drill string buckling (Eulerian instability) inside the cylindrical cavity of an inclined bore-hole attracts attention of many specialists, it is far from completion. This peculiarity can be explained by the complexity of its mathematic model which is described by singularly perturbed equations. Their solutions (eigen modes) have the shapes of boundary effects or buckles (harmonic wavelets) localized in zones of the bore-hole that are not specified in advance. Therefore, the problem should be stated in the domain of entire length of the drill string or in some separated part including an expected zone of its buckling. In the paper, a mathematic model for computer analysis of incipient buckling of a drill string in cylindrical channel of an inclined bore-hole is elaborated. The constitutive equation is deduced with allowance made for action of gravity, contact, and friction forces. Computer simulation of the drill string buckling is performed for different values of the bore-hole inclination angle, its length, friction coefficient, and clearance. The eigen values (critical loads) are found and modes of stability loss are constructed. The numerical results for the case when the inclination angle equals friction angle coincide with ones obtained analytically. Key words: Deep drilling, inclined bore-holes, drill strings, stability, singularly perturbed problem.

1. Introduction At the present time, most of the easy oil and gas is produced. Inasmuch as the readily accessible deposits of hydrocarbon fuels are practically depleted in the result of their intensive extraction in preceding two centenaries, their drawing out from deeper reservoirs holds much promise. An effective means to enlarge the oil and gas extraction efficiency is to drill the bore-holes in inclined and horizontal directions. Yet, drivage of bore-holes of this type is associated with great technological difficulties. They are conditioned by geometric and structural complication of these systems, as well as by redistribution of internal and external forces providing basic cause of decrease of the DS (drill string) mobility in the bore-hole cavity. These factors may be responsible for the next negative features of the drilling process: Corresponding author: Nabil Musa, Ph.D., research field: mechianics of drilling.

 orientation of the gravity forces relative the DS axis changes, bringing to reduction of axial tensile forces (stabilizing the DS tube) and enlargement of longitudinal compressive forces (destabilizing the system);  in this connection, the forces of contact interaction of the DS tube with the bore-hole wall enlarge essentially;  during drilling and tripping operations, the axial and rotary motions of the DS lead to generation of essential distributed axial friction forces and torques;  these friction forces and torques entail the deterioration of the WOB (weight on bit) and TOB (torque on bit) permeability to the bore-hole bottom and reduce the drilling efficiency;  in the bore-hole sections, where the DS is compressed, it can lose its Eularian stability with subsequent buckling and so additional stability analysis should accompany the drilling maintenance;  as shown below, the problem of the DS buckling

26

Critical Buckling of Drill Strings in Cylindrical Cavities of Inclined Bore-Holes

in the channel of a directed bore-hole is multiparametric, its principal feature is associated with variability of the internal compressive axial force. Therefore, the zone of the DS buckling is not known in advance and so the stability analysis should be performed in the entire length of the DS. This problem is singularly perturbed, that is why the modes of stability loss represent localized or distributed harmonic wavelets;  the generated zones of enlarged contact and friction forces can be also responsible for dead or locked states of the DSs. The outlined peculiarities of the bifurcational buckling of the DSs in the inclined DSs channels render detection of this phenomenon hardly predictable that is why the problem of their theoretic modeling is of current importance. The first systematic analysis of helical buckling of a DS was performed by Lubinski et al. [1]. They discovered the mechanism of the DS buckling in vertical bore-holes and established the critical buckling conditions. Since then, different models of the DS buckling in bore-hole channels under action of gravity, contact, and friction forces, as well as torque and axial external force have been considered. Special attention was paid to analysis of directed bore-holes. Inasmuch as the inclined and horizontal bore-holes permeate the oil- and gas- bearing strata along the stratified structure of the underground reservoirs, they cover larger zones of fuel deposits and are effective expedients to enlarge the extraction efficiency [2-5]. Analysis of the DS stability in the bore-holes of these types was initiated after the pioneer paper by Dawsen and Pasley [6]. Later, a lot of refinements were introduced in theoretical models of the buckling effects [7-12]. Analysis of whirl interaction of a drill bit with the bore-hole bottom was performed by Musa et al. [13]. Detailed review of this problem state was presented by Cunha [14], Gao and Huang [15], and Mitchell [16]. It can be concluded from these surveys that, basically, the approaches used by researchers attacking this

problem were based on the buckling mode approximation by sinusoidal or helical curves, while as shown by Gulyayev et al. [17-19], the problem of the DS buckling in channels of long bore-holes is singularly perturbed and therefore, the DS buckling occurs through forming harmonic or spiral wavelets of variable steps in unknown segments of the DS length. Sometimes, they represent high-frequency beating harmonics distributed throughout the total length of the DS. That is why the buckling analysis of these DSs should be performed with the use of their large segments. In this paper, the DS stability in the lower rectilinear segment of an inclined bore-hole is analyzed with account made for constraining effect by cylindrical channel of the bore-hole wall with different clearances as well as distributed gravity, contact, and friction forces.

2. Geometric Prerequisites to the Bending Analysis of a Drill String inside Cylindrical Cavity Let a rectilinear DS lie on the lower generatrix of the cylindrical surface of an inclined bore-hole. Its axis is located in the XOZ plane of fixed coordinate system OXYZ and is inclined under angle β with respect to vertical OZ (Fig. 1). The internal geometry of the DS is specified by coordinate s , measured as the length of axial line from the initial to the current point. Assume that if the DS is immovable, it is loaded by external distributed gravity ( f gr ) and contact ( f cont ) forces, and at its ends axial forces Fz (0) and Fz (S ) are applied. Here, S is the DS length. In the state of the DS movement, unknown distributed frictional force f fr is added which is determined through the contact force with the help of the Coulomb law f fr ( s ) = ± μf cont ( s ) (1) where, μ is the coefficient of friction and the choice of signs “+” and “−” depends on the direction of the DS movement.


27

Bore-hole wall surface

Fz (0)

X

O

f cont

s

Drill string

Y

β f fr Z

Fz ( S )

f gr Bore-hole wall Fig. 1 Schematic of a drill string in an inclined bore-hole.

As the results of these factors action, compressive axial forces are induced in some zones of the DS. On attainment by them of critical values, the DS buckles and its axial line L assumes new equilibrium shape inside the cylinder of radius a equal the bore-hole

surface theory and differential geometry with the use of the model of curvilinear flexible rods [19]. To chase the DS geometry transformation inside cylindrical channel of an inclined bore-hole, introduce a moving right-handed coordinate system oxyz with

clearance. It is required to establish by theoretic simulation the critical state and to construct the mode of the bifurcational stability loss. This study will be performed by methods of non-linear analysis with the use of the linearization procedure. For this purpose, construct the non-linear differential equations of the DS equilibrium and linearize them in the vicinity of the considered stress-strain state. The external loads, corresponding to degeneration of the linearized operator, are considered to be bifurcational and eigen mode of this operator is the mode of the DS buckling [17-19]. Feature peculiar to this effect lies in the fact that if angle β of the bore-hole inclination is not small, the

axis ox oriented along internal normal to the surface G and axis oz directed along the tangent to the curve L . Unit vectors of this system are i, j, k (Fig. 2). In

DS is compressed to the bore-hole wall by gravitation forces f gr (s) which impede its raising on the bore-hole channel surface during buckling process and stabilize its equilibrium. In consequence of this, the DS is kept on this surface and therefore its geometry cannot change arbitrary because now it is determined by the geometry of the cylindrical surface where it lies. In analysis of the geometric transformation of the buckling DS, that compels to invoke the methods of the

parallel with this system, the Frenet trihedron is used [18]. Its tangent unit vector t , unit vector of principal normal n , and unit vector of binormal b are calculated by the formulae t=

dt dρ , n = R , b = t ×n ds ds

(2)

Here, R is the curvature radius of the DS axis line, is the curve L radius-vector in the fixed coordinate system OXYZ . These vectors determine

ρ(s )

orientations of the rod elements and the curve shape. With their use the Darboux vector can be introduced Ω = k R b + kT t (3) where, k R = 1 / R is the curve curvature and kT is its torsion. These parameters are calculated with the help of formulas [20] kR  n

d 2ρ dn   , kT  τ  n   ds  ds 2 

(4)

But it is more rational to express the k R and kT parameters and to study the DS bending in the movable coordinate system oxyz because its use permits to

28


Fig. 2 Axial line L of the DS in its buckling in the cylindrical channel of a bore-hole.

convent the problem difficulty, connected with existence of constraining surface G , into advantage, conditioned by the fact that the L curve geometry can be described in the known terms of the surface G parameters. With this feature in mind, introduce vector ω = kxi + k y j + kzk ,

(5)

representing angular velocity of the oxyz system in its movement along the L curve. Here, k x and k y are the curvatures of the L curve in planes yoz , xoz , correspondingly; k z is its torsion. They are expressed via the known curvatures of the cylindrical surface G parameterized by means of parameter u directed along the surface generatrix and parameter v , determining the position of a point at the generating circle of radius a (Fig. 2). Then, the G surface

surface and it can be expressed as follows [17, 20]: k x  k geod   a(uv  vu) ,

where, symbol prime denotes the operation of differentiation with respect to s . Plane xoz is orthogonal to the G surface, therefore, the k y curvature of the curve L equals normal curvature k norm of the surface in the direction of unit vector t. It is determined through the principal curvatures k1 , k 2 of cylindrical surface with the use of the Euler theorem: k y = k norm = k1 cos 2 θ + k 2 sin 2 θ ,

(6)

In this case, the k x curvature represents the geodesical curvature k

geod

of the L curve in the G

(8)

where, k1 = 0 , k 2 = 1 / a , and θ is the angle between the direction of unit vector t and coordinate line u . Inasmuch as sin θ = adv / ds , it follows: k y  a (v ) 2 .

metrics is determined by the formula (ds ) 2 = (du ) 2 + a 2 (dv) 2

(7)

(9)

Torsion k z of the L curve is calculated with the use of equality [19] k z  u v 

(10)

The constructed geometric correlations permit one to

29


deduce constitutive equations of the DS bending in a cylindrical cavity.

dM x / ds  k y M z  k z M y  Fy ,

3. Constitutive Equations of the DS Bending inside Inclined Bore-Hole Cavity

dM z / ds  k x M y  k y M x .

Consider the problem about elastic bending of a DS inside the cylindrical channel of an inclined bore-hole. The DS is preloaded by distributed gravity forces f gr ( s ) throughout its length and by axial compressive force Fz (s) at its lower end s = S . Action of these forces is associated with generation of internal force F(s) and moment M(s), as well as external contact ( f cont (x) ) and friction ( f fr (x) ) forces. Particular emphasis should be placed on the question of friction forces effects. In our case, two situations are considered when the DS is immovable at the precritical state and when it buckles during lowering and drilling. It can be assumed that at the former case the DS is exposed to action of different dynamic perturbations (for example, by mud flows) which relieve friction forces and then f fr ( s) = 0 . Whereas, during axial motion of the DS this force is defined by Eq. (1). So, the challenge is to establish typical regularities of friction forces influence on the buckling process. In the result of these forces action, the DS can be stretched in its upper zone and compressed in its lower segment. Therefore, its critical buckling predominates below, where the bore-hole axis, as a rule, is nearly rectilinear. During critical deforming, the DS can acquire complicated shape, so the theory of curvilinear flexible rods is used for its analysis. The bifurcation modeling is based on the analyses of non-linear equations of the curvilinear rod equilibrium. They are represented in scalar form in the moving coordinate system oxyz [18, 19] as equations of equilibrium of forces dFx / ds  k y Fz  k z Fy  f

gr x

f

cont x

dFy / ds  k z Fx  k x Fz  f ygr ,

and moments

fr

(12)

Here, the benefits of the chosen reference frame oxyz and vector ω became distinct. Only one component f xcont ( s ) of the unknown contact force f cont (s ) is present in the first equation of system (11) and one component f z fr ( s) of friction force f fr ( s) enters into its third equation. These factors permit to simplify Eqs. (11) and (12). Since, bending moments M x , M y in Eq. (12) are expressed through curvatures k x , k y with the use of Eqs. (7) and (9), one has M x = EIk x , M y = EIk y and shear forces Fx and Fy can be calculated proceeding from two first equations of system (12) Fx  2 EIav v   a ( M z  EIu v)(u v   v u ) Fy   EIa

(13) d (u v   v u )  a ( M z  EIu v)(v) 2 ds

The terms of the right side of the third equation of system (12) equal zero and so torque M z is constant throughout the DS length. From Eqs. (6), (7), (9)-(13), the constitutive system of six first order equations is received dFy

 2 EIau (v) 2 v  ( M z  EIu v)u vk x  k x Fz  f ygr ds dFz  k x Fy  2 EIa 2 (v) 3 v  a( M z  EIu v)(v) 2 k x  f zgr  f z fr ds dk x 1 1  a (v) 2 M z  au (v) 3  Fy ds EI EI dv  v ds du  1  a 2 (v) 2 ds

In this system, variables

Fx

and

My

(14) are

eliminated from consideration because they can be represented through geometry parameters of the G surface, whereas the components of the gravity force are determined by the formulas

,

(11)

dFz / ds  k x Fy  k y Fx  f z  f z , gr

dM y / ds  k z M x  k x M z  Fx ,

f xgr   f f

gr y

gr

sin  cos v

 f (cos   av  sin  sin v  u ) gr

f z  f (cos   u   sin  sin v  av) gr

gr

(15)

30


The first equation of system (11) is not included into system (12) but it is used for calculation of the contact force f xc  

dFx  k y Fz  u vFy  f xgr ds

(16)

Eq. (14) with appropriate boundary conditions describe non-linear bending of a DS under action of gravity and friction forces as well as external axial forces applied to the DS ends inside the channel of an inclined rectilinear bore-hole. The states of the DS loading when the linearized operator of system (14) is degenerated are critical (bifurcational). The eigen values and eigen modes of this system represent critical loads and modes of stability loss (buckling) at these states.

4. Equations of Critical States of the DS inside Inclined Bore-Hole In this paper, it is assumed that a rectilinear DS is freely lying or sliding along its axis in the bottom u = 0 of a rectilinear bore-hole. It is necessary to calculate its critical load and to construct its buckling mode. With this aim in view, linearize Eq. (14) in the vicinity of the state u ( s) = s , v(s) = 0 , k x ( s ) = k y ( s) = k z ( s ) = 0 , M x ( s) = M y ( s) = 0 . At this state, the contact force f xcont ( s ) is constant and easily defined by Eq. (16)

Fz (0)  ( f zgr  f z fr ) S

(17)

Then, in a similar manner, friction force f z fr is calculated as follows:

R

is

prescribed

by

compressive force, acting at the lower end of the DS. In consequence of these remarks, after linearization of system (14), only four equations are suitable for further use. Rewrite them in the linearized form: dFy / ds  Fz k x  af gr cos v , dFz / ds  f zgr  0, dk x / ds  (1 / EI )Fy , dv / ds  v, dv / ds  (1 / a )k x ,

(20)

du / ds  0. Take into consideration that k x  av , Fy  EIav , f xgr  0 , f cont ( s )  f gr sin  , f z fr ( s )   f gr sin  , f gr  g (  t   m ) F , where g  9.81 m/s2;  t ,  m are densities of the tube

material and mud; F is area of the DS tube cross-section; sign “+” is selected for the hoisting operation, sign “−” corresponds to the DS lowering. Further, the DS lowering regime will be considered, therefore Fz ( s )  f gr (cos    sin  )( S  s )  R

(21)

The second and sixth equations of system (20) are trivial and so they will not be considered, the other four equations can be recast in a more convenient form 

y IV   

f xcont ( s )   f xgr

and



f gr (cos    sin  ) R (S  s)  y  EI EI 

f (cos    sin  ) f gr sin  y  y  0, EI aEI gr

(22)

where, δy ( s) = aδv( s) .

(19) Here, Fz (0) is the Fz force value at the suspension

This fourth order homogeneous differential equation is similar to the equation of stability of a beam on elastic foundation and so their solutions have similar properties. In the first place, both of them are singularly perturbed [17, 21] and for this reason, their modes of stability loss have the shapes of boundary effects, usually localized in boundary zones. Secondly, as a rule, these modes represent damping out oscillating harmonics. Very important property of this equation consists in the fact that torque M z , presenting in

point s = 0 . If the DS lowering regime is chosen, then

system (14), disappeared in the result of its

f z fr ( s )   f xcont   f xgr

(18)

Thereafter, function Fz ( s) is found from the second equation of system (14) s



Fz ( s )  Fz (0)   ( f zgr  f z fr )ds  ( f zgr  f z fr ) s  R 0

31


linearization in the vicinity of the considered state. This fact testifies the system insensitivity to the DS torsion in this position.

5. Bifurcation Buckling of a DS in the Channel of Inclined Bore-Hole It should be emphasized that Eq. (22) has variable coefficients, therefore its eigen values and eigen modes can be analyzed only by numerical methods. In the case under consideration, the finite difference method was used for this purpose. In what follows, the results of computer simulation are represented. First and foremost, the remark should be concentrated on the fact that the stated problem is multiparametric. Indeed, the buckling proceeding depends on the DS length, cross-section dimensions, angle of inclination, clearance value, presence or absence of friction effects and friction coefficient value, value of the boundary compressive force R , boundary conditions, and so on. Therefore, below particular cases are studied under next values of characteristic parameters: 4 3 11 4 Pa, m ,   7 . 8  103 kg/m , E  2.1  10 I  2.7  10 t  m  1.3  103 kg/m3, d1 = 0.2 m, d 2 = 0.18 m, F   (d12  d 22 ) / 4  0.00597 m2, μ = 0.2 . The boundary conditions at the top and lower edges correspond to pinned ends δy (0) = δy ( S ) = 0 , y (0)  y ( S )  0 (23)

boundary effect (Fig. 3). As this takes place, the friction forces only slightly influence on the critical value Rcr and function δy (s) . But when the β angle tends to the value β = arcctg μ , the gravity and friction forces balance cos    sin   0

values of inclination angle β . It can be seen that if the β angle is not very large (β = 45° and 60°), the tensile gravity forces provoke decrease of axial force Fz (s) in the upper zone of the DS and the mode of bifurcational buckling δy (s) acquires the shape of

other, the equality place, function Fz (s)

becomes constant, and Eq. (22) takes the simplified form:

y IV 

R f gr sin  y   y  0 EI aEI

(24)

This equation with conditions (23) can be solved analytically. Indeed, assume δy ( s ) = δC sin

πns S

(25)

Then, one can receive from Eqs. (24) and (25) 4

2

R  n  f gr sin   n  0 (26)       aEI  S  EI  S  This equality gives eigen values Rn for different

numbers n 2

2

f gr sin   S   n  Rn  EI    (27)   a  S   n  To calculate critical value of R , it is necessary to minimize Rn with respect to n . Use the condition dRn / dn = 0 . Then, 2

2

dRn 2 f gr sin   S     2 EI   n    0 dn an 3 S  

(28)

and

Initially, stability of the DS of lengths S = 500 and 1,000 m was treated for the clearance value a = 0.166 m. In Table 1, the calculation results for the bore-hole of 500 m in length are demonstrated. Two left columns of thisTable are related to the frictionless model, two right ones contain data associated with influence of friction effect. The diagrams of axial force Fz (s ) , lateral displacement δy (s ) and critical value Rcr are given for every considered case under different

each takes

ncr =

S π

4

f

gr

sin β aEI

(29)

sin β / a

(30)

Therefore, Rcr = 2 EIf

gr

Note that this force does not depend on the DS length. In this instant,   90  arctg  78.69 and the values of these parameters are equal to ncr = 22.45 , Rcr = 225856 N. The considered state is represented by position 4 in Table 1. As may be seen, the critical force Rcr and buckling mode do not exhibit any essential changes for the frictionless model, but under conditions

32


Fig. 3 Boundary effect in the bifurcational mode of a DS in an inclined bore-hole.

Fig. 4 Expanding of the boundary effect with enlargement of the bore-hole inclination angle.

Fig. 5 Harmonic mode of stability loss of the DS inclined under friction angle.

33

Critical Buckling of Drill Strings in Cylindrical Cavities of Inclined Bore-Holes Table 1

Critical force Rcr and buckling mode δy (s ) for the case S = 500 m and a = 0.166 m. Frictionless model

Frictional model Inclination angle β = 45°

1

Rcr = 203.772 kN y

Fz , kN

200

Rcr = 202.129 kN y

Fz , kN

200 0

0 -200 0

250

s,m 500

0

250

s, m 500

-200 250

0

s, m 500

0

s, m 500

250

β = 60°

2

Rcr  219.441 kN

Rcr = 221.771 kN 200

200

0

0

-200

-200 0

250

500

0

250

500

0

250

500

0

250

500

β = 78.495°

3

Rcr = 230.962 kN

Rcr = 224.922 kN

200

200

0

0

-200

-200 0

250

500

0

250

500

0

250

500

0

β = 78.69° Rcr = 230.942 kN

4 200

200

0

0

-200

250

500

Rcr = 225.856 kN

-200 0

250

500

0

250

500

0

250

500

0

β = 79.06824° Rcr = 230.997 kN

5 200

200

0

0

-200

250

500

Rcr = 227.518 kN

-200 0

250

500

0

250

500

0

250

500

0

250

500

β = 85°

6

Rcr = 230.962 kN

Rcr = 229.450 kN

200

200

0

0

-200

-200 0

250

500

0

250

500

0

250

500

0

250

500

34


of the friction force presence, the boundary harmonic wavelet expands with the β enlargement (Fig. 4). It propagates throughout the whole length of the DS (position 3) and becomes a simple sinusoid when angle of its inclination equals the friction angle (position 4). Schematic of the bifurcation mode for this state is shown in Fig. 5. After transition through this state, the buckling modes are less ordered (positions 5 and 6). At the same time, if friction forces equal zero, the buckling mode appears as boundary wavelet and the Rcr value enlarges with angle β enlargement. It issues from Eq. (29) that sinusoid semi wave lengths are defined by the formula λcr = S / n = π 4 aEI /( f

gr

sin β )

(31)

As this formula and numeric calculations testify, the stability loss mode semi step cr  22.72 m for all examples represented in Table 1. It is mentioned above that the stated problem is singularly perturbed and so its solutions, as a rule, have the shapes of boundary effects concentrated in small vicinity of the DS end. The problems of this type are known as non-classical ones [22]. That is why one would expect that they are not sensitive to enlargement of the DS length. Really, this conjecture is corroborated by results of analysis of the DS 1,000 m in length. As evident from Table 2, the critical axial forces Rcr retained their values just as for frictionless model, so also for the case of the friction presence, though they slightly enlarged with the angle β enlargement. The modes of stability loss likewise did not change their shapes and step lengths. Of some interest is the question of how the clearance magnitude influences on the stability loss process. In Tables 3 and 4, the calculation results for the DS buckling in the bore-hole channels of clearance 0.08 m are presented. As the data of these Tables suggest, the clearance decrease is associated with increase of the critical forces Rcr and again, the bifurcational values of the R force nearly coincide for the short ( S = 500 m) and long (S = 1,000 m) DSs. Particular

attention should be given to the effect of the bifurcation mode transformation of the DS 500 m in length. When the DS is immovable and friction forces are eliminated, the Rcr forces enlarge with the β angle increase, though the modes of stability loss transform insignificantly. But in the presence of friction forces, the effect of gradual transformation of the bifurcation mode from boundary effect to disordered harmonic is more obvious with the β enlargement. It is also interesting to note that with the β enlargement, the distance between two zero points of the bifurcation mode reduces from   40.5 m for β = 45° to   31 m for β = 85°. The noted peculiarities of the DS buckling are associated with several factors. When the β angle is not large, the DS is preloaded by tensile axial force in its upper zone and by compressive force in its lower part. In this case the stress-strain state of the DS is essentially heterogeneous. At the same time, the normal component the gravity force, compressing the DS to the bore-hole wall and impeding its buckling, is not large and the DS freely buckles below. With enlargement of the β angle the tensile forces diminish, the DS stress-strain state becomes more homogeneous, and stabilizing effect of the tensile force decreases. But contact and friction forces, as well as the normal component of the gravity force, enlarge. This feature is responsible for the stabilizing effect up growth. Interaction of these conflicting properties brings to insignificant enlargement of critical force Fcr with angle β rise.

6. Conclusions (1) In the paper, a mathematic model for computer analysis of bifurcational buckling of a drill string in cylindrical channel of an inclined bore-hole is elaborated. The constitutive equation is deduced with allowance made for action of gravity, contact, and friction forces; (2) On the basis of this equation, the eigen value problem is stated. The techniques for its numerical solution are proposed;

35


Critical force Rcr and buckling mode δy (s ) for the case S = 1,000 m and a = 0.166 m.

Table 2

Frictionless model

Frictional model

Inclination angle β = 45° Rcr = 203.772 kN

1 Fz , kN

200

y

Fz , kN

200

0

Rcr = 202.129 kN y

0

-200 0

500

s,m 1000

0

500

s,m 1000

-200 0

500

s,m 1000

0

500

β = 60°

2

Rcr = 221.771 kN

Rcr = 219.441 kN

200

200

0

0

-200

-200 0

500

1000

0

500

s,m 1000

0

1000

500

1000

0

500

1000

β = 78.495°

3

Rcr = 230.942 kN

Rcr = 227.993 kN

200

200

0

0

-200

-200 0

500

1000

0

500

0

1000

500

1000

0

500

1000

β = 78.69°

4

Rcr = 230.962 kN

Rcr = 225.856 kN

200

200

0

0

-200

-200 0

500

1000

0

500

0

1000

500

1000

0

β = 79.06824° Rcr = 230.995 kN

5 200

200

0

0

-200

-200 0

500

1000

0

500

0

1000

500

1000

Rcr = 227.684 kN

500

1000

0

500

1000

β = 85°

6

Rcr = 230.622 kN

Rcr = 228.841 kN

200

200

0

0

-200

-200 0

500

1000

0

500

1000

0

500

1000

0

500

1000

36


Table 3

Critical force Rcr and buckling mode δy (s ) for the case S = 500 m and a = 0.08 m. Frictionless model

Frictional model Inclination angle β = 45°

1

Rcr = 288.267 kN 200 Fz , kN

Rcr = 286.618 kN

y

Fz , kN

200

0

y

0

-200

-200 0

250

s,m 500

0

250

s,m 500

0

β = 60°

2

Rcr = 315.273 kN

200

0

-200

-200 250

500

0

250

s,m 500

0

0

500

250

s,m 500

Rcr = 312.936 kN

200

0

0

250

250

500

0

250

500

β = 78.495°

3

Rcr = 330.396 kN

200 0

0

-200

-200 0

250

500

0

250

Rcr = 325.342 kN

200

0

500

250

500

0

250

500

β = 78.69°

4

Rcr = 330.450 kN

200 0

0

-200

-200 0

250

500

0

250

Rcr = 325.342 kN

200

0

500

250

500

0

250

500

β = 79.06824°

5

Rcr = 330.548 kN

200 0

0

-200

-200 0

250

500

0

250

0

500

β = 85

6

Rcr = 330.898 kN

200

0 -200 500

0

250

500

500

0

250

500

Rcr = 325.406 kN

200

0

250

250



-200 0

Rcr = 327.035 kN

200

0

250

500

0

250

500

37


Table 4

Critical force

Rcr

and buckling mode

y (s)

for the case S = 1,000 m and a = 0.08 m.

Frictionless model

Frictional model

Inclination angle β = 45° Rcr = 288.267 kN

1 200 Fz , kN

Rcr = 286.618 kN

200 Fz , kN

y

0

y

0

-200

-200 0

500

s,m 1000

0

500

s,m 1000

0

500

s,m

s,m 1000

0

500

1000

β = 60°

2

Rcr = 315.273 kN

200 0

0

-200

-200 0

500

1000

0

500

Rcr = 312.936 kN

200

0

1000

500

1000

0

500

1000

β = 78.495°

3

Rcr = 330.390 kN

200 0

0

-200

-200 0

500

1000

0

500

Rcr = 327.364 kN

200

0

1000

500

1000

0

β = 78.69° Rcr = 330.450 kN

4 200

0

-200

-200 0

500

1000

0

500

0

1000

1000

Rcr = 325.342 kN

200

0

500

500

1000

0

500

1000

β = 79.06824°

5

Rcr = 330.548 kN

200 0

0

-200

-200 0

500

1000

0

500

Rcr = 327.171 kN

200

0

1000

500

1000

0

500

1000

β = 85°

6

Rcr = 330.898 kN

200 0

0

-200

-200 0

500

1000

0

500

1000

Rcr = 329.199 kN

200

0

500

1000

0

500

1000

38


(3) The problem is shown to be singularly perturbed and hence its solutions (eigen modes) are represented as boundary effects (harmonic wavelets) localized at the vicinity of the lower end of the drill string; (4) Influence of friction presence and values of the bore-hole inclination angle, its length and clearance on the evolution of the bifurcation mode is studied. The mode shape transformation is demonstrated can be accompanied by its expanding and displacing to upper zones of the drill string;

References [1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

Lubinski, A., Althouse, W. S., and Logan, J. L. 1962. “Helical Buckling of Tubing Sealed in Packers.” Journal of Petroleum Technology 14 (6): 655-70. Aadnoy, S. B., and Andersen, K. 2001. “Design of Oil Wells Using Analytical Friction Models.” Journal of Petroleum Science and Engineering 32: 53-71. Brett, J. F., Beckett, A. D., Holt, C. A., and Smith, D. L. 1989. “Uses and Limitations of Drillstring Tension and Torque Models for Monitoring Hole Conditions.” SPE Drilling Engineering 4: 223-9. Jonggeun, C., Schubert, J. J., and Juvkam-Wold, H. C. 2005. “Well-Control Analyses on Extended-Reach and Multilateral Trajectories.” SPE Drilling and Completion 20 (2): 101-8. Sawaryn, S. J., Sanstrom, B., and McColpin, G. 2006. “The Management of Drilling-Engineering and Well-Services Software as Safety-Critical Systems.” SPE Drilling and Completion 21 (2): 141-7. Dawson, R., and Paslay, R. R. 1984. “Drill Pipe Buckling in Inclined Holes.” Journal of Petroleum Technology 36: 1734-8. Gao, D. L., and Liu, F. W. 2013. “The Post-Buckling Behavior of a Tubular String in an Inclined Wellbore.” Computer Modeling in Engineering and Sciences 90 (1): 17-36. Gulyayev, V. I., Gaidaichuk, V. V., Solovjov, I. L., and Gorbunovich, I. V. 2009. “The Buckling of Elongated Rotating Drill Strings.” Journal of Petroleum Science and Engineering 67: 140-8. Huang, W. J., and Gao, D. L. 2014. “Helical Buckling of a Thin Rod with Connectors Constrained in a Cylinder.” International Journal of Mechanical Sciences 84: 189-98.

[10] Kyllingstad, A. 1995. “Buckling of Tubular Strings in Curved Wells.” Journal of Petroleum Science and Engineering 12 (3): 209-18. [11] Mitchell, R. F., and Samuel, R. 2009. “How Good is the Torque/Drag Model?” SPE Drilling and Completion 24 (1): 62-71. [12] Wang, X., and Yuan, Z. 2012. “Investigation of Frictional Effects on the Nonlinear Buckling Behavior of a Circular Rod Laterally Constrained in a Horizontal Rigid Cylinder.” Journal of Petroleum Science and Engineering 90-91: 70-8. [13] Musa, N. W., Gulyayev, V. I., Shevchuk, L. V., and Aldabas, H. 2015. “Whirl Interaction of a Drill Bit with the Bore-Hole Bottom.” Modern Mechanical Engineering 5: 1-20. [14] Cunha, J. C. 2004. “Buckling of Tubulars inside Wellbores: A Review on Recent Theoretical and Experimental Works.” SPE Drilling and Completion (March): 13-8. [15] Gao, D. L., and Huang, W. J. 2015. “A Review of Down-Hole Tubular String Buckling in Well Engineering.” Petroleum Science 12 (3): 443-57. [16] Mitchell, R. F. 2008. “Tubing Buckling—The State of the Art.” SPE Drilling and Comlpetion (December): 361-70. [17] Gulyayev, V. I., Andrusenko, E. N., and Shlyun, N. V. 2014. “Theoretical Modelling of Post-Buckling Contact Interaction of a Drill String with Inclined Bore-Hole Surface.” Structural Engineering and Mechanics 49 (4): 427-48. [18] Gulyayev, V. I., Gaidaichuk, V. V., Andrusenko, E. N., and Shlyun, N. V. 2015. “Critical Buckling of Drill Strings in Curvilinear Channels of Directed Bore-Holes.” Journal of Petroleum Science and Engineering 129: 168-77. [19] Gulyayev, V. I., Gaidaichuk, V. V., and Koshkin, V. L. 1992. Elastic Deforming, Stability and Vibrations of Flexible Curvilinear Rods. Kiev: Naukova Dumka. (in Russian) [20] Dubrovin, B. A., Novikov, S. P., and Fomenko, A. T. 1992. Modern Geometry-Methods and Applications. Berlin, Heidelberg, New York: Springer-Verlag. [21] Chang, K. W., and Howes, F. A. 1984. Nonlinear Singular Perturbation Phenomena. New York, Berlin, Heidelborg, Tokyo: Springer-Verlag. [22] Elishakoff, I., Li, Y., and Starnes, J. H. 2001. Non-Classical Problems in the Theory of Elastic Stability. Cambridge: Cambridge University Press.

D


DAVID

PUBLISHING

Long Distance GIL PD Fault Localization Method Based on Amplitude Difference and Time Difference Calculation of UHF Coupling Signal Zhang Hui1, Hu Po2 and Tao Ke1 1. Administration Section, China Yangtze Power Co., Ltd, ChengDu 610041, China 2. School of Electrical Engineering, Wuhan University, WuHan 430072, China Abstract: In the long distance GIL under certain conditions, this paper researches and realizes detection of PD characters and accurate fault localization through UHF coupling sensors at different positions of the GIL pipeline. The main methods for the detection are UHF signal amplitude difference (DOA) and time difference (TOF). We analyze the localization error by using TE and TEM component and high order TE mode component in electromagnetic coaxial wave guide theory. Research and field test prove the DOA detection error can meet the requirements of real-time online diagnosis and for history tracking analysis. The error of TOF detection method can be controlled within 3% and can be applied to the site. Key words: GIL, partial discharge, UHF, EM-wave, amplitude difference, time difference, fault localization.

1. Introduction The advantages of GIS (gas insulted switchgear) make it widely used in power system while the GIL (gas insulted line) has been widely used in modern power system gradually. The GIL principle is almost the same with GIS. Compared with GIS, GIL is the main channel of the power flow. The electric breakdown of GIL caused by dielectric breakdown will not only do great harm to GIL itself, but also influence the power transmission greatly. Thus, the insulation test of GIL is more important than that of GIS. Similar to the insulation test and diagnosis of GIS, one effective insulation test method of GIL is the signal detection of PD (partial discharge). The detection of UHF (ultra high frequency) coupling signal generated by PD is currently the most widely used online/offline detection method [1], and proved to be effective. There are already studies on the signal sampling of UHF generated by PD of GIS. We can achieve the resolution Corresponding author: Zhang Hui, senior engineer, doctor of engineering, research fields: power system control and security, automatic control, system simulation and analyisis.

of insulation defects at a high recognition rate in a laboratory environment [2]. The studies of UHF generated by PD are mainly for GIS, the methods include: The characteristic signal of PD is acquired and analyzed by methods of analyzing corona ultrasonic signals of steel body acoustic oscillations, or the high-frequency pulse current of pulse current signals, along with the methods of wavelet transform or complex wavelet transform of single PD signal, or multiple grayscale image fractal spectrum analysis. The main goal of these methods is to analyze the causes of discharge caused by insulation deterioration, such as metal particles (fixed projection), surface contaminants and so on [3-7]. One difference between GIL and GIS is the length of GIL is much greater than GIS. The possibility of the occurrence of defects inside GIL increases greatly restricted to the installation crafts and conditions. The insulation accidents caused by remaining foreign body, dielectric breakdown and the drop of equipments or devices accounts for more than 57.3% of the total, what is more, the number rises in exponential trend when the

Long Distance GIL PD Fault Localization Method Based on Amplitude Difference and Time Difference Calculation of UHF Coupling Signal

equipments run for over 25 years. When insulation deterioration occurs, it is very important to locate the insulation failure parts precisely, especially for long distance GIL, no matter what kind of insulation defect it is. However, the studies in this area are very few. This paper analyzes the characteristics of UHF coupling signal waveform generated by PD. Online detection and location can be achieved by detecting the DOA of UHF using PDM, and high-precision positioning in the way of TOF using the method of ultra-high-speed dual track wave record.

2. Partial Discharge Signal 2.1 The Sources and Transmission of PD PD belongs to the category of the electric breakdown of insulated gas. The electric breakdown of SF6 results, in a short time (nanosecond level), current flowing through the conductor. The characteristic impedance of the gas insulated equipment results in a pulse voltage which spreads from the source of PD when the current is flowing through it. The rise time of PD is very short (less than a nanosecond) and the frequency bandwidth is very wide (more than 1 GHz), of which the propagation will cause the electric resonance and stimulate electromagnetic. The propagation path of the electromagnetic pulse spreading in the long gas insulated cavity is shown in Fig. 1: ε1 is the airtight insulator attenuation coefficient, ε2 is the attenuation coefficient of 90 degree angle bend, and ε3 is the coupling attenuation coefficient [8]. 2.2 The Detection of PD Signal Using UHF The frequency of the PD signal generated in SF6 gas insulated cavity is much higher than that in the air. As

can be seen in the propagation map, it is necessary for the PD to stimulate electromagnetic in a sealed metal chamber so that the coupler is able to detect the PD pulse, and eliminate the interference of inherent external air discharge whose frequency is within the range of HF and VHF. GIL meets the requirements [9]. The test model of UHF partial discharge signal detection in closed cavity is shown in Fig. 2. As shown in Fig. 2, 3 represents for air; 4 represents for a closed metal tank with the volume of 1 m3; 5 represents for a columnar high voltage bushing, of which the attenuation coefficient εr equals to 5.5; 1 and 2 represent for the positive and negative AC field; 8 represents for a UHF coupler. The PD pulse is generated in the place of 7, and the UHF coupling wave is detected in the place of 8. The comparison of PD pulse in air and SF6 in the closed metal tank is shown in Fig. 3, with the test discharge capacity q equals to 500 pC. In the UHF wave band (500-3,000 MHz), the

Fig. 2 Test model of UHF PD signal detection.

PD pulse (m

40

1 0.5 0

0

2

4

8

6

10

magnitude

Time (ns) 10 1 .1 .01 .001

Fig. 1 Diagram of pulse dispersion & attenuation.

UHF

1

10 102 frequency (MHz)

103

Fig. 3 Contrast diagram of pulse spectrum.

104


1  2 dB

m

6 4 2 2

4 6 Time (ns)

8

(2)

Assume that the shell cylinder signal attenuation ε4 equals to 0, and the ventilation insulator attenuation is shown as:

0 0

41

10

0   5  0.4 dB

(3)

amplitude

Use the middle frequency band of UHF as the coupling signal, namely the signal frequency is 1,500 MHz. When coax is used as the transmission medium, the attenuation coefficient is shown as: 0

750 frequency（MHz）

 6  17.04 dB /100 m

1500

Fig. 4 Pulse current waveform and amplitude spectrum.

PD pulse generated in the air attenuates rapidly. While using SF6 as the medium, when the PD pulse generates a rising pulse, the UHF coupler is able to detect the corresponding time-domain wave. The map of the pulse current and amplitude spectrum is shown in Fig. 4. The time of PD pulse is in the level of nanosecond, and the rising pulse time is 0.5 ns. The UHF spectrum is mainly within the frequency band of 1 GHz or more than 1 GHz [10].

3. Online Detection and Location of PD Using DOA 3.1 UHD Coupler Settings and PDM System The real-time detected UHF coupler signal of GIL is introduced into the monitoring system PDM. For GIL with long distance, whether the built-in coupler or the window-type coupler is used as the isolation coupler, the signal transmission link is necessary for the signal to be introduced into PDM. The Inherent signal attenuation of straight GIL pipeline is shown as following:

1 dB   0  2 dB

(1)

A typical reference value can be chosen as the airtight insulator attenuation:

(4)

Assume that there are two airtight insulators each one hundred meters on average, thus the total transmission attenuation of the straight line is shown as:  L   0  21   4   5  6100 (5) 21.04   L  23.44 The basic requirement for the PDM to achieve UHF coupling signal detection is that the maximum attenuation is 12 dB each one hundred meters of single path. However, according to Eq. (5), the minimum attenuation of GIL is about 21.04 dB each one hundred meters. For GIL with long distance, if coax is used to transport the signal, the total attenuation exceeds the allowed attenuation requirements. Thus the electrical/optical and optical/electrical conversion link is necessary in order to reduce the transmission attenuation of UHF coupling signal when transported in copper cable path. As shown in Fig. 1, the attenuation coefficient of 90 degree elbow:

 2  6 dB

(6)

This is detrimental to the transmission and location detection of UHF coupling signal in long distance, thus, we can install two couplers at the ninety degree elbow, one in the horizontal direction and the other in the vertical direction, in order to reduce the attenuation of the elbow.


Fig. 5 shows a typical single-phase GIL structure, which is the same as the other two phases. The line LA and LB are two typical pipelines with corner, and each endpoint of the line segment is installed with a coupler. According to the requirements of the signal attenuation mentioned above, if the corner angle is 90 degrees, then it is necessary to install a UHF coupler to reduce the signal measurement attenuation; if the corner angle is greater than 90 degrees, we can just regard it as line segment and there is no need to install a coupler. The coupler transmission signal is converted through the OCU (optical convert unit), and the signal of three phases are combined into one group and filtered by OCU in order to filter out the radio interference signal or the other discharging signal coming through the interface of the equipment which is insulated from the outside air, and detect the amplitude signal of UHF. The digital signal is converted into optical pulse signal by OCU and transferred to the PDM system by optical fiber. The signal is on-line detected, displayed and recorded in the system, as shown in Fig. 6. 3.2 On-Line Detection Method of DOA According to the sketch map of single GIL pipeline shown in Fig. 7, the two endpoints of the pipeline are installed with UHF couplers, and the way of the signal introduced into PDM system is as mentioned before. Assume that the actual distance of the two couplers is L, and the distance between the UHF coupler A and the place where PD occurs is La, and the distance between the UHF coupler B and the place where PD occurs is Lb. We also assume that the actual intensity amplitude of the place where PD occurs is i0, and that of the UHF coupler A and B are ia and ib. The airtight insulator attenuation coefficient is shown in Section 3.1, which is ε1, and the ventilation insulator attenuation coefficient is ε5. Assume that the number of the ventilation Insulator between the place where PD occurs and the UHF coupler A is x, and that of the UHF coupler B is y. Then:

L  La  Lb

(7)

Fig. 5 UHF coupler adapt to GIL pipeline structure.

Fig. 6 UHF coupler signal link into PDM. ϕ2

Lb

La

Intensity (dBm)

42

i1 i2 i3 i 4 ia i5 0

ϕ1

i0

L1

L2 L3 L4 Length (m)

ib

L5

L6

Fig. 7 DOA method detection and calculation.

As for the intensity amplitude of the UHF coupler A, we can get the following formula:

ia  i0  1  La   5  x

(8)

As for the intensity amplitude of the UHF coupler A, we can get the following formula:

ib  i0  1  Lb   5  y

(9)

Eliminating the variable i0 by using Eqs. (5), (8) and (9), we can get the following:

ib  1  Lb   5  y  ia  1  La   5  x La 

ib  ia   1   y  x 5  L  2 1 1 

Lb 

ia  ib   1   x  y 5  L  2 1 1 

(10)


From Eq. (10), we can conclude that we can achieve on-line detection by calculating the distances between the place where PD occurs and the two UHF couplers directly using the following parameters: the number of the airtight insulator and ventilation insulator, which is fixed due to the design of the pipeline; the airtight insulator attenuation coefficient ε1 and the ventilation insulator attenuation coefficient ε5 acquired by experiment, and the PD intensity amplitude ia and ib acquired by the PDM system. 3.3 The Analysis of Detection Error The GIL pipeline conductor is a kind of waveguide system composed of coaxial cable, of which the excitation waves generated by partial discharge include transverse electromagnetic wave and higher order TE, TM wave [11, 12]. Assume that the PD source is a point discharge source, the transverse TEM wave can be expressed as: ETEM 

 

ln  R2 R1  4 R2

I   e i z

(11)

In Eq. (11), ω is the pulse current angular frequency, R1 is the inner radius of the coaxial conductor, μ is the magnetic permeability, ε is the dielectric constant, β is the cavity gain constant, and   is the wave impedance. Assume that the angle of the point where PD occurs and the vertical direction is φ，then the transverse component of the TM wave magnetic field can be expressed as Eq. (12).   kc2 Bmn  Xm  kcr  cos  m e j z ETMmn   8    (12)  2 0m  Jm2  kcR2  Xm  kcR2  I  Bmn   2 2 Jm  kc R1   Jm  kc R 2   X  k r   J  k r  N  k R   J  k R  N  k r  m c m c 1 m c 1 m c  m c  In Eq. (12), δm0 is Kronecker delta, Jm(kcr)、Nm(kcr)

are the first and second kind of m-order Bessel function. Similarly, we can get the transverse component of the TE wave electric field as Eq. (13).

 m2 e j z   cos E A  Z k r m        mn m c  TEmn 8R2   m '2   2 0  Jm  kcR2  Zm  kcR2  I  Amn    m2   m2   Jm'2  kc R1  1 2 2   Jm'2  kc R2  1 2 2    kc R2   kc R1   ' ' Zm  kcr   Jm  kcr  Nm  kc R1   Jm  kc R1  Nm  kcr 

43

(13)

When the boundary conditions are r equals to R1 and r equals to R2, we assume that ETM equals to 0 and ETE equals to 0, then we can get the characteristic mode equations as following: J m  kR1  Nm  kR2   J m  kR2  Nm  kR1   0

(14)

J m'  kR1  N m'  kR2   J m'  kR2  N m'  kR1   0

(15)

The m-order equation solution of Eqs. (14) and (15) is the characteristic modulus value kc of Eqs. (12) and (13). The study and research of the system expressed in Eqs. (11)-(15) show that, the amplitude of each transverse component of the electromagnetic wave generated by PD increases with the increasing length of the waveguide system, which can be applied in long distance GIL pipeline. In the case of proceeding program calculation by using FFT (fast Fourier transform), the relationship of the dominant components TE11, TE21, TE31 of high-order TE wave, the TEM wave and the PD pulse width is weak. However, they change with the change of the PD amplitude synchronously, and the changes of each wave and transverse component are inconsistent, which is the main reason for causing the positioning error based on signal amplitude difference calculation. For example, in the PD signal area whose frequency is with range of 1 GHz ± 200 MHz. The proportion of high modulus component of TE wave changes up to five percent, and the ratio of high amplitude and low amplitude can reach two to three times after decomposition. According to Eq. (10), the amplitude calculation of the same-order high-order wave is the most accurate in

44


theory, however, after acquisition and transform, the amplitudes are not in the same order or same mode. We assume that the ratio of high amplitude and low amplitude after decomposition is two times, and ignore the sign bit of the photoelectric conversion in Fig. 7. The A to D effective value digit m is 13 according to Table 1. According to Eq. (10), the maximum error of measuring and positioning is 7.5 percent every one hundred meters of GIL. Taken the angle of PD source and UHF sensor into consideration [13-15], the comprehensive error can be abbreviated as formula:       DOA  2  R2  R1  sin   cos    2 2 2 

La L  b  100  7.5% cos 1 cos 2

(16)

 3R2  7.5

4. TOF (Time of Flight) Detecting Method The DOA method can not only detect the occurrence of PD in the long distance GIL pipeline, but also detect the place where PD occurs on line. The maximum error of the method DOA can reach ±9.0 m away from the place where PD actually happens every 100 m of GIL pipeline with the pipe diameter of 50 cm. Such positioning accuracy needs to be improved. As the basis of the disintegration overhaul of GIL, the method to improve the positioning accuracy is TOF method by using ultra high speed double channel signal acquisition. 4.1 The TOF Detection and Positioning Method The hardware structure of the TOF method is the same with the DOA method, namely the already installed UHF coupler, of which the signal is introduced into the high speed optical oscilloscope. The PD signal is acquired while the GIL pipeline is under the high pressure testing, of which the principle is detecting the time difference of the PD signal reaching the two couplers installed at the beginning and end of the GIL pipeline. The structure diagram is shown in Fig. 8, PT is the photoelectric transducer.

Table 1 Error relationship table with different A-D bits. Δ (%) 0.39 0.77 1.50 3.00 6.00

m 15 14 13 12 11

Leb1

Lea1

Lfa

Lfb

tf Lea2

Leb2

Fig. 8 Structure diagram of TOF method.

The cable distance of the UHF coupler A and PT is Lea1, and that of the UHF coupler B and PT is Leb1; the optical fiber distance of the two PTs connected to the coupler A is Lfa, and that of the two PTs connected to the coupler B is Lfb; the distance of the cable that connects the PT of coupler A to the dual trace oscilloscope is Lea2, and the distance of the cable that connects the PT of coupler B to the dual trace oscilloscope is Leb2; the time difference of the waveforms of coupler A and coupler B is tf. Assume that the PD signal is electromagnetic wave, of which the propagation velocity in SF6 gas or copper medium is the speed of light c in the vacuum; we also assume that the signal conversion time of the PTs is the same, namely tPT. In order to improve the detection accuracy, the intensity amplitude of the DOA method needs to be ignored, thus the TOF method is shown as following:   Lea1  Lea 2  L fa  La   tf    2tPT  c     Leb1  Leb 2  L fb  Lb     2tPT  (17) c    

 La  Lb 

c L  ea1  Lea 2  L fa    Leb1  Leb 2  L fb  c


10

L  tf c 2

(18)

When the value of tf is negative, the fault point is on the left of the GIL pipeline, and positive is on the right. Eq. (18) has proved that the main error of the TOF method exits in the measurement of tf in experiment. The GIL pipeline is filled with SF6 with the pressure of 0.6 MPa. The length of the pipeline is 200 m, and the outside diameter of the pipeline R2 is 510 mm. The inner conductor is a cavity, of which the outside diameter is 150 mm, and the inner thickness of the conductor is 10 mm. The PT is 15 bits with symbol. The sampling rate of the dual trace oscilloscope is 5 GS/s. The waveform record of the two groups is shown in Fig. 9. The calculating results are tf in the first group is 11.6 ns in the first group, and tf in the second group is 6.12 ns. Using these results and Eq. (17) or (18), we can locate the place where PD occurs in GIL pipeline in experiment. The error of the measuring link is set as 0 in the previous sections for convenience of calculation, however, this error needs to be taken into consideration in the practical application. The TOF method is used to record the flight wave in experiment, and the PD signal of the UHF coupler is near complete transmission. The high-order TE wave and TEM wave of PD can be traced directly, and can be acquired and recognized according to the theoretical amplitude. Thus, the main error includes the transforming link and the first and second part in Eq. (16).

0 -10

100 0

0

4

8 12 16 Time（ns）

-100 20

1 amplit ude(V)

As shown in Eq. (17), the first part is the time difference of the PD signal transmitting in different distances, and the second part is the time difference of the signal transformation and measurement. The conditions that Lea1=Leb1, Lea2=Leb2, Lfa=Lfb need to be complied with strictly in the process of the positioning experiment to set the data of the measurement link. Thus, the second part of Eq. (17) equals to zero, then location of the fault point is as following:

amplit ude(mV)

4.2 Analysis of the Positioning Method

La 

45

0 -1

1 0

0

10

20 30 40 Time（ns）

-1 50

Fig. 9 Wave record of TOF method.

     TOF  2  R2  R1  sin   cos    2   2 2 La L   b  0.77% L cos 1 cos 2

(19)

 3R2  0.77% L

According to Eq. (19), we can calculate that the error of the TOF method is 2.3% in the experimenting pipeline, of which the accuracy can meet the requirements of the strip inspection of GIL. In particular, the TOF method can achieve the positioning of linear closed pipe; if the PD occurs outside the linear closed pipe, the positioning location of PD using the TOF method will be at the two UHF couplers at the both ends of the pipeline; if there is a T connector in the pipe, the positioning location will be at the T connector.

5. Conclusions (1) The two kinds of detecting and positioning method of the location where PD occurs in the long distance GIL pipeline are analyzed in this paper, and the hardware structure for the detecting and positioning is described. The error of the two methods is analyzed using the analysis of the TEM and TE wave in


46

waveguide theory. The intelligent analysis methods of UHF signal needs to be studied and discussed in the future work; (2) The positioning of UHF signal is achieved by detecting the PD signal wave amplitude using the DOA method, which is an on-line continuous detecting method and ran in the PDM system to judge the position signal of the PD in the GIL pipeline and output the alarm. The method can also achieve the acquisition and record of the PD wave acquired by any single UHF coupler for further diagnosis and trend analysis; (3) Compared with the DOA method, the TOF method based on the existing hardware can achieve the high speed acquisition and display of the wave, of which the effective detection accuracy is improved from 7.5% to 2.3%, which meets the requirements of experiment and maintenance, thus it can improve the economical efficiency and continuity of the operating system greatly.

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Lu, F. C., Jin, H., Wang, Z. J., and Zhang, B. 2014. “GIS Partial Discharge Detection and Recognition Based on the Kernel Combination and Multiple Feature Fusion Method.” Transactions of China Electrotechnical Society 29: 334-40. Yin, H., and Qiu, Y. C. 2004. “Study on UHF Method for GIS Partial Discharge Detection.” High Voltage Engineering 30: 19-20. Yao, Y., Yue, Y. F., and Huang, X. Q. 2008. “Application of GIS Ultra High Frequency Ultrasonic PD Detection Method.” High Voltage Engineering 34: 422-4. Chen, J., Liu, W. H., Lu, J., Chen, M., Li, J. H., and Li, Y. M. 2011. “Acoustic Signal Characteristics of Corona Discharge in Different Location of GIS.” High Voltage Engineering 37: 3006-11. Zhang, X. X., Tang, J. Z., Tang, J., Luo, Y., and Xie, Y. B. 2012. “Relationship between UHF Signals and Discharge

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Magnitude from Typical Partial Discharge Defects in GIS.” High Voltage Engineering 38: 59-65. Tang, J., Fan, M., Tan, Z. H., and Sun, C. X. 2013. “Crossover Response Processing Technology of Photoacoustic Spectroscopy Signal of SF6 Decomposition Components Under Partial Discharge.” High Voltage Engineering 39: 257-64. Tang, J., Zeng, F. P., Fan, Q. T., Liu, Y. G., and Zhang, X. X. 2014. “Multifractal Spectrum Identification of Partial Discharge in GIS Based on Fluorescence Optical Fiber Detection.” High Voltage Engineering 40: 465-73. Liu, J. H., Xu, M. H., Huang, C. J., Guo, C. X., Yao, L. P., and Jiang, X. C. 2010. “Investigation on the Attenuation Characteristics of Electromagnetic Waves in GIS.” Transactions of China Electrotechnical Society 25: 52-8. Tang, J., Zhou, Q., Xu, Z. R., Liu, M. J., and Sun, C. X. 2005. “Establishment of Mathematical Model for Partial Discharge in GIS Using UHF Method.” Proceedings of the CSEE 25 (19): 106-10. Li, L. X., Teng, L. T., Huang, C. J., Zeng, Y., and Jiang, X. C. 2009. “Envelope Analysis and Defects Identification of Partial Discharge UHF Signals in GIS.” High Voltage Engineering 35: 260-5. Liu, J. H., Yao, M., Huang, C. J., Duan, D. P., Qian, Y., and Jiang, X. X. 2009. “Characteristics of PD EM-Wave Modes in GIS.” High Voltage Engineering 35: 1654-60. Ding, D. W., Gao, W. S., Yao, S. J., Liu, W. D., and He, J. X. 2013. “Analysis of Excitation Characteristics of Ultra High Frequency Electromagnetic Waves Induced by PD in GIS.” High Voltage Engineering 39: 1893-901. Zhang, L., Lin, Q., Ding, D. W., and Gao, W. S. 2011. “Simulation Analysis on the Attenuation Characteristics of Partial Discharge Ultra-high Frequency Signals in GIS.” High Voltage Engineering 37: 726-31. Hu, H. B., Wu, J. W., Zhang, L. M., and Lian, S. J. 2012. “Composite Measurement Error Analysis and Model Research of Electrical Signals RMS.” Transactions of China Electrotechnical Society 27: 172-7. Yao, C. G., Zhou, D. B., Chen, P., Xing, L., and Sun, C. X. 2011. “UHF-Based Monitoring for Equipment PD within the Substation and Early Warning.” High Voltage Engineering 37: 1670-6.


D

DAVID

PUBLISHING

Analysis of Percolation of the Stabilized Suspensions of TiO2 and SiO2 Nanoparticles in Soil Columns Simulating Landfill Layers Elizabeth Mendes de Oliveira1, Daniele Aparecida Nogueira2, Luis CarlosRolim Lopes2, José Flávio Silveira Feiteira2 and Jose Adilson de Castro2 1. Escola de Engenharia de Alimentos, Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Valença 27600-000, Rio de Janeiro, Brasil 2. Escola de Engenharia Industrial Metalúrgica, Universidade Federal Fluminense, Volta Redonda 27255-125, Rio de Janeiro, Brasil Abstract: It studied the behavior of transport and stability of TiO2 and SiO2 nanoparticles suspensions percolating through soil columns aiming at simulating municipal waste landfills covering soil layers performance. Experimental columns were constructed with landfill soils and water suspensions with nanoparticles percolation runs were carried out. The experimental columns were constructed with 100 mm and 200 mm of diameter and height, respectively. Outlet concentrations were measured along the percolation time using ICP-OES and nanoparticles tracking analyzer. It was observed that SiO2 nanoparticles acts as a stabilizer of TiO2 nanoparticles suspensions and promotes its transport through the soil columns, which simulates the conditions of the controlled landfills layers. The interaction of the suspensions of SiO2 nanoparticles with nanoparticles of TiO2, promote a high stability of the emulsions, which confers the high zeta potential present in SiO2 suspensions, promoting greater mobility and transport through the soil columns. The experimental results demonstrated that TiO2 nanoparticles were kept suspended, even after 10 days, which indicates good stability. It was observed that both TiO2 and SiO2 were kept in suspensions with negligible nanoparticles clustering and decantation. It was confirmed that the TiO2 and SiO2 of the outflow of soil columns are strongly affected by the soil pH, organic carbon and clay content of the soils. It was observed that the soil columns behave as a retention barrier for both TiO2 and SiO2 nanoparticles. Key words: Stabilization, column experiment and nanofluids.

1. Introduction The so-called nanotechnology-based products are constituted of engineered nanomaterials or nanoparticles size structures. The amount of these materials released into the environment is continuously increasing. Thus, growing attention from different regulatory agencies interested in minimizing the environmental impact of these novel materials are observed [1]. To assess the risk, it is necessary to consider the likelihood of exposure to engineered nanoparticles through aqueous media, as it is a receptacle to these materials during their life cycle [2]. Consequently, in real aquatic systems, the probability Corresponding author: Elizabeth Mendes de Oliveira, Dr., research field: transport phenomena in soils contamination.

that nanoparticles interact with each other may be considered since they are presented at substantially higher concentrations [3]. Many factors influence the balance between nanoparticle dispersion/transport and aggregation/deposition in aqueous systems, both environmental and intrinsic to the nanoparticles properly [4]. The particulate in suspension on surface water with a high surface area and the reaction of colloids with other factors, can act as a carrier in the water column could affect the fate and transport of nanoparticles. The significant differences in the properties of nanoparticles and bulk materials are due to the relative increased on surface area and quantum effects that are usually neglected at the macro scale. The increase of applications of nanomaterials and

48

Analysis of Percolation of the Stabilized Suspensions of TiO2 and SiO2 Nanoparticles in Soil Columns Simulating Landfill Layers

consequent increased of production are expected to cause exponentially and uncontrolled emissions in the environment (air, water and soil ecosystems) [5]. The stability of aqueous suspensions are governed by the balance of various forces acting on the interaction between nanomaterials present in suspension, and so existing contaminants in the active sites of the soil or suspensions, such as van der Waals attraction, double-layer repulsion and steric interaction [6]. The transport of colloids and nanoparticles in porous media is restricted by two processes: (1) straining or physical filtration where the particle is larger than the pore and is trapped into the soil; and (2) true filtration where the particle is removed from solution by interception, diffusion and sedimentation [7]. The nanofluids emulsions are obtained by adding the nanoparticles in the base fluid. The current interest in the study of nanofluids is in natural phenomena that are emitted from the nanoparticles in the environment, as well as knowledge on the transport and deposition and their influence on its chemical behavior in the environment, especially for the soil ecosystem. In this investigation nanoparticles of TiO2 (NPTiO2) present in the controlled landfill soil and released with the garbage are studied, the choice of titanium dioxide is due to the fact that it is one of the most widely used nanomaterials in the industrial scale applications. In order to analyze the interactions of NPTiO2 and nanoparticles of SiO2 (NPSiO2) in suspensions which are harmful to human health, which according to the literature are largely emitted by industries. The objectives of this study were to investigate the mobility of TiO2 nanoparticles (NPTiO2) in water suspensions and their interactions with the silica nanoparticles (NPSiO2) in natural soil. The concentrations of nanoparticles of the TiO2 and SiO2 were analyzed using spectrophotometry analysis (ICP-OES) and the size distributions of their aggregates using nanosight equipment (NTA—Nanoparticle Tracking Analyzer). Therefore, this study is focused on the behavior of NPTiO2 in suspensions with

uncontaminated soils and the interactions of NPTiO2 and NPSiO2 with soil columns and the effectiveness of the soil column to retain and complexation of these materials is determined.

2. Methodology In the first step, the nanoparticles of TiO2 (NPTiO2) and SiO2 (NPSiO2) were obtained from Sigma-Aldrich (USA) with an anatase phase purity 99.7%, specific surface area of 200-220 m2/g and the average size of 25 nm particle. The NPSiO2 has purity of 99.5%, specific surface area of 220-240 m2/g particle size 30 nm in average, respectively. It was prepared NPTiO2 and NPSiO2 suspensions by stirring at 300 rpm and Milli-Q water during 24 h. The mixtures were transferred to containers and allowed to stand undisturbed for 10 days to obtain stable solutions. The concentration of TiO2 and SiO2 were determined using a spectrophotometric technique. Two experimental columns were prepared and percolation of the suspensions was carried out using NPTiO2 and NPTiO2 + NPSiO2 suspensions. During the stabilization period, the suspensions were monitored and suspensions aliquots were periodically collected on day 0, 2, 4, 6, 8 and 10 days and analyzed to determine the size distribution of the aggregate, NPTiO2 and NPSiO2 concentrations. The aggregate size distributions were determined using a NTA (Nanoparticle Tracking Analyzer). The percolation column experiments were conducted with soil samples that are used as layers in Municipal Waste Landfill of Volta Redonda, RJ, Brazil. The column was mounted in PVC with 20 cm length and inner diameter of 25 mm was uniformly packed with 10 cm of air-dried soil. At the beginning of the experiment, the soil column was initially saturated with DDW from the bottom of the column gradually upward through the entire length of the column, and then the column was leached with 100 mL of DDW. After that the turbidity of outflow was measured, and it was found that the turbidity was