Multi-objective optimization of process parameters for the helical gear precision forging by using Taguchi method

Transcription

1 Journal of Mechanical Science and Technology 5 (6) (0) 59~57 DOI 0.007/s z Multi-objective optimization of process parameters for the helical gear precision forging by using Taguchi method Wei Feng and Lin Hua,* School of Materials Science and Engineering, Wuhan University of Technology, China School of Automotive Engineering, Hubei Key Laboratory of Advanced Technology of Automotive Parts, Wuhan University of Technology, Wuhan 40070, China (Manuscript Received June 4, 00; Revised March 0, 0; Accepted March 0, 0) Abstract Precision forging of the helical gear is a complex metal forming process under coupled effects with multi-factors. The various process parameters such as deformation temperature, punch velocity and friction conditions affect the forming process differently, thus the optimization design of process parameters is necessary to obtain a good product. In this paper, an optimization method for the helical gear precision forging is proposed based on the finite element method (FEM) and Taguchi method with multi-objective design. The maximum forging force and the die-fill quality are considered as the optimal objectives. The optimal parameters combination is obtained through S/N analysis and the analysis of variance (ANOVA). It is shown that, for helical gears precision forging, the most significant parameters affecting the maximum forging force and the die-fill quality are deformation temperature and friction coefficient. The verified experimental result agrees with the predictive value well, which demonstrates the effectiveness of the proposed optimization method. Keywords: Helical gear precision forging; Multi-objective optimization; Taguchi method; Finite element method; Orthogonal design Introduction This paper was recommended for publication in revised form by Editor Dae-Eun Kim * Corresponding author. Tel.: , Fax.: address: fw7757@sina.com; huasvs@yahoo.com.cn KSME & Springer 0 Helical gears are widely applied as an important transmission component in most of the mechanical and automotive industry. In recent years, there has been an increased interest in the production of gears by the precision forming technique. This is because of their inherent advantages compared with conventional cutting methods. The advantages include the excellent mechanical properties, less raw material, good tolerance, high productivity and cost savings [, ]. The precision forging of the helical gear is a very complicated metal forming process under coupled effects with multifactors. The various process parameters such as deformation temperature, punch velocity and friction affect the forming quality differently, thus the reasonable process parameter design is very important. Actually, for lack of theoretical instruction, the process parameters of gears precision forging were determined by repeated experiments with artificial experience, which consume a large amount of materials and time. As a result, the optimization design of process parameters is significant to obtain the desired goals such as achieving good diefill quality, reducing the forging force, increasing the die life, obtaining favorable grain size. In recent years, many scholars have made a lot of research on the forming of helical gears. Samanta [] proposed a process for cold extrusion of helical gears. Choi et al. [, 4, 5] developed a new method of cold extrusion for helical gears and analyzed it by using the upper-bound method. Lange et al. [6, 7] made a deformation analysis for the cold forging of helical gears by D FEM and analyzed the elastic deformation of the die by D-BEM. Yang [8] investigated the clamping-type forging of helical gears through experiments and analysis by FEM. Jung [9] proposed the extrusion of helical gears by twostep process to reducing the forming load. However, previous methods mainly focused on the formability of helical gears by cold extrusion. Optimization technique with multi-objective design of process parameters for a helical gear warm precision forging has not been reported. Due to the inherent complexity of forming processes, the helical gear forging is of high forging pressure which causes failure, plastic deformation and wear of die. Moreover, it is difficult to fill the teeth corner because of the helical shape. The forging pressure and filling conditions can be predicted by rigid-plastic finite element simulation. This is performed by combining the FEM with an optimization technique allowing the adjustment of process parameters in order to meet the

2 50 W. Feng and L. Hua / Journal of Mechanical Science and Technology 5 (6) (0) 59~57 specified demand. In this way, the control of process parameters is possible and allows us to obtain products with the desired demand, such as the shape and so on. Thus, many researchers have paid attention to combining the FEM with an optimization technique to optimize process parameters. Guoqun Zhao and Xinhai Zhao [, ] used a finite elementbased sensitivity analysis method to optimize the preform die shape for metal forming processes to minimize the difference between the realized and the desired final forging shapes and to minimize the effective strain variation within the final forging, respectively. X. Chen [] proposed a process parameters optimization method for the hot forging process of gear based on FEM and Taguchi method to minimize the forging force during gear hot forging process. Y.K. Lee [4] simulated the bevel gear forging process by three dimensional FEM based on rigid-plastic material modeling and found a defect-free forging process to improve the product quality and to secure the effective material flow by optimizing the die. Xiaoming He [5] proposed a robust parameters control methodology based on Taguchi method and numerical simulation to control the microstructure of heavy forgings, uniform and small microstructure of the final forging was considered as the objective function. In this paper, the multi-objective optimization of the helical gear warm precision forging process is studied using a weighting factor in the signal-to-noise ratio of the Taguchi method. The multi-objective design includes smaller forging force and better filling condition of gear teeth. Taguchi method determines the optimal values of deformation temperature, punch velocity, friction factor for a given helical gear to minimize forging force and to improve filling condition of gear teeth. The helical gear precision forming process is studied using a FEM to provide the solutions of the deformation, the stress and the internal variable fields under different forming processes. The analysis of variance is also investigated for the multi-objective design parameters. In this study, we propose a method to analyze the effects of the process parameters on precision forging helical gear by combining finite element analysis with the Taguchi method.. Description of Taguchi method Taguchi method [6] was developed by Taguchi, it is utilized widely in designing and analysis of experimental method to optimize the performance characteristics through the setting of process parameters. It provides an integrated approach to determine the best range of designs simply and efficiently for quality, performance, and cost [7, 8]. In Taguchi method, three-stages such as system design, parameter design, and tolerance design are employed. Parameter design is the key stage, which used to obtain the optimum levels of process parameters for developing the quality characteristics and to determine the product parameter values depending optimum process parameter values [9]. Based on orthogonal arrays, the number of experiments which may lead Table. Dimension of the helical gear. Number of teeth 4 Normal Module.745 Normal pressure angle 0 Helix angle 0. Modification coefficients 0.8 Width 0mm. Fig.. D-FE model of helical gear warm forging. to the increasing of the time and cost can be reduced by using Taguchi method. It employs a special design of orthogonal arrays to learn the whole parameters space with the least experiments only. Taguchi method employs the S/N ratio to identify the quality characteristics applied for engineering design problems. Usually, the S/N ratio characteristics can be divided into three types: the-lower-the-better, the-higher-thebetter, and the-nominal-the-better [6]. A statistical analysis of variance (ANOVA) can be utilized to present the influence of process parameters on forging force and filling condition. In this way, the optimum levels of process parameters can be predicted.. Optimal design problem of the helical gear precision forging. FE modeling for precision forging of the helical gear In this study, the helical gear product used as a component of the automobile transmission was formed by the clampingtype closed-die forging. The specification and dimensions of the adopted helical gear are shown in Table. The authors have built a D-FE model of isothermal precision forging of the helical gear in DEFORM-D software as shown in Fig.. The process conditions in the FE-simulation are: () due to high temperature and large deformation in the process, elastic deformation is negligible and all the dies are regarded as the rigid body and the billet is the deformed body; () the friction at the billet-dies interfaces was assumed to be of shear type; () the temperature of environment is assumed as the room temperature, 0 C; (4) the initial tetrahedral solid elements of the billet were around 00,000 and automatic remeshing tech-

3 W. Feng and L. Hua / Journal of Mechanical Science and Technology 5 (6) (0) 59~57 5 nique was adopted during simulation; (5) for the complexity of forming processes, the mesh density around the teeth is considered higher to improve the deformation accuracy in these area; (6) the billet material used in the model is the AISI-40; (7) the governing equations for the solution of the mechanics of rigid-plastic deformation do not consider the volume force and satisfy with the equilibrium equation, the geometrical equation, volume constancy, and the material obeying the Mises yield criterion; (8) using the penalty function method to handle the condition of volume constancy. (a) (b). Selection of design parameter based on the Taguchi method The goal of the parameter design is to optimize the process parameter values for improving objective functions so as to obtain the desired high quality component without increasing cost under the optimal process parameter. During warm forging processes of helical gear, process parameters such as deformation temperatures of the billet, interface friction, punch velocity, punch stroke, and flow stress of the billet material have a great influence on the mechanical and metallurgical properties of the final products. Deformation temperature (T) greatly affects the flow and deformation pressure of material, performance and surface quality of the final forging product. Many materials are very sensitive to strain rate, and the distribution of strain rate in the forging process greatly affects the deformation behavior. The control of strain rate is usually realized by controlling punch velocity (v). The friction coefficient (µ) of the interface between billet and tools affect tool wear and deformation pressure. Therefore, deformation temperature, punch velocity and interface friction coefficient are chosen as optimal process parameters design variables in this study.. Objective functions In the helical gear forging process, the high forging force significantly cause failure, plastic deformation and wear of dies. It is one of the most essential factors to take into account when choosing forging equipment. For the same forging, if the maximum forging force can be lessened, small tonnage equipment can be used. This will help to lengthen the life span, and reduce the cost of forging. Therefore, a smaller forging force is one objective that should be looked forward to in forging technology and the process of die design. Hence the maximum forging force F max is selected as the optimal objective. The maximum forging force can be defined as the sum of the forces of all the element nodes that have contacted with the upper die along the Z direction. It is expressed as: F max n = f () i= iz Fig.. The meshed FE model (a) initial billet; (b) deformed block. where f iz is the maximum Z direction force of the element node i that is in contact with the upper die. n is the total node number that is in contact with the upper die. In addition, the die-fill condition is also selected as another optimal objective in this work. Incompletely filling of gear teeth is one of the main forging defects. The primary shape requirement in forging design is to make the billet to fill the die cavity adequately and obtain the forging product with less or no flash. The quality of the gear teeth will directly affect the accuracy of dimension and geometry for the final forging part. There are many different evaluation criteria for predicting the filling of gear teeth in gear forging processes, such as the shape difference of the desired final forging and the actual final forging, and the volume difference between them. The minimum distance D min is used here as a measure of the filling condition, and it can be defined as: ( ) ( ) min ib jd ib jd D = x x + y y () where D min displays the minimum distance from the surface of the workpiece to the nearest tool, x ib, y ib is the element node i coordinate values on the surface of the workpiece, x jd, y jd is the element node j coordinate values on the tool surface. The smaller the value of D min is, the more adequate the filling of gear teeth..4 Construction of orthogonal array experiment A large number of experiments need to be carried out when the number of the process parameters increases. To solve this problem, the Taguchi method uses a special design of orthogonal arrays to study the entire parameter space with only a small number of experiments. In the process parameter design of the helical gear, four levels of the process parameters were selected, as shown in Table. Because the interaction between the deformation temperature and velocity is considered, the interaction of two factors can be treated as a new factor according to Taguchi s suggestion. For four factors with four levels, the experimental layout of an L 6 (4 5 ) orthogonal array is selected for the present research. Table shows the L 6 orthogonal array in which the 6 rows are carried out to investigate the effects of the four fac-

4 5 W. Feng and L. Hua / Journal of Mechanical Science and Technology 5 (6) (0) 59~57 Table. Process parameters and their levels. Symbol A B C Process parameters T ( ) v (mm/sec) µ Level Table. Experimental L 6 orthogonal array. Exp. No Level Level Process parameters A B A B C Level Table 4. Simulation results for maximum forging force F max and minimum distance D min. Exp. No F max (KN) D min (mm) S/N S/N for F max (db) for D min (db) tors. The FEM software Deform-D is used to simulate the gear warm forging process and to calculate the optimal objective function value. Table 4 shows the simulation results of maximum forging force F max and minimum distance D min. 4. The Taguchi method with multi-objective design 4. Signal-to-noise ratio (S/N ratio) Taguchi method utilizes the S/N ratio approach instead of the average value to transform the FEM results into a value for the evaluation characteristic in the optimum parameter analysis. This value can estimate the main effect of each factor and their levels on the optimization object. The S/N ratio η is expressed in db units and it can be defined as below: η = 0log( MSD) () where MSD is the mean-square deviation for the output characteristic. Usually, there are three types of quality characteristics in the analysis of the S/N ratio: the nominal-the-better, the smaller-the-better, and the higher-the-better. To obtain optimal process parameters, the smaller-the-better quality characteristics for the maximum forging force F max and the minimum distance D min should be taken. The MSD for the smaller-the-better quality characteristic can be expressed as below: n MSD = S (4) n i = i where S i is the value of maximum forging force F max and minimum distance D min for the ith experiment and n is the number of tests of data points in an experiment. After conducting S/N analysis, S/N ratio values of the maximum forging force F max and the minimum distance D min are listed in Table Taguchi multiple objective optimization based on weighting method It is suitable for the optimization of only single object to use Taguchi method, so it must be modified to solve multiobjective optimization problems. A weighting method is made use of to determine the importance of each optimum object in this paper. Then the optimization of multiple objective is converted into that of single objective by weighting method. The multi-objective S/N ratio η j in the jth experiment is defined as follows: ηj = ω k ηkj (5) k = ωk = (6) k = where η j is the multi-objective S/N ratio in the jth experiment, η jk is the kth single objective S/N ratio for the jth experiment. ω k is the weighting factor in the kth single objective S/N ratio and k is the number of optimization objective. Table 5 shows the multi-objective S/N ratio with different combinations of the weighting factors. 4. S/N and ANOVA analysis The larger the multi-objective S/N ratio is, the smaller the

5 W. Feng and L. Hua / Journal of Mechanical Science and Technology 5 (6) (0) 59~57 5 Table 5. Multi-objective S/N ratio with different weighting factors. Exp. No Multi-objective S/N ratio(db) Case Case Case ω =0.5 ω =0.4 ω =0.6 ω =0.5 ω =0.6 ω = Fig.. Average values of S/N rations for case. variance of performance characteristics around the desired value is. The multi-objective S/N ratio for case to for each parameter at different levels is plotted in Figs., 4 and 5, respectively. From Figs. -5, it can be easily find that the optimum factor level combination is A4BCfor each case, that is the maximum forging force F max and minimum distance D min are minimum at forth level of deformation temperature (A4), first level of punch velocity (B), first level of friction coefficient (C). In order to investigate the effects of the process parameters on the optimization objective quantitatively, analysis of variance (ANOVA) is carried out. It utilizes the total sum of squares SS T, which is a deviation of the multi- objective S/N ratio from the total average S/N ratio η, to evaluate the significance of process parameters on optimization objective. SS T can be calculated as below: Fig. 4. Average values of S/N rations for case. m T = ( j ) j= m ( ) ηj m j= SS η η (7) η = (8) where m is the number of experiments in the orthogonal array (m=6 in this study) and η j is the multi-objective S/N ratio in the jth experiment. The sum of squares due to the variation from the average S/N ratio for factor p is given by SS p r ( S ) m ηkp ( ) j r m η (9) k= j= = where p represents one of the process parameters, k is the level Fig. 5. Average values of S/N rations for case. number of this parameter p, r is the repetition of each level of the parameter p, and S η is the sum of the multi-response S/N ip ratio involving this parameter p and level k. The sum of squares for error SS e is given by SSe = SST ( SSA + SSB + SSC + SS A B) (0) where SS A, SS B, SS C, SS A B is sum of squares for factor A,B,C,A B, respectively. Sum of squares divided by corresponding degree of freedom (DOF) can give the mean square. Mean square for each factor MS p and error mean square are given respectively by

6 54 W. Feng and L. Hua / Journal of Mechanical Science and Technology 5 (6) (0) 59~57 Table 6. Results of ANOVA for case. Table 9. Results of the confirmation test for case. Source A B C A B Error Total Sum of squares DOF 5 Mean square Table 7. Results of ANOVA for case. F- ratio Contribution(%) T ( ) v (mm/sec) µ F max (kn) D min (mm) S/N ration(db) Relative error of S/N Improvement of S/N Initial parameters (A4BC) db Optimal parameters (A4BC) Prediction Experiment % Source A B C A B Error Total MS p MS SS p df p = () SS Sum of squares DOF 5 Mean square Table 8. Results of ANOVA for case. Source A B C A B Error Total Sum of squares DOF 5 Mean square F- ratio F- ratio Contribution(%) Contribution(%) e e = () dfe where df p, df e represents degree of freedom for a factor p and error, respectively. The F-ratio value for each process parameter is the ratio of mean square for a factor p to error mean square, it can be calculated as MS p FP =. () MSe The percentage contribution C p for a factor p can be calculated as SS p df p MSe Cp =. (4) SST Table 0. Results of the confirmation test for case. T ( ) v (mm/sec) µ F max (kn) D min (mm) S/N ration (db) Relative error of S/N Improvement of S/N Tables 6, 7 and 8 show the results of ANOVA for cases, and respectively. It can be seen from the F-ratio value and the percentage contribution result that the significant parameters influencing multi-objective optimization design are deformation temperature and friction coefficient. The effect of punch velocity is very small compared to that of deformation temperature and friction coefficient. The effect of interaction between deformation temperature and punch velocity in each case is very small, so they could be ignored. 5. Confirmation test Based on the S/N ratio and ANOVA analysis, the optimal process parameters combination for cases, and are A4BC. However, the optimum factor level combination is A4BC according to visual analysis from Table 5. Therefore, a confirmation test should be carried out to evaluate the optimal combination. Confirmation test was carried out to predict and verify the improvement of optimization objective, after the optimal level of the design parameters has been selected. The estimated optimum value of S/N ratio η opt of A4BC for each case can be calculated as ηopt = ηa4 + ηb+ ηc ( P ) η (5) where A4 Initial parameters Optimal process Parameters (A4BC) (A4BC) Prediction Experiment db % η is the average S/N ratio for factor A at level 4 obtained from Table 5, η B is the average S/N ratio for factor B at level obtained from Table 5, η C is the average S/N ratio for factor C at level obtained from Table 5, η is the mean of S/N ratio obtained from Table. Executing forging FEM simulation under the optimum setting condition, that is deformation temperature is, punch velocity is

7 W. Feng and L. Hua / Journal of Mechanical Science and Technology 5 (6) (0) 59~57 55 (a) (b) Fig. 6. The minimum distance D min distribution before optimization (a) isoregion distribution; (b) distribution of deformed block. Fig. 8. Comparing of the forging Load-Stroke curve after optimization with before. (a) Fig. 7. The minimum distance D min distribution after optimization (a) isoregion distribution; (b) distribution of deformed block. (b) 0mm/s, friction coefficient is, the optimum result can be obtained. Tables 9, 0 and show the results of the confirmation test. The obtained maximum forging force F max is 550kN and its S/N ratio is -6.8, the obtained minimum distance D min is and its S/N ratio is 0.4. Compared with the results obtained in the initial process parameters A4BC, i.e., deformation temperature is, punch velocity is 50mm/s, and friction coefficient is, it shows that both the maximum forging force F max and the minimum distance D min are improved under the optimal setting of the process parameters which is determined by the approach presented in this study. The increase of the multi-objective S/N ratio from the initial process parameters to the optimal process parameter is 0.8 db, 0.dB and 0.4dB for case to, respectively. Based on the result of the confirmation test, the relative error between the estimated optimum value and the optimum experiment value of the multi-objective S/N ratio for case to is 0.6%, 0.59% and 0.6%, respectively, they are within the engineering requirement. This indicates that the optimal settings of process parameters obtained by modified Taguchi approach are reliable, i.e., deformation temperature is, punch velocity is 0mm/s, and friction coefficient is. The minimum distance D min distribution and the forging Load-Stroke curve after optimization with before are shown in Figs. 6, 7 and 8, respectively. Fig. 6(a) shows the percentage of the nodes with the same minimum distance D min of the total nodes, and Fig. 6(b) shows the D min distribution in the deformed block before optimization. It can be seen from Fig. 6(a) that the range of the same D min is 0~0.0mm and their percentage of nodes is 50.7%, moreover, the filling condition isn t good in the bottom of the forged gear, as shown in Fig. 6(b). Fig. 7(a) shows the percentage of the nodes with the same minimum distance D min of the total nodes, and Fig. 7(b) shows the D min distribution in the deformed block after optimization. It can be seen from Fig. 7(a) that the range of the same D min is 0~mm and their percentage of nodes is 50.94%, moreover, the filling condition is very good in the whole forged gear, as shown in Fig. 7(b). Fig. 8 gives the comparison of the forging Load-Stroke curve for the initial and the optimized parameters. It can be observed from Fig. 8 that the forging load after optimization is hardly less than before during forging. Furthermore, after optimization, the maximum forging force F max is 550kN in helical gear forming which is 6% lower than before. 6. Conclusions Multi-objective optimization design based on the Taguchi method and the finite element method has been implemented for the helical gear warm forging process in this paper. In the light of S/N ratio analysis, variance analysis and FEM simulation results, the following conclusions can be drawn: () The significant forming parameters affecting the helical gear warm forging process such as deformation temperature, friction coefficient, and punch velocity can be easily recognized by performing the experiments which are designed based on the orthogonal array of the Taguchi method. () Deformation temperature and friction coefficient affect the helical gear warm forging process greatly regardless of case to, they contribute about 86% together, while punch velocity does not affect the helical gear warm forging process too much, it only contributes about 5%, and interaction between deformation temperature and punch velocity has little effect on the helical gear warm forging process. () For a given helical gear forming process, the optimal combination of process parameters can be determined through the modified Taguchi method to obtain the minimum values of the maximum forging force F max and the minimum distance

8 56 W. Feng and L. Hua / Journal of Mechanical Science and Technology 5 (6) (0) 59~57 D min. That is when forming process parameters deformation temperature is, friction coefficient is, and punch velocity is 0mm/s, the maximum forging force F max and the minimum distance D min are the smallest simultaneously. (4) The optimal process parameters were confirmed with confirmatory experiments. Acknowledgment This work has been supported by the Natural Science Foundation of China for Distinguished Young Scholars (No ). Nomenclature T : Deformation temperature ( ) v : Punch velocity(mm/s) µ : Friction coefficient F max : Maximum forging force (kn) x, y, z : Cartesian coordinates f iz : z direction force of the element node i D min : The minimum distance (mm) x ib, y ib : Coordinate value of node i on the workpiece surface x jd, y jd : Coordinate value of node j on the tool surface η, η j : Signal-to-noise ratio(db), multi-objective S/N ratio in the jth experiment(db) η : The total average S/N ratio(db) η opt : The estimated optimum value of S/N ratio MSD : Mean square deviation S i : The ith experiment value of optimal objective ω k : Weighting factor in the kth single objective S/N ratio SS T : The total sum of squares SS p : The sum of squares for factor p SS e : The sum of squares for error MS p : Mean square for factor p MS e : Mean square for error df p : Degree of freedom for factor p df e : Degree of freedom for error F p : F-ratio value for factor p : Percentage contribution for factor p C p References [] J. C. Choi and Y. Choi, Precision forging of spur gears with inside relief, Int. J. Mach. Tools Manuf., 9 (999) [] J. C. CHoi, Y. Choi and S. J. TAK, The forging of helical gears (I): experiments and upper-bound analysis, Int. J. Mech. Sci., 40 (998) 5-7. [] S. K. Samanta, Helical gear: a noble method of manufacturing it, Proc. of the 4th North American Metalworking Research Conf., USA (976) [4] J. C. Choi, H. Cho and H. Kwon, A new extrusion process for helical-gears:experiment study, J. Mate.r Process Tech- nol., 4 (994) 5-5. [5] J. C. Choi, Y. Choi and S. J. Tak, The forging of helical gears (Ⅱ): comparisons of the forging processes, Int. J. Mech. Sci., 4(999) [6] V. Szentmihalyi, K. Lange, Y. Tronel, J. L. Chenot and R. Ducloux, -D finite-element simulation of the cold forging of helical gears, J. Mater. Process Technol., 4 (994) [7] K. Lange and V. Szentmihalyi, Optimized cold forging of helical gears by FEM-simulation, Proc. of 9th International Cold Forging Congress, U.K. (995) [8] Y. B. Park and D. Y. Yang, Finite element analysis for precision cold forging of helical gear using recurrent boundary conditions, Proc. of the KSME(Ⅰ), Korean (995) [9] S.-Y. Jung, M.-C. Kang, C. Kim and C.-H. Kim et al., A study on the Extrusion by a two-step process for manufacturing helical gear, Int. J. Adv. Manuf. Technol., 4 (009) [0] G. Zhao, E. Wright and R. V. Grandhi, Sensitivity analysis based preform die shape design for net-shape forging, Int. J. Mach. Tools Manuf., 7 (997) 5-7. [] G. Zhao, X. Ma, X. Zhao and R. V.Grandhi, Studies on optimization of metal forming processes using sensitivity analysis methods, J. Mater. Process Technol., 47(004) 7-8. [] X. Zhao, G. Zhao, G. Wang and T. Wang, Preform die shape design for uniformity of deformation in forging based on preform sensitivity analysis, J. Mater. Process Technol., 8 (00) 5-. [] X. Chen and J. D. Won, Gear hot forging process robust design based on finite element method, J. Mech. Sci. Tech., (008) [4] Y. K. Lee, S. R. Lee, C. H. Lee and D. Y, Yang, Process modification of bevel gear foging using three-dimensional finite element analysis, J. Mater. Process Technol., (00) [5] X. He, Z. Yu and X. Lai, Robust parameters control methodology of microstructure for heavy forgings based on Taguchi method, Materials & Design, 0 (009) [6] H. Zhijun, Three design, China Mechanical Industry Press, Beijing (99). [7] H. Oktem, T. Erzurumlu and I. Uzman, Application of Taguchi optimization technique in determining plastic injection molding process parameters for a thin-shell part, Materials & Design, 8 (007) [8] T.-R. Lin, Optimisation technique for face milling stainless steel with multiple performance characteristics, Int. J. Adv. Manuf. Technol., 9 (00) 0-5. [9] C. Y. Nian, W. H. Yang and Y. S. Tarng, Optimization of turning operations with multiple performance characteristics, J. Mater. Process Technol., 95 (999) [0] M. Ogura and K. Kondo, Precision forging of helical gears utilizing divided-flow method, The Seventh Aisa Symposium on Precision Forging, China (000)

9 W. Feng and L. Hua / Journal of Mechanical Science and Technology 5 (6) (0) 59~57 57 applications. Wei Feng is a Ph.D candidate and is also a lecturer of Material processing Engineering at Wuhan University of Technology. She received her M.S. degree in Pressure Processing from Wuhan University of Technology, China, in 00. Her research areas include advanced forming and its Lin Hua received his M.S. degree in Pressure Processing from Wuhan University of Technology, China, in 985. He then received his Ph.D. degree in Mechanical Engineering from Xi an Jiaotong University, China, in 000. Dr. Hua is currently a professor at the School of Automotive Engineering, Hubei Key Laboratory of Advanced Technology of Automotive Parts at Wuhan University of Technology, China. Dr. Hua s research interests include advanced forming and equipment technology.