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May 2, 200814:31WSPC/180-JAMS00100 Journal of Advanced Manufacturing Systems Vol. 7, No. 1 (2008) 1520 c ? World Scientifi c Publishing Company A STUDY ON STEPWISE OPTIMIZATION OF FORMING PARAMETERS FOR THIN-WALLED TUBE NC BENDING JIE XU, HE YANG, MEI ZHAN and HENG LI Department of Materials Forming and Control Engineering Northwestern Polytechnical University, P.O. Box 542 Xian 710072, Shaanxi, P. R. China jennyxjl 2931126.com The optimization design of forming parameters for thin-walled tube NC bending is a complicated problem with multi-objectives, multi-variables and multi-constraints. A stepwise optimizing strategy is proposed to solve the problem. Initial values are deter- mined according to the databases and expert knowledge, and then the forming param- eters are optimized by adopting diverse methods after reducing their range gradually. The optimization processes implementing the strategy are carried out for the bending of stainless steel and aluminum alloy tubes with thickness of 1mm, outside diameter of 38mm, and bending radius of 57mm. The FEM model established by ABAQUS/Explicit is used. Free wrinkling, the allowed cross-section distortion degree and other engineering demands are constraint conditions, and the minimum wall thinning ratio is defi ned as the optimization objective. The optimal values of the number of mandrel balls and the clearance between mandrel balls are obtained step by step respectively. Then the man- drel extension length and the boosting velocity of the pressure die are optimized by the complex method. The experiments are performed to verify the optimization results. Keywords: Thin-walled tube NC bending; forming parameter optimization; FEM. 1. Introduction The thin-walled tube NC precision bending process is a complex process with cou- pling interactive multi-factorial eff ects. If the forming parameters are inappropriate, excessive wall thinning even cracking, wrinkling, wall fl attening and inaccuracy of bending angle caused by spring-back will occur easily, especially for thin-walled tubes. Thus, the optimization of the forming parameters has become an important subject to be resolved urgently. In this research, through analyzing and describing, a stepwise strategy is proposed, and forming parameters are optimized by com- bining FEM with the engineering optimization method and the virtual experiment design method, on the basis of experiential data and expert knowledge based on previous research.1 15 May 2, 200814:31WSPC/180-JAMS00100 16J. Xu et al. 2. Analysis and Description In engineering application of thin-walled tube NC bending process, the optimiza- tion problem is how to select reasonable forming parameters in order to satisfy the demanded bending radius and ensure the forming quality under given dimension and material of tubes. Hence, the minimum wall thinning ratio is determined as the optimization objective, while free wrinkling, the allowed cross-section distor- tion degree as the constraints conditions, without considering springback. The wall thinning ratio (T) is expressed by Eq. (2.1), and the cross-section distortion degree () is expressed by Eq. (2.2). T = t0 tmin t0 100%(2.1) = D0 D0 D0 100%(2.2) where D0is the outer layer length of vertical axes after bending, D0is the original outside diameter of tube, t0is the original wall thickness of tube, and tminis the minimum wall thickness of tube after bending. The independent variables of the process parameters, which can be controlled directly and have signifi cant eff ect on the objective, are selected as the design variables. The constraint conditions, which come from the requirement of forming quality, forming conditions and geometry constraints, contain much expert knowledge and experiential data used to determine the initial values of variables. 3. Strategy and Its Realization of Stepwise Optimization Through the above analysis, the strategy for stepwise optimization of the forming parameters is proposed. Detailed steps of its realization are described as follows, and the fl ow chart is shown in Fig. 1. Input D0, t0, R (bending radius), query the database of the forming limit, judge whether the bending radius is larger than the minimum bending radius without wrinkling. If yes, go on the next step, and if no, output information of instability and change the bending radius. Query the database to fi nd the corresponding forming parameters. If it does not exist, analyze by expert knowledge to obtain initial forming parameters, establish a FEM model, and then determine the optimum friction coeffi cients and clearances between tools and tube by the wrinkling criterion. Change the number of mandrel balls (n) and the clearance between mandrel balls (p0) in the allowed range, and optimize them through the FEM calcula- tion for the minimum wall thinning ratio in the allowed cross-section distortion degree. Do virtual uniform distribution experiments. Uniform distribution design is an experiment design method only by considering the uniform experiment points.2 May 2, 200814:31WSPC/180-JAMS00100 Stepwise Optimization of Forming Parameters for Thin-Walled Tube NC Bending17 Query forming limit database Whether exist corresponding forming limit Input material parameters, D0t0, R Forming limit database Determination module of forming limit Whether RRmin Query database of forming parameters Establish FEM model and calculate Output instability information No Yes Analysis by expert knowledge No No Yes No manufacturingEnd Determine forming parameters range and their initial values Whether satisfy wrinkling criteria Caculate Whether max n=n+1 No obtain the optimum of p Change clearance and friction Virtul experiment in the determined range Optimize e and Vp by the complex method Whether the result satisfy the requirement Whether exist corresponding forming parameters Yes Yes Yes No No Yes Calculate T nnmax NoYes Whether TTmax Forming parameter database Yes Fig. 1.Flow chart of stepwise optimization. According to the results, the relationship of wall thinning ratio with the mandrel extension length (e) and the boosting velocity of pressure die (Vp) is regressed by the quadric polynomial: y = a0+a1x1+a2x2+a3x2 1+a4x22. Then they are opti- mized by the complex method, which is a direct search method, to resolve multi- dimension nonlinear problems with constraints without computing the grads of the objective.3 We use the established data management system in Ref. 4 to conclude the rationality of forming parameters and determine the range of the parameters in the whole optimization process, and the FEM models established under ABAQUS/ Explicit software in Ref. 5 to calculate. The optimization algorithm and the FEM software transmit information by programs developed in Visual C+. 4. Results and Discussion The optimization strategy proposed is applied to the bending tubes of 38 1 stainless steel and aluminum alloy with bending radius of 57mm in order to verify May 2, 200814:31WSPC/180-JAMS00100 18J. Xu et al. its feasibility. For stainless steel tubes, the results under diff erent clearance and mandrel ball conditions in obtained range are shown in Figs. 2 and 3. Virtual uniform distribution experiment results are shown in Table 1. The optimal values of the mandrel extension length and the boosting velocity of the pressure die are 7.62mm and 51.07mm/s, respectively. The wall thinning ratio has been improved by 4% after optimization. The contour plots of equivalent plastic strain and stress are shown in Figs. 4 and 5, and the plastic deformation is more uniform after ? ? ? ? ? ? ? ? (mm)?X clearance between mandrel balls? (%)? ? ?maximum cross section distortion? three mandrel balls? two mandrel balls? one mandrel ball? Fig. 2. Wall thinning ratios under diff erent mandrel balls and diff erent clearance between mandrel balls. ? ? ? ? ? ? ? ? (mm) X clearance between mandrel balls (%) ? ?maximum cross section distortion three mandrel balls two mandrel balls one mandrel ball Fig. 3. Maximum cross section distortion degree under diff erent mandrel balls and diff erent clearance between mandrel balls. May 2, 200814:31WSPC/180-JAMS00100 Stepwise Optimization of Forming Parameters for Thin-Walled Tube NC Bending19 Table 1. Results of the virtual uniform experiment under diff erent e and Vp. Numbere (mm)Vp(mm/s)MaximumMinimumT(%) Thickness (mm)Thickness (mm) 16.0036.481.1810.802119.79 26.5041.041.1810.818618.14 37.0045.601.2080.830416.96 47.5050.161.2030.835616.44 58.0054.721.1970.837616.24 67.0036.481.1960.80919.10 77.5041.041.1860.819318.07 88.0045.601.2060.833116.69 98.0036.481.1990.810518.95 106.0045.601.2060.829517.05 116.5050.161.1940.843215.68 127.0054.721.2010.840515.95 136.0054.721.1960.839216.08 Fig. 4.Equivalent plastic strain distribution: (left) e = 8.00mm, Vp= 45.60mm/s; (right) e = 7.62mm, Vp= 51.07mm/s. Fig. 5.Stress distribution: (left) e = 8.00mm, Vp= 45.60mm/s; (right) e = 7.62mm, Vp= 51.07mm/s. May 2, 200814:31WSPC/180-JAMS00100 20J. Xu et al. Table 2.Comparison between stainless steel tube bending and aluminum alloy tube bending. MaterialVp(mm/s)e (mm)T inT in Simulation (%)Experiment (%) 1Cr18Ni9Ti51.077.6216.0919.22 LF2M52.126.0020.5822.74 Material in inWhether Simulation (%)Experiment (%)Wrinkling 1Cr18Ni9Ti4.026.89no LF2M4.687.93no optimization. Similarly, for thin-walled aluminum alloy tubes, the optimum values of e and Vpare acquired as 6.00mm and 52.12mm/s, respectively. Experiments have been done on PLC controlled hydraulic bender W27YPC-63NC. Adopting the optimum values, eligible products are acquired, and the results of the stainless steel tubes have been compared with those of the aluminum alloy, both without drawbacks and satisfying the quality requirement, as shown in Table 2. 5. Conclusion A stepwise optimization strategy is proposed to solve the optimization problem for thin-walled tube NC bending, in which, parameters are optimized gradually. Forming parameters have been optimized for the NC bending of stainless steel a