可双向弯管的弯管机设计【说明书+CAD+SOLIDWORKS】
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May 2, 200814:31WSPC/180-JAMS00100Journal of Advanced Manufacturing SystemsVol. 7, No. 1 (2008) 1520c ? World Scientific Publishing CompanyA STUDY ON STEPWISE OPTIMIZATION OFFORMING PARAMETERS FOR THIN-WALLEDTUBE NC BENDINGJIE XU, HE YANG, MEI ZHAN and HENG LIDepartment of Materials Forming and Control EngineeringNorthwestern Polytechnical University, P.O. Box 542Xian 710072, Shaanxi, P. R. Chinajennyxjl 2931126.comyangheThe optimization design of forming parameters for thin-walled tube NC bending isa complicated problem with multi-objectives, multi-variables and multi-constraints. Astepwise 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 bendingof stainless steel and aluminum alloy tubes with thickness of 1mm, outside diameter of38mm, and bending radius of 57mm. The FEM model established by ABAQUS/Explicitis used. Free wrinkling, the allowed cross-section distortion degree and other engineeringdemands are constraint conditions, and the minimum wall thinning ratio is defined asthe optimization objective. The optimal values of the number of mandrel balls and theclearance 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 thecomplex method. The experiments are performed to verify the optimization results.Keywords: Thin-walled tube NC bending; forming parameter optimization; FEM.1. IntroductionThe thin-walled tube NC precision bending process is a complex process with cou-pling interactive multi-factorial effects. If the forming parameters are inappropriate,excessive wall thinning even cracking, wrinkling, wall flattening and inaccuracy ofbending angle caused by spring-back will occur easily, especially for thin-walledtubes. Thus, the optimization of the forming parameters has become an importantsubject 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 experimentdesign method, on the basis of experiential data and expert knowledge based onprevious research.115May 2, 200814:31WSPC/180-JAMS0010016J. Xu et al.2. Analysis and DescriptionIn engineering application of thin-walled tube NC bending process, the optimiza-tion problem is how to select reasonable forming parameters in order to satisfy thedemanded bending radius and ensure the forming quality under given dimensionand material of tubes. Hence, the minimum wall thinning ratio is determined asthe optimization objective, while free wrinkling, the allowed cross-section distor-tion degree as the constraints conditions, without considering springback. The wallthinning ratio (T) is expressed by Eq. (2.1), and the cross-section distortion degree() is expressed by Eq. (2.2).T =t0 tmint0 100%(2.1) =D0 D0D0 100%(2.2)where D0is the outer layer length of vertical axes after bending, D0is the originaloutside diameter of tube, t0is the original wall thickness of tube, and tminis theminimum wall thickness of tube after bending. The independent variables of theprocess parameters, which can be controlled directly and have significant effect onthe objective, are selected as the design variables. The constraint conditions, whichcome from the requirement of forming quality, forming conditions and geometryconstraints, contain much expert knowledge and experiential data used to determinethe initial values of variables.3. Strategy and Its Realization of Stepwise OptimizationThrough the above analysis, the strategy for stepwise optimization of the formingparameters is proposed. Detailed steps of its realization are described as follows,and the flow chart is shown in Fig. 1. Input D0, t0, R (bending radius), query the database of the forming limit, judgewhether the bending radius is larger than the minimum bending radius withoutwrinkling. If yes, go on the next step, and if no, output information of instabilityand change the bending radius. Query the database to find the corresponding forming parameters. If it doesnot exist, analyze by expert knowledge to obtain initial forming parameters,establish a FEM model, and then determine the optimum friction coefficientsand clearances between tools and tube by the wrinkling criterion. Change the number of mandrel balls (n) and the clearance between mandrelballs (p0) in the allowed range, and optimize them through the FEM calcula-tion for the minimum wall thinning ratio in the allowed cross-section distortiondegree. Do virtual uniform distribution experiments. Uniform distribution design is anexperiment design method only by considering the uniform experiment points.2May 2, 200814:31WSPC/180-JAMS00100Stepwise Optimization of Forming Parameters for Thin-Walled Tube NC Bending17Query forming limit database Whether exist corresponding forming limit Input material parameters, D0t0, RForming limit databaseDetermination module of forming limit Whether RRminQuery database of forming parametersEstablish FEM model and calculateOutput instability informationNoYesAnalysis by expert knowledgeNoNoYesNomanufacturingEndDetermine forming parameters range and their initial valuesWhether satisfy wrinkling criteriaCaculate Whether maxn=n+1Noobtain the optimum of p Change clearance and frictionVirtul experiment in the determined rangeOptimize e and Vpby the complex methodWhether the result satisfy the requirementWhether exist corresponding forming parametersYesYesYesNoNoYesCalculate TnnmaxNoYesWhether TTmaxForming parameterdatabaseYesFig. 1.Flow chart of stepwise optimization.According to the results, the relationship of wall thinning ratio with the mandrelextension length (e) and the boosting velocity of pressure die (Vp) is regressed bythe quadric polynomial: y = a0+a1x1+a2x2+a3x21+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 ofthe objective.3We use the established data management system in Ref. 4 to conclude therationality of forming parameters and determine the range of the parameters inthe whole optimization process, and the FEM models established under ABAQUS/Explicit software in Ref. 5 to calculate. The optimization algorithm and the FEMsoftware transmit information by programs developed in Visual C+.4. Results and DiscussionThe optimization strategy proposed is applied to the bending tubes of 38 1stainless steel and aluminum alloy with bending radius of 57mm in order to verifyMay 2, 200814:31WSPC/180-JAMS0010018J. Xu et al.its feasibility. For stainless steel tubes, the results under different clearance andmandrel ball conditions in obtained range are shown in Figs. 2 and 3. Virtualuniform distribution experiment results are shown in Table 1. The optimal valuesof the mandrel extension length and the boosting velocity of the pressure die are7.62mm and 51.07mm/s, respectively. The wall thinning ratio has been improvedby 4% after optimization. The contour plots of equivalent plastic strain and stressare 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 different mandrel balls and different clearance between mandrelballs.?(mm)X clearance between mandrel balls(%)? ?maximum cross section distortionthree mandrel balls two mandrel ballsone mandrel ballFig. 3.Maximum cross section distortion degree under different mandrel balls and differentclearance between mandrel balls.May 2, 200814:31WSPC/180-JAMS00100Stepwise Optimization of Forming Parameters for Thin-Walled Tube NC Bending19Table 1.Results of the virtual uniform experiment under different e and Vp.Numbere (mm)Vp(mm/s)MaximumMinimumT(%)Thickness (mm)Thickness (mm)16.0036.481.1810.802119.7926.5041.041.1810.818618.1437.0045.601.2080.830416.9647.5050.161.2030.835616.4458.0054.721.1970.837616.2467.0036.481.1960.80919.1077.5041.041.1860.819318.0788.0045.601.2060.833116.6998.0036.481.1990.810518.95106.0045.601.2060.829517.05116.5050.161.1940.843215.68127.0054.721.2010.840515.95136.0054.721.1960.839216.08Fig. 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-JAMS0010020J. Xu et al.Table 2.Comparison between stainless steel tube bending and aluminumalloy tube bending.MaterialVp(mm/s)e (mm)T inT inSimulation (%)Experiment (%)1Cr18Ni9Ti51.077.6216.0919.22LF2M52.126.0020.5822.74Material in inWhetherSimulation (%)Experiment (%)Wrinkling1Cr18Ni9Ti4.026.89noLF2M4.687.93nooptimization. Similarly, for thin-walled aluminum alloy tubes, the optimum valuesof e and Vpare acquired as 6.00mm and 52.12mm/s, respectively. Experimentshave been done on PLC controlled hydraulic bender W27YPC-63NC. Adoptingthe optimum values, eligible products are acquired, and the results of the stainlesssteel tubes have been compared with those of the aluminum alloy, both withoutdrawbacks and satisfying the quality requirement, as shown in Table 2.5. ConclusionA stepwise optimization strategy is proposed to solve the optimization problemfor thin-walled tube NC bending, in which, parameters are optimized gradually.Forming parameters have been optimized for the NC bending of stainless steel andalumin
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