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内容简介：: ORIGINAL ARTICLECold extrusion of a long trapezium splineand its forming analysisYuan AnfuReceived: 21 August 2007 /Accepted: 10 March 2008 / Published online: 15 April 2008#Springer-Verlag London Limited 2008Abstract The machining of a long trapezium spline isdifficult due to its stiffness. In this paper, a special coldextrusion technique has been adopted on the basis ofanalyzing its three-dimensional velocity field and simula-tion using the software programme Deform-3D 5.0tomake a qualified trapezium spline of12840 with 16teeth.Keywords Coldextrusion.Trapeziumspline.Forminglimit.Deform1 IntroductionThe rectangle spline is mainly used to hold heavy loads dueto its thick root. Therefore it is widely used to transmitpower in the auto industry. This papers mainly focuses onthe forming of a long trapezium spline, which is a difficultproblem to solve in the machining industry. Traditionalmachining methods, such as milling, hobbling, etc., are notcapable of forming such spline in batches due to their lowefficiency and quality; therefore special manufacturingmethods such as twisting, extruding, etc. have becomemore and more widely used. Still, for long trapeziumspline, as shown in Fig. 1, both of them have somedifficulties to form a qualified part 17.2 Details of part to be formedThe drawing of a trapezium spline to be formed refers toFig. 1. Its details are as follows:Teeth :16Thick of Tooth :1:3Material : 20Cr GBElasticModule : 205GpaPossionRatio : 0:29Density : 7850Kg?m3YieldStrength : 685MpaTopdia:of tooth : Dt 12:8mmRootdia:of tooth : 10:86mm3 Steps to solveThere are two problems which need to be solved in order toform a qualified product:3.1 Structure of the die cavityThe structure of the die cavity directly influences deforma-tion of the workpiece and stress and strain distributionduring extrusion. Therefore it is necessary to design areasonable die structure according to the actual formingInt J Adv Manuf Technol (2009) 41:461467DOI 10.1007/s00170-008-1480-yY. Anfu (*)Information and Control College,Nanjing University of Information Science & Technology,No.114 Pancheng New Street Pukou District,Nanjing, Jiangsu Province 210044, Chinae-mail: conditions to obtain a minimum forming force. In thispaper, based on the analysis to the three-dimensionalvelocity field in metal extrusion according to assumptionof isoextrusion ratio flow, a reasonable die structure can bedesigned. And then forming of extrusion under the sameconditions with actual extrusion is simulated with Deform.Finally the extrusion die is machined according to theabove two results.3.2 Stiffness of part to be formedAs to the thin long the workpiece to be formed in thispaper, how to keep enough stiffness of the workpieceduring cold extrusion becomes an overwhelming problem.So in actual extrusion, traditional push force is changed to apull force and, at the same time, supported by specialmechanism. These techniques above are proved to beeffective.4 Analysis of extrusionIn this paper, all analysis is made on the basis of open dieextrusion.4.1 Shape function of spline shaftDue to the symmetry of the trapezium spline, only half thestructure of its shape is drawn in Fig. 2. According to theworking principle of trapezium spline, its shape function ofsurface can be obtained as follows:f r;Z g ? Rb?Z=L Rb1whereLValid length of working zone of die cavity;RbRadius of base circle, i.e., radius of raw bar;g()is defined as follows:g Rt0 ? 81SR 81 ? 82Rr81 ? 828:2whereRtRadius of top circle of splineRrRadius of root circle of splineSR()Equation of trapezium spline which is describedas follows:SR : Rrr sin 81? Rtrsin ? 82 RtRrsin 81? 823whereakPressure angle of the splinetPolar angle when top circle of spline is polar radiusFig. 2 Shape function of trapezium spline and its coordination systemFig. 3 Deforming zone of trapezium splineFig. 1 Part drawing to beformed462Int J Adv Manuf Technol (2009) 41:4614674.2 Actual anglesAccording to actual dimensions of trapezium spline,Eqs. (1, 2 and 3)can be transferred as follows:81 5:830;82 6:88082 12:30ZoneI : f r;Z Rt? RbZ=L Rb4ZoneII : f r;Z :r RtRrsin 81?82Rrsin 81?Rtsin ?82 Z Z:8:174.4 Power calculation by upper bound analysisDuring extrusion, there are three powers of deformationpower inside the workpiece, friction power and shearpower, that is:PT Pd Pt Pf18where Pd, Pt, Pfare powers of deformation power insidethe workpiece, shear power and friction power on thecontacting surface of the spline respectively. They are asfollows:PdZVsedv19wheree ffiffiffi23qe2rr e2 e2zz 2e2rz?1=2Ptssffiffiffi3pZvjjdS20where is the interrupting surface of velocityPfmssffiffiffi3pZvjjDA21Fig. 5 Simulation objectFig. 6 Simulation model464Int J Adv Manuf Technol (2009) 41:461467where is the inner surface of extrusion dieThe total deformation power:Pf pV0D2r?422From 1822, the following equation can be obtained:ffiffiffi23rZVe2rr e2 e2zz 2e2rz?1=2sdvsffiffiffi3pZvjjdS msffiffiffi3pZvjjdA pV0D2r?423whereerVrr;e1rV Vr?;ezVzz;ezr12VzrVrz?The calculating result of guide angle according topower is 23.5.5 Simulation of extrusionIn this paper, Deform software is used to simulate extrusionforming to verify the above calculation results 810. Thesimulation environment is similar to actual conditionswhich are stated as follows:5.1 The purpose of simulationIn order to reduce manufacturing cost, save time and obtaina qualified spline as soon as possible, In this paper,simulation of extrusion has been made. Therefore, thepurpose of this simulation is to obtain the optical guideFig. 7 (a) Strain distribution with extrusion depth of 5 mm. (b) Strain distribution with extrusion depth of 5 mm. (c) Strain distribution withextrusion depth of 5 mmFig. 8 (a) Stress distribution with extrusion depth of 12 mm. (b) Stress distribution with extrusion depth of 12 mm. (c) Stress distribution withextrusion depth of 12 mmInt J Adv Manuf Technol (2009) 41:461467465angle a (ref. to Fig. 5) according to the value of stress andstrain of the workpiece during extrusion.5.2 Simulation environmentAnalysis softwareDeform-3D 5.0Analysis modeHeat transfer &deformationWorkpiece materialAISI-1045 similar with20 Cr (GB)Number of mesh70000Nodes14452Element62766Analysis steps100Time increment0.5Frication coefficient between topand the workpiece0.3Frication coefficient betweenbottom and the workpiece0.085.3 Setup of model and simulationThe model of simulation is as Fig. 6 in which the structureof the bottom die is as Fig. 5. Diameters of the bottom dieand top die are 45 and 25, respectively, and theirthicknesses are all 10 mm. In this model, both the bottomdie and top die are rigid and the workpiece is plastic.During extrusion, the top die moves down at constant speedof 1.0 mm/s. The diameter and length of the workpiece are12.9 and 25 mm, respectively.Three simulations are made whose bottom die are 20,25 and 30, respectively, in the same conditions.5.4 Results of simulationStrain distribution of the workpiece at step 10 and Stressdistribution of the workpiece at step 24 are shown in Figs. 7and 8, respectively. The other maximum stress and strainvalues at these two steps are listed at Table 1. Figure 9 isthe simulation result at step 82. From these results, thefollowing points can be obtained:(1)From the point of stress of the workpiece, thedifference at different guide angles is not so obvious.However, the strain at different guide angle changesnoticeably and the best one is the bottom die with 25guide angle.(2)From the point of extrusion, it is the best when theguide angle is 25 since, at this angle, no “forgingreduction” appeared and the workpiece extrudedqualifies (see Fig. 9).6 Actual extrusion forming 11, 12Combining with results of simulation and analysis, weopened the bottom die with a guide angle of 25. The actualmachining conditions are as follows:Extrusion machineSpecial-purpose made machinePowerHigh pressure hydraulic oilDimension of oilcylinder4001000Working pressure15 MpaMaterial of theworkpiece20Cr (GB-Standard of China) withtypical surface treatmentLubricationOil lubricationSpeedAbout 1.4 mm/sDie materialSintered alloyLoad mode ofextrusion forcePull not pushTable 1 Maximum stress and strain at step 10 and 24Guide angle Step 10Step 24Max.stressMax.strainMax.stressMax.strain2014503.4313203.032514002.0914601.683013207.3014407.25Fig. 9 A spline extruded at step82 with 25 guide angleFig. 10 Photos of trapezium spline shafts466Int J Adv Manuf Technol (2009) 41:461467In order to obtain qualified product, one point must bepaid attention to, i.e., how to keep the stability of theworkpiece during extrusion. In this test, special equipmentis assembled with which the part can be kept stable and willnot bend during extrusion. In addition, guiding accuracy isvery important, otherwise extrusion force cannot be stableand a fracture will appear on the surface of the workpiece(refer to Fig. 10).7 ConclusionMore and more attention is being paid to extrusion in themanufacturing industry because of its advantages of highefficiency, high accuracy. This, therefore, is called no chipmachining. Especially, extrusion becomes the only formingmethod for some parts in batch production. From this paper,the following conclusions can be made:(1)Upper bound analysis is a useful and effective methodto calculate in theory power needed during extrusion,and its analysis result is accurate as long as the modelestablished is similar to actual forming conditions.(2)With the help of some reasonable software such asDeform, simulation of some forming process has beenfound on a wide daily application. According tosimulation results, some structure or parameters canbe modified or adjusted as necessary before extrusiondie is put into production.(3)Regarding the forming of thin long spline shaft, itsstiffness and stability are the first consideration need tobe solved besides common factors in extrusion must beconsidered. Otherwise, qualified part cant be made.(4)CAE technology is a very useful tool, with whichmuch time and much cost can be saved.(5)Up to now, in test periods, a qualified product can bemachined,althoughtherearestillsomeproblemsthatneedto be solved such as production efficiency and optimumextrusion technique. After further modification, thismachining method should be put into batch production.References1. Jia LL, Gao JZ (2002) Study on extrusion forming limits of longsplines. China Mechanical Engineering 22:197419762. Xu H, Jia SS, Tun HC, Li RZ, Yu G (2005) Numerical simulationof cold extrusion molding process of propeller shaft involutespline. Vehicle Technology 4:32353. Luo YH, Li LX (2006) Study on isothermal extrusion using thedeform. Journal of Hunan Industry Polytechnic 16:13154. Lv L, Tan L (2004) Research on mould of spline in cold extrusion.Mechanical Worker (Cold Machining) 8:27285. Gao J (2004) Research on knowledge-based intelligent system andkey technologies of cold extr

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