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ORIGINAL ARTICLE Cold extrusion of a long trapezium spline and its forming analysis Yuan Anfu Received: 21 August 2007 /Accepted: 10 March 2008 / Published online: 15 April 2008 # Springer-Verlag London Limited 2008 Abstract The machining of a long trapezium spline is difficult due to its stiffness. In this paper, a special cold extrusion technique has been adopted on the basis of analyzing its three-dimensional velocity field and simula- tion using the software programme Deform-3D 5.0 to make a qualified trapezium spline of12840 with 16 teeth. Keywords Coldextrusion . Trapeziumspline . Forming limit . Deform 1 Introduction The rectangle spline is mainly used to hold heavy loads due to its thick root. Therefore it is widely used to transmit power in the auto industry. This papers mainly focuses on the forming of a long trapezium spline, which is a difficult problem to solve in the machining industry. Traditional machining methods, such as milling, hobbling, etc., are not capable of forming such spline in batches due to their low efficiency and quality; therefore special manufacturing methods such as twisting, extruding, etc. have become more and more widely used. Still, for long trapezium spline, as shown in Fig. 1, both of them have some difficulties to form a qualified part 17. 2 Details of part to be formed The drawing of a trapezium spline to be formed refers to Fig. 1. Its details are as follows: Teeth : 16 Thick of Tooth :1:3 Material : 20Cr GB ElasticModule : 205Gpa PossionRatio : 0:29 Density : 7850Kg C14 m 3 YieldStrength : 685Mpa Topdia:of tooth : D t 12:8mm Rootdia:of tooth : 10:86mm 3 Steps to solve There are two problems which need to be solved in order to form a qualified product: 3.1 Structure of the die cavity The structure of the die cavity directly influences deforma- tion of the workpiece and stress and strain distribution during extrusion. Therefore it is necessary to design a reasonable die structure according to the actual forming Int J Adv Manuf Technol (2009) 41:461467 DOI 10.1007/s00170-008-1480-y Y. Anfu (*) Information and Control College, Nanjing University of Information Science ;Zg C0R b C138Z=L R b 1 where L Valid length of working zone of die cavity; R b Radius of base circle, i.e., radius of raw bar; g() is defined as follows: g R t 0 C20 8 1 SR 8 1 C20 8 2 R r 8 1 C20 8 2 8 : 2 where R t Radius of top circle of spline R r Radius of root circle of spline SR() Equation of trapezium spline which is described as follows: SR : R r r sin 8 1 C0R t rsin C0 8 2 R t R r sin 8 1 C08 2 3 where a k Pressure angle of the spline t Polar angle when top circle of spline is polar radius Fig. 2 Shape function of trapezium spline and its coordination system Fig. 3 Deforming zone of trapezium spline Fig. 1 Partdrawingtobe formed 462 Int J Adv Manuf Technol (2009) 41:461467 4.2 Actual angles According to actual dimensions of trapezium spline, Eqs. (1, 2 and 3)can be transferred as follows: 8 1 5:83 0 ; 8 2 6:88 0 8 2 12:3 0 ZoneI : fr;ZR t C0 R b Z=L R b 4 ZoneII : fr;Z: r R t R r sin 8 1 C08 2 R r sin 8 1 C0R t sin C08 2 Z Z : 8 : 17 4.4 Power calculation by upper bound analysis During extrusion, there are three powers of deformation power inside the workpiece, friction power and shear power, that is: P T P d P t P f 18 where P d , P t , P f are powers of deformation power inside the workpiece, shear power and friction power on the contacting surface of the spline respectively. They are as follows: P d Z V s edv 19 where e 2 3 q e 2 rr e 2 e 2 zz 2e 2 rz C2C3 1=2 P t s s 3 p Z vjjdS 20 where is the interrupting surface of velocity P f ms s 3 p Z vjjDA 21 Fig. 5 Simulation object Fig. 6 Simulation model 464 Int J Adv Manuf Technol (2009) 41:461467 where is the inner surface of extrusion die The total deformation power: P f pV 0 D 2 r C14 4 22 From 1822, the following equation can be obtained: 2 3 r Z V e 2 rr e 2 e 2 zz 2e 2 rz C2C3 1=2 s dv s 3 p Z vjjdS m s 3 p Z vjjdA pV 0 D 2 r C14 4 23 where e r V r r ; e 1 r V V r C18C19 ; e z V z z ; e zr 1 2 V z r V r z C18C19 The calculating result of guide angle according to power is 23.5. 5 Simulation of extrusion In this paper, Deform software is used to simulate extrusion forming to verify the above calculation results 810. The simulation environment is similar to actual conditions which are stated as follows: 5.1 The purpose of simulation In order to reduce manufacturing cost, save time and obtain a qualified spline as soon as possible, In this paper, simulation of extrusion has been made. Therefore, the purpose of this simulation is to obtain the optical guide Fig. 7 (a) Strain distribution with extrusion depth of 5 mm. (b) Strain distribution with extrusion depth of 5 mm. (c) Strain distribution with extrusion depth of 5 mm Fig. 8 (a) Stress distribution with extrusion depth of 12 mm. (b) Stress distribution with extrusion depth of 12 mm. (c) Stress distribution with extrusion depth of 12 mm Int J Adv Manuf Technol (2009) 41:461467 465 angle a (ref. to Fig. 5) according to the value of stress and strain of the workpiece during extrusion. 5.2 Simulation environment Analysis software Deform-3D 5.0 Analysis mode Heat transfer & deformation Workpiece material AISI-1045 similar with 20 Cr (GB) Number of mesh 70000 Nodes 14452 Element 62766 Analysis steps 100 Time increment 0.5 Frication coefficient between top and the workpiece 0.3 Frication coefficient between bottom and the workpiece 0.08 5.3 Setup of model and simulation The model of simulation is as Fig. 6 in which the structure of the bottom die is as Fig. 5. Diameters of the bottom die and top die are 45 and 25, respectively, and their thicknesses are all 10 mm. In this model, both the bottom die and top die are rigid and the workpiece is plastic. During extrusion, the top die moves down at constant speed of 1.0 mm/s. The diameter and length of the workpiece are 12.9 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 simulation Strain distribution of the workpiece at step 10 and Stress distribution of the workpiece at step 24 are shown in Figs. 7 and 8, respectively. The other maximum stress and strain values at these two steps are listed at Table 1. Figure 9 is the simulation result at step 82. From these results, the following points can be obtained: (1) From the point of stress of the workpiece, the difference at different guide angles is not so obvious. However, the strain at different guide angle changes noticeably and the best one is the bottom die with 25 guide angle. (2) From the point of extrusion, it is the best when the guide angle is 25 since, at this angle, no “forging reduction” appeared and the workpiece extruded qualifies (see Fig. 9). 6 Actual extrusion forming 11, 12 Combining with results of simulation and analysis, we opened the bottom die with a guide angle of 25. The actual machining conditions are as follows: Extrusion machine Special-purpose made machine Power High pressure hydraulic oil Dimension of oil cylinder 4001000 Working pressure 15 Mpa Material of the workpiece 20Cr (GB-Standard of China) with typical surface treatment Lubrication Oil lubrication Speed About 1.4 mm/s Die material Sintered alloy Load mode of extrusion force Pull not push Table 1 Maximum stress and strain at step 10 and 24 Guide angle Step 10 Step 24 Max. stress Max. strain Max. stress Max. strain 20 1450 3.43 1320 3.03 25 1400 2.09 1460 1.68 30 1320 7.30 1440 7.25 Fig. 9 A spline extruded at step 82 with 25 guide angle Fig. 10 Photos of trapezium spline shafts 466 Int J Adv Manuf Technol (2009) 41:461467 In order to obtain qualified product, one point must be paid attention to, i.e., how to keep the stability of the workpiece during extrusion. In this test, special equipment is assembled with which the part can be kept stable and will not bend during extrusion. In addition, guiding accuracy is very important, otherwise extrusion force cannot be stable and a fracture will appear on the surface of the workpiece (refer to Fig. 10). 7 Conclusion More and more attention is being paid to extrusion in the manufacturing industry because of its advantages of high efficiency, high accuracy. This, therefore, is called no chip machining. Especially, extrusion becomes the only forming method for some parts in batch production. From this paper, the following conclusions can be made: (1) Upper bound analysis is a useful and effective method to calculate in theory power needed during extrusion, and its analysis result is accurate as long as the model established is similar to actual forming conditions. (2) With the help of some reasonable software such as Deform, simulation of some forming process has been found on a wide daily application. According to simulation results, some structure or parameters can be modified or adjusted as necessary before extrusion die is put into production. (3) Regarding the forming of thin long spline shaft, its stiffness and stability are the first consideration need to be solved besides common factors in extrusion must be considered. Otherwise, qualified part cant be made. (4) CAE technology is a very useful tool, with which much time and much cost can be saved. (5) Up to now, in test periods, a qualified product can be machined,althoughtherearestillsomeproblemsthatneed to be solved such as production efficiency and optimum extrusion technique. After further modification, this machining method should be put into batch production. References 1. Jia LL, Gao JZ (2002) Study on extrusion forming limits of long splines. China Mechanical Engineering 22:19741976 2. Xu H, Jia SS, Tun HC, Li RZ, Yu G (2005) Numerical simulation of cold extrusion molding process of propeller shaft involute spline. 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