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1、附录3 翻译原文Blank design and formability prediction of complicated progressive die stamping part using a multi-step unfolding methodZhang Zhibing, Liu Yuqi,Du Ting,Li ZhigangState Key Lab of Material Processing and Die&Mould Technology,Huazhong University of Science&Technology, Wunan,Hubei 430074,Chinaa
2、 r t i c l e i n f oArticle history:Received 17 March 2007Received in revised form12 July 2007Accepted 24 November 2007AbstractA multi-step unfolding method (MSUM) is developed for blank design and formability prediction of complicated progressive die stamping part .In the method ,a finite element m
3、odel of the inverse approach(IA)is developed at a local area according to the stamping process, and the intermediate shape is unfolded on a reference surface at the local area .Not only the influence of the connection ,blank-holder force and the friction ,but also the influence of the offsetting of
4、the strain neutral layer with different radius of curvature at local area, are considered in the model ,which improves the calculation precision of the blank shape at each step .The key intermediate blank shapes and initial blank shape can be generated using the method with many times in an inverse
5、sequence .The optimum blank shape also can be designed according to the formability of the forming part .The MSUM is illustrated to the blank design of a progressive die stamping part ,and a benchmark test is compared with experimental and other numerical results.Keywords: Blank design Progressive d
6、ie Multi-step unfolding method Inverse approach1.IntroductionA large number of parts on automobile body are deformed by stamping ,and sometimes the features of the stamping parts are very complicated .In order to improve the quality and the efficiency of products ,many parts are formed using progres
7、sive die process .Comparing with simple press tool, progressive die has the advantages of high quality and efficiency of product ,which is especially suitable for large-lot production in a short delivery time .However ,it is very difficult to design strip layout in progressive die design ,and only t
8、he rich experience and technical engineers are competent to do it well.In the strip layout design, firstly, the stamping process sequence is designed according to the part features with experience and simple theoretical formula. Secondly, the shape at each step is designed with the process sequence
9、and all shapes are assembled into a strip. After finishing the die structure design with strip layout, it is very important to validate the design of strip layout and the die structure in a real production condition to find out potential defects. It is necessary to modify the design of strip layout
10、and the die structure until the defects is removed. So it is a rather difficult task to obtain an optimum strip layout. If the optimal blank shape and size at each step and the formability are predicted at the design stage, which will greatly reduce the trial and error time of the whole progressive
11、die design.However, at the design stage of strip layout, intermediate shape and boundary conditions of process are unknown. It is impossible to use finite element incremental approach to simulate the sheet metal forming at each step (Jian et al.,2002).And the most important thing for the designer is
12、 to calculate the intermediate shapes and to predict the formability of each step from the final shape of the part to initial blank. Up to now, the inverse approach(IA)(Guo et al.,1990,2000,2001;Naceur et al.,2001)or one step(Lee and Huh,1998)is a better solution for the problem. But the inverse app
13、roach can only calculate the initial shape from the final shape without taking into account intermediate forming process, and sometimes there is a big error even wrong result for complex shape, especially at upright wall or undercut conditions.Many authors used the IA to predict the initial blank sh
14、ape of the complete part, and it is an effective method for many stamping part with simple process. But for complicated forming parts or progressive die stamping parts, the intermediate forming process has great effect on the initial blank shape, and it is difficult to set the boundary conditions fo
15、r different local forming areas with complete unfolding. It is feasible method to calculate inversely the local forming area according to the practical forming processes step by step, and the upright wall or undercut conditions can be avoided to some extent.In the sheet metal forming simulation syst
16、em, FASTAMP (Yuqi et al.,2004),a multi-step unfolding method(MSUM) is developed to assist the progressive die design. Firstly, a finite element model of the inverse approach is developed at a local area according to the stamping process, and the intermediate shape is unfolded inversely from final sh
17、ape to initial shape on a reference surface at each step. In calculation model, the reference surface may be generated according to the process and feature surface. The influences of stamping process such as the connection, blank-holder force, the friction and the offsetting of the strain neutral la
18、yer with different radius of curvature at local area, are also considered. Then these shapes are assembled into a strip layout. The forming defects can be predicted with the numerical results and the optimum blank shape also can be generated using the unfolding method.In this paper, some finite elem
19、ent aspects in the IA are recalled firstly. One example is illustrated to the blank design of a progressive die stamping part, and the initial shape of another example is compared with experimental and other numerical results.2.Some finite element aspects in MSUMThe finite element model of MSUM is b
20、ased on IA. The details of the finite element formulation can be found in the papers (Guo et al.,1990,2000;Naceur et al.,2001).The mixed element types of DKT (Batoz et al.,1980) and DKQ(Batoz et al.,2000)with bending effect are used in the analytical model to improve the calculation precision. The t
21、reatments(Yuqi and Junhua,2006)of the boundary conditions such as displacement constraint and external nodal force transformed from blank-holder force, friction force and the total restraining force of draw bead are introduced to improve the conditioning of the tangent stiffness matrix Using MSUM at
22、 the local area, the upright wall or undercut conditions will become weak with practical stamping direction, the conditioning of tangent matrix will be increased and the convergence speed is improved. 3.The procedure of MSUMA typical progressive die part (Fig.1) and the strip layout(Fig.2) are desig
23、ned with the progressive die wizard(PDW)in UG NX software. At the process design stage, only the final shape is known and the intermediate shape should be designed according to the process requirements and shape features. For example, it is necessary to cut the sheet on the intermediate reference su
24、rface and then to flange it at the flanging design process. If there is a large deformation at flanging area, it is necessary to calculate the cutting line precisely and previously. Moreover, if there will be a large deformation at local area, such as drawing, flanging or bulging ,it is very useful
25、to estimate formability and check process conditions in advance, which is helpful to avoid forming defects, such as rupture and severe wrinkling. Therefore, progressive die design process is a difficult and complex task even for rich experienced engineers.A MSUM based on the inverse approach is prop
26、osed against the difficulty of progressive die design. The intermediate shape and cutting lines are calculated with process and shape features. The formability can also be estimate with the numerical results. The method mainly involves the following detailed techniques:3.1. Intermediate reference su
27、rfaceIn the calculation model, most of the intermediate reference surface can be calculated automatically according to shape features at local forming area. For example, the reference surface can be generated at the tangent direction along the border of forming area. If the forming process is more c
28、omplicated, the surface can also be generated manually with experience. However, it is difficult to design the intermediate shape of each step in the opposite sequence of processing step from final shape to initial blank shape, especially for complex shape and forming process. When design the shape
29、at current step, the reference surface should be generated from the shape of previous step and the formability should be validated to avoid defects. Sometimes not only the shape and forming process of current step but also the shapes of previous steps must be modified.At the design stage of progress
30、ive die stamping part, the design engineers can generate relatively easily the intermediate reference surface with the CAD software, such as UGNX and CATIA. It is difficult to predict precisely the intermediate shape on the reference surface. Up to now, although there are many authors try to optimiz
31、e the shape of the intermediate reference surface with many optimization algorithms, the algorithms are only suit to the specific shape part and the optimization time is too long, which is unable to meet the application requirements. Currently the intermediate reference surface is generated by the d
32、esigners and the intermediate shape is calculated using IA.3.2. Process conditionsIn the finite element model, many process conditions can be considered. For example, the fixed constrains will be added at the nodes to assume that the relative displacement is very little at the connection area. At be
33、nding or flanging area, the influences of blank-holder force and friction are considered to simulate the deformation of sheet metal. For large deformation at local area, the conditions treatment is different between deep drawing and bulging. If the forming process is bulging, the restraint force or
34、blank-holder force at flanging area is very big, the material of sheet metal is almost stiff, even fixed. If the forming process is deep drawing, the restraint force or blank-holder force at flanging area is relatively slightly, the material can flow at flanging area. In MUSM, the constraint or big
35、blank-holder force should be added on the nodes at flanging area for bulging deformation. And the proper blank-holder force will be added to corresponding nodes.3.3. Strain neutral layer offsettingAs shown in Fig.3,the strain neutral layer(SNL)(Yingping and Jun,2002)will offset from the geometry neu
36、tral layer(GNL) to an inner layer along radial direction. Neutral layer offsetting has a great influence on the blank shape size especially when the rate between the thickness and radius of curvature is bigger. When considering the SNL offsetting in MSUM, the shape size calculated and the experiment
37、al result will be more closely.3.4. Procedure of MUSMAs we know, material of sheet metal will flow in a different way for different stamping process, and the formability of the final part will be also different. The sequence of MUSM must meet with the requirement of actual stamping process in strip
38、layout. Therefore, the stamping process must be designed firstly according to the geometry feature and process requirement of the final part. Secondly, the intermediate shape will be calculated using MUSM. And the formability will be evaluated to avoid the defects such as crack and wrinkling. The re
39、ference surface and boundary conditions should be modified until the formability is perfect.Sometimes the surface should be modified again if the shapes calculated at previous steps are not good from the full view of the strip layout. Finally, the optimum strip layout will be obtained after modify t
40、he stamping process many times.3.5. Formability analysisThe distribution of various physical quantities and the deformation of the inner holes can be calculated with the results. And the formability can be predicted to assist the design of the stamping process.3.6. LimitationsThe influence of restri
41、king and springback are ignored during unfolding process, and there are errors of the simulation result for the choice of shell element, which cannot simulate the deformation of restriking and springback precisely.4.Examples4.1. Example 1:Aided design of strip layoutAs shown in Fig.4(a),the dominati
42、ng forming process of a progressive die forming part involves bulging, bending, flanging and restriking. The strip layout is assembled with six key intermediate shapes (Fig.2)and other auxiliary shapes. As shown in Fig.4(bg),the operation of MSUM is six steps. As show in Fig.4(a),the counterpart of
43、final shape is the 17th step in strip layout(Fig.2).As shown in Fig.4(a),H is at the connection area and the fixed constraint will be added on the nodes at this area. The material of the part is SPCC and the initial thickness is 0.75 mm.1st step. As shown in Fig. 4(b), the bending area(Fig.4(a), D a
44、rea)will be unfolded. The counterpart shape is the 15th step in strip layout. Before bending at this local area, the cutting line will be calculated and then to bend the sheet metal. So, when unfolding the local bending area, the intermediate shape will be projected on the reference surface(plane su
45、rface at current step)at the previous step. The offsetting of strain neutral layer is calculated. At the local area, the bending radius is 1.5 mm, the offsetting size is 0.03 mm with the theoretical formula (Shuobeng et al.,2002).The error between the size of cutting line with offsetting and the exp
46、erimental result is relatively little.2nd step. As shown in Fig.4(c),the flanging area(Fig.4(a), C and E area)will be unfolded. The counterpart shape is the 13th step in strip layout. When unfolding the flanging area, the reference surface is calculated automatically with the feature surface of prev
47、ious unfolding shape. Generally, the reference surface is extruded from the boundary curves (feature curves) in the tangent direction of the feature surface. As shown in Fig.5, the flanging contains compression deformation and stretch forming, and it is difficult to determine the cutting line on the
48、 3D reference surface with experience.Many physical quantities can be obtained with the result, such as the distribution of stress, strain, thickness and forming limited diagram(FLD).As shown in Fig.6,the distribution of thickness strain show that the larger thickness thinning is 10.7% at the stretc
49、h deformation area with good formability, and the larger thickness strain is 10.7% at the compression deformation area with a little of wrinkle risk.3rd step. As shown in Fig. 4(d),the bending area(Fig.4(a), F area)will be unfolded. The counterpart shape is the 11th step in strip layout. The unfolding ope