外文资料
Application of Data Mining Method to Improve the Accuracy of Springback Prediction in Sheet Metal Forming
Xu Jing—ring(许京荆)，ZHANG Zhi—wei(张志伟)，Wu，Yi—min(吴益敏) School of Electrornechanical Engineering and Automation，Shanghai University，Shanghai 200072，P．R．China
Abstract: A new method was worked out to improve the precision of springback prediction in sheet metal forming by combining the finite element method(FEM)with the data mining(DM)technique．First the genetic algorithm (GA) was adopted for recognizing the materia1 parameters．Then according to the even design idea，the suitable calculation scheme was confirmed，and FEM was ud for calculating the springback．The computation results were compared with experiment data，the difference between them was taken as source data，and a new pattern recognition method of DM called hierarchical optimal map recognition method(HOMR)is applied for summarizing the calculation regulation in FEM ．At the end．the mathematics model of the springback simulation was established．Bad on the model，the calculation errors of springback can be controlled within 10％compared with the experimental results．
Key words :springback prediction，pattern recognition，genetic algorithm，FEM ，even design idea，H0MR，data mining．
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第2页 1 Introduction
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The springback in sheet metal forming can be described as the change of sheet metal shape compared with the shape of the tools after forming process. Sheet metals with high strength--to--modulus ratio such as high strength steels and aluminum alloys are particularly prone to springback ， and the materials are becoming more important in automotive industry to reduce the car weight and increa fuel efficiency ．The final component shape does not conform to the tool geometry due to the springback of parts ，so the die design becomes very difficult ．In order to compensate springback ，die tryout is required in current automotive die development and construction process ．Die designs and construction is one of the most time-consuming steps in new car-type developing process ．Therefore ， how to find an effective and reliable method for springback prediction is of great significance ．
Currently ，the finite element method(FEM )has been ud to calculate the springback of sheet met
绝望的亲情als in forming process[2-7],but the results of calculation are not correct ，and the calculation results of U —shape component show that the average error is 62％. It cannot be directly ud for die design ．房产经济人
There are a lot of nonlinear factors ，such as large deformation, friction, impact and materia1 characters, which will influence the sheet metal forming and springback. Becau the data mining technique is a good method to treat the complex factors and data,in order to predict the springback correctly in sheet metal forming , a new method is developed for springback prediction in the prent paper ．The FEM is ud to calculate the springback ．The computation results are compared with experimental data ，the difference between the two results is taken as source data, and a new HOMR pattern recognition method of data mining is adopted for summarizing the calculation orderliness in
FEM ．According to the hierarchical optimal map recognition method(HOMR)to build the
第3页 hyper-polyhedron model ，the mathematical model for the springback simulation is established ．Bad on the mathematical model ，the springback can be predicted and its errors can be controlled within 10％ compared with the experimental results ． 2 FEM Calculation Model
Sheet metal forming process is a typical topic related to impact and contact treatment, which refers to non-linear problems, such as large displacement ，large rotation , friction and contact[11] .From the mechanics viewpoint the forming process is a dynamic and interactive action of multi-body contact system ，and for the forming process ，the respon of the system vs the time has to be examined ．The respon can be determined by the following governing equation.
(1) Sheet metal forming process can be described by the dynamic equation ：ij i i f x σρρ+= （1） where ij σ is the Cauchy stress ，i f is the body force density ，i x is the acceleration ，and ρ is the current density.
(2)The solution of dynamic equation should satisfy the following traction boundary conditions ：
()ij j i n t t σ= （2）
奶酪和黄油的区别Where j n ，j =1，2，3，is the unit outward normal to current boundary ，and i t ，i = 1，2，3，is the surface force.
(3)The displacement boundary condition can be expresd as follows ：
画小狗()(),i j x a t D t = （3）
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where ()i D t ，i =1，2，3，are the given displacement functions ，and (),i j x a t are the initial coordinates of particle j a at moment t ．
(4)The contact discontinuity condition along the sliding contact surface area is
()0ij ij j n σσ+
--= （4）
According to the above equation and boundary conditions ，a formula can be obtained by the principle of virtual work ，given as
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i i ij i j i i i i V V V S x x dV x dV f x dV t x dS δπρδσδρδδ=+--=⎰⎰⎰⎰ (5)
where δπmeans virtual work ．i x δ is virtual displacement ，I S is the boundary of surface force ．
手机声音小After discretization ， the following equation can be solved by the FEM ：
()()(),,Mx
修心修身
t P x t F x x =- （6） where M is the global mass matrix ，()x
t is the vector of global nodal acceleration,P is the vector of global forces(including nodal forces ，surface loads and body
loads)，and F is the vector of equivalent nodal forces compod by element stress ，x
means the vector of velocity ．
3 Mathematical Model of Springback Prediction in Sheet
Metal Forming
3.1 The parameters lection for FEM calculation
Metal stamping process includes forming and springback．The stress status of the two steps are different．So the simulation techniques for the two steps are also different in the application of FEM .
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First．the dynamic explicit method is ud for calculating the forming，and then the previous calculation results are input to calculate the springback with the static implicit method adopted．According to this procedure the computation efficiency is improved．But the final calculation results are different from the experimental results due to different inputting parameters in the FEM calculation．In order to study the effect of inputting parameters on the FEM results, the appropriate parameters should be lected. The following five parameters，such as the virtual stamping speed v，the penalty factor fc，the ratio of die mesh density to blank mesh density ed,the ratio of die fillet radius to blank mesh density eb，and the friction coefficient f，are examined．
3.2 Determining the source data
(1) Determination of material model coefficients and FEM calculation
Bad on the stamping experiment in Fig.1, a quarter of experiment device is taken for the FEM calculation as shown in Fig.2.
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The stamping experiment was carried out on the Zwick testing machine．The
