# 考虑变形热和摩擦热效应的热力耦合冲压研究

1.湖南大学汽车车身先进设计制造国家重点试验室，长沙， 4100822.湖南湖大艾盛汽车技术开发有限公司，长沙， 410082

## 1 变形热及摩擦热理论

### 1.1 变形热机理及计算

1.1.1 应变能产生机理

(1)

(2)

Fig.1 Uniform tensile strain energy distribution

1.1.2 变形热转化机理

(3)

(4)

(5)

(6)

1.1.3 变形热应用机理

(7)

(8)

n=n0exp(-Cn(T-T0))

m=m0exp(-Cm(T-T0))

(9)

(10)

(11)

### 1.2 摩擦热机理及计算

1.2.1 摩擦热产生机理

(12)

(13)

1.2.2 变摩擦力模型

μ(p)=μ0(p/p0)np-1

(14)

Fig.2 Variable friction coefficient model at
different temperature

μ(θ)=(T0)(T/T0)nT+b

(15)

Fig.3 Variable friction coefficient model at
different pressures

μ(p,θ)=0(p/p0)np-1(θ/θ0)nT+b

(16)

(17)

### 1.3 热耗散与热传递机理

(18)

T(x,y,z,t=0)=T0(x,y,z)

(19)

(1)第一类边界条件是指某给定表面上质点的温度值在传热过程中保持不变，即温度值为给定的边界条件，设该表面为S1，则表示为

T(x,y,z,t)=T0 (t>0,SS1)

(20)

(2)若物体表面S2给定热流密度q，则称之为第二类边界条件，即

(21)

(22)

(3)第三类边界条件。板料与模具温度升高后，高于室温的边界面与空气接触，即开始与环境对流换热，即

(23)

### 1.4 数值模拟应用方法

(24)

Q=Qp+Qc+Qd+Qf

(25)

(26)

(27)

Fig.4 Solutions considering deformation heat and
friction heat

## 2 双相钢热拉伸试验

### 2.1 热拉伸试验过程

Tab.1 Chemical composition of DP780
(mass fraction) %

Fig.5 MT5105 microcomputer controlled electronic
universal testing machine

Fig.6 Size of the tensile specimen

### 2.2 热拉伸试验结果

Fig.7 True stress-strain curve at 20 ℃

Fig.8 True stress-strain curve at 70 ℃

Fig.9 True stress-strain curve at 140 ℃

### 2.3 考虑温度的塑性本构方程的求解

(28)

n=0.215 4exp(-0.000 9(T-T0))
m=60.021 3exp(-0.007 9(T-T0))

## 3 数值模拟研究

### 3.1 变形热效应数值模拟研究

3.1.1 变形热数值模拟过程

Tab.2 Material parameters

3.1.2 变形热效应结果讨论

Fig.10 Stress distribution before fracture

Fig.11 Temperature distribution before fracture

Fig.12 Comparison of true stress-strain curve and
constitutive curve at the center of the specimen

### 3.2 热效应数值模拟研究

3.2.1 摩擦热数值模拟过程

(a)t=0.025 s (b)t=0.05 s

(c)t=0.075 s (d) t=0.1 s

Fig.13 Temperature change during the test

Tab.3 Mold parameter settings

3.2.2 摩擦热效应结果讨论

Fig.14 Temperature change with time at the
point of sheet

Fig.15 Reflexive forces under different
friction models

### 3.3 考虑热效应的冲压成形仿真

3.3.1 新式冲压成形方法

Fig.16 U-shaped stamping die pictures

3.3.2 新式冲压成形结果讨论

3.3.2.1 冲压过程温度变化

(a)t=0.25 s (b)t=0.5 s

(c)t=0.75 s (d) t=1.0 s

Fig.17 Temperature change of the stamping process
with fully thermal coupling

3.3.2.2 凸模力结果对比

Fig.18 Comparison of punch force changes

3.3.2.3 回弹结果对比

(a)考虑热效应

(b)不考虑热效应

Fig.19 Comparison of final stress distribution

(a)考虑热效应

(b)不考虑热效应

Fig.20 Side-view comparison of springback distribution

Fig.21 Comparison of springback calculation results

Fig.22 Stamping U-shaped part and maximum
springback measurement

Tab.4 Comparison of springback angle size

## 4 结论

(1)考虑变形热条件下的拉伸结果明显与恒温下的拉伸结果不同，热效应导致流变应力曲线低于恒温下的应力曲线，变形热导致金属塑性增强，且不可忽略不计。

(2)金属钣金冲压过程中摩擦区域的摩擦热近似与摩擦面的相对位移成正比增长，一旦脱离摩擦面，温升不再产生，产生的摩擦热对金属塑性存在明显的影响。

(3)将变形热和摩擦热同时考虑进模型中，通过钣金冲压热力耦合分析发现，同时考虑变形热和摩擦热的情况下，U形件的厚度变化更小，最终步长下的残余应力相对较小，且冲压所需的凸模力也更小。

(4)对计算模型下的U形件进行试制，对比两种模型下的回弹结果与实际回弹量贴合性,发现传统的冷冲压模型和考虑自发热效应的新式模型下分析的回弹结果差异明显，考虑自发热效应的模型下，侧壁回弹的准确率提高10.08%，法兰处回弹准确率提高23.26%，明显更加贴合实际生产的测量结果。

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# ResearchonThermal-mechanicalStampingFormingConsideringDeformationHeatandFrictionHeatEffects

NIE Xin1 XIAO Bingbing1 SHEN Danfeng2 GUO Wenfeng1

1.State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,Hunan University,Changsha，410082 2.Hunan Huda Aisn Automotive Technology Development Co.,Ltd.，Changsha,410082

Abstract The DP780 material was subjected to constant temperature tensile test in the temperature range of 20～140 ℃ and the strain rate range of 0.001～0.1s-1, and the true stress and strain change trends were analyzed. The constitutive equations of materials were established based on the Norton-Hoff model, which might better reflect the shaping constitutive relationship of DP780 during different cold forming processes. Combined with the Norton-Hoff constitutive model and friction model related to temperature and pressure，the combination of theoretical research and numerical simulation was used to study the mechanism and macroscopic characteristics of deformation heating and friction heating of DP780 steel plates. According to the theory of complete thermal coupling numerical simulation, considering the coupling analysis of temperature field, stress field and strain field, a research method of stamping was proposed considering deformation heat and friction heat effects. Through the stamping experiments, the forming results and springback characterization of DP780 steel plates applied to U-shaped parts were obtained. Comparing the simulation results of the traditional cold stamping and the new analytical method considering self-heating effects, it is found that the new stamping forming research method improves the accuracy by 10.1% on the sidewall and the accuracy by 23.2% at the flange.

Key words high-strength steel; stamping; Norton-Hoff constitutive model; deformation heat; friction heat; thermal-mechanical coupling

DOI：10.3969/j.issn.1004-132X.2020.16.014

(编辑 王艳丽)