﻿ T形管内高压成形过程加载路径的优化方法
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 哈尔滨工程大学学报  2020, Vol. 41 Issue (6): 929-936  DOI: 10.11990/jheu.201901021 0

### 引用本文

FENG Yingying, LUO Zongan, ZHANG Hongge, et al. Optimization method for the loading path of a T tube in the hydroforming process[J]. Journal of Harbin Engineering University, 2020, 41(6): 929-936. DOI: 10.11990/jheu.201901021.

### 文章历史

T形管内高压成形过程加载路径的优化方法

1. 东北大学 轧制技术及连轧自动化国家重点实验室, 辽宁 沈阳 110819;
2. 一汽轿车股份有限公司, 吉林 长春 130012

Optimization method for the loading path of a T tube in the hydroforming process
FENG Yingying 1, LUO Zongan 1, ZHANG Hongge 2, MAO Lanyu 1
1. State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110819, China;
2. FAW CAR Co., Ltd., Changchun 130012, China
Keywords: T tube    hydroforming    loading path    numerical simulation    orthogonal test    BP neural network    average performance index function    intelligent optimization

1 材料和方法

1.1 材料特性

1.2 有限元模型的建立

 Download: 图 1 T形管有限元分析模型 Fig. 1 Finite element analysis model of T tube

1.3 加载路径的智能控制方法

1.3.1 加载路径初始值的确定

 Download: 图 2 正交试验优选区域 Fig. 2 The drawing of orthogonal test preferred area
1.3.2 智能控制方法

 $Q_j^{(1)} = x(j),j = 1,2, \cdots ,M$ (1)

 ${\rm{ net}} _i^{(2)}(k) = \sum\limits_{j = 1}^M {\omega _{ij}^{(2)}} Q_j^{(1)}$ (2)
 $Q_i^{(2)}(k) = f({\rm{ net }}_i^{(2)}(k)),i,j = 1,2, \cdots ,M$ (3)

 ${ {\rm{net}} _l^{(3)}(k) = \sum\limits_{i = 1}^Q {\omega _{li}^{(3)}} \cdot Q_i^{(2)}(k)}$ (4)
 ${Q_l^{(3)}(k) = g( {\rm{net}} _l^{(3)}(k))}$ (5)
 $\begin{array}{l} Q_1^{(3)}(k) = {T_{{\rm{max}}}};Q_2^{(3)}(k) = {T_{{\rm{min}}}};\\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} Q_3^{(3)}(k) = H;Q_4^{(3)}(k) = S \end{array}$ (6)

 ${E{{(k)}_1} = \frac{1}{2}{{({r_1}(k) - {y_1}(k))}^2}}$ (7)
 ${E{{(k)}_2} = \frac{1}{2}{{({r_2}(k) - {y_2}(k))}^2}}$ (8)
 ${E{{(k)}_3} = \frac{1}{2}{{({r_3}(k) - {y_3}(k))}^2}}$ (9)
 ${E{{(k)}_4} = \frac{1}{2}{{({r_4}(k) - {y_4}(k))}^2}}$ (10)

 $E(k) = \frac{1}{4}(E{(k)_1} + E{(k)_2} + E{(k)_3} + E{(k)_4})$ (11)

 $\Delta \omega _{{\rm{li}}}^{(3)}(k) = - \eta \cdot \frac{{\partial E(k)}}{{\partial \omega _{{\rm{li}}}^{(3)}}} + \alpha \Delta \omega _{{\rm{li}}}^{(3)}(k - 1)$ (12)

 $\Delta \omega _{li}^{(3)}(k) = \alpha \Delta \omega _{li}^{(3)}(k - 1) + \eta \delta _1^{(3)}Q_i^{(2)}(k)$ (13)
 $\begin{array}{l} \delta _l^{(3)} = {\rm{error}} (k) \cdot {\rm{sgn}} \left( {\frac{{\partial y(k)}}{{\partial \Delta u(k)}}} \right) \cdot \frac{{\partial \Delta u(k)}}{{\partial Q_l^{(3)}(k)}} \cdot \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {g^\prime }( {\rm{net}} _l^{(3)}(k)),l = 1,2,3 \end{array}$ (14)
 ${g^\prime }( \cdot ) = g(x) \cdot (1 - g(x))$ (15)

1.3.3 智能控制方法在有限元仿真中的应用

 $S = \pi {\left( {\frac{{{D_1}}}{2} - {R_2}} \right)^2}$ (16)

 Download: 图 3 T形管示意图以及支管与背向冲头之间的接触面积 Fig. 3 The schematic of T shaped tube and contact area between branch tube and back punch

 Download: 图 4 自适应仿真与基于遗传算法的BP神经网络控制算法流程 Fig. 4 Flow chart of adaptive simulation and BP neural network control algorithm based on genetic algorithm 注：L为轴向进给；P为内压力；B为背向位移；S为支管顶部和背向冲头的接触面积。
2 有限元模拟的结果和讨论

 Download: 图 6 优化前后路径A的管材内高压成形极限 Fig. 6 Tube hydroforming limit diagram of path A before and after optimization
 Download: 图 7 优化前后圆角切线两点与支管高度之间的距离 Fig. 7 The distance between two points of the fillet tangent and height of branch tube before and after optimization
 Download: 图 8 加载路径A优化前后的壁厚度分布 Fig. 8 The tube wall thickness distribution of path A before and after optimization
 Download: 图 9 加载路径A优化前后的主应变分布 Fig. 9 The tube principal strain distribution of path A before and after optimization

3 模拟结果验证实验

 Download: 图 10 200 MPa内高压成形机 Fig. 10 The 200 MPa hydroforming machine

 Download: 图 11 有限元模拟的截面厚度分布图和实验样品的截面 Fig. 11 The axial section thickness distribution of finite element simulation and experimental sample
4 结论

1) 将背向位移纳入加载路径的主要因素，有效缓解了支管顶端边部减薄，避免支管破裂等缺陷的发生。

2) 采用正交试验方法确定加载路径的初始值，采用基于遗传算法的BP神经网络控制方法优化T形管的加载路径，通过建立平均性能指标函数，优化了学习效率，提高了计算精度。此方法可以有效解决T形管内高压成形过程加载路径的匹配和优化问题。

3) 通过实验验证，模拟与实验结果的误差精度在±5%以内，说明此方法具有较高的精度和可行性。