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 应用科技  2018, Vol. 45 Issue (5): 22-25  DOI: 10.11991/yykj.201711013 0

### 引用本文

XU Jian'an, GAO Xin, HU Faguo, et al. Optimization of the frame of towing winch based on multi-objective topology optimization[J]. Applied Science and Technology, 2018, 45(5), 22-25. DOI: 10.11991/yykj.201711013.

### 文章历史

1. 哈尔滨工程大学 机电工程学院，黑龙江 哈尔滨 150001;
2. 武汉船用机械有限公司 技术中心，湖北 武汉 430084

Optimization of the frame of towing winch based on multi-objective topology optimization
XU Jian'an1, GAO Xin1, HU Faguo2, ZHANG Yongyong2, QU Dongyue1
1. College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China;
2. Technique Center, Wuhan Marine Machinery Plant Co., Ltd., Wuhan 430084, China
Abstract: In view of the structure optimization problem of large towing winch in ships, this paper presents a multi-objective topology optimization method for conceptual design of the frame of large towing winch. The optimization objective for the frame of towing winch mainly includes three aspects: weight, stiffness, and natural frequency. Derive the optimal solution and the worst solution respectively in these three aspects, and calculate the object function by compromise programming method, realizing the multi-objective topology optimization of the frame structure of towing winch under complicated working condition. The frame of towing winch after optimization is improved to a certain extent in aspects of mass, stiffness and natural frequency. The optimization results show utility of the dynamic and static multi-objective topology optimization method in the design process of marine equipment, providing a theoretical reference for the structure optimization design of marine equipment.
Keywords: multi-objective    towing winch    compromise programming method    quality    frame    natural frequency    compliance    topology optimization

1 静载荷多工况拓扑优化

 \begin{aligned}C\left( X \right) = & {\left( {\sum\limits_{K = 1}^m {\omega _k^q{{\left( {\frac{{{C_x}\left( X \right) - C_k^{\min }}}{{C_k^{\max } - C_k^{\min }}}} \right)}^q}} } \right)^{\frac{1}{q}}} = \\& \left( {\omega _1^q} \right.{\left( {\frac{{{C_1}\left( X \right) - C_1^{\min }}}{{C_1^{\max } - C_1^{\min }}}} \right)^q} + \cdots + \\& {\left. {\omega _m^q{{\left( {\frac{{{C_m}\left( X \right) - C_m^{\min }}}{{C_m^{\max } - C_m^{\min }}}} \right)}^q}} \right)^{\frac{1}{q}}}\end{aligned}

 $\begin{gathered} {\rm{Min}}:C\left( X \right) = {\left( {\sum\limits_{k = 1}^m {\omega _k^q{{\left( {\frac{{{C_k}\left( X \right) - C_k^{\min }}}{{C_k^{\max } - C_k^{\min }}}} \right)}^q}} } \right)^{\frac{1}{q}}} \\ \operatorname{s} .{\rm t}.\left\{ \begin{gathered} \sum\nolimits_{k = 1}^m {\left( {\sum\nolimits_{j = 1}^n {{V_j}x_j^k} } \right) - \overline V \leqslant 0} \\ 0 < {x_{\min }} \leqslant {x_j} < 1 \\ j = 1,2, \cdots ,n;k = 1,2, \cdots ,m \\ \end{gathered} \right. \\ \end{gathered}$ (1)

2 动态载荷拓扑优化

 $\left\{ \begin{gathered} \max :{\lambda _n} \\ {\rm{s}}{\rm{.t}}{\rm{.}}\left\{ \begin{gathered} \sum\nolimits_{j = 1}^n {{V_j}{x_j} - \overline V \leqslant 0,j = 1,2, \cdots ,n} \\ 0 < {x_{\min }} \leqslant {x_j} < 1,j = 1,2, \cdots ,n \\ \left( {{K} - {\lambda _n}{M}} \right){{\phi }_n} = \left\{ 0 \right\} \\ \end{gathered} \right. \\ \end{gathered} \right.$

3 静态与动态载荷联合多目标优化

 $\begin{array}{l}\min F\left( X \right) = \left( {\sum\limits_{k = 1}^m {{\omega _k}{{\left( {\displaystyle \frac{{{C_K}\left( X \right) - C_K^{\min }}}{{C_K^{\max } - C_K^{\min }}}} \right)}^2}} } \right. + \\{\kern 1pt}\;\;\; \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\left. {\;\left( {1 - \sum\limits_{k = 1}^m {{\omega _k}} } \right){{\left( {\displaystyle \frac{{{\varLambda _{\max }} - {\varLambda _\lambda }}}{{{\varLambda _{\max }} - {\varLambda _{\min }}}}} \right)}^2}} \right)^{\frac{1}{2}}}\end{array}$ (2)

4 拖缆机机架多目标优化设计 4.1 边界条件及载荷工况

4.2 优化结果