基于多目标遗传算法的二自由度动力吸振器优化设计

doi:10.13229/j.cnki.jdxbgxb20180924

摘要/Abstract

摘要：

针对实际工况中常见的具有平移和绕质心转动两个自由度的无阻尼主系统，提出了一种二自由度动力吸振器，通过对吸振器刚度和阻尼的优化，使主系统获得良好的减振效果。用位移、加速度、角位移和角加速度对主系统振动进行评价并作为优化目标。采用带精英策略的非支配排序遗传算法（NSGA-Ⅱ）解决4个优化目标、3个设计变量的多目标优化问题，得到含有60个解的Pareto最优解集。用熵权TOPSIS法对Pareto最优解进行排序，选取最优解作为动力吸振器优化设计的解。对动力吸振器进行仿真分析，频域仿真结果和随机激励下的时域仿真结果表明：参数优化后的动力吸振器使得主系统的4个振动评价指标均大幅降低，二自由度动力吸振器的振动控制效果良好，NSGA-Ⅱ和熵权TOPSIS联合优化方法适用于二自由度动力吸振器的优化设计。

关键词: 机械设计, 二自由度动力吸振器, 多目标优化, 遗传算法, 多属性决策

Abstract:

This paper presents a 2-DOF dynamic vibration absorber to reduce the vibration of 2-DOF main system which possesses translation and rotation around the centroiding. The main system obtains a good damping effect by optimizing the stiffness and damping of the dynamic vibration absorber. The evaluation and optimization indexes are displacement, acceleration, angular displacement and angular acceleration. The nondominated sorting genetic algorithm (NSGA-Ⅱ) is used to solve the multi-objective optimization problem including four optimization objectives and three design variables. The 60 Pareto optimal solutions are ordered by entropy weight TOPSIS. The optimal solution is selected as the dynamic vibration absorber optimization design solution and a simulation analysis is carried out to obtain the frequency domain simulation results and time domain simulation results. The results show that the dynamic vibration absorber with optimized parameters greatly reduce the four vibration evaluation indexes of the main system and the vibration control effect of the two-DOF dynamic vibration absorber is good. The NSGA-Ⅱ and Entropy TOPSIS joint optimization method is suitable for optimal design of two-DOF dynamic vibration absorber.

Key words: mechanical design, two-DOF dynamic vibration absorber, multi-objective optimization, genetic algorithm, multi-attribute decision making

中图分类号:

TH113.1

贾富淳,孟宪皆,雷雨龙. 基于多目标遗传算法的二自由度动力吸振器优化设计[J]. 吉林大学学报(工学版), 2019, 49(6): 1969-1976.

Fu-chun JIA,Xian-jie MENG,Yu-long LEI. Optimal design of two degrees of freedom dynamic vibration absorber based on multi-objective genetic algorithm[J]. Journal of Jilin University(Engineering and Technology Edition), 2019, 49(6): 1969-1976.

图/表 9

图1

图2

图3

表1

决策结果"

序数	方案
序数	1	2	3	4	5
sum(max\|x ₁/f\|)/（10^-4 m·N^-1）	1.88	1.78	1.96	2	1.74
sum(max\|θ ₁/f\|)/（10^-4 rad·N^-1）	6.17	6.43	5.98	5.87	6.55
sum(max\| $x ¨$ ₁/f\|)/（10^-2 m·s^-2·N^-1）	6.43	6.25	6.58	6.64	6.2
sum(max\| $θ ¨ 1$ /f \|)/（rad·s^-2·N^-1）	1.217	1.31	1.146	1.107	1.35
k ₃/(10⁴ N·m^-1)	2.865	2.47	3.074	3.335	2.387
k ₄/(10⁴ N·m^-1)	1.019	1.015	1.019	1.015	1.014
c/(10³ N·s·m^-1)	1.296	1.291	1.443	1.438	1.241
综合评价指数方正汇总行C	0.153	0.154	0.155	0.156	0.162

表1

图4

图5

表2

幅频特性峰值"

幅频特性	峰	幅频特性峰值/dB
幅频特性	峰	主系统	附加DVA	降幅
max\|x ₁/f \|	1	-85.5	-172.1	86.6
max\|x ₁/f \|	2	-197.7	-242.1	45
max\|θ ₁/f \|	1	-85.4	-107.9	22
max\|θ ₁/f \|	2	-154.7	-172.3	17.6
max\| $x ¨$ ₁/f \|	1	29.42	-59.9	88.9
max\| $x ¨$ ₁/f \|	2	-39.50	-84.7	45.2
max\| $θ ¨ 1$ /f \|	1	29.5	-60.2	89.7
max\| $θ ¨ 1$ /f \|	2	50.2	3.1	46.9

表2

图6

图7

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