基于响应面与遗传算法的主轴系统动力学建模及参数修正

doi:10.13229/j.cnki.jdxbgxb20210311

摘要/Abstract

摘要：

针对在建立主轴系统的动力学模型时采用简化处理带来较大的误差问题，提出了一种融合响应面与遗传算法的主轴系统动力学建模方法。首先，考虑切削过程中主轴与刀柄之间的结合面刚度以及主轴轴承的支撑刚度，建立主轴系统的动力学模型；其次，通过对比刚性连接和柔性连接时主轴系统的前三阶固有频率，分析影响主轴系统动力学特性的主要因素；然后，基于主轴系统的动力学模型构造接触刚度的样本点，以样本点中的主轴与刀柄的结合面刚度作为输入参数，主轴系统的一阶、二阶和三阶固有频率作为输出参数，采用非参数回归方法构造响应面模型，利用决定系数和均方根误差的相对值检验响应面的精度；最后，通过多目标遗传算法修正主轴-刀柄结合面的刚度，以此为基础修正主轴系统的动力学模型，从而提高主轴系统动力学模型的精度。以某主轴系统为例，通过对比修正前后的分析精度，验证基于响应面和遗传算法的主轴动力学分析的准确性。

关键词: 主轴系统, 动力学分析, 响应面, 多目标遗传算法

Abstract:

Considering that the simplified processing in the process of establishing the dynamic model of the spindle system will lead to a large error， a dynamic modeling method based on response surface and genetic algorithm is proposed. Firstly， the dynamic model of the spindle system is established by considering the stiffness of the spindle-holder joint surface and the bearing support stiffness. Secondly， the main factors that affect the accuracy of dynamics analysis are developed by comparing the first three natural frequencies of the spindle system model with rigid and flexible connections. Then， sample points of contact stiffness are constructed based on the dynamics model of the spindle system， and the stiffness of the spindle-holder joint in the sample point is used as the input parameter， then the first， second， and third order natural frequency are used as the output parameters， and the non-parametric regression method is used to fit the response surface. The relative value of the determination coefficient and the root mean square error is used to test the accuracy of the response surface. The multi-objective genetic algorithm is used to update the stiffness of spindle-holder joint， which is used to update the dynamic model of the spindle system. Finally， a case study shows that the proposed method based on the fusion response surface methodology and optimization algorithm has higher analysis accuracy.

Key words: spindle system, dynamics analysis, response surface, multi-objective genetic algorithm

中图分类号:

TG659

陈传海,姚国祥,金桐彤,申桂香,于立娟,田海龙. 基于响应面与遗传算法的主轴系统动力学建模及参数修正[J]. 吉林大学学报(工学版), 2022, 52(10): 2278-2286.

Chuan-hai CHEN,Guo-xiang YAO,Tong-tong JIN,Gui-xiang SHEN,Li-juan YU,Hai-long TIAN. Dynamic modeling and parameter updating of machine tool spindle system based on response surface methodology and genetic algorithm[J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(10): 2278-2286.

图/表 18

图1

图2

图3

图4

图5

表1

主轴-刀柄结合面的刚度"

参数	接触刚度/（N·m^-1）	参数	转动刚度/（N·m^-1）
k₁_xk₁_y	1.5×10⁷	$k 1 ψ k 1 θ$	1.66×10⁴
k₂_xk₂_y	1.22×10⁷	$k 2 ψ k 2 θ$	1.38×10⁴
k₃_xk₃_y	9.95×10⁷	$k 3 ψ k 3 θ$	1.15×10⁴
k₄_xk₄_y	8.07×10⁷	$k 4 ψ k 4 θ$	9.62×10³

表1

图6

图7

图8

图9

图10

表2

表3

图11

图12

表4

修正后的主轴-刀柄结合面刚度"

参数	接触刚度/（N·m^-1）	参数	转动刚度/（N·m^-1）
k₁_xk₁_y	9.28×10⁶	$k 1 ψ k 1 θ$	3.5×10⁴
k₂_xk₂_y	5.77×10⁶	$k 2 ψ k 2 θ$	3.04×10⁴
k₃_xk₃_y	2.917×10⁶	$k 3 ψ k 3 θ$	2.3×10⁴
k₄_xk₄_y	5.212×10⁶	$k 4 ψ k 4 θ$	2.21×10⁴

表4

表5

图13

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验证条件	一阶频率	二阶频率	三阶频率
相对误差/%	30.3	15.5	35.4
仿真值/Hz	395	1157	1414
试验值/Hz	303	1002	1044

验证条件	一阶频率	二阶频率	三阶频率
相对误差/%	23.7	16.1	28.4
仿真值/Hz	231	1163	1341
试验值/Hz	303	1002	1044

验证条件	一阶频率	二阶频率	三阶频率
相对误差/%	4.6	5.59	3.2
优化后的仿真值/Hz	289	1058	1077
实验值/Hz	303	1002	1044