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

Abstract

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

CLC Number:

TG659

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.

Figures/Tables 18

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Table 1

Stiffness of spindle-holder joint"

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

Table 1

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Table 2

Table 3

Fig.11

Fig.12

Table 4

Revised calculation result of spindle-holder joint"

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

Table 4

Table 5

Fig.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

Dynamic modeling and parameter updating of machine tool spindle system based on response surface methodology and genetic algorithm

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