Journal of Jilin University(Engineering and Technology Edition) ›› 2022, Vol. 52 ›› Issue (10): 2278-2286.doi: 10.13229/j.cnki.jdxbgxb20210311

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

Chuan-hai CHEN(),Guo-xiang YAO,Tong-tong JIN,Gui-xiang SHEN,Li-juan YU(),Hai-long TIAN   

  1. Key Laboratory of CNC Equipment Reliability,Ministry of Education,Jilin University,Changchun 130022,China
  • Received:2021-03-06 Online:2022-10-01 Published:2022-11-11
  • Contact: Li-juan YU E-mail:cchchina@jlu.edu.cn;tallyu@163.com

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

Fig.1

Discretization of spindle system"

Fig.2

Spindle-holder joint model"

Fig.3

Spindle-holder joint unit"

Fig.4

Spindle-holder joint"

Fig.5

Measuring holder force with tension gauge"

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
k1xk1y1.5×107k1ψk1θ1.66×104
k2xk2y1.22×107k2ψk2θ1.38×104
k3xk3y9.95×107k3ψk3θ1.15×104
k4xk4y8.07×107k4ψk4θ9.62×103

Fig.6

Position between bearing roller and raceway"

Fig.7

Bearing stiffness varies with speed"

Fig.8

Natural frequency test of spindle"

Fig.9

FRF of spindle acceleration imaginary and real parts"

Fig.10

FRF of spindle acceleration imaginary and real parts after noise reduction"

Table 2

First three natural frequencies of the rigid connection of the spindle-holder joint"

验证条件一阶频率二阶频率三阶频率
相对误差/%30.315.535.4
仿真值/Hz39511571414
试验值/Hz30310021044

Table 3

First three natural frequencies of the flexible connection of the spindle-holder joint"

验证条件一阶频率二阶频率三阶频率
相对误差/%23.716.128.4
仿真值/Hz23111631341
试验值/Hz30310021044

Fig.11

Generation process of response surface"

Fig.12

Response surface fitting evaluation"

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
k1xk1y9.28×106k1ψk1θ3.5×104
k2xk2y5.77×106k2ψk2θ3.04×104
k3xk3y2.917×106k3ψk3θ2.3×104
k4xk4y5.212×106k4ψk4θ2.21×104

Table 5

Verification of the optimizing results"

验证条件一阶频率二阶频率三阶频率
相对误差/%4.65.593.2
优化后的仿真值/Hz28910581077
实验值/Hz30310021044

Fig.13

Comparison of spindle acceleration frequency response curve between modified model andtest"

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