Measurement of radial rotation error of electric spindle based on vibration response reconstruction

doi:10.3785/j.issn.1008-973X.2025.04.020

Journal of ZheJiang University (Engineering Science)

2025, Vol. 59

Issue (4): 842-852 DOI: 10.3785/j.issn.1008-973X.2025.04.020

Measurement of radial rotation error of electric spindle based on vibration response reconstruction

Jiahao RUAN1,2(

),Weimin KANG1,2,Jianzhong FU1,2,*(

)

1. School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China
2. Key Laboratory of 3D Printing Process and Equipment of Zhejiang Province, Hangzhou 310027, China

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Abstract

Existing methods of measuring radial rotation error of the electric spindle apply to low rotational speeds and fail to realize the online measurement of the machining process. The intrinsic mechanism of the vibration response and radial rotation error of a machine tool electric spindle was studied, the mechanism of online measurement of radial rotation error by vibration reconstruction of the electric spindle was revealed, and a new method of online measurement of radial rotation error by vibration signal was proposed for the electric spindle under high-speed rotation. The vibration response of the mandrel was reconstructed from the vibration signals collected from the electric spindle housing by modal expansion equation. During the reconstruction process, the initial extraction of the modal vibration pattern of the spindle was realized by finite element simulation, the modal vibration pattern was corrected by modal vibration experiment, and a mathematical model of the vibration response of the mandrel and radial rotation error of the spindle was established to realize the solution of the radial rotation error of the spindle. Comparison tests were conducted with the three-point method of spindle radial error measurement. Results showed that the error of the proposed method was within 6.49% at electric spindle speeds below 10 000 r/min. The proposed method provides a technical path for realizing the online measurement of the radial rotation error of the electric spindle during the machining process of CNC machine tools.

Key words： CNC machine tool electric spindle radial rotation error vibration response reconstruction modal extension

Received: 31 January 2024 Published: 25 April 2025

CLC:

TH 113.1

Fund: 浙江省自然科学基金资助项目（DT23E0501，DT23E050005）；国家自然科学基金资助项目（52175440）；浙江省科技计划项目（2023C01059）.

Corresponding Authors: Jianzhong FU E-mail: 22125091@zju.edu.cn;fjz@zju.edu.cn

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Cite this article:

Jiahao RUAN,Weimin KANG,Jianzhong FU. Measurement of radial rotation error of electric spindle based on vibration response reconstruction. Journal of ZheJiang University (Engineering Science), 2025, 59(4): 842-852.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.04.020 OR https://www.zjujournals.com/eng/Y2025/V59/I4/842

基于振动响应重构的电主轴径向回转误差测量

现有测量电主轴径向回转误差的方法适用于低转速，无法实现加工过程的在线测量. 开展机床电主轴振动响应与径向回转误差的内在机理研究，揭示电主轴振动重构在线测量径向回转误差机制，提出电主轴在高速转动下通过振动信号获取在线测量径向回转误差的新方法. 应用模态扩展方程，基于电主轴机壳上采集的振动信号，重构芯轴的振动响应. 在重构过程中，利用有限元仿真实现电主轴模态振型初步提取，采用模态振型实验校正电主轴模态振型，建立芯轴振动响应与电主轴径向回转误差的数学模型，实现电主轴径向回转误差的求解. 对比实验结果表明，相比主轴径向误差测量的三点法，所提方法在主轴转速低于10 000 r/min时，误差不超过6.49%. 所提方法为实现数控机床加工过程中电主轴径向回转误差在线测量提供了技术路径.

关键词： 数控机床, 电主轴, 径向回转误差, 振动响应重构, 模态扩展

Tab.1 Material-mechanical property parameters of key components of electric spindle

Fig.1 First two orders of modal vibration pattern of electric spindle

Fig.2 Excitation experiment setup

Fig.3 Accelerance frequency response function diagram

Tab.2 Inherent frequency of each order before and after modification of finite element model of electric spindle

Fig.4 Arrangement of measurement points of electric spindle sensor

Fig.5 Variation of rate of change of Fisher information matrix 2-norm with modal analysis order for different spindle vibration directions

Fig.6 Schematic rationalization of effect of rotational speed on modal vibration pattern

Fig.7 Size distribution of mandrel reconfiguration points

Fig.8 Axis fitting schematic

Fig.9 First six orders of vibration pattern of electric spindle mandrel

Fig.10 Calculation method of rotation error

Fig.11 Modal vibration pattern correction test rig

Fig.12 Knocking position of force hammer

Fig.13 Comparison of reconstructed and measured responses

Fig.14 Comparison of reconstruction errors of vibration response at different reconstruction points (before modal vibration pattern correction)

Fig.15 Flowchart of modal vibration pattern correction algorithm for electric spindle housing

Fig.16 Comparison of reconstruction errors of vibration response at different reconstruction points (after modal vibration pattern correction)

Fig.17 Test program for modal vibration pattern correction of electric spindle mandrel

Fig.18 Modal vibration pattern of electric spindle mandrel

Fig.19 Polar coordinates of repeated measurement part of vibration response reconstruction method

Tab.3 Measured values of radial rotation error by vibration field reconstruction method for tested electric spindle

Fig.20 Distribution of measurement results of vibration response reconstruction method at different rotational speeds of electric spindle

Tab.4 Measurement results of radial rotation error of electric spindle vibration response reconstruction method

Fig.21 Test rig for high rotational speed three-point method

Fig.22 Distribution of measurement results of three-point method at different rotational speeds of electric spindle

Tab.5 Measurement error results of vibration response reconstruction method of measured electric spindle at different rotational speeds


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