Operation Modal Analysis Method of Gear Grinding Machine Spindle Operations under Complex Working Conditions

doi:10.3969/j.issn.1004-132X.2026.01.006

Abstract

Abstract:

Aiming at the problems that the spindle vibrations in grinding machines were complex and the modal characteristics were difficult to effectively identified under the service states. Based on adaptive noise complete ensemble empirical mode decomposition and correlation analysis， a method was proposed. The finite element modal analysis was used to define the frequency band range， and the wavelet threshold classification method was used to retain the modal feature information. In order to identify and eliminate the harmonic response generated by rotor， a method was used in signal cepstrum editing. Different noise reduction methods and 2-DOF examples show that the modal identification errors are reduced to 1.3% after processing by the proposed method， the fitting order is reduced 76.7% as the poles are stable， and the modal characteristics of the rotating parts are accurately identified for the machine tool in service.

Key words: operational modal analysis, complete ensemble empirical mode decomposition with adaptive noise, wavelet threshold grading criterion, cepstrum editing, grinding machine, parameter identification

摘要：

针对磨齿机主轴服役状态下振动形式复杂、模态特征难以有效识别的问题，提出一种基于自适应噪声完备集合经验模态分解与相关性分析的方法。采用有限元模态分析方法定义频带范围，采用小波阈值分级法保留模态特征信息。采用倒频谱法编辑信号，以识别并剔除转子产生的谐波响应。不同降噪方法与二自由度算例的验证结果表明，所提方法处理后的模态识别误差减小至1.3%，极点稳定时的拟合阶次降低76.7%，可准确识别服役状态下机床旋转部件的模态特征。

关键词: 工作模态分析, 自适应噪声完备集合经验模态分解, 小波阈值分级准则, 倒频谱编辑, 磨齿机, 参数识别

CLC Number:

TH133.2

LI Guolong, ZHAO Xiaoliang, WANG Yu, TAO Yijie. Operation Modal Analysis Method of Gear Grinding Machine Spindle Operations under Complex Working Conditions[J]. China Mechanical Engineering, 2026, 37(1): 51-59.

李国龙, 赵晓亮, 王玉, 陶一杰. 复杂工况下磨齿机主轴运行模态的分析方法[J]. 中国机械工程, 2026, 37(1): 51-59.

Figures/Tables 19

Fig.1 Cepstrum editing process

Fig.2 Process of modal parameter identification for a gear grinding machine spindle

Fig.3 Spindle finite element model

Tab.1 The first three natural frequencies and vibration modes

阶次	频率/Hz	振型
1	97.264	主轴中部摆动
2	178.522	主轴沿X轴负晃动
3	221.521	主轴左端沿X轴负晃动，变形明显

Fig.4 The first three order formation diagram of the spindle mode

Tab.2 The first three order modal parameters of gear grinding machine spindle

阶次	频率/Hz	阻尼比/%
1	96.178	1.02
2	179.633	0.45
3	225.873	0.64

Fig.5 Time and frequency domain diagram of initial vibration signal

Fig.6 Vibration signal CEEMDAN decomposition results

Tab.3 The correlation coefficient of IMF components

分量	相关系数C	分量	相关系数C
IMF₁	0.7344	IMF₈	0.0684
IMF₂	0.4428	IMF₉	0.1225
IMF₃	0.3946	IMF₁₀	0.0958
IMF₄	0.2811	IMF₁₁	0.0239
IMF₅	0.1914	IMF₁₂	0.0129
IMF₆	0.1781	IMF₁₃	0.0059
IMF₇	0.1006	IMF₁₄	0.0085

Fig.7 Signals before and after hierarchical noise reduction

Fig.8 Signal frequency domain diagram of different noise reduction processing

Tab.4 Second-order modal parameters of the simulation system

参数	一阶	二阶
固有频率/Hz	30.835	49.932
阻尼比/%	1.0	2.0

Fig.9 Self-power spectrum under harmonic interference

Fig.10 Simulation system signals before and after cepstrum editing

Fig.11 SSI-DATA modal identification stability diagram

Fig.12 Modal identification steady state diagram

Tab.5 The start order for stable poles in the stable graph

	信号A	信号B	信号C
1阶	133	58	31
2阶	128	52	28
3阶	120	55	24
识别速度	慢	中	快
识别准确性	低	低	高

Tab.6 The natural frequency and damping ratio identified by different pre-processing signals

	固有频率/Hz			阻尼比
	1阶	2阶	3阶	1阶	2阶	3阶
直接识别	45.86	132.01	196.51	2.51	0.12	0.21
仅降噪识别	91.51	160.82	240.22	0.81	0.40	0.58
降噪-倒频谱	97.46	178.83	227.01	4.13	0.02	0.04

Tab.7 Relative errors between modal parameters from differently processed signals and experimental results %

	固有频率/Hz			阻尼比
	1阶	2阶	3阶	1阶	2阶	3阶
直接识别	52.31	26.52	13.00	4.13	0.02	0.04
仅降噪识别	4.86	10.48	6.34	2.51	0.12	0.21
降噪-倒频谱	1.31	0.46	0.68	0.81	0.40	0.58

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