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浙江大学学报(工学版)
浙江大学学报(工学版)  2025, Vol. 59 Issue (4): 842-852    DOI: 10.3785/j.issn.1008-973X.2025.04.020
机械与能源工程     
基于振动响应重构的电主轴径向回转误差测量
阮佳豪1,2(),康为民1,2,傅建中1,2,*()
1. 浙江大学 机械工程学院，浙江 杭州 310027
2. 浙江省三维打印工艺与装备重点实验室，浙江 杭州 310027
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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摘要：

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    
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
收稿日期: 2024-01-31 出版日期: 2025-04-25
CLC:  TH 113.1  
基金资助: 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）.
通讯作者: 傅建中     E-mail: 22125091@zju.edu.cn;fjz@zju.edu.cn
作者简介: 阮佳豪（1998—），男，硕士生，从事高精度数控机床精度测量研究. orcid.org/0009-0003-9681-8148. E-mail：22125091@zju.edu.cn
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引用本文:

阮佳豪,康为民,傅建中. 基于振动响应重构的电主轴径向回转误差测量[J]. 浙江大学学报(工学版), 2025, 59(4): 842-852.

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.

链接本文:

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

结构材料ρ/(kg·m?3)E/GPaμ
芯轴45#78502100.31
基座铸铝2700700.30
轴承内圈轴承钢78002080.30
轴承外圈轴承钢78002080.30
表 1  电主轴关键部件材料力学特性参数
图 1  电主轴前2阶模态振型图
图 2  激振实验装置
图 3  加速度导纳频率响应图
模态阶数f/Hz
ε/%
修正前修正后实验结果
1270.53275.92282.550.93
2445.54452.21460.271.98
3538.54554.38564.331.76
4820.58826.15832.460.76
5924.59947.24950.780.37
61 042.611 048.751 050.590.18
表 2  电主轴有限元模型修正前后各阶固有频率
图 4  电主轴传感器测点布置图
图 5  不同电主轴振动方向的费舍尔信息矩阵的2-范数变化率随模态分析阶数的变化
图 6  转速对模态振型影响的合理性示意图
图 7  芯轴重构点尺寸分布
图 8  轴线拟合原理图
图 9  电主轴芯轴前6阶振型
图 10  回转误差计算方法
图 11  模态振型修正实验台
图 12  力锤敲击位置
图 13  重构响应和实测响应比较
图 14  不同重构点振动响应重构误差对比（模态振型修正前）
图 15  电主轴机壳模态振型修正算法的流程图
图 16  不同重构点振动响应重构误差对比（模态振型修正后）
图 17  电主轴芯轴模态振型修正实验方案
图 18  电主轴芯轴模态振型图
图 19  振动响应重构法重复测量部分极坐标图
序号${{\varepsilon}}_{\text{rr}} $/μm序号${{\varepsilon}}_{\text{rr}} $/μm序号${{\varepsilon}}_{\text{rr}} $/μm
11.3081.11151.39
21.2991.35161.26
31.28101.31171.29
41.20111.35181.38
51.23121.22191.28
61.15131.21201.12
71.26141.36211.32
表 3  被测电主轴振动场重构法径向回转误差测量值
图 20  电主轴不同转速下振动响应重构法测量结果分布图
vs/(103 r·min?1)$\varepsilon_{\mathrm{rr}} $/μmR/μm$\sigma $/μm
10.820.140.056
21.060.160.048
31.960.290.059
41.480.250.085
51.380.190.063
61.060.180.076
71.190.220.082
81.230.270.103
91.220.300.099
101.270.280.080
表 4  电主轴振动响应重构法径向回转误差测量结果
图 21  高转速三点法实验台
图 22  电主轴不同转速下三点法测量结果分布图
vs/(103 r·min?1)Ea/μm$\varepsilon _{\mathrm{r}} $/%
10.056.49
20.054.95
30.083.92
40.064.23
50.032.13
60.066.00
70.051.71
800
90.021.67
100.021.55
表 5  不同转速下被测电主轴振动响应重构法测量误差结果
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