一种五轴机床旋转轴位置无关几何误差辨识方法

doi:10.3969/j.issn.1004-132X.2025.11.016

摘要/Abstract

摘要：

为快速辨识五轴机床旋转轴位置无关几何误差（PIGEs），提高旋转轴几何误差辨识精度，提出了一种采用三种球杆仪安装模式的旋转轴PIGEs简便辨识方法。在三种球杆仪安装模式下，通过齐次坐标变换建立了包含安装误差与旋转轴PIGEs的杆长变化模型。利用仿真分析了PIGEs对三种安装模式下球杆仪轨迹的影响，结果表明三种安装模式下控制单轴运动可以实现8项PIGEs的辨识。在辨识实验中，通过对球杆仪安装误差的测量来消除其对辨识精度的影响，以实现旋转轴8项PIGEs的辨识。最后对旋转轴8项PIGEs进行了补偿，实验结果表明，补偿后的误差最大绝对值由103.9 μm减小至 0.46 μm，验证了所提辨识方法的有效性和准确性。

关键词: 五轴机床, 旋转轴, 位置无关几何误差, 球杆仪, 安装模式

Abstract:

In order to quickly identify PIGEs of rotary axis of five-axis machine tools， and improve the accuracy in identifying geometric errors of rotary axis， a simple identification method was proposed for PIGEs of rotary axis using three installation modes of DBB. The mathematical model of bar length changes included installation errors and PIGEs of rotary axis was established based on homogeneous coordinate transformation under three installation modes of DBB. The effects of PIGEs on the paths of DBB were analyzed by simulation under three installation modes， and the results show that eight PIGEs may be identified by controlling uniaxial motion under three installation modes. In the identification experiments， the influences of identification accuracy were eliminated by measuring the installation errors of DBB， and the identification of eight PIGEs of rotary axis was realized. Finally， eight PIGEs of rotary axis were compensated， and the experimental results show that the maximum absolute value of the compensated errors is reduced from 103.9 μm to 0.46 μm， which verifies the effectiveness and accuracy of the proposed identification method.

Key words: five-axis machine tool, rotary axis, position-independent geometric error（PIGE）, double ball bar（DBB）, installation mode

中图分类号:

TH161

李想, 刘焕牢, 王宇林, 戴鑫. 一种五轴机床旋转轴位置无关几何误差辨识方法[J]. 中国机械工程, 2025, 36(11): 2609-2617.

Xiang LI, Huanlao LIU, Yulin WANG, Xin DAI. An Identification Method of PIGEs for Rotary Axes of Five-axis Machine Tools[J]. China Mechanical Engineering, 2025, 36(11): 2609-2617.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2025.11.016

https://www.cmemo.org.cn/CN/Y2025/V36/I11/2609

图/表 12

图1 五轴机床结构及坐标系建立

Fig.1 Structure diagram of five-axis machine tool mode and coordinate system establishment

图2 PIGEs的定义

Fig.2 Definition of PIGEs

图3 三种安装模式

Fig.3 Three installation modes

图4 刀具球安装误差

Fig.4 Tool ball installation error

表1 仿真基本参数

Tab.1 Basic parameters of simulation

参数	数值
球杆仪标称长度L/mm	100
工件球球心相对于刀具球球心在X方向上的偏移量L_X /mm	60
工件球球心相对于刀具球球心在Y方向上的偏移量L_Y /mm	80
刀具球球心到C轴轴线的距离l/mm	100
刀具球球心到A轴轴线的距离h/mm	100
A轴旋转范围	［-15°，70°］
C轴旋转范围	［0°，360°］
ACS与CCS间的距离Z_AC /mm	50
位置误差δ_YA，δ_ZA，δ_XC，δ_YC /μm	±10
垂直度误差S_YA，S_ZA，S_XC，S_YC /（°）	±0.005

表2 PIGEs对各安装模式下杆长的影响

Tab.2 The influence of PIGEs on each installation mode

误差	$δ Y A = ± 10 μ m$	$δ Z A = ± 10 μ m$	$S Y A = ± 0.005 °$	$S Z A = ± 0.005 °$
模式一仅A轴旋转
模式二
模式一仅C轴旋转
模式三
误差	$δ X C = ± 10 μ m$	$δ Y C = ± 10 μ m$	$S X C = ± 0.005 °$	$S Y C = ± 0.005 °$
模式一仅C轴旋转
模式三

表2 PIGEs对各安装模式下杆长的影响

Tab.2 The influence of PIGEs on each installation mode

误差	$δ Y A = ± 10 μ m$	$δ Z A = ± 10 μ m$	$S Y A = ± 0.005 °$	$S Z A = ± 0.005 °$
模式一仅A轴旋转
模式二
模式一仅C轴旋转
模式三
误差	$δ X C = ± 10 μ m$	$δ Y C = ± 10 μ m$	$S X C = ± 0.005 °$	$S Y C = ± 0.005 °$
模式一仅C轴旋转
模式三

图5 球杆仪安装误差测量原理

Fig.5 Principle of measuring DBB installation error

图6 安装误差测量

Fig.6 Measurement for installation error

图7 安装测量现场

Fig.7 Installation and measurement scenes

表3 PIGEs补偿前后的数值

Tab.3 Values of PIGEs before and after compensation

误差项	补偿前	补偿后	误差降低率/%
δ_YA /μm	28.69	-1.54	94.63
δ_ZA /μm	-103.90	0.46	99.56
S_YA /（″）	-6.68	-2.16	67.66
S_ZA /（″）	-13.60	-4.06	70.15
δ_XC /μm	5.14	0.80	84.44
δ_YC /μm	-6.73	1.22	81.87
S_XC /（″）	-16.03	-3.64	77.29
S_YC /（″）	-26.34	3.05	88.42

图8 球杆仪长度数据

Fig.8 Length data of DBB

表4 PIGEs辨识方法的对比

Tab.4 Comparision among PIGEs identification methods

辨识方法	安装次数	指标	δ_YA	δ_ZA	S_YA	S_ZA	δ_XC	δ_YC	S_XC	S_YC
文献［5］	3	补偿前	-27.13 μm	1.90 μm	-12.47″	-1.26″	-23.36 μm	214.20 μm	103.99″	343.15″
		补偿后	-8.01 μm	0.68 μm	-4.91″	-0.40″	-8.09 μm	68.12 μm	39.12″	115.68″
		降低率	70.48%	64.21%	60.62%	68.25%	65.37%	68.20%	62.38%	66.29%
		平均降低率	65.73%
文献［13］	4	补偿前	25.40 μm	-9.10 μm	6.33″	-0.93″	22.30 μm	3.30 μm	4.17″	-0.95″
		补偿后	-1.00 μm	-0.20 μm	-0.83″	-0.08″	4.00 μm	-2.00 μm	0″	3.82″
		降低率	96.06%	97.80%	86.89%	91.40%	82.06%	39.39%	100.00%	0
		平均降低率	74.20%
本文方法	3	补偿前	28.69 μm	-103.90 μm	-6.68″	-13.60″	5.14 μm	-6.73 μm	-16.03″	-26.34″
		补偿后	-1.54 μm	0.46 μm	-2.16″	-4.06″	0.80 μm	1.22 μm	-3.64″	3.05″
		降低率	94.63%	99.56%	67.66%	70.15%	84.44%	81.87%	77.29%	88.42%
		平均降低率	83.00%

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