五轴机床旋转轴位置无关几何误差的快速辨识方法

doi:10.3969/j.issn.1004-132X.2026.08.012

摘要/Abstract

摘要：

为简化五轴机床旋转轴位置无关几何误差（PIGEs）的辨识过程，并减少安装误差的引入，提出了一种基于球杆仪的单轴控制测量方法，仅需两种安装模式即可实现对旋转轴8项PIGEs的快速辨识。通过减少球杆仪的安装次数降低了因球杆仪安装误差引起的辨识精度损失，提高了辨识精度和效率。采用旋量理论构建运动矩阵，建立旋转轴PIGEs误差模型和球杆仪杆长模型。通过仿真分析各项PIGEs对球杆仪轨迹的影响，验证了该辨识方法的有效性。分析了安装误差对实验结果的影响，完成了旋转轴8项PIGEs的辨识。最后进行了补偿实验对比验证，结果表明补偿后的整体精度提高87.38%，所提球杆仪辨识方法不仅简化了辨识过程，而且具有较高的准确性。

关键词: 五轴机床, 旋转轴, 球杆仪, 旋量理论, 位置无关几何误差

Abstract:

To simplify the identification process of PIGEs in the rotary axes of five-axis machine tools and to minimize the introduction of installation errors， this paper proposes a single-axis controlled measurement method based on a double ball bar （DBB）. The method enables rapid identification of all eight PIGEs for a rotary axis using only two installation configurations， thereby reducing accuracy loss caused by repeated DBB setups and improving both efficiency and precision. A kinematic model based on screw theory is developed to establish the PIGE error model and the DBB displacement relationship. The influence of individual PIGEs on the DBB trajectory is analyzed through simulation， which validates the effectiveness of the proposed identification method. The effect of installation errors on experimental results is quantitatively investigated， and all eight PIGEs are successfully identified. Comparative compensation experiments demonstrate an 87.38% improvement in overall positioning accuracy. The proposed DBB-based method not only streamlines the identification procedure but also achieves high accuracy.

Key words: five-axis machine tool, rotary axes, ballbar, screw theory, position-independent geometric errors （PIGEs）

中图分类号:

TH161

鲍玺宇, 刘焕牢, 王宇林, 张泽堃. 五轴机床旋转轴位置无关几何误差的快速辨识方法[J]. 中国机械工程, 2026, 37(8): 1928-1936.

BAO Xiyu, LIU Huanlao, WANG Yulin, ZHANG Zekun. Rapid Identification of Position-Independent Geometric Errors of Rotary Axes in Five-axis Machine Tools[J]. China Mechanical Engineering, 2026, 37(8): 1928-1936.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2026.08.012

https://www.cmemo.org.cn/CN/Y2026/V37/I8/1928

图/表 18

图1 五轴机床机床结构及坐标系的建立示意图

Fig.1 Schematic diagram of five-axis machine tool structure and coordinate system establishment

图2 PIGEs的定义

Fig.2 Definition of PIGEs

图3 安装误差示意图

Fig.3 Schematic diagram of installation error

图4 误差旋量定义

Fig.4 Definition of error screw

图5 两种安装模式

Fig.5 Two installation modes

表1 安装模式参数 (mm)

Tab.1 Installation mode parameters

模式	球杆仪长度	X方向偏置量	Y方向偏置量	Z方向偏置量H
1	100	80	60	0
2	100	60	0	80

表2 关键尺寸与误差

Tab.2 Key dimensions and errors

球杆仪的标称长度L/mm	100
模式一的偏移量	X_w1=80 mm，Y=60 mm
模式二的偏移量	X_w2=60 mm，H=80 mm
A轴的旋转范围	［-15°，70°］
A轴与机床距离Z_CA /mm	50
C轴的旋转范围	［0°，360°］
位置误差假设值	δ_ya，δ_za，δ_xc，δ_yc =±10μm
垂直度误差假设值	ε_ya，ε_za，ε_xc，ε_yc =±0.005°

图6 模式一：仅A轴旋转

Fig.6 Mode 1： Only A-axis rotation

图7 模式二：仅A轴旋转

Fig. 7 Mode 2： Only A-axis rotation

图8 模式一：仅C轴旋转

Fig. 8 Mode 1： Only C-axis rotation

图9 模式二：仅C轴旋转

Fig. 9 Mode 2： Only C-axis rotation

表3 球杆仪规格

Tab.3 Ball bar specifications

球杆仪的型号	Renishaw QC20-W
球杆仪的标称长度/mm	100
球杆仪的校准长度/mm	99.9957
分辨率x/μm	0.1
测量范围/mm	±1
测量精度	±0.5 μm（20 ℃）
测量精度	±（0.8+0.4%L）（0～40 ℃）

图10 测量安装误差

Fig.10 Measurement of installation error

图11 安装误差测量原理

Fig. 11 Measurement principle of installation error

图12 实验测量过程

Fig.12 Experimental measurement process

表4 本文方法补偿前后的PIGEs数据

Tab.4 PIGEs data before and after compensation using the proposed method

误差参数	补偿前	补偿后	补偿提升比/%
δ_ya /μm	22.62	$-$ 4.80	78.78
δ_za /μm	$-$ 90.01	2.42	97.31
ε_ya /（″）	158.99	$-$ 25.41	84.02
ε_za /（″）	248.76	2.41	99.03
δ_xc /μm	21.98	4.20	80.89
δ_yc /μm	$-$ 10.17	1.63	83.97
ε_xc /（″）	$-$ 21.37	$-$ 4.01	81.26
ε_yc /（″）	47.21	2.94	93.77

表4 本文方法补偿前后的PIGEs数据

Tab.4 PIGEs data before and after compensation using the proposed method

误差参数	补偿前	补偿后	补偿提升比/%
δ_ya /μm	22.62	$-$ 4.80	78.78
δ_za /μm	$-$ 90.01	2.42	97.31
ε_ya /（″）	158.99	$-$ 25.41	84.02
ε_za /（″）	248.76	2.41	99.03
δ_xc /μm	21.98	4.20	80.89
δ_yc /μm	$-$ 10.17	1.63	83.97
ε_xc /（″）	$-$ 21.37	$-$ 4.01	81.26
ε_yc /（″）	47.21	2.94	93.77

图13 误差补偿前后球杆仪杆长变化量对比

Fig.13 Comparison of ball bar length variations before and after error compensation

表5 不同PIGEs辨识方法比较

Tab.5 Comparison of different PIGEs identification methods

参考文献	球杆仪安装模式的数量	是否有延长杆	补偿提升比/%
文献［26］	4	是	82.74
文献［28］	3	否	68.06
文献［29］	3	否	83.00
本文方法	2	否	87.38

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