Citation: Wu, S.; Dong, Z.; Qi, F.; Fan,
Z. Prediction of the Comprehensive
Error Field in the Machining Space of
the Five-Axis Machine Tool Based on
the “S”-Shaped Specimen Family.
Machines 2022, 10, 408.
https://doi.org/10.3390/
machines10050408
Academic Editors: Kelvin K.L. Wong,
Dhanjoo N. Ghista, Andrew W.H. Ip
and Wenjun (Chris) Zhang
Received: 17 February 2022
Accepted: 18 April 2022
Published: 23 May 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Prediction of the Comprehensive Error Field in the Machining
Space of the Five-Axis Machine Tool Based on the “S”-Shaped
Specimen Family
Shi Wu * , Zeyu Dong , Fei Qi and Zhendong Fan
Key Laboratory of Advanced Manufacturing and Intelligent Technology, Ministry of Education, Harbin
University of Science and Technology, Harbin 150080, China; 18845041407@163.com (Z.D.);
qifei368@163.com (F.Q.); fzd1778417460@163.com (Z.F.)
* Correspondence: swu@hrbust.edu.cn; Tel.: +86-187-4568-7640
Abstract:
In order to quickly and accurately predict the spatial geometric error field of the five-axis
machine tool processing, a method for predicting the comprehensive error field of the five-axis
machine tool processing space based on the “S”-shaped specimen family is studied. Firstly, for the
five-axis CNC machine tool in the form of A-C dual turntable, the geometric error model of the
rotating axis is established based on the multi-body dynamics theory; the error mapping relationship
between the processing technology system and the workpiece is analyzed based on the “S”-shaped
specimen family, and the identification of 12 geometric errors of the two rotating shafts. Then,
the error value of the sampling point is measured based on the “S”-shaped test piece in machine
contact, and the double-circle center coordinate value is determined according to the curvature of the
measured wire of the test piece, in order to identify the geometric errors of the two rotation axes of
the five-axis machine tool. Finally, based on the prediction method, the comprehensive error field of
the five-axis CNC machine tool processing space is analyzed. Compared with other geometric error
identification methods, the measurement accuracy of this method meets the processing requirements
and can further evaluate the comprehensive performance of the machine tool.
Keywords: five-axis CNC machine tool; “S”-shaped sample; machining error; spatial error field
1. Introduction
The continuous development of processing technology has contributed toward the
widespread use of five-axis CNC machine tools in the processing of complex parts. Five-
axis CNC machine tools involve many errors in the processing of such parts. These errors
can be categorised into thermal errors, geometric errors, dynamic cutting force errors, and
servo control errors.
Geometric errors account for a large proportion of these errors. They are mainly
caused by issues in the process of machine tool part manufacturing and assembly. There
are many geometric errors in machine tools, and research on such errors mainly focuses on
their modelling, measurement, and identification.
Various methods are adopted for modelling geometric errors in machine tools. Cur-
rently, geometric error modelling is mainly based on multi-body system theory, which has
the characteristics of high versatility and accuracy. Qiao et al. proposed a new calibration
model based on the exponential product rotation theory of five-axis machine position-
independent geometric errors (PIGEs), which requires only four independent parameters
of the rotating axis and two independent parameters of the moving axis; thus, dimensional
reduction of the recognition coefficient matrix can reduce the amount of calculation to a
certain extent [
1
]. Zhong et al. regarded a multi-body system. They established a model of
the geometric error related to the position of the axis of rotation and proposed an improved
virtual rigid body recognition method to calculate the positioning error of the moving
Machines 2022, 10, 408. https://doi.org/10.3390/machines10050408 https://www.mdpi.com/journal/machines
