Quasistatic Error Modeling and Model Testing for a 5-Axis Machine with a Redundant Axis


This paper presents an approach to modeling the quasistatic errors of a 5-axis machine tool with one redundant axis. By introducing errors to the ideal joints and shape transforms of the kinematics of the machine, an error model is obtained. First order error characteristics are used to parameterize the introduced errors. It is found that of the 52 introduced error parameters, only 32 have a linearly independent effect on the volumetric errors observed in the machine's workspace. To identify these error parameters, the volumetric error components at 290 randomly chosen points are measured with a laser tracker. The unknown parameters are obtained by least-squares estimation, and the resulting model able to reduce average magnitude of the volumetric error vectors at these points by an average of 90% of their original values. Further, the identified model was used to predict the errors observed in two independent test point sets (each set consisting of 48 points). A 75% reduction in the average magnitude of the error vectors was observed. A large fraction of the residual errors was found to be attributable to the thermal drift of the machine during the experiments, which were not conducted in a thermally controlled environment and the positioning repeatability of the machine.


Mechanical and Aerospace Engineering


This work was performed with support from the Digital Manufacturing and Design Innovation Institute (DMDII) under project DMDII14-07-02: Integrated Manufacturing Variation Management. The project is sponsored in part by the Department of Army . The authors would also like to acknowledge inputs and supports from Nien Lee, Richard Eirhart, Keith Egland, Mike Vogler and Craig Habeger of Caterpillar Inc. and Jorge E. Correa of UIUC.

Keywords and Phrases

Errors; Machine tools; 5-axis machine tool; Controlled environment; Error characteristics; Least squares estimation; Linearly independents; Machine tool accuracies; Machine tool errors; Volumetric errors; Error compensation; Machine-tool accuracy; Machine-tools; Quasistatic machine-tool errors

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version


File Type





© 2018 Elsevier, All rights reserved.

Publication Date

01 Jan 2018