A complete, continuous, and minimal product of exponentials-based model for five-axis machine tools calibration with a single laser tracker, an R-test, or a double ball-bar

Peng Xu, Benny C.F. Cheung, Bing Li

Research output: Journal article publicationJournal articleAcademic researchpeer-review

8 Citations (Scopus)


Calibration is an important way to improve and guarantee the accuracy of machine tools. This paper presents a systematic approach for position independent geometric errors (PIGEs) calibration of five-axis machine tools based on the product of exponentials (POE) formula. Instead of using 4 × 4 homogeneous transformation matrices (HTMs), it establishes the error model by transforming the 6 × 1 error vectors of rigid bodies between different frames resorting to 6 × 6 adjoint transformation matrices. A stable and efficient error model for the iterative identification of PIGEs should satisfy the requirements of completeness, continuity, and minimality. Since the POE-based error models for five-axis machine tools calibration are naturally complete and continuous, the key issue is to ensure the minimality by eliminating the redundant parameters. Three kinds of redundant parameters, which are caused by joint symmetry information, tool-workpiece metrology, and incomplete measuring data, are illustrated and explained in a geometrically intuitive way. Hence, a straightforward process is presented to select the complete and minimal set of PIGEs for five-axis machine tools. Based on the established unified and compact error Jacobian matrices, observability analyses which quantitatively describe the identification efficiency are conducted and compared for different kinds of tool tip deviations obtained from several commonly used measuring devices, including the laser tracker, R-test, and double ball-bar. Simulations are conducted on a five-axis machine tool to illustrate the application of the calibration model. The effectiveness of the model is also verified by experiments on a five-axis machine tool by using a double ball-bar.

Original languageEnglish
Article number041010
Number of pages15
JournalJournal of Manufacturing Science and Engineering, Transactions of the ASME
Issue number4
Publication statusPublished - 1 Apr 2019

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Mechanical Engineering
  • Computer Science Applications
  • Industrial and Manufacturing Engineering

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