This study proposes an identification and compensation method for the geometric errors of the rotary axes in five-axis machining centers, based on the on-machine measurement results of the machined workpiece. Geometric errors can be identified from the shape geometry of the workpiece machined by five-axis motions because the influence of the errors appears on the shape geometry. An observation equation can be obtained based on the geometric error model and machined shape. The actual geometric errors can be identified by the least square matching of the measured and simulated machined shapes. In order to confirm the effectiveness of the proposed method, an actual cutting test and a simulation are performed. Based on their results, it is confirmed that the proposed method can successfully identify the geometric errors in the simulation. However, these errors cannot be identified in the experiments because a few of them do not have sufficient influences onto the machined shape. On the other hand, although the geometric errors cannot be correctly identified, it is confirmed that the they can be adequately compensated for based on the identified errors in both the simulation and experiment.

1. [1] “Test Code for Machine Tools – Part 1: Geometric Accuracy of Machines Operating under No-load or Quasi-static Conditions,” ISO230-1, 2012.
2. [2] S. Ibaraki and W. Knapp, “Indirect Measurement of Volumetric Accuracy for Three-Axis and Five-axis Machine Tools: A Review,” Int. J. of Automation Technology, Vol.6, No.2, pp. 110-124, 2012.
3. [3] M. Tsutsumi and A. Saito, “Identification and Compensation of Systematic Deviations Particular to 5-Axis Machining Centers,” Int. J. of Machine Tools & Manufacture, Vol.43, pp. 771-780, 2003.
4. [4] M. Tsutsumi and A. Saito, “Identification of Angular and Positional Deviations Inherent to 5-Axis Machining Centers with a Tilting-Rotary Table by Simultaneous Four-Axis Control Movements,” Int. J. of Machine Tools & Manufacture, Vol.44, pp. 1333-1342, 2004.
5. [5] M. Tsutsumi, S. Tone, N. Kato, and R. Sato, “Enhancement of Geometric Accuracy of Five-Axis Machining Centers Based on Identification and Compensation of Geometric Deviations,” Int. J. of Machine Tools & Manufacture, Vol.68, pp. 11-20, 2013.
6. [6] B. Bringmann and W. Knapp, “Model-Based ‘Chace-the-Ball’ Calibration of a 5-Axis Machining Center,” CIRP Annals – Manufacturing Technology, Vol.55-1, pp. 431-534, 2006.
7. [7] S. Weikert, “R-test, A New Device for Accuracy Measurements on Five Axis Machine Tools,” CIRP Annals – Manufacturing Technology, Vol.53-1, pp. 429-432, 2004.
8. [8] S. Xiang and Y. Altintas, “Modeling and Compensation of Volumetric Errors for Five-Axis Machine Tools,” Int. J. of Machine Tools & Manufacture, Vol.101, pp. 65-78, 2016.
9. [9] S. Ibaraki, M. Sawada, A. Matsubara, and T. Matsushita, “Machining Tests to Identify Kinematic Errors on Five-Axis Machine Tools,” Precision Engineering, Vol.34, No.3, pp. 387-398, 2010.
10. [10] S. Ibaraki and Y. Ota, “A Machining Test to Calibrate Rotary Axis Error Motions of Five-Axis Machine Tools and its Application to Thermal Deformation Test,” Int. J. of Machine Tools & Manufacture, Vol.86, pp. 81-88, 2014.
11. [11] A. Velenosi, G. Campatelli, and A. Scippa, “Axis Geometrical Errors Analysis Through a Performance Test to Evaluate Kinematic Error in a Five Axis Tilting-Rotary Table Machine Tool,” Precision Engineering, Vol.39, pp. 224-233, 2015.
12. [12] J. Bryan, “Int. Status of Thermal Error Research,” CIRP Annals – Manufacturing Technology, Vol.39-2, pp. 645-656, 1990.
13. [13] C. Brecher, P. Hirsh, and M. Weck, “Compensation of Thermo-Elastic Machine Tool Deformation Based on Control Internal Data,” CIRP Annals – Manufacturing Technology, Vol.53-1, pp. 299-304, 2004.
14. [14] Y. Li, W. Zhao, S. Lan, J. Ni, W. Wu, and B. Lu, “A Review on Spindle Thermal Error Compensation in Machine Tools,” Int. J. of Machine Tools & Manufacture, Vol.95, pp. 20-38, 2015.
15. [15] M. Gebhardt, S. Capparelli, M. Ess, W. Knapp, and K. Wegener, “Physical and Phenomenological Simulation Models for the Thermal Compensation of Rotary Axis of Machine Tools,” Proc. of the 13th EUSPEN Int. Conf., pp. 304-309, 2013.
16. [16] S. Ibaraki and Y. Ota, “Error Calibration for Five-Axis Machine Tools by On-the-Machine Measurement Using a Touch-Trigger Probe,” Int. J. of Automation Technology, Vol.8, No.1, pp. 20-27, 2014.
17. [17] Y. Kimura, A. Matsubara, and Y. Koike, “Analysis of Measurement Errors of a Diffuse-Reflection-Type Laser Displacement Sensor for Profile Measurement,” Int. J. of Automation Technology, Vol.6, No.6, pp. 724-727, 2012.
18. [18] M. A. Fischler and R. C. Bolles, “Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography,” Communications of the ACM, Vol.24, No.6, pp. 381-395, 1981.
19. [19] Y. Nagai, S. Ibaraki, and S. Nishikawa, “Error Calibration of 5-Axis Machine Tools by On-Machine Measurement System Using a Laser Displacement Sensor,” J. of Advanced Mechanical Design, Systems, and Manufacturing, Vol.8, No.4, No.14-00115, 2014.
20. [20] R. Sato, Y. Sato, K. Shirase, G. Campatelli, and A. Scippa, “Finished Surface Simulation Method to Predicting the Effects of Machine Tool Motion Errors,” Int. J. of Automation Technology, Vol.6, No.8, pp. 801-810, 2014.
21. [21] S. Hasegawa, R. Sato, and K. Shirase, “Influences of Geometric and Dynamic Synchronous Errors onto Machined Surface in 5-Axis Machining Center,” J. of Advanced Mechanical Design, Systems, and Manufacturing, Vol.10, No.5, No.16-00133, 2016.
22. [22] S. Ibaraki, Y. Kimura, Y. Nagai, and S. Nishikawa, “Formulation on Influence of Machine Geometric Errors on Five-Axis On-Machine Scanning Measurement by Using a Laser Displacement Sensor,” J. of Manufacturing Science and Engineering, Vol.137, No.2, 021013-1/11, 2015.