Geometric Errors Estimation of a Rotary Table using Double Ball-bar

볼바를 사용한 회전 테이블의 기하학적 오차 추정

  • Received : 2010.05.25
  • Accepted : 2010.09.02
  • Published : 2010.11.01

Abstract

In this paper, double ball-bar is used to estimate the geometric errors of a rotary table, which includes one-axial motion, two-radial motions and two-tilt motions, except the angular positioning error. To simplify the measurement procedures, three measurement steps have been designed and developed. At each measurement step, one end of the double ball-bar is fixed at the nose of spindle and the other end is located on the rotary table. And specific circular test path is planned to keep the distance between two balls as constant at ideal case. The relationship including the geometric errors of a rotary table and the measured distance between two balls which is distorted by the geometric errors is defined by using ball-bar equation. Each geometric error is modeled as $4^{th}$ order polynomial considering $C^1$-continuity. Finally the coefficients of polynomial are calculated by least-square method. Simulation is done to check the validation of the suggested method considering set-up errors and measurement noise. Suggested method is applied to estimate geometric errors of a rotary table of a 5-axis machine tool.

Keywords

References

  1. Uddin, M. S., Ibaraki, S., Matsubara, A. and Matsushita, T., "Prediction and Compensation of Machining Geometric Errors of Five-axis Machining Centers with Kinematic Errors," Precision Engineering, Vol. 33, No. 2, pp. 194-201 , 2009. https://doi.org/10.1016/j.precisioneng.2008.06.001
  2. ISO 230-1, "Test Code for Machine Tools-Part 1: Geometric Accuracy of Machines Operating under No-load or Finishing Conditions," ISO, 1996.
  3. Chen, G., Yuan, J. and Ni, J., "A Displacement Measurement Approach for Machine Geometric Error Assessment," International Journal of Machine Tools and Manufacture, Vol. 41, No. 1, pp. 149-161, 2001. https://doi.org/10.1016/S0890-6955(00)00049-3
  4. Lee, J. H., Liu, Y. and Yang, S. H., "Accuracy Improvement of Miniaturized Machine Tool: Geometric Error Modeling and Compensation," International Journal of Machine Tools and Manufacture, Vol. 46, No. 12-13, pp. 1508-1516, 2006. https://doi.org/10.1016/j.ijmachtools.2005.09.004
  5. Park, S. R., Hoang, T. K. and Yang, S. H., "A New Optical Measurement System for Determining the Geometrical Errors of Rotary Axis of a 5-axis Miniaturized Machine Tool," Journal of Mechanical Science and Technology, Vol. 24, No. 1, pp. 175-179, 2010. https://doi.org/10.1007/s12206-009-1139-0
  6. Lee, D. M. and Yang, S. H., "Mathematical Analysis for Geometrical Error Synthesis Modeling of Machine Tools," Proceeding of the KSPE Spring Conference, pp. 71-72, 2008.
  7. Eman, K. F. and Wu, B. T., "A Generalized Geometric Error Model for Multi-axis Machines," Annals of CIRP, Vol. 36, No. 1, pp. 253-256, 1987. https://doi.org/10.1016/S0007-8506(07)62598-0
  8. Yang, S. H., Yuan, J. and Ni, J., "Accuracy Enhancement of a Horizontal Machining Center by Real' time Error Compensation," Journal of Manufacturing Systems, Vol. 15, No. 2, pp. 113-124, 1996. https://doi.org/10.1016/0278-6125(96)82336-3
  9. Lee, K. I., Lee, D. M. and Yang, S. H., "Estimation of Geometric Errors for a Rotary Table with Double Ball-bar Measurements," Proceeding of the KSPE Spring Conference, pp. 239-240, 2009.
  10. ISO 230-7,"Test Code for Machine Tools-Part 7: Geometric Accuracy of Axes of Rotation," ISO, 2006.
  11. Ball-Suh, S. H., Lee, E. S. and Jung, S. Y., "Error Modelling and Measurement for the Rotary Table of Five-axis Machine Tools," International Journal of Advanced Manufacturing Technology, Vol. 14, No. 9, pp. 656-663, 1998. https://doi.org/10.1007/BF01192286
  12. Ihara, Y., Lin, S. and Kakino, Y., "Analysis of the Motion Accuracy of 5-axis Controlled Machining Centers using DBB Method," International Journal of Japan Society for Precision Engineering, Vol. 32, No. 3, pp. 188-193, 1998.
  13. Knapp, W., "Testing Rotary Axes on NC Machine Tools," Annals of CIRP, Vol. 39, No. 1, pp. 549-552, 1990. https://doi.org/10.1016/S0007-8506(07)61116-0
  14. Hai, N., Yuan, J. and Ni, J., "Reverse Kinematic Analysis of Machine Tool Error using Telescoping BaIl Bar," ASME, PED, 68-1, pp. 277-286, 1994.
  15. Lee, D. M. and Yang, S. H., "Analysis for Singularity Problem in the Ball-bar Equation," Proceeding of the KSPE Spring Conference, pp. 241-242, 2009.