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Position-dependent geometric errors measurement and identification for rotary axis of multi-axis machine tools based on optimization method using double ball bar

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Abstract

Geometric errors measurement and identification for rotary table are important. However, precisely adjustment for the setup position of a double ball bar in each measurement pattern is inconvenient. This study proposes a novel optimization identification method using a double ball bar to recognize the position-dependent geometric errors (PDGEs) of rotary axis. A mathematical model for ball bar measurement is firstly constructed to map the relationship between measurement direction and position of the double ball bar. And then, the setup positions of the double ball bar for PDGEs identification are analyzed. According to analysis for setup positions of the double ball bar, simplified measurement patterns would be conducted by adjusting only two setup positions for the ball bar and thus reduce the procedure of accurate adjustment for the ball bar. The PDGEs can be fitted as an nth B-spline curve, on the account of its being smooth and continuous. To identify the PDGEs, an optimization method, by computing the suitable value of control points of nth B-spline curve of errors to minimize the optimal value of the target function between the actual measured value and the value derived from a theoretical measurement model, is proposed. Moreover, in order to obtain the accurate value of control points of the error curve, the sensitivity analysis is conducted to acquire the sensitivity matrix with respect to control points of errors. The PDGEs are able to be identified simultaneously after calculating the appropriate values of control points of errors. The proposed identification method is validated by simulation and experiment. The results prove the effectiveness of the proposed method.

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References

  1. Qiao Y, Chen Y, Yang J, Chen B (2017) A five-axis geometric errors calibration model based on the common perpendicular line (CPL) transformation using the product of exponentials (POE) formula. Int J Mach Tools Manuf 118–119:49–60

    Article  Google Scholar 

  2. Ramesh R, Mannan MA, Poo AN (2000) Error compensation in machine tools — a review: part I: geometric, cutting-force induced and fixture-dependent errors. Int J Mach Tool Manu 40(9):1235–1256

    Article  Google Scholar 

  3. Schwenke H, Knapp W, Haitjema H, Weckenmann A, Schmitt R, Delbressine F (2008) Geometric error measurement and compensation of machines—an update. CIRP Ann Manuf Technol 57(2):660–675

    Article  Google Scholar 

  4. Zhu S, Ding G, Qin S, Lei J, Zhuang L, Yan K (2012) Integrated geometric error modeling, identification and compensation of CNC machine tools. Int J Mach Tool Manu 52(1):24–29

    Article  Google Scholar 

  5. Chen G, Yuan J, Ni J (2001) A displacement measurement approach for machine geometric error assessment. Int J Mach Tool Manu 41(1):149–161

    Article  Google Scholar 

  6. Peng W, Xia H, Wang S, Chen X (2017) Measurement and identification of geometric errors of translational axis based on sensitivity analysis for ultra-precision machine tools. Int J Adv Manuf Technol 94(5–8):2905–2917

    Google Scholar 

  7. ISO 230-7-2006, Test Code for Machine Tools-Part 7: Geometric Accuracy of Axes of Rotation (2006). ISO

  8. Chen JX, Lin SW, Zhou XL, Gu TQ (2016) A ballbar test for measurement and identification the comprehensive error of tilt table. Int J Mach Tool Manu 103:1–12

    Article  Google Scholar 

  9. Xiang S, Altintas Y (2016) Modeling and compensation of volumetric errors for five-axis machine tools. Int J Mach Tool Manu 101:65–78

    Article  Google Scholar 

  10. Lasemi A, Xue D, Gu P (2016) Accurate identification and compensation of geometric errors of 5-axis CNC machine tools using double ball bar. Meas Sci Technol 27(5):055004

    Article  Google Scholar 

  11. Yang J, Ding H (2016) A new position independent geometric errors identification model of five-axis serial machine tools based on differential motion matrices. Int J Mach Tool Manu 104:68–77

    Article  Google Scholar 

  12. Tsutsumi M, Tone S, Kato N, Sato R (2013) Enhancement of geometric accuracy of five-axis machining centers based on identification and compensation of geometric deviations. Int J Mach Tool Manu 68(68):11–20

    Article  Google Scholar 

  13. Lee DM, Zhu Z, Lee KI, Yang SH (2011) Identification and measurement of geometric errors for a five-axis machine tool with a tilting head using a double ball-bar. Int J Precis Eng Manuf 12(2):337–343

    Article  Google Scholar 

  14. Lee KI, Yang SH (2016) Compensation of position-independent and position-dependent geometric errors in the rotary axes of five-axis machine tools with a tilting rotary table. Int J Adv Manuf Technol 85(5–8):1677–1685

    Article  Google Scholar 

  15. Tsutsumi M, Saito A (2003) Identification and compensation of systematic deviations particular to 5-axis machining centers. Int J Mach Tool Manu 43(8):771–780

    Article  Google Scholar 

  16. Tsutsumi M, Saito A (2004) 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 Mach Tool Manu 44(12–13):1333–1342

    Article  Google Scholar 

  17. Ibaraki S, Knapp W (2012) Indirect measurement of volumetric accuracy for three-axis and five-axis machine tools: A review

  18. Zhang Z, Hu H (2013) A general strategy for geometric error identification of multi-axis machine tools based on point measurement. Int J Adv Manuf Technol 69(5–8):1483–1497

    Article  Google Scholar 

  19. Li H, Guo J, Deng Y, Wang J, He X (2016) Identification of geometric deviations inherent to multi-axis machine tools based on the pose measurement principle. Meas Technol 27(12)

  20. Jiang Z, Bao S, Zhou X, Tang X, Zheng S (2015) Identification of location errors by a touch-trigger probe on five-axis machine tools with a tilting head. Int J Adv Manuf Technol 81(1–4):149–158

    Article  Google Scholar 

  21. Jiang Z, Song B, Zhou X, Tang X, Zheng S (2015) Single setup identification of component errors for rotary axes on five-axis machine tools based on pre-layout of target points and shift of measuring reference. Int J Mach Tool Manu 98(4/5):1–11

    Google Scholar 

  22. Ibaraki S, Oyama C, Otsubo H (2011) Construction of an error map of rotary axes on a five-axis machining center by static R-test. Int J Mach Tool Manu 51(3):190–200

    Article  Google Scholar 

  23. Jiang X, Cripps RJ (2015) A method of testing position independent geometric errors in rotary axes of a five-axis machine tool using a double ball bar. Int J Mach Tool Manu 89:151–158

    Article  Google Scholar 

  24. Lee KI, Yang SH (2013) Measurement and verification of position-independent geometric errors of a five-axis machine tool using a double ball-bar. Int J Mach Tool Manu 70(4):45–52

    Article  Google Scholar 

  25. Chen JX, Lin SW, He BW (2014) Geometric error measurement and identification for rotary table of multi-axis machine tool using double ballbar. Int J Mach Tool Manu 77(77):47–55

    Article  Google Scholar 

  26. Xiang S, Yang J (2014) Using a double ball bar to measure 10 position-dependent geometric errors for rotary axes on five-axis machine tools. Int J Adv Manuf Technol 75(1–4):559–572

    Article  Google Scholar 

  27. Fu G, Fu J, Xu Y, Chen Z, Lai J (2015) Accuracy enhancement of five-axis machine tool based on differential motion matrix: geometric error modeling, identification and compensation. Int J Mach Tool Manu 89:170–181

    Article  Google Scholar 

  28. Xia HJ, Peng WC, Ouyang XB, Chen XD, Wang SJ, Chen X (2017) Identification of geometric errors of rotary axis on multi-axis machine tool based on kinematic analysis method using double ball bar. Int J Mach Tool Manu 122:161–175

    Article  Google Scholar 

  29. Haug EJ (1989) Computer-Aided Kinematics and Dynamics of Mechanical Systems Volume-I Basic Methods Allyn 1

  30. Kong LB, Cheung CF, To S, Lee WB, Du JJ, Zhang ZJ (2008) A kinematics and experimental analysis of form error compensation in ultra-precision machining. Int J Mach Tool Manu 48(12–13):1408–1419

    Article  Google Scholar 

  31. Nering ED, Henney DR (1970) Linear algebra and matrix theory. Wiley

  32. Fu G, Fu J, Shen H, Sha J, Xu Y (2016) Numerical solution of simultaneous equations based geometric error compensation for CNC machine tools with workpiece model reconstruction. Int J Adv Manuf Technol 86(5–8):2265–2278

    Article  Google Scholar 

  33. Fu G, Fu J, Shen H, Yao X, Chen Z (2015) NC codes optimization for geometric error compensation of five-axis machine tools with one novel mathematical model. Int J Adv Manuf Technol 80(9–12):1879–1894

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to express their sincere thanks to the support of the National Natural Science Foundation of China (No.51775116), the Open Operation of Guangdong Provincial Key Laboratory of Micro-nano Manufacturing Technology and Equipment (No. 2017B030314178), and the Guangdong Science and Technology Planning Project (No. 2015B010102011, No. 2015B090921007 and No. 2016B090911001).

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Authors and Affiliations

  1. Guangdong Provincial Key Laboratory of Micro-nano Manufacturing Technology and Equipment, School of Electromechanical Engineering, Guangdong University of Technology, Guangzhou, 510006, Guangdong, China

    Weichao Peng, Hongjian Xia, Xindu Chen, Zeqin Lin, Zhifeng Wang & Haiyan Li

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  1. Weichao Peng
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  2. Hongjian Xia
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  3. Xindu Chen
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  4. Zeqin Lin
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  5. Zhifeng Wang
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Correspondence to Hongjian Xia.

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Peng, W., Xia, H., Chen, X. et al. Position-dependent geometric errors measurement and identification for rotary axis of multi-axis machine tools based on optimization method using double ball bar. Int J Adv Manuf Technol 99, 2295–2307 (2018). https://doi.org/10.1007/s00170-018-2583-8

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  • DOI: https://doi.org/10.1007/s00170-018-2583-8

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