Skip to main content
SpringerLink
Log in

Kinematic errors prediction for multi-axis machine tools’ guideways based on tolerance

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

In this paper, a systematic approach on how to predict kinematic errors based on tolerance of machine tools’ guideways is introduced. Firstly, the truncated Fourier series function is applied to fit curve of guideways surface. Since geometric profile errors are regarded as a bridge between tolerance and kinematic errors of machine tools’ guideways, the mapping relationship between tolerance and geometric profile errors of machine tools’ guideways is formulated, and the mapping relationship between geometric profile errors and kinematic errors of guideways is established. Then, kinematic errors prediction model based on tolerance of guideways is subsequently proposed. Finally, simulation verification is conducted with this method. Simulation results show the range of the predicted kinematic errors (positioning error, y direction and z direction straightness error, roll error, pitch error, and yaw error) is 17.12 μm, 56.57 μm, 70.71 μm, 28.28 μrad, 141.42 μrad, and 113.14 μrad, respectively. In order to verify the feasibility and effectiveness of the presented method, a measuring experiment is carried out on guideways of a gantry-type five-axis milling machine tools by using a dual-frequency laser interferometer. The measured and identified discrete data can be fitted precisely by Fourier curve fitting method. The fitting results show the range of the measured kinematic errors is 16.96 μm, 59.43 μm, 68.63 μm, 28.65 μrad, 135.40 μrad, and 111.58 μrad, respectively. The maximum residual errors between the predicted and measured values of kinematic errors are 1.67 μm, 5.19 μm, 5.50 μm, 1.87 μrad, 9.81 μrad, and 7.07μrad, respectively. Comparing with the measured results of kinematic errors, residual errors are considerably small and can be neglected. Therefore, there is no doubt that this method is effective enough for predicting kinematic errors and can be used to replace the measurement of kinematic errors. In the design stage of machine tools, this approach is convenient for engineers to derive the distribution of kinematic errors. And its basic idea can be applied to other type of machine tools’ guideways.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Sharif Uddin M, Ibaraki S, Matsubara A, Matsushita T (2009) Prediction and compensation of machining geometric errors of five-axis machining centers with kinematic errors. Precis Eng 33:194–201

    Article  Google Scholar 

  2. Chen GS, Mei XS, Li HL (2013) Geometric error modeling and compensation for large-scale grinding machine tools with multi-axes. Int J Adv Manuf Technol 69(9–12):2583–2592

    Article  Google Scholar 

  3. Feng WL, Yao XD, Arynov A, Yang JG (2015) Straightness error compensation for large CNC gantry type milling centers based on B-spline curves modeling. Int J Mach Tools Manuf 88:165–174

    Article  Google Scholar 

  4. Wu CJ, Fan JW, Wang QH, Pan R, Tang YH, Li ZS (2018) Prediction and compensation of geometric error for translational axes in multi-axis machine tools. Int J Adv Manuf Technol 95:3413–3435

    Article  Google Scholar 

  5. Chen G, Liang Y, Sun Y, Chen W, Wang B (2013) Volumetric error modeling and sensitivity analysis for designing a five-axis ultra-precision machine tool. Int J Adv Manuf Technol 68(9–12):2525–2534

    Article  Google Scholar 

  6. Wang Z, Wang DL, Wu Y, Dong HM, Yu SD (2017) Error calibration of controlled rotary pairs in five-axis machining centers based on the mechanism model and kinematic invariants. Int J Mach Tools Manuf 120:1–11

    Article  Google Scholar 

  7. Du SW, Hu JC, Zhu Y, Hu CX (2017) Analysis and compensation of synchronous measurement error for multi-channel laser interferometer. Meas Sci Technol 28:1–7

    Google Scholar 

  8. Huang ND, Jin YQ, Bin QZ, Wang YH (2015) Integrated post-processor for 5-axis machine tools with geometric errors compensation. Int J Mach Tools Manuf 94:65–73

    Article  Google Scholar 

  9. Qiao Y, Chen YP, Yang JX, 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 

  10. Li J, Xie FG, Liu X-J, Li WD, Zhu SW (2016) Geometric error identification and compensation of linear axes based on a novel 13-line method. Int J Adv Manuf Technol 87:2269–2283

    Article  Google Scholar 

  11. Yang JX, Mayer JRR, Altintas Y (2015) A position independent geometric errors identification and correction method for five-axis serial machines based on screw theory. Int J Mach Tools Manuf 95:52–66

    Article  Google Scholar 

  12. Zhu SW, Ding GF, Qin SF, Lei J, Zhuang L, Yan KY (2012) Integrated geometric error modeling, identification and compensation of CNC machine tools. Int J Mach Tools Manuf 52(2012):24–29

    Article  Google Scholar 

  13. Gao HM, Fang FZ, Zhang XD (2014) Reverse analysis on the geometric errors of ultra-precision machine. Int J Adv Manuf Technol 73:1615–1624

    Article  Google Scholar 

  14. Fan JW, Guan JL, Wang WC, Luo Q, Zhang XL, Wang LY (2002) A universal modeling method for enhancement the volumetric accuracy of CNC machine tools. J Mater Process Technol 129(1–3):624–628

    Article  Google Scholar 

  15. Fu GQ, Fu JZ, Shen HY, Xu YT, Jin YA (2015) Product-of-exponential formulas for precision enhancement of five-axis machine tools via geometric error modeling and compensation. Int J Adv Manuf Technol 81(1–4):289–305

    Article  Google Scholar 

  16. Wu C, Fan J, Wang Q, Chen D (2018) Machining accuracy improvement of non-orthogonal five-axis machine tools by a new iterative compensation methodology based on the relative motion constraint equation. Int J Mach Tools Manuf 124(1):80–98

    Article  Google Scholar 

  17. Chen GQ, Yuan JX, Ni J (2001) A displacement measurement approach for machine geometric error assessment. Int J Mach Tools Manuf 41:149–161

    Article  Google Scholar 

  18. Liu YC, Zhang HH, Wang XS (2017) Analysis on influence of perpendicularity error of five axis NC machine tool error modeling accuracy and complexity. Procedia Eng 174:557–565

    Article  Google Scholar 

  19. Chen DJ, Dong LH, Bian YH, Fan JW (2015) Prediction and identification of rotary axes error of non-orthogonal five-axis machine tool. Int J Mach Tools Manuf 94:74–87

    Article  Google Scholar 

  20. Fan JW, Tang YH, Chen DJ, Wu CJ (2017) A geometric error tracing method based on the Monte Carlo theory of the five-axis gantry machining center. Adv Mech Eng 9(7):1–14

    Google Scholar 

  21. Hwang J, Park C-H, Gao W, Kim S-W (2007) A three-probe system for measuring the parallelism and straightness of a pair of rails for ultra-precision guideways. Int J Mach Tools Manuf 47:1053–1058

    Article  Google Scholar 

  22. Ekinci TO, Mayer JRR, Cloutier GM (2009) Investigation of accuracy of aerostatic guideways. Int J Mach Tools Manuf 49:478–487

    Article  Google Scholar 

  23. Zha J, Xue F, Chen YL (2017) Straightness error modeling and compensation for gantry type open hydrostatic guideways in grinding machine. Int J Mach Tools Manuf 112:1–6

    Article  Google Scholar 

  24. Ekinci TO, Mayer JRR (2007) Relationships between straightness and angular kinematic errors in machines. Int J Mach Tools Manuf 47:1997–2004

    Article  Google Scholar 

  25. He GY, Sun GM, Zhang HS, Huang C, Zhang DW (2017) Hierarchical error model to estimate motion error of linear motion bearing table. Int J Adv Manuf Technol 93:1915–1927

    Article  Google Scholar 

  26. Hwang J, Park C-H, Kim S-W (2010) Estimation method for errors of an aerostatic planar XY stage based on measured profiles errors. Int J Adv Manuf Technol 46:877–883

    Article  Google Scholar 

  27. Majda P (2012) Modeling of geometric errors of linear guideway and their influence on joint kinematic error in machine tools. Precis Eng 6:369–378

    Article  Google Scholar 

  28. Qi EB, Fang ZY, Sun T, Chen JC, Liu CZ, Wang J (2016) A method for predicting hydrostatic guide error averaging effects based on three-dimensional profile error. Tribol Int 95:279–289

    Article  Google Scholar 

  29. Tang H, Duan J-A, Zhao QC (2017) A systematic approach on analyzing the relationship between straightness & angular errors and guideway surface in precise linear stage. Int J Mach Tools Manuf 120:12–19

    Article  Google Scholar 

  30. 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 Tools Manuf 40:1235–1256

    Article  Google Scholar 

  31. ISO 230-1:2012. (2012). Test code for machine tools—part 1: geometric accuracy of machines operating under no-load or quasi-static conditions, 1–11

  32. Cheng Q, Zhao HW, Liu ZF, Zhang C, Gu PH (2016) Robust geometric accuracy allocation of machine tools to minimize manufacturing costs and quality loss. Proc Inst Mech Eng Part C-J Mech Eng Sci 230(15):2728–2744

    Article  Google Scholar 

  33. Wang SK (2007) The positioning accuracy analysis of ball screw feeding system abstract [D]. Dalian University of Technology, Dalian

    Google Scholar 

  34. ISO 8636–2:2007. (2007). Machine tools—test conditions for bridge-type milling machines—testing of the accuracy—Part 2: Travelling bridge (gantry-type) machines, 6–37

Download references

Funding

This work is financially supported by the National Natural Science Foundation of China (No. 51775010 and 51705011) and Science and Technology Major Projects of High-end CNC Machine Tools and Basic Manufacturing Equipment of China (No. 2014ZX04011031).

Author information

Authors and Affiliations

  1. Beijing Key Laboratory of Advanced Manufacturing Technology, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Jinwei Fan, Haohao Tao, Changjun Wu, Ri Pan, Yuhang Tang & Zhongsheng Li

Authors
  1. Jinwei Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haohao Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Changjun Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ri Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yuhang Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Zhongsheng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haohao Tao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, J., Tao, H., Wu, C. et al. Kinematic errors prediction for multi-axis machine tools’ guideways based on tolerance. Int J Adv Manuf Technol 98, 1131–1144 (2018). https://doi.org/10.1007/s00170-018-2335-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-018-2335-9

Keywords

Search

Navigation