Thermal error regression modeling of the real-time deformation coefficient of the moving shaft of a gantry milling machine

Abstract

This paper describes a novel modeling method for determining the thermal deformation coefficient of the moving shaft of a machine tool. Firstly, the relation between the thermal deformation coefficient and the thermal expansion coefficient is expounded, revealing that the coefficient of thermal deformation is an important factor affecting the precision of moving shaft feed systems. Then, thermal errors and current boundary and machining conditions are measured using sensors to obtain the first set of parameters for a thermal prediction model. The dynamic characteristics of the positioning and straightness thermal errors of the moving axis of a machine tool are analyzed under different feed speeds and mounting modes of the moving shaft and bearing. Finally, the theoretical model is derived from experimental data, and the axial and radial thermal deformation coefficients at different time and positions are obtained. The expressions for the axial and radial thermal deformation of the moving shaft are modified according to theoretical considerations, and the thermal positioning and straightness error models are established and experimentally verified. This modeling method can be easily extended to other machine tools to determine thermal deformation coefficients that are robust and self-correcting.

Keywords

Moving shaft / Ball screw / Thermal expansion / Thermal deformation coefficient / Error modeling

References

[1] Mayr J, Jedrzejewski J, Uhlmann E, et al. Thermal issues in machine tools. CIRP Ann Manuf Technol, 2012, 61: 771-791.

[2] Putz M, Richter C, Regel J et al (2018) Industrial relevance and causes of thermal issues in machine tools. In: Proceedings of the conference on thermal issues in machine tools, 21–23 March, Dresden, pp 723–736

[3] Liu K, Liu H, Li T, et al. Prediction of comprehensive thermal error of a preloaded ball screw on a gantry milling machine. J Manuf Sci Eng, 2018, 140(2): 021004.

[4] Wang HT, Li TM, Wang LP, et al. Review on thermal error modeling of machine tools. J Mech Eng, 2015, 51(9): 119-128.

[5] Chen JS. A study of thermally induced machine tool errors in real cutting conditions. Int J Mach Tools Manuf, 1996, 36(12): 1401-1411.

[6] Mize CD, Ziegert JC. Neural network thermal error compensation of a machining center. Precis Eng, 2000, 24(4): 338-346.

[7] Zhang Y, Yang JG. Modeling for machine tool thermal error based on grey model preprocessing neural network. J Mech Eng, 2011, 47(7): 134-139.

[8] Zhang Y, Yang JG, Xiang ST, et al. Volumetric error modeling and compensation considering thermal effect on five-axis machine tools. Proc Inst Mech Eng Part C J Mech Eng Sci, 2013, 227(5): 1102-1115.

[9] Blaser P, Pavliček F, Mori K, et al. Adaptive learning control for thermal error compensation of 5-axis machine tools. J Manuf Syst, 2017, 44(2): 302-309.

[10] Wei X, Gao F, Li Y, et al. Study on optimal independent variables for the thermal error model of CNC machine tools. Int J Adv Manuf Technol, 2018, 98(1/4): 657-669.

[11] Yongjin K, Jeong MK, Omitaomub OA. Adaptive support vector regression analysis of closed-loop inspection accuracy. Int J Mach Tools Manuf, 2006, 46(6): 603-610.

[12] Liu H, Miao EM, Wei XY, et al. Robust modeling method for thermal error of CNC machine tools based on ridge regression algorithm. Int J Mach Tools Manuf, 2017, 113: 35-48.

[13] Bai FY (2008) Research on thermal error modeling of machine tools based on Bayesian network. Dissertation, Zhejiang University, Hangzhou

[14] Kim SK, Cho DW. Real-time estimation of temperature distribution in a ball-screw system. Int J Mach Tools Manuf, 1997, 37(4): 451-464.

[15] Xu ZZ, Liu XJ, Choi CH, et al. A study on improvement of ball screw system positioning error with liquid-cooling. Int J Precis Eng Manuf, 2012, 13(12): 2173-2181.

[16] Horejs O (2007) Thermo-mechanical model of ball screw with non-steady heat sources. In: International conference on thermal issues in emerging technologies-theory and applications, 3–6 January 2007, Cairo, Egypt, pp 126–130

[17] Mori M, Mizuguchi H, Fujishima M, et al. Design optimization and development of CNC lathe headstock to minimize thermal deformation. CIRP Ann Manuf Technol, 2009, 58(1): 331-334.

[18] Sun L, Ren M, Hong H, et al. Thermal error reduction based on thermodynamics structure optimization method for an ultra-precision machine tool. Int J Adv Manuf Technol, 2017, 88(5/8): 1267-1277.

[19] Shi H, Ma C, Yang J, et al. Investigation into effect of thermal expansion on thermally induced error of ball screw feed drive system of precision machine tools. Int J Mach Tools Manuf, 2015, 97: 60-71.

[20] Xu YY, Zu L, Wang YY et al (2018) Theoretical analysis and experimental study of thermal deformation model of ball screw and its influence on positioning accuracy. Modul Mach Tool Autom Manuf Tech 1:1–3, 7

[21] Chen C, Qiu ZR, Li XF, et al. Temperature field model of ball screws used in servo systems. Optics Precis Eng, 2011, 19(5): 1151-1158.

[22] Mayr J, Blaser P, Ryser A, et al. An adaptive self-learning compensation approach for thermal errors on 5-axis machine tools handling an arbitrary set of sample rates. CIRP Ann, 2018, 67(1): 551-554.

[23] Yang JG, Fan KG, Du ZC. Technique of real-time error compensation on NC machine tools, 2013, Beijing: China Machine Press

Funding

National Natural Science Foundation of China http://dx.doi.org/10.13039/501100001809(51575272)