Simulation of Thermal Behaviors of Motorized Spindle Based on Fractal Theory and Monte Carlo Method

Abstract

Abstract:

Abstract： The finite element analysis thermal-structure model of a spindle was proposed at the design stage to avoid the sudden failure in actual machining caused by the high temperature rise in the spindle components. The calculation method of bearing heat power, which regarded the contact angle as the iterative variable, was proposed to avoid the disadvantages of the traditional Newton-Raphson algorithm when the bearing quasistatic was analyzed, such as the poor convergence, slow convergence speed and low accuracy. The motor efficiency analysis method was applied to calculate the heat power of the built-in motor. To avoid the inaccuracy of the statistical methods and the poor generality of the experiment methods, the fractal theory and Monte Carlo method were utilized to calculate the thermal contact conductance between joint surfaces. Besides, the convective heat transfer coefficients of different components were calculated according to the Nusselt number. Furthermore, the spindle thermal deformation and temperature distribution were simulated by applying the above boundary conditions to the FEA model. The results show that the modeling approach of high-speed spindle thermal characteristics is correct and the FEA model can accurately predict the temperature distribution and thermal deformation.

Key words: motorized spindle, bearing quasistatics analysis, NewtonRaphson, thermal contact conductance, thermal errors

MA Chi,YANG Jun,MEI Xuesong,ZHAO Liang,WANG Xinmeng,SHI Hu. Simulation of Thermal Behaviors of Motorized Spindle Based on Fractal Theory and Monte Carlo Method[J]. Journal of Shanghai Jiaotong University, 2015, 49(09): 1324-1331.

References

［1］Bryan J. International status of thermal error research ［J］. CIRP AnnalsManufacturing Technology, 1990, 39(2): 645656.

［2］Zhao Haitao, Yang Jianguo, Shen Jinhua. Simulation of thermal behavior of a CNC machine tool spindle ［J］. International Journal of Machine Tools and Manufacture, 2007, 47(6): 10031010.

［3］Chen J S. Neural networkbased modelling and error compensation of thermallyinduced spindle errors ［J］. The International Journal of Advanced Manufacturing Technology, 1996, 12(4): 303308.

［4］杨军, 梅雪松, 赵亮, 等. 基于模糊聚类测点优化与向量机的坐标镗床热误差建模［J］. 上海交通大学学报, 2014，48(8): 11751182.

YANG Jun, MEI Xuesong, ZHAO Liang, et al. Thermal error modeling of coordinate boring based on fuzzy clustering measuring point optimization and support vector machine ［J］. Journal of Shanghai Jiaotong University, 2014，48(8): 11751182.

［5］杨军, 施虎, 梅雪松, 等. 双驱伺服进给系统热误差的试验测量与预测模型构建［J］. 西安交通大学学报, 2013, 47(11): 5359.

YANG Jun, SHI Hu, MEI Xuesong, et al. Experimental measurement and construction of prediction model and of the dualdrive servo feed system thermal error ［J］. Journal of Xi’an Jiaotong University, 2013, 47(11): 5359.

［6］Bossmanns B, Tu J F. A thermal model for high speed motorized spindles ［J］. International Journal of Machine Tools and Manufacture, 1999, 39(9): 13451366.

［7］Creighton E, Honegger A, Tulsian A, et al. Analysis of thermal errors in a highspeed micromilling spindle ［J］. International Journal of Machine Tools and Manufacture, 2010, 50(4): 386393.

［8］Greenwood J A, Williamson J B P. Contact of nominally flat surfaces ［J］. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1966, 295(1442): 300319.

［9］McWaid T, Marschall E. A comparison of elastic and plastic contact models for the prediction of thermal contact conductance ［J］. Wrmeund Stoffübertragung, 1993, 28(8): 441448.

［10］Harris T A. Rolling bearing analysis ［M］. New York: Wiley, 1984.

［11］Kylander G. Thermal modelling of small cage induction motors ［D］. Sweden： Chalmers University of Technology, 1995.

［12］Incropera F P, Lavine A S, DeWitt D P. Fundamentals of heat and mass transfer ［M］. New York：John Wiley & Sons, 2011.

［13］Berry M V, Lewis Z V. On the WeierstrassMandelbrot fractal function ［J］. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1980, 370 (1743): 459484.

［14］Cooper M G, Mikic B B, Yovanovich M M. Thermal contact conductance ［J］. International Journal of Heat and Mass Transfer, 1969, 12(3): 279300.

［15］Zou Mingqing, Yu Boming, Cai Jianchao, et al. Fractal model for thermal contact conductance ［J］. Journal of Heat Transfer, 2008, 130(10): 10130111013019.