Thermal Model of a Ball Bearing using the State-Space approach and Light Gray-Box Lumped Parameter Thermal Network

¹ Institute of Machine Tools and Mechatronics, Faculty of Mechanical Engineering and Information Technology, University of Miskolc, Miskolc-Egyetemváros, Hungary
^2,3 Institute of Machine Tools and Mechatronics, Faculty of Mechanical Engineering and Information Technology, University of Miskolc, Miskolc-Egyetemváros, Hungary
⁴ Institute of Energy Engineering and Chemical Machinery, Faculty of Mechanical Engineering and Information Technology, University of Miskolc, Miskolc-Egyetemváros, Hungary

^* Corresponding author: szgtscab@uni-miskolc.hu
Email: hegedus.gyorgy@uni-miskolc.hu, Email: daniel.toth1@uni-miskolc.hu
Email: peter.bencs@uni-miskolc.hu

Abstract

In this paper, a thermal model of a ball bearing subjected to radial loads is presented. By the application of the State-Space approach and the Light Gray-Box lumped parameter thermal network, the temperature of the inner components of a ball bearing, these are: outer-race T_o; balls T_b and inner-race T_i; and the temperature of the housing T_h were determined. The relation between the external force, rotational speed, lubrication type, were investigated for the purpose of determining the total frictional moment M_f that occurs among the elements comprising the ball bearing. Subsequently, the total heat losses Q_f were calculated together with the heat distribution along the elements of the ball bearing. The analytical results were validated experimentally. It could be seen that the standard deviation of temperature between the thermal model and the experimental measurements over the outer-race T_o and housing T_h were sd = 5.06 % and sd = 0.33 % . Moreover, the temperature of the balls T_b and the inner-race T_i were predicted. In this context, the results show good agreement with real data, therefore, the thermal model can be utilized to foresee the thermal behavior of bearings with similar geometry that undergo effects of radial loads.