Dark Gray Box Lumped Parameter Thermal Network for High Speed Spindle Rolling Bearings

The paper proposes the application of an innovative methodology for creating thermal circuits called Dark Gray Box Lumped Parameter Thermal Network, through which the thermal fields of high speed spindle rolling bearings can be predicted. During machining operations, radial and thrust loads will be exerted in the spindle system. These loads, at high rotational speeds will produce frictional moments, hence, generating heat losses that are absorbed by the inner components of the rolling bearing. In this study, the thermal resistances between the inner race and balls, and the outer race and balls were calculated applying the theory of fast moving elliptic thermal resistances. Additionally, the heat convection coefficients were independently calculated for the determination of the thermal resistances by convection between the inner race and the lubricant film, outer race and lubricant film and the balls and the lubricant film in order to create a more accurate model of the system. The solution of the Dark Gray Box LPTN was obtained applying the State Space approach, determining the temperature variations of the inner race, balls and the assembly consisting of the outer race and housing. The findings of this study were compared with Finite Element Analysis using Ansys transient thermal and with experimental tests performed by preceding studies, showing to be consistent. In conclusion, the method is effective as an observer, meaning that the thermal fields of the inner components of a ball bearing can be determined by input factors including, frictional moments, the thermal properties of the material, external loads and the high rotational speed.