Theoretical analysis and experimental validation demonstrate improved torque prediction in ball bearings, suggesting enhanced design for energy efficiency.
Improving the accuracy of ball bearing torque prediction is essential to design energy-efficient rotating machines. Because the viscous rolling resistance dominates the torque of the ball bearings, regression formula is proposed in previous study. In the previous report (part 1: Viscous Rolling Resistance Formulas for Contact and Non-Contact Zones), the authors propose the viscous rolling resistance formula accounts for variations in Hertzian contact ellipse position and size, and raceway width. This study proposes a more accurate method for calculating ball bearing torque by applying the formula established in the previous report (Part 1). The model considers viscous rolling resistance, traction, cage friction, and drag force. The validity of this method is demonstrated through comparison with experimental results using deep groove ball bearings under fully lubricated conditions. It shows that the error between the calculated and the experimental values is generally within 10%, and the viscous rolling resistance of the non-contact zone accounted for up to 27% of the bearing torque. These results revealed that accurate estimation of rolling resistance not only in the contact zone but also in the non-contact zone of the raceway improves the accuracy of ball bearing torque calculations.
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Egawa et al. (2026) studied this question.
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