A Time-Dependent Reliability-Based Design Optimization Method for Rolling Bearings with Thermal Failure Probability Constraints

Thermal failure is a critical failure mode in rolling bearings, particularly under high-speed or heavy-load conditions, resulting in severe consequences such as lubrication failure or bearing seizure. However, existing optimization approaches that consider thermal characteristics frequently neglect time-dependent uncertainties, including dynamic loads and ambient temperature variations, which influence thermal failure risk. This study proposes a reliability-based design optimization framework to derive structural parameter designs for rolling bearings that satisfy thermal failure probability constraints. First, a thermal network model is established to capture the bearing's dynamic thermal response using a quasi-static mechanical model combined with a thermal resistance approach. Subsequently, a two-stage time-series sampling method is developed for time-dependent reliability analysis, enabling efficient evaluation of thermal failure probability under dynamic operating conditions. To maximize the bearing's dynamic load capacity, an optimization formulation is introduced that decouples the optimization loop from failure probability estimation. Finally, the effectiveness of the proposed method is demonstrated in a case study involving a deep-groove ball bearing for an electric motor.