Reliability Modeling of Complex Ball Mill Systems with Stress–Strength Interference Theory

The ball mill is a critical size reduction equipment in industries such as mining and metallurgy. However, the sustainable reliability modeling of the entire system is challenging due to its complex service conditions. This paper presents a systematic framework for the reliability analysis of ball mills based on Stress–Strength Interference Theory (SSIT). Based on a reliability block diagram (RBD), this study establishes a system-level reliability model for the ball mill. Within this framework, the cylinder model is developed using the energy conservation principle between impact energy and strain energy; the gear model comprehensively considers both contact and bending fatigue failure modes; and the bolt model is constructed through mechanical analysis in conjunction with Hooke’s law. In the case study, a laboratory-scale mill (Φ5.5 × 2.6 m shell, effective grinding chamber: 5.3 m inner diameter × 2.376 m length) operating at 14 RPM under dry grinding conditions is analyzed. The reliability of individual components and the entire system is computed using Monte Carlo simulation. The results indicate that the overall system reliability increases when one of the following three conditions is met: the surface hardness of the gear is higher and the tangential force is lower; the impact velocity on the cylinder is lower and the impacted area is larger; or the tensile force on the bolt is reduced.