Development of a Statistical Reliability-Based Model for the Estimation and Optimization of a Spur Gear System

Abstract

In this paper, a statistical model, which is based on the stress–strength theorem, has been proposed for the estimation and optimization of spur gear systems embedded (running) in a mechanical device. First, the model is used for the estimation of the variation of the bending stress and the contact pressure distribution in the spur gear systems, which several studies have confirmed as the main source of failure (failure modes) in the spur gear system. The optimal variation values of the stress and strength distribution as well as the reliability of the spur gear systems are then determined via a statistical reliability analysis method embedded in model, which is otherwise referred to as the proactive approach. The proactive approach is mainly applied to evaluate and predict the system failures. The computational results from the analysis show that the higher the stress distribution function, the lower the reliability of the spur gear system. Also, with a distributed strength function of 696.3 MPa and a mean value of 100 MPa of the spur gear system, the optimal stress value is between the range 0–369.5 MPa.