Comparative analysis of tooth-root strength using stress-strength interference (SSI) theory with FEM-based verification

Gear geometry plays a significant role in deciding the tooth deflection, magnitude of stress induced and stress distribution. Accurate evaluation of the stress state and distribution of stresses at the tooth root requires application of experimental methods to determine, such as electric resistance wire strain gauges, or photoelastic gauges, etc. These experimental methods are especially complicated, expensive, and laborious. Therefore, they are applied mainly in special cases. In the recent years, the methods of probabilistic design have been commonly accepted in the design of mechanical components and systems to assist the designer in making decisions on the best balanced design with respect to several design criteria. In probabilistic design, it is common to use parametric statistical models to calculate the probability of failure obtained from the Stress-Strength Interference (SSI) theory, which more nearly models the true situation. This paper discusses the application of the SSI theory that has been used to support the detailed gear design as part of the "Design for Reliability" approach to evaluate the tooth-root strength with finite element method-based verification. The SSI theory is formulated to predict the effect of the root fillet generated by rack or hob tool with and without protuberance on the gear system reliability. The results indicate the high fillet root stresses and gear tooth deflection in gears with the lowest tip radius of the generating tool.