Estimating beam strength of metallic gear materials

Expressions for the pulsating or beam strengths of many popular metallic gear materials are derived based on the tensile strength and endurance ratio. The strength values predicted are for a reliability of 99% at load cycles corresponding to that of the endurance strength of the materials. The expressions are based on the consideration of the revised Lewis gear root stress formula by treating the design parameters as random variables associated with the lognormal probability density function and application of the Gerber fatigue failure rule. Pulsating strength predictions are compared with those of AGMA estimates for through-hardened steels and other materials. The variances between model predictions and AGMA values for steel and ductile cast iron materials are reasonably low. Low variances between model and AGMA values for high-strength gray cast iron and cast bronze were also observed. However, high variances between model and AGMA values for low-strength gray cast iron and cast bronze were found. Overall, the model estimates are considered sufficiently accurate for preliminary design applications where initial sizes of gears are generated. The study showed that for many metallic gear materials, the average pulsating strength ratio is 0.36 at 99% reliability. Therefore, the suggestion by Buckingham, that the fatigue strength of a gear tooth is approximately one-third (0.333) of the tensile strength of the material is justified.