Effect of backup ratio on root stresses in spur gear design

This article studies the effect of backup ratio in spur gear root stress analysis and design. Backup ratio is important in understanding rim failures that start at the tooth root. Such failures can become the critical failure mode in gears with low rim thickness such as those used in turboprops, helicopters, and other applications where compact size and low weight are important design considerations. Here an analytical approach, based on theory of elasticity, is used to provide a computational formulation for root stress calculations in spur gears based on their bending capacity both as a function of tooth strength as well as rim strength. Sensitivity analysis is then applied (due to the analytic nature of the formulation) to evaluate the effect of backup ratio on root stresses as well as on the American Gear Manufacturers Association's (AGMA) geometry factor used in standardized design methods. It is shown that there exists an optimal backup ratio that would minimize root stresses. The sensitivity analysis leads to a simple design rule for spur gears based on the backup ratio consideration.