Impact of Tooth Spacing Errors on the Root Stresses of Spur Gear Pairs

In this study, experimental and theoretical investigations of the effect of tooth spacing errors on the root stresses of spur gear pairs are performed. A test setup with instrumentation for the measurement of root stresses has been developed. A number of experiments were performed with gears having deterministic (at one or two teeth only) and random spacing errors (all teeth having a random distribution of errors as in a typical production gear). These experiments were simulated using a deformable-body gear contact model to describe the empirical trends physically. A methodology is proposed to relate increases in root stresses to the spacing error magnitudes directly. Closed-form expressions resulting from this methodology permit the determination of the stress amplification factors due to a certain range of spacing error tolerances as well as quantifying how much spacing error can be tolerated within a user defined stress limit.