Gear-Tooth Stresses at High Speed

Abstract

If the maximum stress in a gear tooth is less than the fatigue limit for the material, the tooth should not fail even after indefinitely prolonged running. Fatigue data collected in the conventional way suggest that the number of stress cycles required to cause failure of a given material under any particular stress is independent of the time-rate of repetition of stress. It should therefore be permissible to stress any gear, regardless of its speed, up to the fatigue limit for its material, although this suggestion may need modification because of the difference between the impulsive nature of the application of load to a gear, and the more gradual fluctuation of stress in a fatigue-test specimen of the Wöhler type. Where high-speed gears have failed under stresses apparently lower than the fatigue limit, it becomes necessary to consider whether the actual stress was as low as had been supposed. Errors of pitch and profile in gear teeth may cause actual stresses to be higher than nominal stresses by an amount that increases with speed in any particular installation, up to a limit that would not be exceeded even at infinite speed. The nominal permissible stress (corresponding to the mean transmitted torque) should therefore take account of probable errors in the teeth. High tooth-loads may also be induced by running a geared system in a condition approaching that of resonance with some type of vibration. In general, this danger is more likely in high-speed installations than in others, and it is not always wise to follow the usual practice of ignoring its possibility.