An analytical determination of speed factor in gear designs

Abstract

In practical gear design, the “speed factor” is usually employed which is defined as a ratio of the allow-able stress at required running speed of the gear system to the stress at zero speed. At present, several expressions for the speed factor are recommended by several authorities; however, those are almost all empirical and not analytical. The present paper aims to contribute to an analytical determination of the speed factor for spur gears as stated below. First, from a dynamic photoelastic test of a pair of spur gears, the following results were obtained: Next, flexural fatigue testing was conducted with the epoxy resin, the photoelastic material, and the S-N diagram was determined. Finally, the cumulative-damage concept was applied into the fatigue failure of the gear tooth where the above-determined hystogram of fillet stresses and the S-N diagram were used; then, the allowable mean stress which ensures 107 endurance was estimated for each running speed. An analytical value of the speed factor was then determined by dividing the allowable stress by the fatigue strength of the material at 107 cycles. The speed factor thus obtained was compared with the conventional expressions for the speed factor.