Influence of Certain Variables on the Stresses in Gear Teeth

Abstract

A photoelastic study was made to obtain a more accurate picture of the localized stresses in gear tooth fillets than can be obtained from the commonly used Lewis equation. A set of approximate stress concentration factors are presented for fillets in gear teeth based upon a set of variables such as the radius r of the fillets, thickness t of tooth, height h of load position on the tooth, etc. The problem was attacked by making a series of tests of ``conventionalized gear teeth'' in the form of short cantilever beams in which one factor at a time could be varied. The values of stress concentration factor were computed as the ratio of the maximum stress in the fillet to the calculated stress at the ``assumed weakest section,'' as defined by Lewis' equation. In general, it was noted that as the height of load position (h/t) was increased, the maximum stress increased, but the stress concentration factor decreased. An approximate equation for the tensile stress concentration factors, k, for the conventionalized models with sides of the tooth parallel is: k=1.25(t′/r)0.2(t/h)0.3. A definite decrease in the tensile stress concentration factor was observed as the tooth model was gradually tapered inward to approach Lewis' ideal shape of the parabola of uniform strength, whereas no change in the compressive stress concentration factor occurred as the angle was varied over a 25° range. Tests now in progress on generated gear teeth having a 14½-degree pressure angle and a diametral pitch of 2 indicate that the stress concentration factor for the tensile fillet is given fairly accurately by the formula: K=0.22(t/r)0.2(t/h)0.4.