Safety of Spur Gear Design Under Non-Ideal Conditions With Uncertainty

The current practice of gear design is based on the Lewis bending and Hertzian contact models. The former provides the maximum stress on the gear base, while the latter calculates the contact pressure at the contact point between the gear and pinion. Both calculations are obtained at the reference configuration with ideal conditions; i.e., no tolerances and clearances. The first purpose of this paper is to compare these two analytical models with the numerical results, in particular, using finite element analysis. It turns out that the estimations from the two analytical equations are closely matched with those of the numerical analysis. The numerical analysis also yields the variation of contact pressures and bending stresses according to the change in the relative position between gear and pinion. It has been shown that both the maximum bending stress and contact pressure occur at non-reference configurations, which should be considered in the calculation of a safety factor. In reality, the pinion-gear assembly is under the tolerance of each part and clearance between the parts. The second purpose of this report is to estimate the effect of these uncertain parameters on the maximum bending stress and contact pressure. For the case of the selected gear-pinion assembly, it turns out that due to a 0.57% increase of clearance, the maximum bending stress is increased by 4.4%. Due to a 0.57% increase of clearance, the maximum contact pressure is increased by 17.9%.