A novel semi-analytical method for fillet foundation deflection calculation in presence of a tooth crack propagating into the rim of a spur gear

Abstract

Existing analytical approaches for calculating fillet foundation deflections in spur gear struggle to adequately address the complexities introduced by tooth cracks, particularly as cracks propagate into the gear body. The finite element methods are accurate but computationally expensive. In response to these challenges, the paper introduces a novel semi-analytical method based on elastic circular ring theory that is capable of calculating the fillet foundation deflection for both healthy and cracked conditions. To establish the usefulness of the method, the fillet foundation deflections obtained are further used to obtain the time-varying mesh stiffness. A methodology centered on compatibility conditions is employed to achieve load distribution during double tooth engagement. The results are verified using two three-dimensional finite element models. In addition, the effect of different hub hole radii, crack lengths and orientations on the fillet foundation deflections and TVMS are investigated. The outcomes suggest that the proposed semi-analytical approach demonstrates superior accuracy in the calculation of spur gear mesh stiffness compared to alternative methods.