Analytical calculation of mesh stiffness for spiral bevel gears with an improved global tooth deformation model

The paper proposes an efficient and accurate analytical calculation model of time-varying mesh stiffness (TVMS) for the spiral bevel gear. Firstly, an enhanced numerical loaded tooth contact analysis (NLTCA) model that considers both the global tooth and local contact deformations is developed. Based on Tredgold's approximation, spiral bevel gears are sliced into a series of spur gears. An improved global tooth deformation model is developed by accounting for axial tooth deformation and the effect of non-contacting tooth slices. The influence coefficient method is utilized to determine the local contact deformation. Subsequently, based on the results of the NLTCA model, a detailed calculation procedure for determining the TVMS of spiral bevel gears is described. Finally, some numerical examples are provided to illustrate the efficiency and accuracy of the proposed model through comparisons to finite element analysis (FEA) results. The proposed model can achieve satisfactory accuracy without FEA modification. Furthermore, ignoring the effects of the non-contacting tooth slices will lead to excessive elastic deformation when the length of the contact area across the tooth width is significantly shorter than the tooth width.