Study on excitation and time-varying mesh characteristics of straight bevel gears considering modification and friction

An accurate and numerically efficient nonlinear coupled excitation model for straight bevel gears (SBG) with linear and point contact is proposed. This model incorporates stiffness, load distribution, and transmission error (TE) models. Considering root fillet and axial mesh force components, energy equivalence principle, accumulated integral potential energy method, and segment coupling theory, single mesh stiffness (SMS) models with and without coupling effect are proposed. On this basis, the formula for calculating SMS under the action of friction is given. Time-varying mesh stiffness (TVMS), load distribution, and TE models were established using the deformation compatibility condition and principle of force balance. The proposed model was verified by comparing the calculation results with those obtained using the finite element method (FEM). The semi-analytical TVMS model used in this study could be solved accurately and quickly. The meshing characteristics and changing rules of SBG under the influence of different modification methods, modification amounts, and friction coefficients were analyzed. This study is expected to help further enrich and develop gear stiffness theory and provide a theoretical tool for gear dynamics research.