Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack

Gear tooth deviations are the main excitation sources for gear dynamic responses. However, it is seldom considered in the analytical mesh stiffness model except for some computational analysis like finite element method. To make up this gap, a general analytical mesh stiffness model is proposed in this paper to include the effect of the gear tooth errors. This proposed model establishes the relationship between the gear tooth errors and the total mesh stiffness, load sharing among different tooth pairs in mesh and loaded static transmission errors (LSTE). It is suitable for not only the gear pairs with low contact ratio (LCR), but also the gear pairs with high contact ratio (HCR). Two spur gear pair models, namely one with LCR between 1 and 2 and the other one with HCR between 2 and 3, are used to demonstrate the effectiveness of the proposed mesh stiffness model. Influences of the TPM, applied torque and gear tooth root crack on the mesh stiffness, load sharing and loaded static transmission errors are also investigated.