Calculation of mesh stiffness of spur gears considering complex foundation types and crack propagation paths

Based on the finite element theory and the loaded tooth contact analysis, an analytical-finite-element model considering the complex foundation types and the crack propagation paths is proposed to calculate the mesh stiffness of spur gears. The complex gear foundation types (including web foundation and slots foundation) and the crack propagation paths (including tooth fracture and rim fracture) are considered in the proposed method, and the effects of various foundation types, crack propagation paths and crack lengths on the mesh stiffness are analyzed. In order to verify the proposed method, the simulated crack paths are confirmed by those derived from the experimental and the extended finite element methods, and the mesh stiffness obtained from the proposed method is validated by that of the potential energy method and the three-dimensional finite element method. Compared with the potential energy method, the proposed model can be used to calculate the mesh stiffness of spur gears with different gear foundation types and real crack propagation paths. Meanwhile, the proposed method has higher computational efficiency compared with the finite element method (e.g., the finite element method takes about 3.5 h for a mesh cycle and the proposed method costs 25 s). The results indicate that the web thickness has greater influence on the mesh stiffness of spur gears than the rim thickness. The results show that two crack types, namely the tooth fracture and rim fracture, have more obvious influence on the mesh stiffness of single-tooth contact zone relative to that of the double-tooth contact zone. (C) 2019 Elsevier Ltd. All rights reserved.