An Improved Model for Calculating the Mesh Stiffness of Helical Gears

Time-varying mesh stiffness (TVMS) is one of the important internal excitations of gear transmission systems. Accurate solution of meshing stiffness is the key to research the vibration response of gear transmission system. In the traditional analytical method (TAM), the TVMS of single-teeth engaged region consist of bending, shearing, axial compression deformation stiffness, fillet-foundation stiffness, and Hertzian contact stiffness, the TVMS of double-tooth engaged region is the sum of the single-tooth engaged region, which will lead to repeated calculation of the fillet-foundation stiffness. In order to overcome this shortcoming, considering the coupling effect between two pairs of meshing tooth, an improved method of fillet-foundation is adopted to calculate to TVMS of each slice gear. According to the ‘slicing method’, the helical gear is divided into slice gear. Considering the coupling effect of each slice gear, the TVMS of helical gear can be obtained. The improved analytical method (IAM) is verified by comparing with finite element method (FEM) and TAM. Based on the IAM, the effects of the helical angle, face width, the number of gear, and modification coefficient on the mesh characteristics are analyzed. The results show that the IAM is consistent with the FEM and also consistent with TAM in single-tooth engagement. However, there is obviously error with the TAM in double-tooth or multi-tooth engagement.