Numerical Calculation Method of Meshing Stiffness for the Beveloid Gear considering the Effect of Surface Topography

Abstract

The tooth surfaces of beveloid gears have different topography features due to machining methods, manufacturing accuracies, and surface wear, which will affect the contact state of the tooth surface, thereby affecting time-varying mesh stiffness between mating gear pairs. Therefore, a slice grouping method was proposed in this paper on the basis of potential energy to calculate the total meshing stiffness of beveloid gears with the surface topography. The method in this paper was verified by finite element method (FEM). Compared with the calculation results of this paper, the relative error is 5.9%, which demonstrated the feasibility and accuracy of the method in this paper. Then, the influence of parameters such as pressure angle, helix angle, pitch angle, tooth width, fractal dimension, and fractal roughness on meshing stiffness was investigated, of which results show that pressure angle, pitch angle, tooth width, and fractal dimension have an incremental impact on the mean value of mesh stiffness. However, the fluctuating value of mesh stiffness has also increased as the pressure angle, tooth width, and pitch cone angle increase. Both the helix angle and the fractal roughness have a depressive impact on the total stiffness. But the difference is that, with the increase of the helix angle, the fluctuation of meshing stiffness has been decreased. Conversely, with the increase of the fractal roughness, the fluctuation of meshing stiffness has been increased.

Stiffness analysis of nutation face gear considering roughness

“…Nutation face gear belongs to a kind of face gear, and the rough surface in the contact area is a series of discrete points when the nutation face gear transmission engages, so the meshing line can be approximated as a curve. Through literature analysis (Mao, 2022), it can be concluded that in practical calculations, the three-dimensional fractal function needs to be improved and dimensionally reduced before using. Therefore, when calculating the meshing stiffness of the nutation face gear considering roughness, the rough surface three-dimensional fractal function was not used to characterize the model.…”

Nonlinear dynamics analysis of gear system considering time-varying meshing stiffness and backlash with fractal characteristics

“…A slice grouping method based on potential energy was advanced to calculate the TVMS considering fractal tooth surface in Ref. [36]. Yang et al [37] developed a contact stiffness calculation model of two arc gears considering friction based on an improved fractal contact model.…”

Research on Time-Varying Meshing Stiffness of Marine Beveloid Gear System

“…Therefore, Wu et al [32] proposed an improvement to the elastic deformation formula for calculating the meshing stiffness of cylindrical gears. Mao et al [33] improved the Weber method based on the slicing principle. However, these methods can only accomplish the calculation of the meshing stiffness of variable beveloid gears with specific parameters and the systematic and generalized approach still presents a gap.…”

“…The finite element method (FEM) is the widely-chosen method among the various numerical methods for calculating the meshing stiffness of beveloid gears [34][35][36][37]. However, these researchers only analyzed models with specific parameters.…”