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.
Highlights
Involute beveloid gears, which were first proposed by Mettitt in 1954, have the variable profile shift modification coefficient along axes direction
To accurately and efficiently calculate the time-varying meshing stiffness of gears, domestic and foreign scholars have done a lot of research. e current methods for calculating the time-varying meshing stiffness of gears generally include the potential energy method and the finite element method (FEM) from the literature in recent years
It can be found that the total meshing stiffness has increased with the adding of the pressure angle, and the total mesh stiffness improved by 6% when the pressure angle increased from 17° to 21°. e reasonable explanation of this is that the tooth thickness at the root of the tooth increases. e radius of curvature of the tooth surface increases as the pressure angle increases. erefore, the total mesh stiffness of the beveloid gear has increased
Summary
Involute beveloid gears, which were first proposed by Mettitt in 1954, have the variable profile shift modification coefficient along axes direction. Song et al proposed the potential energy-based slice grouping method to calculate the mesh stiffness for straight beveloid gears with parallel axes [13]. E slice grouping method was proposed on the basis of potential energy to calculate the total meshing stiffness of beveloid gears with the rough surface topography. An improved potential energy method based on fractal theory was proposed to calculate the total meshing stiffness for beveloid gears of a rough surface in this paper. Due to the fact that the effective contact part of the beveloid gear teeth can be regarded as the trapezoidal section in the axial direction, the calculation formula of Ii, Ai, and G can be expressed as
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