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In this paper, a potential energy based slice grouping method was proposed to calculate the mesh stiffness for straight beveloid gears with parallel axes. The mathematical mesh stiffness model was derived. The finite element tooth contact model was developed and the loaded tooth contact analysis was conducted to calculate the mesh stiffness. The verification for the mesh stiffness was conducted with the error 3 %, which proves the feasibility and accuracy. Then, the effects of parameters such as pressure angle, pitch cone angle, and profile shift coefficient on the mesh stiffness were investigated. Results show that the normal pressure angle and the tooth width have obvious effects both on the single tooth and synthesized mesh stiffness. When pressure angle is less than 20°, mesh stiffness will be increased with the increase of pressure angle. However, it decreases rapidly when the pressure angle exceeds 20°. Both the single tooth and synthesized mesh stiffness increase obviously as the tooth width increases. The increase of the cone angle and addendum coefficient have a little effect on the single tooth mesh stiffness, but have the obvious incremental effects on the synthesized mesh stiffness. The contact ratio increases obviously with the increase of the addendum coefficient. The profile shift coefficient and the clearance coefficient have unsubstantial effects both on the single and synthesized mesh stiffness.

Tool errors are inevitable in an actual gear-manufacturing environment and may directly affect the accuracy of machined tooth surfaces. In this paper, tool errors including spheric radius, pressure angle, rake angle, regrind angle, and cutting side relief angle errors for three-face blade are defined and considered to establish the accurate tooth surface mathematical model for face-hobbed hypoid gears based on the manufacturing process and the meshing theory. The simulation flowchart for tooth surface modeling and tooth surface topography deviation analysis are proposed and performed. Results show that the tooth surface deviation is positive with positive spheric radius and rake angle errors and contrary results can be found for other three tool errors. In addition, the impact of the pressure angle error is the strongest. In addition, the rake angle error has the weakest effect and the influence of spheric radius error on the tooth surface deviation is unsubstantial. For location of tooth surface deviation, the maximum deviation is at the top on the heel and the minimum deviation is at the middle on the toe for spheric radius error. The maximum and minimum deviations are at the top and the middle tooth on the heel for other factors, respectively.

This paper proposed a new tooth surface modeling method for beveloid gear based on the real cutter surface using two orthogonal variables. Then, the analytical mesh model with and without misalignments were derived and solved to study the influences of geometry design parameters on contact behaviors for paralleled beveloid gear pair. Loaded tooth contact analysis is used to validate the proposed mesh model by abaqus software, and the error is below 5%. Results suggest that the increase in pressure, cone, and helical angles enlarge the contact area for meshing without misalignments. The addendum coefficient has unsubstantial impacts on the contact behaviors. For meshing with axis error in the horizontal direction, the growth of pressure angle, cone angle, helical angle, and addendum coefficient improves the carrying capacity of single tooth. But the transmission error deteriorates with the increase in pressure, cone, and helical angles. All three types of misalignments have little influence on the size of the contact ellipse. The growth of axis errors in horizontal and vertical directions significantly increases the transmission error, but the center distance error has a little influence on the transmission precision.

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