Tooth contact analysis of crossed beveloid gear transmission with parabolic modification

Considering the gear manufacturing and meshing theory, a numerical design approach with parabolic modifications was proposed to improve the mesh behaviors of crossed beveloid gear transmission. The generating procedure with parabolic modifications for the crossed beveloid gears with small shaft angle was proposed. And the analytical mesh model with misalignments of crossed beveloid gear transmission was developed. Then the effects of parabolic modifications on contact path and contact ratio were investigated. Also, the misalignments sensitivity was analyzed for the beveloid gears with and without parabolic modifications. Results show that the design situation with a positive parabola coefficient for the pinion and a negative parabola coefficient for the gear is better than other combinations of the parabola coefficients. Both the offset error and shaft angle error tend to deviate the contact path from the theoretical middle region. The parabolic modifications can reduce the sensitivity of contact path to the offset error and shaft angle error for crossed beveloid gear transmission effectively. Both axial pinion and gear position error has little influence on the mesh behaviors for the crossed beveloid gear pair with and without parabolic modifications.