Calculation of line and point contact ratio for orthogonal spur-face gear drive

The contact ratio of face gear drive is hard to calculate precisely because it is point contact adjusted from line contact to avoid jamming. To obtain the calculation methods and improvement measures for the contact ratio of face gear drive, the line contact ratio (LCR) in shaping and the point contact ratio (PCR) in meshing are investigated in this paper. Tooth surface equations of face gear shaping are established based on its generation principle and the contact line midpoint tracks are obtained. Iterative equations to accurately calculate restrictive conditions (undercutting and pointing) for face gear tooth are constructed and verified, their approximate equations are given further. Meshing tracks in face gear drive are obtained by solving the established meshing equations. Calculation methods of the LCR and PCR are elaborated according to their definitions and the fitting equations are given for engineering application. The results show that the PCR is markedly lower than the LCR. The advantage of high contact ratio of face gear drive is significantly affected because it is very sensitive to the realization of point contact. It is acceptable to use the LCR to approximate the PCR when the distribution range of the meshing track on the face gear tooth surface is determined. It provides a theoretical basis for the design and optimization of orthogonal spur-face gear drive.