A slotting method for cosine gears was proposed by using the involute cutter based on the conjugate theories of digital surface and gear meshing. The slotting model between the cosine tooth surface represented by discrete points and the cutter figuration determined by analytic function was built for their geometrical relationship and conjugate motion during the machining process. Conjugate points in the cutter section corresponding to the discrete points on the cosine gear tooth surface and the conjugate movements were solved. By using the flexible control of the CNC procedure, the active control of the cutting trace of the slotting cutter was accomplished and the envelop forming of the cosine gear was obtained. Based on the software C++ and Matlab, the computer aided manufacturing(CAM) system of the cosine gear was developed, and the simulation of the slotting process was accomplished. Several examples were provided to illustrate the approach. The result of the simulation demonstrates that the proposed slotting method is feasible.
A mathematical model of gear tooth profiles using the ellipse curve, whose curvature is convenient to control by changing the mathematical parameters as its line of action, was built based on the meshing theory. The equation of undercutting condition was derived from the model. A special epicycloidal tooth profile was also presented. An example gear drive with variation of the ellipse parameters was taken to illustrate the proposed method. The contact ratio of the gear drive designed by the proposed method was analyzed. A comparison of the property of the gear drive designed with the involute gear drive was also carried out. The results confirm that the proposed gear drive has higher contact ratio in comparison with the involute gear drive.
