The second envelope method of point-vector and its application on worm wheel grinding modified gear

A conventional worm wheel profile is obtained by establishing the meshing equation of the wheel and gear and determining the contact trace, which is difficult to use in calculating the non-standard profile gear. The second envelope method of point-vector (PV) is then proposed, which is actually a digital calculation method. The grinding wheel profile is formed by generating motion of the gear surface. The generating motion is divided into the first and second envelope motion. Using a PV approximation method, a gear profile is dispersed into a series of PVs to establish the PV envelope principle and the envelope approximation algorithm, determine the envelope point with the minimal orientation-distance to the wheel in the PV group, and obtain the wheel profile by fitting all the envelope points. In this paper, a detailed description of the wheel profile forward and gear profile backward calculation processes is provided using the second envelope method of PV. Experimental verification of the calculation results demonstrates that this method can be employed to calculate and machine any gear profile and achieve high accuracy.