Based on the roller thread equation, the spur tooth profile equation, and coordinate transformation relationships, the surface equations of the incomplete gear pairs in the planetary roller screw mechanism were established. Combining the gear meshing principle with the surface equations of incomplete gear pairs, a model for calculating the contact point positions and contact line lengths of incomplete gear pairs was proposed. A finite element model for incomplete gear pair was introduced to validate the correctness of the present model. The influence of the initial angle and width of the spur gear on the meshing characteristics of incomplete gear pairs was analyzed. The results show that under the same meshing radius, the maximum and minimum contact line lengths on each spur tooth structure are not affected by the initial angles of the roller's spur tooth profile and the roller's spur thread. The analysis shows that when the tooth width of the incomplete gear pair is an integer multiple of the roller thread lead, under the same meshing radius, the contact line lengths on any spur tooth structure are identical.
A Mon, study studied this question.