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To explore the meshing mechanism of classic conic worm drive and provide a theoretical basis for creating other types of worm drive, a complete meshing theory on the proposed worm pair and its meshing performance are investigated. A new mathematical model containing a full set of geometric parameters on this drive is established using differential geometry. The formulae for calculating the reference point coordinates in different coordinate systems are attained, and then the blank size of the conical worm wheel is given. To build tooth surface boundaries, the meshing theory based on reference point is applied, which ensures the location of this point on the tooth surface. By solving multivariate nonlinear equation system in MATLAB environment, these conjugate regions and instantaneous contact lines are plotted within the axial section of the conic worm pair, at the same time, these values of sliding angle and induced principal curvature at meshing points are calculated. Finally, a numerical study is performed and the results verify that the conic worm pair has a relatively high tooth surface utilization ratio and favorable conditions for contact stress and lubrication, which is consistent with the practical application.
Zhu et al. (Fri,) studied this question.