Research On Meshing Principle Of Planar Enveloping Conical Worm Drive

Compared with traditional Archemides conical worm drive,the enveloping worm drive has the advantages of large transmission ratio,compact structure,large number of teeth meshing,large coincidence degree and smooth transmission.If enveloped worm drive could be manufactured successfully,the tooth surface of cone and cone of the worm wheel can be grind,thus there is a hope to change the material of the cone worm wheel from copper to steel,for more excellent study of the cone worm transmission has not to be started up very well.Related research shows that the study of enveloping worm drive is still in the embryonic stage,so it needs to be improved and perfected.According to the theory of gear meshing,the basic and the basic quantities of the first kind of tooth surfaces are calculated.The equations of the enveloping helical worm helix are written out,and the unit normal vector is derived.The meshing boundary function and the curvature interference boundary function of the meshing engagement of the enveloping worm worm tooth,and deduces the calculation formula of the curvature parameter of the spiral surface of the enveloping worm.According to the gear meshing theory,the envelope equation of the enveloping worm wheel is deduced and the unit normal vector of the tooth surface is obtained.The formulas of the curvature parameters of the enveloping worm gear tooth surface are established,and the induced principal curvature and sliding angle of the enveloping worm pair are obtained.According to the results of the study,the computer-aided meshing analysis of the enveloping worms was carried out.The working length of the enveloping worm,the range of the conjugate region of the enveloping worm tooth and the distribution of the instantaneous contact line of the enveloping worm are analyzed.At the same time,the main meshing characteristics such as the induced principal curvature and the sliding angle of the conical worm pair at the meshing point of the instantaneous contact line are analyzed.The influence of design parameters and processing parameters on the global and local meshing characteristics of the conical worm worms are investigated,and a reasonable geometric design method for the enveloping worm drive is summarized.The mathematical equations of conical worm and conical worm gear tooth surface and the conjugate tooth profile equation of conical worm drive are deduced by using the knowledge of gear meshing theory,and the formation method of tooth surface is put forward.The tooth shape of the conical worm,the conjugate area of the conical worm’s tooth surface and the instantaneous contact line distribution of the conical worm’s transmission are drawn in MATLAB.The optimal design parameters of the original parameters are given according to the meshing analysis.The results show that the planar enveloping worm drive has a series of excellent meshing characteristics.And the parameters of the flat grinding wheel are adjustable,which provides a vast space for further improving the performance of the conical worm pair.