Digital Modeling of Cone-generated Enveloping Torus Worm - Zhi Liu; Hong Lu; Xin Kuang; Liang Xia (Jixie chuandong)
The meshing performance of enveloping tours worm drive requires the envelope lines to be matched strictly in accordance with the established relationship， the accuracy of tooth profile will directly affect its application performance. Aiming at the complicate meshing surface representation issue of cone-generated enveloping torus worm， the digital modeling method of this worm is proposed. The modeling frame is established firstly， and the meshing equations of the working tooth profile in different coordinate systems for the worm are deduced by applying differential geometry， kinematics， envelope theory and space coordinate transformation method， and the digital models of the working tooth profile of the worm are established， simultaneously， the generatrices equation of bottom and addendum surface are worked out. In addition， the constraint conditions of the worm digital models are constructed according to the enveloping process and boundary conditions of tooth profile. The solving algorithm for the complex nonlinear mathematical models is also designed based on the forming principle of the envelope surface， the instantaneous contact line and all meshing point cloud for the tooth profile are calculated， the distribution of contact line of worm tooth profile is also given. The digital solid model of worm is obtained by using curve and surface fitting technology based on the point cloud of worm tooth profile. The modeling experiment demonstrate that the digital model of worm is accurate， the designed solving algorithm of the model is effective as well as convergence， the worm tooth profile is of high precision， and the error of the worm tooth profile is at the level of 10-9. The research results can lay an accurate model foundation for precision digital manufacturing of cone-generated envelope torus worm and corresponding cone-generated double-envelope worm gear hob.