关键词: 环面蜗杆副, 数字模型, 啮合型面, 算法, 三维实体

Abstract: To solve the modeling accuracy of planar double-enveloping torus worm pair,the three dimensional (3D) digital entity modeling method was proposed.The digital models of tooth profile and addendum as well as bottom surface of worm pair were established by using analytic methods such as space envelope theory and coordinate transformation method.According to the surface's forming characteristic,the solving algorithms for complex multivariate nonlinear mathematical models were designed,which could calculate the meshing point cloud of tooth profile.The precision of tooth profile were also analyzed with envelope theory.In 3D modeling software system,the curve and surface model of tooth profile for worm pair were fitted and built with envelope pattern on the basis of point cloud.The addendum and bottom models for worm pair were constructed while the surface generatrix revolved around each axis simultaneously,and the 3D entity models of worm pair were constructed.The modeling results demonstrated the validity and accuracy of the proposed modeling method and designed algorithms.

Key words: torus worm pair, digital model, meshing surface, algorithms, 3D entity