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

摘要： 为解决平面二次包络环面蜗杆副建模精度问题,提出其三维实体模型的数字构建方法。运用空间包络原理和坐标转换等解析方法构建了表征平面二次包络环面蜗杆和蜗轮的齿廓、齿顶与齿底环面的数字模型,根据蜗杆副成型特征设计了表征其齿廓复杂多元非线性数学模型的求解算法,计算出了该环面蜗杆副齿廓的全部啮合点云。逆向应用包络原理检验分析了算法求解蜗杆副齿廓点云的计算精度。在三维造型软件系统中应用包络方式对蜗杆副齿廓点云进行曲线、曲面拟合,构建了蜗杆副齿廓曲面模型,同时将计算的蜗杆副齿顶与齿底环面母线导入并绕各自轴线旋转构建了其齿顶与齿底环面模型,最后将齿廓与齿顶齿底环面封闭并实体化得到蜗杆副三维实体模型。通过建模实例验证了建模方法及设计算法的有效性与准确性。

关键词: 环面蜗杆副, 数字模型, 啮合型面, 算法, 三维实体