平面二次包络环面蜗杆数字化实体建模研究

Digital Entity Modeling of Planar Double-Enveloping Torus Worm

为提升平面二次包络环面蜗杆建模精度,提出其三维实体模型的数字构建方法。运用包络原理和坐标转换方法构建了表征平面二次包络环面蜗杆齿廓、齿底与齿顶环面的解析模型,设计了表征齿廓复杂非线性数学模型的求解算法,获取了表征环面蜗杆齿廓的点云,并分析了齿廓特征点云的计算精度。将蜗杆齿廓点云导入三维造型软件,应用包络方式构建蜗杆齿廓曲线、曲面模型,同时将表征蜗杆齿底与齿顶环面母线导入并构建齿底与齿顶曲面模型,最后实体化得到蜗杆三维实体模型。建模实例验证了建模方法及设计算法的有效性与准确性。

In order to improve the modeling accuracy, the three dimensional digital entity modeling method of planar double- enveloping torus worm pair has been proposed. The analytic models of the tooth profile and bottom as well as addendum surface of the worm are established appliedenvelope theoryand coordinate transformation method,in addition, the solving algorithm for the complex nonlinear mathematical model is also designed, next, the point cloud forthe tooth profile are obtained, and the calculation precision of the tooth profile is also analyzed. Finally, the curve and surface model of the worm tooth profile are built applied envelope pattern on the basis of the point cloud while inputting the points into the modeling software, simultaneously, the bottom and addendum models are constructed based on the surface generatrix, the three dimensional entity model is obtained at last.The modeling results demonstrate the validity and accuracy of the modeling method and designed algorithm.