平面二次包络环面蜗轮理论齿面重构数字化造型算法研究

Study on an Algorithm for Rebuilding Tooth Surfaces of Planar Double-Enveloping Toroid Worm Gear

为了实现平面二次包络环面蜗轮的数控加工,必须对蜗轮理论齿面进行精确数字化造型。本文提出了1种齿面离散与重构算法,即运用一族截平面将蜗轮单齿理论齿面沿接触线进行离散,获得离散型值点云;在严格限定蜗轮齿面各边界约束的基础上,运用Bernstein-Bézier三角片插值法对上述离散型值点云进行插值重构,获得G1级光顺的高度近似蜗轮齿面,该建模方法适用于大多数CAD数据接口。对这一算法进行了计算机仿真,结果表明该算法是可行的。

To manufacture Planar Double-Enveloping Toroid Worm Gear by CNC technology,a 3-D computer model of it must be constructed.This paper introduces an algorithm for rebuilding tooth surfaces of the worm gear.Firstly,a series of planes,which have the same axis with the worm gear,are used to intersect with the theoretical contact lines on a tooth surface to obtain a sequence of contact points(also called interpolation points).Surfaces on a tooth are separated into lots of scattered data points.This is the discrete model of the worm gear.Then,based on strictly depicting all the boundaries on the tooth,Bernstein-Bézier triangle pitches are used to interpolate all the scattered data points to rebuild the tooth surfaces.During this interpolating processing,an algorithm for smoothing edges of every two adjacent pitches is used and the whole surface of a tooth can obtain G1 smoothness except boundaries.A 3-D computer model of the worm gear is constructed and has enough preciseness for CNC manufacturing.This 3-D computer model fits to most CAD data ports and is easy to generate cutter traces in CNC manufacturing.Simulations have proven the reasonability of the algorithm.