螺旋锥齿轮实体建模及齿面形状评价方法研究  

Research on Method of Solid Modeling and Tooth Surface Shape Evaluating for Spiral Bevel Gear

作　　者：魏巍[1] 张连洪[2] 

机构地区：[1]长江大学机械工程学院,湖北荆州434023 [2]天津大学教育部机构理论与装备设计重点实验室,天津300072

出　　处：《机床与液压》2017年第23期128-131,166,共5页Machine Tool & Hydraulics

基　　金：国家自然科学基金资助项目(51275347);长江大学青年基金资助项目(2015cqn47);湖北省属高校优势特色学科群省级立项建设项目(石油天然气)

摘　　要：提出了一种基于点阵计算的螺旋锥齿轮实体建模方法,可准确描述共轭齿面和过渡曲面的形状,通过改变点阵密度,可创建齿面精度可变的齿轮实体模型。针对常用的单点评价方法随机性大的问题,提出了一种基于接触椭圆尺寸分析的共轭齿面形状精度评价方法,在齿面上选定测量点后,以圆球切入齿面形成接触椭圆。采用诱导法曲率和短程挠率公式,计算测量点两个主曲率和主方向,沿主方向测量接触椭圆半径并计算评价结果。根据评价结果调整点阵密度,从而获得齿面形状精度满足接触分析要求的齿轮实体模型。A method of solid modeling for spiral bevel gear is purposed based on points cloud calculation, conjugate tooth surface and transitional surface of spiral bevel gear can be described exactly by this method. Solid model of gear with variable precision was established by changing density of points cloud. A method for shape evaluating of conjugate tooth surface was purposed by dimensional analyzing of contact ellipse, which was used to weaken randomness of the conventional evaluating method. Some measuring positions were chosen on the tooth surface, tooth surface was cut into a certain distance by sphere and contact ellipse was obtained by Boolean operation between solid model of gear and sphere. The principal curvatures and principal directions of measuring points were calculated by using formulas of induced normal curvature and induced geodesic torsion, radii of contact ellipse were measured along principal directions of measuring points. Solid model of gear which satisfies the requirement of tooth contact analysis is obtained by adjusting density of points cloud.

关 键 词：螺旋锥齿轮 点阵 实体建模 曲率 接触椭圆 

分 类 号：TG0[金属学及工艺]