计及刀尖圆角和根切的螺旋锥齿轮实体建模

Solid modeling of spiral bevel gear considering cutter fillet and undercutting

考虑刀尖圆角对齿面形状的影响,建立了螺旋锥齿轮啮合齿面和齿根过渡曲面的数学模型。通过分析齿面根切和未根切时齿面形状的两种拓扑形式,引入齿高方向的比例变量,提出了一种判别根切的数值算法。通过在轴截面上对离散点进行规划,提出了一种基于离散点求解的螺旋锥齿轮建模方法,该方法具有较好的通用性,无论是否发生根切都能准确描述齿面形状。通过编制齿轮计算程序,实现了齿面离散点和轮坯尺寸自动化计算,建立了齿轮副实体模型。采用有限元方法进行了齿轮副加载分析,获得的应力云图可准确显示接触椭圆的位置和形状,验证了文中建模方法的可行性。

Taking influence of cutter fillet on tooth surface into consideration,the mathematical models of meshing surface and root transition surface of spiral bevel gear were established.A kind of numerical algorithm for judging undercutting was proposed by introducing a proportional variable in the direction of tooth height and analyzing two topology modes of tooth shapes when undercutting occurred and not occurred.Through planning discrete points on axial cross section,a solid modeling method of spiral bevel gear based on discrete point solution was developed, which has much better generality and can describe the tooth shape precisely regardless undercutting occurred or not.By making tooth calculation program,the automatic calculation of discrete points and dimensions of gear blank are carried out,and the solid model of gear pairs was also built.The stress cloud diagram obtained by using the finite element analysis method to carry out gear pairs torque loading analysis can show the position and shape of contact ellipse,verifying the feasibility of the solid modeling method presented in this paper.