非正交非对称面齿轮啮合原理与齿面设计

Meshing principle and tooth surface design of non-orthogonal asymmetric face gear

为了增加面齿轮的有效齿宽,研究一种任意轴交角传动且齿廓双侧压力角不等的非正交非对称面齿轮副。首先,设计出非对称齿条形刀具,根据齿条和插齿刀的运动关系,推导出非对称插齿刀的齿面方程;其次,基于啮合原理,建立非正交非对称面齿轮的插齿加工坐标系,并借助数据可视化软件对非正交非对称面齿轮的工作曲面和过渡曲面进行离散求解,建立了完整齿面的数学模型;第三,确定了非正交非对称面齿轮齿宽的限制条件,并分析了轴交角和压力角对齿宽的影响,得到不同压力角组合的面齿轮的齿面接触路径;最后,将求解得到的点云导入三维软件,曲面拟合得到非正交非对称面齿轮的复杂曲面模型。研究结果表明:非正交非对称面齿轮的根切界限与从动侧齿面相关,从动侧齿面压力角越大,产生根切的内径越小;增大轴交角或者减小从动侧的齿面压力角能有效避免齿顶变尖,增加有效齿宽;面齿轮采用非对称齿形能获得较长的接触路径,拥有更好的传动性能,但更容易发生边缘接触。

In order to increase the effective tooth width of the face gear,a non-orthogonal asymmetric face gear pair with arbitrary shaft angle transmission and unequal pressure angles on both sides of the tooth profile was studied.Firstly,the asymmetrical rack was designed and the tooth surface equation of the asymmetrical shaper was deduced according to the motion relationship between the rack and the shaper.Secondly,based on the meshing principle,the gear shaping coordinate system of non-orthogonal asymmetric face gear was established.The working surface and fillet surface of non-orthogonal asymmetric face gear were discretely solved by using the data visualization software.The mathematical model of complete tooth surface was established.Thirdly,the limiting conditions of tooth width of non-orthogonal asymmetric face gear were determined,the influence of shaft angle and pressure angle on tooth width was analyzed and the tooth contact path of face gear with different pressure angles was obtained.Finally,the point cloud was imported into 3D software and the complex surface model of non-orthogonal asymmetric face gear was obtained by surface fitting.The results show that the undercutting limit of the non-orthogonal asymmetric face gear is related with the driven side tooth surface.The larger the pressure angle of the driven side tooth surface is,the smaller the inner diameter of the undercutting is.Increasing the shaft angle or decreasing the tooth surface pressure angle on the driven side can effectively avoid pointing of the tooth tip and increase the effective tooth width.The asymmetrical tooth profile of the face gear can obtain a longer contact path and have better transmission performance,but it is more prone to edge contact.