平行轴纯滚动内啮合线齿轮设计方法

A Designing Method for Parallel Shaft Internal-Meshing Line Gear with Pure-Rolling Contact

为了提高线齿轮的传动效率,提出了一种平行轴纯滚动内啮合线齿轮的设计方法。基于线齿轮啮合理论,求解空间共轭曲线方程,并分析纯滚动啮合需满足的约束条件;建立过接触点且垂直于角速度方向的齿廓截面,通过齿廓截面方程和接触线方程构建凸凸、凸凹和凸平接触齿面数学模型。以圆柱螺旋线为例,分析纯滚动啮合的设计参数选取原则,构建凸凹接触的内啮合线齿轮齿面,利用三维软件建模并进行运动学分析,结果表明:当设定理论传动比为2、重合度为1.5、小齿轮齿数为6时,凸凹接触相对曲率半径最小,齿面接触应力最小,其他条件不变的情况下,凸凹齿面的接触应力相对凸凸接触和凸平接触分别降低了28.95%和19.17%。通过该方法构建的内啮合线齿轮副平均传动比为2.00,瞬时传动比最大变化值仅为0.07,能够实现平稳、连续的速度传递。

To improve the transmission efficiency of line gear,a designing method for pure-rolling internal line gear mechanism is proposed for parallel shaft transmission.Following the line gear meshing theory,the equations of spatial conjugate curves are solved and the constraint conditions for pure-rolling meshing are analyzed.The profile cross-section located on the contact point and perpendicular to the direction of angular velocity is established.The mathematical models of tooth surface of convex-convex,convex-concave and convex-flat contacts are constructed according to the profile cross-section equations and contact curve equations.Taking cylindrical helix as an example,the selection criterion of designing parameters for pure-rolling meshing state is analyzed and the pure-rolling internal meshing tooth surface is constructed.The contact stress of tooth surface with different contact forms is analyzed.Meanwhile,the modeling of convex-concave surface and the kinematics analysis are carried out with 3D software.The results show that when the theoretical transmission ratio,the contact ratio,and the teeth number of pinion are respectively set as 2,1.5 and 6,the convex-concave contact with the relative smallest curvature radius has the lowest contact stress under the same restrictive conditions,and the contact stress is reduced by 28.95%and 19.17%respectively,compared to convex-convex and convex-flat contacts.The average transmission ratio of the internal line gear pair constructed by this method reaches 2.00,and the maximum variation of the instantaneous transmission ratio reaches only 0.07,smooth and continuous speed transmission is thus realized.