渐开线零齿差内啮合齿轮传动齿廓啮合过程理论分析

零齿差内啮合齿轮传动机构由于应用的局限性，其运动学和动力学特征一直没有引起太多的关注。1998年笔者将此机构应用于潜油螺杆泵采油系统中，连接减速器的输出轴和螺杆泵转子，此处转子与定子的相对运动特征要求联轴节的输出相对于输入轴以一定的规律作相对偏心运动，这样，机构中参与啮合的轮齿数的常规的齿轮联轴节相比明显减少并有齿廓之间相对滑移，因此，连带引出强度、效率、振动等问题。为了给这些问题的研究打下基础，本文从齿廓啮合入手进行深入分析，建立了反映啮合点在齿廓上变化规律的16种隶属关系，并给出确定齿廓接触起迄点的解析方法。

Theoretical Analysis of Tooth Engaging Process ofInvolute Internal Gear Drive with Zero - tooth - difference

Because of the limited applying scope of the internal gear drive with zero-tooth-difference, less attention was paid to the kinematic and dynamic features of this mechanism. In 1998, the author of this paper applied it in the submerged-motor-driven progressing cavity pumping system as a coupling to connect the output shaft of reducer and the rotor of pump. The relative motion feature of rotor and stator of the pump requires that the output shaft axis do eccentric motion around the input one of coupling with an eccentricitye, therefore, the meshing teeth number in the mechanism is fewer compared with that generally used in engineering. Furthermore, the sliding motion takes place between the gear-tooth profiles. For such reasons, the problems such as strength, efficiency and vibration must be taken into account. As a premier basic work, the tooth profile engaging process was analyzed deeply in this paper. Altogether 16 kinds of relationships between classifications and attributes were established. At last, the analytical method to determine the starting and ending contact points of tooth profiles, in both polar and rectangular coordinate system, was given.