Principle and Method for Machining Face Gear with Developable Ruled Surface

可展直纹面面齿轮的加工原理与方法

College of Mechanical Engineering, Xi'an University of Science and Technology, Xi'an 710054, China

Received: 24 March 2020

Abstract

The tooth surface of a face gear is recognized as un-developable ruled surface in tradition, which result in the problem that face gear generation using simple cutter with high efficiency and accuracy puzzled people for a long time. Applying the traditional shaping method for face gear generation in derivation of the tooth surface position vector, a space straight line equation was established by using this vector, to illustrate that the tooth surface of the traditional face gear could be considered as developable ruled surface constituted by space lines family, the position vectors of the developable ruled surface were established respectively based on involute, rack and considering the spatial position relationship in meshing. Elaboration and proposition of the principle and method that were used to generate the face gear with the developable ruled surface by straight edged cutter in line contact, and representation of the generated surface model. Furthermore the developable ruled surface was compared to the traditional surface, the normal difference between the two kinds of surfaces is on micro-scale. Numerical examples shows that the normal distance is no more than 1/70 of modulus, the developable ruled surface to which was performed simple longitudinal crowning is able to mesh with the involute surface of the pinion correctly, and demonstrates acceptable geometric meshing performance.

摘要

传统上认为面齿轮的齿面为复杂的非可展直纹面，致使利用简单的刀具高效精准加工面齿轮的问题长期困扰着人们。利用面齿轮传统的插齿方法建立齿面位矢方程，以该位矢为参量建立空间直线方程，说明传统面齿轮齿面可视为空间直线族构成的可展直纹面。考虑空间啮合位置关系，分别基于渐开线和齿条建立了该直纹面的位矢方程。阐述了直刃刀具线接触法加工可展直纹面面齿轮的原理和方法并建立了齿面模型。进一步将该可展齿面与传统齿面进行对比分析，2种齿面的法向差异属于微观量，数值计算结果表明法向距离不到模数的1/70，对可展直纹面进行简单的齿向抛物线修形即可与圆柱齿轮渐开线齿面啮合，并呈现较好的几何啮合性能。