The research on non-circular gears with typical pitch curve is a representative direction of non-circular gear design and manufacturing. The design theory and transmission performance of elliptical gear are studied, and many tooth profile optimization design methods are proposed. It shows that the non-uniform transmission characteristics can be applied to aerospace, agricultural machinery, metrology and other fields; The mathematical model of slotting elliptical gear is established, but it can not be applied to slotting high-order elliptical gear.
In recent years, many scholars have carried out a lot of research work on the optimization design, mechanism application and vibration control of special-shaped complex gears, which has effectively promoted the research on the theory and application of gear transmission. High order elliptic gear can realize periodic variable speed ratio motion, has unique kinematic and geometric transmission characteristics, and has broad application prospects. Gear hobbing is an optimal and efficient technology to realize mass production of high-order elliptic gear. In view of the non-circular characteristics of pitch curve, it is difficult to gear hobbing of high-order elliptic gear. It is necessary to establish an efficient and practical linkage model. It is necessary to use computer for virtual machining verification before practical application. Compared with elliptical gears, high-order elliptical gears are prone to concave pitch curves. At present, the hobbing technology for this kind of gear has not been reported. In order to solve its manufacturing problems, this paper studies the high-order elliptical gear hobbing theory and virtual hobbing core technology, which provides a theoretical basis for the research and development of high-order elliptical gear machining module of hobbing NC system.
According to the non concave condition of pitch curve, the hobbing discriminant function of high-order elliptic gear is established. Through virtual machining and hobbing examples, it is proved that hobbing can be used when all pitch curves f ≥ 0. The gear hobbing models of high-order elliptical spur gear and high-order elliptical helical gear are established, and verified by virtual gear hobbing and example gear hobbing. The model can specify the relationship between the pulse frequencies of each linkage axis, which can be realized by numerical control device. The virtual gear hobbing technology based on the principle of tool (inclined) rack shows the tool path under the control of gear hobbing model, which can pre display the actual tooth profile shape and avoid blind machining. The virtual gear hobbing shows that the high-order elliptical gear meeting the hobbing conditions can be processed by gear hobbing, and the linkage model is correct and feasible; The gear with concave pitch curve cannot be hobbed due to the interference of rack pitch line. The example hobbing and its measurement results are consistent with the simulation conclusion.
In view of the similar principle between worm wheel (honing) and gear hobbing, the theory and results described in this paper can be directly applied to worm wheel (honing) grinding of high-order elliptic gears.