Helical gear transmission is a transmission mode of meshing helical cylindrical gear and helical gear, which can meet the different transmission requirements of orthogonal, non-orthogonal or offset axes of two gears. Its transmission device has the advantages of small mass, large coincidence, compact structure, good transmission stability, low vibration noise and strong bearing capacity, and is widely used in aviation, aerospace and automotive fields, Especially, it is widely used in the split torsion transmission system of the helicopter main reducer.
In recent years, with the rapid development of science and technology, great progress has been made in the research of helical gear at home and abroad. According to the principle of the double-parameter envelope method, Bodzas S. et al. deduced the equation of the cutting edge of the spiral worm hob, obtained the tooth surface equation of the spiral tooth surface gear according to the coordinate transformation, established the three-dimensional geometric model of the spiral worm hob and the spiral tooth surface gear, and verified the correctness of the calculation method and the modeling process. Litvin F.L. and others have made a comprehensive study of the transmission theory and processing technology of the face gear, analyzed the transmission theory of the worm face gear by using differential geometry and meshing principle, deduced the equation of the base worm tooth surface, and solved the problem of the root undercut and the tooth tip of the worm face gear. The domestic research on spiral tooth surface gears started relatively late, and the research is relatively few. Fan Junhui and Guo Hui have studied the grinding principle of the worm wheel of the orthogonal face gears, established the relationship between the shortest distance of the shaft between the base worm and the generating gear and the intersection angle of the shaft, deduced the tooth surface equation of the grinding of the base worm and the face gear, established the three-dimensional geometric model of the grinding of the base worm and the face gear, and studied the singularity of the base worm tooth surface, The tooth surface error of the grinding tooth surface and the theoretical tooth surface is compared through the calculation of the tooth surface error. Tang Jinyuan et al. studied the corresponding relationship between the surface of the worm wheel and the surface of the face gear during the grinding process of the worm wheel, calculated the contact line between the face gear and the imaginary profile wheel, the imaginary profile wheel and the worm wheel, obtained the calculation method of the contact points of the worm wheel and the face gear at different machining positions, and gave the corresponding model of the grinding surface of the worm wheel and the face gear teeth, The method of grinding surface gear with worm wheel is simulated and verified. According to the meshing principle of space staggered axes, Liu Xuangen proposed the shaving method of spiral tooth surface gear for the finishing of spiral tooth surface gear. Through studying the shaving principle of spiral tooth surface gear, he established the shaving motion model of spiral tooth surface gear, gave the tooth surface equation, material and basic parameters of tooth surface of the shaving tool, and carried out the shaving simulation of spiral tooth surface gear using VERICUT software, The experimental study of gear shaving is also carried out. Li Jia et al. and Chen Xinchun put forward the concept of cutting tooth machining for internal helical cylindrical gears, established the motion model of cutting tooth machining, and verified the correctness and technical feasibility of cutting tooth machining.
At present, the domestic research work mainly focuses on internal gears, spur gears and helical gears with small helical angle, while the research on helical gears with large helical angle is very few. In this paper, the method of turning helical gear is proposed. The gear type taper cutter is used to generate the complex tooth surface with two degrees of freedom, namely, “cutting” and “gouging” of gear hobbing, which can cut the helical gear with large helical angle. Taking the straight-tooth conical tooth turning helical gear as the research object, the tooth turning model of the spiral tooth face gear is established, the tooth turning principle of the spiral tooth face gear is studied, the two-degree-of-freedom meshing equation and tooth surface equation of the tooth turning of the spiral tooth face gear are derived, and the tooth surface error and tooth shape error are analyzed to verify the feasibility of the tooth turning principle of the spiral tooth face gear.