The geometric characteristics of variable tooth thicknessare: on different end sections of a gear, the tooth shape has different modification coefficient. The tooth top surface and root surface of variable tooth thickness helical gear are conical. The variable tooth thickness helical gear transmission with parallel shaft can adjust the tooth side clearance by axial movement, so that the transmission without side clearance with precise backlash can be realized. The variable tooth thickness helical gear transmission with intersecting and intersecting shafts can realize the transmission with small shaft angle. In recent years, variable tooth thickness helical gear is widely used in robot arm, speedboat, high-speed production line, radar steering and tracking system and other fields.
Because of the complexity of the tooth surface shape of the variable tooth thickness helical gear, it is difficult to form the accurate tooth surface by using the spatial rotation and translation of the reference tooth profile. The hobbing principle of variable tooth thickness gear is studied. The generation mechanism of profile generating rack in hobbing variable tooth thick gear is studied. Based on the theory of enveloping surface method, the tooth surface equation of variable tooth thickness helical gear is obtained. On the basis of the above research, from the point of view of machining, according to the relative position and motion relationship between the shaped gear rack and the gear to be machined in the actual machining process, we establish the coordinate system of gear tooth cutting engagement; according to the principle of gear engagement, we derive the tooth surface equations of involute spiral surface, transition surface and tooth root surface of variable tooth thickness helical gear from the tooth surface equation of shaped gear rack; The tooth surface of the variable tooth thickness helical gear is directly, accurately and completely generated by MATLAB programming, and the accurate model of the variable tooth thickness helical gear is established by using the three-dimensional coordinate values of the points on the generated tooth surface.
The imaginary rack which is conjugate meshed with the gear is called the profile rack of the gear.
Schematic diagram of variable tooth thickness helical gear machining with profile rack. The inclination angle of the teeth is β C. The indexing plane abc1d1 of the profile generating rack is inclined to the axis of the gear to be cut into an angle δ, but the relative motion of the two is still the same as that of the processing of the helical cylindrical gear, that is, the pitch plane ABCD of the profile generating rack and the indexing cylinder of the variable tooth thickness helical gear are tangent and pure rolling. According to the principle of generating meshing, the teeth of variable tooth thickness helical gear can be determined by the tooth surface of the generating rack.