The generation principle, mathematical models of variable involute, and its application

Abstract

A novel generation method of tooth profile curve is presented in this paper. It introduces the concept of a variable involute whose curve is generated by the generating line rolling and slipping on the base circle simultaneously. The generation principle of variable involute is described and the equation of variable involute is deduced. Then, equations are established to synthesize a conjugate profile for the gear teeth, which include some restrictions to keep the involute meshing properties. With a selectable and arbitrary relative slippage which is defined as a slipping function, the variable involute has desirable properties of controllability and flexibility. By constructing different slipping functions, involute, cycloid and circular-arc gears can be expressed into one unified form. The freedom and unified form of variable involute suggests the possibility of optimal conjugation design. An application example of gear pair with a few teeth is presented, aiming at overcoming the shortcomings of involute gear pair in load-carrying capacity and meshing performance, and its simulation analysis is conducted. Through comparative analysis with the involute gear, the results demonstrate that the variable involute gear pair with a few teeth has larger contact ratio as well as load-carrying capacity, and engagement performance has been effectively improved.