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.

Design and Analysis of Novel Non-Involute Cylindrical Gears with a Curved Path of Contact

“…Involute gears have superior performance and are the most commonly used gears in machines. However, with the development of modern industry, some shortcomings of involute gears have gradually appeared, such as low contact strength and limited bearing capacity [1][2][3][4][5]. Due to an intrinsic property of the involute curve, the curvature radius of the involute profile in the dedendum part approaching the base circle is very small.…”

Geometric Modeling and Manufacturing Method for a few Teeth Involute Gear with Bilateral Modification

“…Chien-fa and Chena [3] studied the selection of the radial displacement coefficient and helix Angle of the gear for the problems of continuous transmission poor and root cutting of the gear with a few teeth and obtained better design parameters. In view of the weak strength of the involute a few gear teeth, Sun Yuehai [4] has studied the tangential and radial displacement, and proposed the equal strength condition design method, and obtained the optimal combination of the variable coefficient under this condition, which has certain application value. However, none of these studies has done research on processing methods and trial production.…”