Geometry design and mathematical model of a new kind of gear transmission with circular arc tooth profiles based on curve contact analysis

Abstract

A new meshing relationship for gear drive to characterize the conjugation geometry is studied in this paper based on conjugate curves. Conjugate curves are described as two smooth curves always keep continuous and tangent contact with each other in given contact direction under motion law. The general principle of curve meshing is developed for the given spatial or plane curve. The meshing equation along arbitrary direction of contact angle is derived. The properties of geometric and motion of the contact of conjugate curves are discussed. According to the equidistance-enveloping method, tubular meshing surfaces are proposed to build up circular arc tooth profiles, which inherit all properties of conjugate curves. The geometry design and mathematical model of the gears are established. Three types of contact pattern of tooth profiles are generated: convex-to-convex, convex-to-plane and convex-to-concave. A calculation example for convex-to-concave tooth profiles of gears is provided. Theoretical and numerical results demonstrate the feasibility and correctness of proposed conjugate curves theory and it lays the foundation for the design of high performance gear transmission.