Study on the pitch curve with minimal rotary inertia for the noncircular gears

Abstract

Aimed at the high load and slow response of the noncircular gears design, a general mathematical model for designing the pitch curve with minimal rotary inertia of the noncircular gear is proposed by resorting to kinematics principle and calculus of variations. To achieve the closure design, the constraint conditions and smoothness characteristics of N-lobed noncircular gear pitch curve with minimal rotary inertia are established and calculated analytically. In addition, the unified design method of the conjugate pitch curves with minimal rotary inertia for the noncircular gears is given in this paper. Unclosed and closed N-lobed conjugate pitch curves that satisfy the desired transmission requirements can be easily solved by using the proposed method, and each lobe has identical profile to ensure the periodical motion of the pitch curves. Numerical examples are implemented in computer and demonstrate the feasibility of the above method.