Centrifugal stiffening analysis of gear pair with generalized component mode synthesis and semi-analytic contact technique

Abstract

Cantilever beam assumption is widely used to estimate gear flexibility for analytical calculation of transmission error of gear pair. Similar to the rotating beam, it is supposed that centrifugal stiffening will also affect dynamic transmission error of gear pair. This work presents an efficient computational procedure for centrifugal stiffening analysis of gear pair. As inertia centrifugal force is distributively applied on gear body, the finite element grid model of gear pair is firstly established. Then, in order to reduce large number of degrees of freedom in finite element grid, the generalized component mode synthesis is employed to establish dynamic equation of flexible gear with constant mass matrix and co-rotated constant stiffness matrix. In order to avoid highly refined grid near contact zone, the semi-analytic contact technique which incorporates advantage of penalty method and Lagrange multiplier method is employed to calculate contact force between non-matching sparse tooth face meshes. After transforming system dynamic differential algebraic equation into ordinary differential equation, dynamic contact analysis of a helical gear pair is carried out, and dynamic transmission error at different rotational speeds are compared. Inflation deformation of gear under inertia centrifugal force is shown as explanation for influence of centrifugal stiffening on dynamic transmission error.