Online state and parameter estimation of a nonlinear gear transmission system

Abstract

This study aims at modeling the nonlinear dynamic response of a gear transmission system, based on substructuring techniques. More specifically, a finite element (FE) model is introduced for the housing of the gearbox, while the essential effects of the gear-pair, the bearings and the shafts are described by a lumped parameter model. The latter is characterized by strongly nonlinear characteristics that account for gear backlash, meshing stiffness, transmission error properties and bearing stiffness nonlinearities. Accordingly, a joint state and parameter estimation (JS&PE) problem is formulated on the basis of the lumped model. The proposed framework uses vibration acceleration measurements from sensors attached on the housing and, through their propagation to the lumped nonlinear model via the FE substructure, an Unscented Kalman Filter (UKF) is activated for the solution of the JS&PE problem. In contrast to other alternatives (e.g., the Extended Kalman Filter), the UKF features a number of advantages in treating nonlinear systems, including a derivative free calculation and a capacity for higher order nonlinearities. The method’s performance is examined using both numerical simulations and experimental tests.