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Non-linear mathematical modeling of gear rotor bearing systems including bearing clearance

Gürkan, Niyazi Ersan
In this study, a non-linear mathematical model of gear-rotor systems which consists of elastic shafts on elastic bearings with clearance and coupled by a non-linear gear mesh interface is developed. The mathematical model and the software (NLGRD 2.0) developed in a previous study is extended to include the non-linear effects due to bearing clearances by using non-linear bearing models. The model developed combines the versatility of using finite element method and the rigorous treatment of non-linear effect of backlash and bearing clearances on the dynamics of the system. The software uses the output of Load Distribution Program (LDP), which computes loaded static transmission error and mesh compliance for the contact points of a typical mesh cycle, as input. Although non-varying mesh compliance is assumed in the model, the excitation effect of time varying mesh stiffness is indirectly included through the loaded static transmission error, which is taken as a displacement input into the system. Previous computer program which was written in Fortran 77 is rewritten by using MatLAB 7.0 and named as NLGRD (Non-Linear Geared Rotor Dynamics) Version 3.0. The program is highly flexible and open to further developments. The program calculates dynamic to static load ratio, dynamic transmission error, forces and displacements at bearings. The mathematical model suggested and the code (NLGRD version 3.0) are validated by comparing the numerical results obtained from the model suggested with experimental data available in literature. The results are also compared with those of previously developed non-linear models. The effects of different system parameters such as bearing stiffness, bearing clearance and backlash on the gears are investigated. The emphasis is placed on the interaction of clearances in bearings with other system parameters.