The mathematical modelling of gearbox vibration under applied lateral misalignment

Abstract

In the mathematical modelling of gear vibrations it is found that there is a gap between the transient models developed in academia and the steady state models frequently used in industry. It is seen that the academic models are adept at modelling the nonlinear phenomena seen during gear contact for system with only a few degrees-of-freedom, whereas the industrial models are capable of solving the linear steady state response of more complex transmission systems. The work presented in this thesis attempts to bridge the gap between the two models, through the development of a transient nonlinear model of a gear pair with increased degrees-of-freedom. An understanding of the gear contact is achieved through the use of advanced static finite element analysis with nonlinear gear contact. Through FEA the effects of gear misalignment on these contact conditions is also investigated. The findings from the FEA are then used in a mathematical model of a single stage spur gear transmission, which is developed as part of the thesis, to determine the system accelerations. The mathematical model includes the time varying mesh stiffness and the time varying and nonlinear bearing stiffness's and frictional forces. The effects of lateral misalignment seen in the FEA results are also included into the model to investigate their effects. The model parameters are then varied to determine their effects and the simulated accelerations are compared against experimental results. It is found from this comparison that although some similarities between the simulated and experimental results are achieved for the aligned case, insufficient corroboration is found for the axially and radially misaligned results to confirm the validity of the mathematical model for modelling misalignment. From this, further experimental results were requested to gain a better con- fidence in the effects of lateral misalignment