Dynamic modeling of parallel shaft gear transmissions using finite element method

In order to obtain more accurate bearing responses to predict the noise of gearbox, a comprehensive fully coupled dynamic model of a parallel-shaft external cylindrical gear-shaft-bearing-case system was proposed. The continuous gear system was divided into discrete shaft element, mesh element, and bearing-base element. The modularized equations of motion for each element were built, and the dynamic model of the system was automatically created according to the relationship between different elements. The shear deformation effect of the shaft element was considered in the model. The dynamic equations with all degrees of freedom coupled (transverse-rotational-axial-pendular) were given as well. The effect of different gear hand direction and rotating direction were considered. Then the coupling vibration between the gear rotor system and the case was also introduced in the analysis. A single-stage helical gear pair was taken as an example to validate the proposed method by comparing the predicted data with the experimental ones. The results show that the finite element method has higher precision than the common lumped mass method to predict the dynamic response for both gears and bearings. A standardized program for the proposed method has been created, which can provide an effective means to predict the vibration and noise of multi-stage complex parallel shaft gear transmissions in engineering practice.