Time-Domain Dynamic Analysis of Helical Gears with Reduced Housing Model

Abstract

Gear noise and vibrations remain key concerns in many transmission applications. The dynamic loads or errors at the gear mesh excite the components in a gear box. Typical transfer path for the noise and vibration includes gears, shafts, bearings, and the housing or the base connected to the housing. Low frequency vibrations propagate through structures as structure-borne noise, and higher frequency vibrations typically manifest as air-borne noise. The housing due to its large surface area acts as a good radiator of sound. Thus, it is imperative that the dynamic analysis of the entire gearbox, including the housing, is essential in understanding its noise and vibration characteristics.Lumped parameter models are commonly used to model gear dynamics, where various components of the gear box are represented by lumped inertias and stiffness. The gear mesh excitation, which is the source for the dynamics, has to be provided externally either as time-varying mesh stiffness or as the static transmission error [1]. General purpose finite element software may also be used to solve gear dynamics. But it requires refined meshes near the contact zone for accurate gear tooth contact modeling. Moreover the local refinement needs to keep moving as the gears rotate, thus making it practically infeasible to solve the time domain gear ABSTRACTIn this paper we present a time-domain dynamic analysis of a helical gear box with different housing models using a unique finite element-contact mechanics solver. The analysis includes detail contact modeling between gear pairs along with the dynamics of gear bodies, shafts, bearings, etc. Inclusion of the housing in the dynamic analysis not only increases the fidelity of the model but also helps estimate important NVH metrics, such as dynamic load and vibration transmission to the base, sound radiation by the gearbox, etc. Two different housing models are considered. In the first, the housing is represented by a full FE mesh, and in the second, the housing is replaced by a reduced model of condensed stiffness and mass matrices. Component Mode Synthesis (CMS) methods are employed to obtain the reduced housing model. Results from both the models are successfully compared to justify the use of reduced housing model for further studies.Steady state sound radiation by the gear box housing is then studied in the frequency domain using a boundary element solver. The housing frequency response, which is the boundary condition for the acoustic analysis, is estimated using two different methods. In one method, the response is computed from the generalized coordinates and component modes using modal superposition, in the other the bearing dynamic loads are used to perform forced response analysis on the full FE mesh of the housing. Thus, a template for end-to-end solution to predict radiated noise from a gear box is established.

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