Modeling of Gearbox Whining Noise

The main source of excitation in gearboxes is generated by the meshing process, which generates vibration transmitted to the casings through shafts and bearings. Casing vibration generates leads to acoustic radiation (whining noise). It is usually assumed that the transmission error and variation of the gear mesh stiffness are the dominant excitation mechanisms. These excitations result from tooth deflection and tooth micro-geometries (voluntary profile modifications and manufacturing errors). For real cases, the prediction of noise induced by the Static Transmission Error (STE) remains a difficult problem.
In this work, an original calculation procedure is implemented by using a finite element method and taking into account the parametric excitations and their coupling (Spectral Iterative Method, developed by the Ecole Centrale de Lyon). The procedure is based on a modal approach developed in the frequency domain, particularly efficient to analyze systems having many degrees of freedom.
In a first step, the static transmission errors and tooth stiffness’s are calculated from the knowledge of the tooth macro and micro geometry. In a second step, these data are used to calculate the dynamic transmission errors, the teeth dynamic loads, and the dynamic response of the gearbox. A finite element model of the gearbox (including housings, shafts and bearings) is used to extract the modal basis necessary for this method.
Measurements carried out on a specific gearbox test bench allow comparison of simulation and experimental results. Accelerometers and optical encoders were used to measure static and dynamic errors of transmission and the vibration response of the casings.
The correlation between calculations and measurements at each stage of the computation chain is used to validate the relevance of these numerical approaches.