WIT Press

A multibody dynamic model for evaluating the vibrating modes of gear train systems


Free (open access)


Volume 5 (2021), Issue 3



Page Range

264 - 277

Paper DOI



WIT Press


R. P. Monteiro, R. Vidoni & F. Concli


Nowadays, the use of gearboxes in the mechanical sector has significantly increased due to the various possible applications and new materials available on the market. Moving through each application, from robotics to the automotive sector, the use of gearboxes ensures high efficiency with a compact structure. Generally, gearboxes are composed by gears, shafts and bearings, and each of these components can be subjected to failures. Therefore, in the analysis of each mechanical component it is central to let the system operate properly. In fact, the presence of a damage can lead to a slight variation of system properties (e.g. stiffness). To design even more reliable gearboxes, it results fundamental to monitor the system’s health state and the damage progress. To better understand these phenomena, a numerical study is here presented. A back-to-back gear rig (fixed-axis two-stage test rig) is used as reference. It was developed an effective multibody dynamic model that exploits a combination of two different approaches – the Lumped Parameter Method (LPM) and the Finite Element Method (FEM). In this work, the effect of different operative and loading conditions was studied. In particular, the effect of damages on the eigenfrequencies and on the vibrational spectra was investigated based on numerical simulations. The stiffnesses of the gear train components, used in the LPM, were estimated by means of dedicated fem simulations. the results of the LPM were validated with experimental data acquired on a real healthy back-to-back rig. Moreover, the effect of a tooth root damage on the vibrational spectra was analysed. The stiffnesses of the system’s components affect considerably the eigenfrequencies. As predicted by the FEM simulations, in presence of damage, the stiffness of the teeth varies significantly, affecting the vibrational spectra. Therefore, this work can be an effective starting point to setup a monitoring strategy of gearboxes.


dynamic modelling, finite element method (FEM), gear trains, gearboxes, gears, lumped parameter method (LPM), multibody modelling (MBM), multibody systems.