Mathematical Modeling of Torsional Vibrations in a Gearbox with Faults Using Distributed Parameters and Bond Graphs

Vibrations are important in machinery since they present the current state of the system and can indicate certain events (like the presence of a fault). To use the vibrations as indicators for fault detection, one must get the system’s ideal response to certain frequencies. To achieve that, mathematical modelling is of great importance. In this paper it is presented a way to model and simulate the response of a gearbox given an input and the presence of a fault. The mathematical approach is based on the distributed parameter model of the shafts and the simulation is done using Bond graphs which is a great way to integrate systems of different nature (electrical, mechanical) in the same model. This approach has the advantage that it is easy to use and integrate in any model and the simulation of faults can greatly reduce costs needed with experimentation.