Modelling and Simulation of Gear Systems Dynamics for Supporting Condition Monitoring Using Mathematica

Modelling and simulation of gear system dynamics to support the condition monitoring is one of the most important issues which should be properly developed. There are many papers on the subject of gearbox dynamic modelling however they are not coherent. Only in few papers a "complete system", which consist of a drive, gearbox and a driven machine is considered. The system which is going to be considered in this paper is complete and its parameters are based on a real system. To present different gear system dynamics problems a nonlinear time-varying model is analysed using Mathematica software. In the model the torsional vibration of the rotating system is considered. The model includes time-varying gear mesh stiffness, gear errors of each meshing tooth pair and non-linearities due to tooth separations. Numerical solution of the system is obtained by Mathematica. Highly optimized superfunctions used in Mathematica analyse model equations and automatically select the right algorithms to get accurate results quickly. Other computation systems (e.g. MATLAB) require manual selection of solution algorithm to apply, whereas in Mathematica we use NDSolve and the risk of wrong results is minimal. The aim of the study is to show that mathematical modelling and computer simulation using Mathematica enable detailed investigation of the dynamic properties of a gearing system.