An Analytical Approach to Gear Mesh Dynamics for the Sustainable Design of Agricultural Machinery Drive Systems

This research aims to advance the understanding and application of dynamic models for gears within agricultural machinery drive trains by developing analytical solutions. Despite the significant advancements in vibration analysis, there is a notable scarcity of comprehensive research that addresses the analytical modeling of gear dynamics, particularly using advanced mathematical techniques such as the multiple scale method (MSM). A new approach to modeling gear meshing is introduced, where the Fourier expansion of a rectangular signal is utilised to simulate the time-varying mesh stiffness (TVMS). Such an approach allows the use of the MSM as an efficient tool to obtain solutions for parametrically induced vibrations. A dynamic model of a simple helical gear system is introduced in the form of Hill’s equation, and a sensitivity analysis is conducted for the main parameters of the system based on the solution obtained with the MSM. The results show the high credibility of the provided method when compared with a well-known state-of-the-art model and that the model reacts to parameter variations as expected. Additionally, an analysis of the energy harvesting possibilities is presented, which shows that, for the default parameter values, the harvester should be tuned to 5694.31 Hz to generate the maximum energy. It is concluded that the proposed model and MSM approach can serve as suitable tools for gear analysis, and the future paths for research are defined.