Nonlinear Dynamics of Traveling Tractor-Implement System Generated by Free Play in the Linkage

Abstract

The requirement for high work rates in order to achieve a high productivity, involves an increase in the tractor forward speed during transportation, thus loads induced during transportation can be extremely high. Load predicting methods would therefore be useful for designers in designing operations. In this study a nonlinear tractor-implement model with a free play in the three-point linkage was developed. Based on the experiments conducted by Collins and Sakai, the tractor-implement system was modeled as an impact oscillator, where the free play of the three-point linkage acted as an impact element. Equations of motion were derived using the method of Lagrange, assuming no rigid connection between the tractor and the implement. In numerical experiments, by varying the excitation frequency; periodic, subharmonic, and chaotic vibrations were observed.