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Stability and Chaotic Behavior of Farm Tractors

Published by the American Society of Agricultural and Biological Engineers, St. Joseph, Michigan

Citation:  Paper number  013136,  2001 ASAE Annual Meeting. (doi: 10.13031/2013.4346) @2001
Authors:   LO Garciano, R Torisu, K Sakai, J Yoshida, J Takeda
Keywords:   Stability, chaotic vibrations, nonlinear tractor dynamics, correlation dimension, Lyapunov exponent, random vibration, quasi-periodic vibration

The stability and chaotic behavior of a farm tractor assumed as a rigid body were investigated from the standpoint of nonlinear tractor dynamics. The investigation was carried out by conducting a frequency response test by running the tractor on an artificial test track over a wide range of forward speeds. The analysis was conducted in the time domain and frequency domain. In the time domain analysis, qualitative changes of the dynamics of the tractor were analyzed using the phase portrait and Poincare section that identified the quasi-periodic vibrations in the middle speed range of 1.50~3.08 m/s. Quantitative analysis using the correlation dimension identified the random vibration in the low speed range of 0.63~1.42 m/s, and chaotic vibrations in the high-speed range of 3.32-4.52 m/s. An almost zero Lyapunov exponent estimate identified marginal stability in the middle speed range and the largest positive Lyapunov exponent estimates in the high-speed range identified the deterministic chaotic vibration. In the frequency domain analysis, nonlinear resonance of the tractor in the middle speed range is where the marginal stability of the dynamic behavior of the tractor occurred.

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