Modeling agricultural tractor motion on sloping ground considering longitu-dinal and lateral gradients

Tractor overturning or rollover is a serious accident owing to its high fatality rate. Reviews of farm tractor rollover incidents indicate that overturns account for over 50% of all tractor-related deaths. To understand a tractor's performance on uneven terrain, a three-dimensional (3D) mathematical model describing the general bouncing and pitching motions of a tractor would be very useful. In this study, we design a rigid-body tractor system with the tires modeled as spring-damper units. To predict the tractor's motion on undulating surfaces, a half sine wave bump is adopted for the front and rear wheels on both the longitudinal and transverse slopes. The tractor's dimensional parameters and physical properties are taken from the work of Takeda et al. (2010). The passing over process is divided into four detailed phases and the attitude of the tractor is obtained by capturing the motion of the vehicle's center of gravity (COG). The displacement, pitch angle, and accelerations of the COG are numerically analyzed by applying the Runge-Kutta method. We introduce in this study three coordinates for the vehicle, slope and horizontal ground-based observations. The results are presented as factors of forward velocity, bump height, and slope gradient. Predictions show that there is a decrease in stability and an increase in danger at higher velocities, higher bump heights, and steep inclines. The specific cases indicating dangerous situations for the tractor are pointed out according to the results.