Dynamic analysis of agricultural wheel tractor driving on uneven surface under the influences of speed and slope angle

A dynamic three-dimensional model of a tractor travelling through a half sine wave obstacle was developed considering bouncing, pitching, and rolling motions. Compared with the case of bouncing on a level road, setting the obstacle on a sideways slope under the upper side of the forwarding tractor could stimulates a much more dangerous scenario, which may lead to tractor overturn. In this model, the tractor was considered as a rigid body, except for the tires, which were regarded as spring-damper units. The entire passing-over process was divided into four periods as done by Yamamoto and Shimada (1957), and Takeda et al. (2010) for dissecting the influence of each specific travelling period on the tractor. Basic dimensional parameters and physical properties of the objective tractor, used as input parameters in our simulation, were cited directly from the work of Takeda et al. (2010). Dynamic behavior of the tractor was described by capturing the motion of its center of gravity, which includes vertical displacement, angle, and angular acceleration for the pitching and rolling phenomena. Using the Runge-Kutta method, the desired mathematical model was numerically simulated through programming in Visual Basic Application language within Microsoft Excel. Tractor dynamic predictions were presented as factors of forward constant speed and lateral slope. The simulation results show fluctuations and increase in danger levels owing to higher velocities and steep lateral slopes. Therefore, this model enables us to explore potential overturning judgment standards.