Analysis of Static Lateral Stability Using Mathematical Simulations for 3-Axis Tractor-Baler System

Purpose: This study aims to evaluate the applicability of a tractor-baler system equipped with a newly developed round baler by conducting stability analyses via static-state mathematical simulations and verification experiments for the tractor equipped with a loader. Methods: The centers of gravity of the tractor and baler were calculated to analyze the transverse overturning of the system. This overturning of the system was analyzed by applying mathematical equations presented in previous research and comparing the results with those obtained by the newly developed mathematical simulation. For the case of the tractor equipped with a loader, mathematical simulation results and experimental values from verification experiments were compared and verified. Results: The center of gravity of the system became lower after the baler was attached to the tractor and the angle of transverse overturning of the system steadily increased or decreased as the deflection angle increased or decreased between $0^{\circ}$ and $180^{\circ}$ on the same gradient. In the results of the simulations performed by applying mathematical equations from previous research, right transverse overturning occurred when the tilt angle was at least $19.5^{\circ}$ and the range of deflection angles was from $82^{\circ}$ to $262^{\circ}$ in counter clockwise. Additionally, left transverse overturning also occurred at tilt angles of at least $19.5^{\circ}$ and the range of deflection angles was from $259^{\circ}$ to $79^{\circ}$ in counter clockwise. Under the $0^{\circ}$ deflection angle condition, in simulations of the tractor equipped with a loader, transverse overturning occurred at $17.9^{\circ}$, which is a 2.3% change from the results of the verification experiment ($17.5^{\circ}$). The simulations applied the center of gravity and the correlations between the tilt angles, formed by individual wheel ground contact points excluding wheel radius and hinge point height, which cannot be easily measured, for the convenient use of mathematical equations. The results indicated that both left and right transverse overturning occurred at $19.5^{\circ}$. Conclusions: The transverse overturning stability evaluation of the system, conducted via mathematical equation modeling, was stable enough to replace the mathematical equations proposed by previous researchers. The verification experiments and their results indicated that the system is workable at $12^{\circ}$, which is the tolerance limit for agricultural machines on the sloped lands in South Korea, and $15^{\circ}$, which is the tolerance limit for agricultural machines on the sloped grasslands of hay in Japan.