Mathematical description of tractor slippage with variable tire inflation pressure

Abstract

Tractor slippage is one of the main economic and environmental indicators for composing of tractor units. It is a key indicator showing the rational interaction of the tire to the road (soil) surface. If it is too big or too small, big energy losses occur. Slippage depends not only on the vertical loads to the driving wheels, but also on the wheel and soil grip area. The grip area between the wheel and soil usually increases by reducing the tire’s air pressure. For the operation of tractor units (especially in agriculture) the preliminary calculation of the slippage, i.e. forecasting of the energy and economic task, is one of the most important. Tractor slippage prediction in most cases is calculated based on the traction coefficients. However, the coefficients mathematical expression does not include indicators that evaluate tire pressure in the tire. From the mathematical point of view, for the ability to optimize the slippage of the driving wheels, while at the same time seeking better ecological and economic performance, it is not enough to evaluate the traction coefficient dependencies on the traction forces and the vertical load of tires, but also dependencies on the tire performance indicators, too. This article will present a mathematical model that allows estimating the slippage of driving wheels at various air pressure in the tractor tires. Based on the experimental tractor slippage dependences on the traction power and air pressure in the tires and the calculations based on the empirical formula, the formulas for calculation of the limiting traction power and the degree of the coefficient of the mathematical model of the towing calculation were made. An expanded calculation method allows to calculate the slippage value of the tractor driven wheel for any permitted tire inflation pressure.