Mathematical description of tractor slippage with variable tire inflation pressure

Abstract

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.Keywords: farm tractor, draw pull, inflation pressure, slippage, traction coefficient. IntroductionThe main purpose of farm tractors is to perform drawbar work. This is defined by draw pull force and run speed. Draw pull and drive wheel slippage are the key indicators affected by interaction between the wheel and the soil surface [1]. Most scientific information sources show that about 20-55 % of the available tractor power is wasted at the tire-soil interface, i.e. because of the drive wheel slippage and tire and soil deformation [2][3][4]. This energy consumes the tires and compacts the soil to a degree that may be detrimental to crop production. Efficient work of agricultural tractors includes: choosing an optimum work speed for a given tractor-implement unit; maximizing the tractive advantage of the traction devices, and minimizing the drive wheel slippage [5; 6]. Among these, minimizing of the fuel consumption could be done with little efforts.The agricultural tractors work at maximum efficiency, if their slippage is maintained in a certain rational range [7; 8]. As per the previous studies, it is recommended that farm tractors and drive wheels should be maintained to rational slippage at 10-15 % to get...

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