Mathematical model to calculate the critical value of the angle of gradient for a tractor-mounted tilther

Abstract

The article is devoted to the search for a mathematical model convenient for practical calculations to determine the critical value of the angle of gradient for the tractor-mounted heavy tilther. It shows the existing mathematical model, which is then refined based on the stiffness of the elastic tractor wheels and their vertical reactions offset. Three methods of solving the resulting equations are analyzed, upon which the optimal one is chosen. As a result, a simple and convenient in practice mathematical model to determine the critical value of the angle of gradient for the tractor-mounted implement is obtained. The analysis of the calculation results showed that depending on the operating conditions and the weight of the tractor counterweight, the differences between the results calculated using the traditional and refined models can reach more than 4 degrees, which is very important to ensure the hill climbing safety.