Optimization of the parameters of tillage units

Among the many methods and techniques for optimizing the soil-cultivating unit parameters, the method of Lagrange multipliers occupies a special place. In this article, the Lagrange method is used to develop analytical dependencies that make it possible to determine the optimal values ​​of the operating width and operating speed of tillage (ploughing and cultivating) units at a set value of tractor engine power and the linear nature of the dependence of its slipping on traction force. As a result, it was found that the decreasing intensity in the ploughing unit operating width ([Formula: see text]) with an increase in the plough's specific resistance coefficient ([Formula: see text]) is practically independent of the ploughing depth ([Formula: see text]). When changing the value of this parameter in the range of 0.22-0.30 m, increasing the value of the [Formula: see text] coefficient from 50 to 65 kN m^{- 2} requires reducing the value of parameter [Formula: see text] by 23%. The maximum performance of the tractor with the plough occurs at the minimum possible values ​​of the [Formula: see text], [Formula: see text] and [Formula: see text] parameters. This result is achieved by increasing the ploughing unit operating width. At the same time, the maximum performance of the tractor with the cultivator is achieved at the maximum possible values ​​of the [Formula: see text] (3.6 kN m^{- 1}) and [Formula: see text] (3.0 m s^{- 1}) parameters and amounts to 8.6 ha h^{- 1}. Compared to the option for the minimum values ​​of the [Formula: see text] (3.0 kN m^{- 1}) and [Formula: see text] (2.0 m s^{- 1}) parameters, this is 28.4% more.