The Results of a Compromise Solution, Which Were Obtained on the Basis of the Method of Uncertain Lagrange Multipliers to Determine the Influence of Design Factors of the Elastic-Damping Mechanism in the Tractor Transmission

The article is devoted to the research of a compromise solution for finding the optimal parameters of the Elastic Damping Mechanism (EDMṇ) in the 14 kN class tractor transmission. The tractor was part of three different machine-tractor units and performed the main agricultural operations: plowing, cultivation and sowing. The task was to define a single function (compromise solution), which can be used to describe the processes in the transmission when performing these operations. The Lagrange multiplier method was used to obtain a compromise solution. It was necessary to create one General mathematical model out of three mathematical models, which should correctly reflect the nature of the ongoing processes. It was necessary to determine the Lagrange multipliers λ1, λ2…λm for this purpose. All calculations were made in the software environment Maple and MatLab. Compromise problem solution was found. The extremum of the «transmission transparency degree» function is found based on Lagrange multipliers. A compromise model is obtained that expresses the influence of the main EDM parameters on the «transmission transparency degree». The values of factors included in the resulting Lagrange function are found.