Elastic Damping Mechanism Optimization by Indefinite Lagrange Multipliers

Abstract

The current paper has presented the study on theoretical dependences of the optimization parameter (the degree of transmission transparency) on the design factors of elastic-damping mechanism (EDM) in the transmission for tractors of small traction class (14 kN). The purpose of the study was to obtain a unified functional relationship that integrates early study results. The determination of a unified function was based on reaching a compromise by the method of indefinite Lagrange multipliers. With the help of the function, there have been obtained the dependences of the effect of EDM design factors on transmission processes when performing the main agricultural operations. Using a method based on finding a compromise solution (method of indefinite Lagrange multipliers), there have been substantiated design parameters of the elastic-damping mechanism in the tractor transmission and there has been identified an optimization parameter of the Lagrange function. For a better understanding of the obtained dependence, there has been carried out a three-dimensional visual analysis. Each factor used in the Lagrange function was a physical parameter of an elastic-damping mechanism. The resulting equation has given an opportunity to control mechanism parameters in natural operating conditions. The obtained Lagrange value has demonstrated that the mechanism absorbs 32% of fluctuations in the external traction load of a tractor, when working with the main agricultural tools.

Keywords

• Compromise problem
• elastic damping mechanism (EDM)
• indefinite Lagrange multipliers
• mechanical power transmission
• optimization
• tractor