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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

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Intelligent Computing and Optimization (ICO 2020)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1324))

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Abstract

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.

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Acknowledgments

The team of authors expresses recognition for the organization of the Conference ICO'2020, Thailand, and personally Dr. Pandian Vasant. The authors are grateful to anonymous referees for their helpful comments.

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Authors and Affiliations

  1. Federal Scientific Agroengineering Center VIM, 1st Institute pas. 5, Moscow, 109428, Russia

    Sergey Senkevich, Ekaterina Ilchenko, Aleksandr Prilukov & Mikhail Chaplygin

Authors
  1. Sergey Senkevich
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  2. Ekaterina Ilchenko
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  3. Aleksandr Prilukov
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  4. Mikhail Chaplygin
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Corresponding author

Correspondence to Sergey Senkevich .

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Editors and Affiliations

  1. Department of Fundamental and Applied Sciences, Universiti Teknologi Petronas, Tronoh, Perak, Malaysia

    Pandian Vasant

  2. Faculty of Electrical Engineering and Computer Science, VŠB TU Ostrava, Ostrava, Czech Republic

    Ivan Zelinka

  3. Faculty of Engineering Management, Poznan University of Technology, Poznan, Poland

    Gerhard-Wilhelm Weber

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Senkevich, S., Ilchenko, E., Prilukov, A., Chaplygin, M. (2021). 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. In: Vasant, P., Zelinka, I., Weber, GW. (eds) Intelligent Computing and Optimization. ICO 2020. Advances in Intelligent Systems and Computing, vol 1324. Springer, Cham. https://doi.org/10.1007/978-3-030-68154-8_14

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