{"title":"Dynamics of a Wheel with a Deformable Periphery","authors":"V. G. Vil’ke, I. F. Kozhevnikov","doi":"10.1134/s1995080224602510","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider a model of a wheel consisting of a disc and a continuous set of rods joined to the disc. The rods are replaced by a continuous set of masses at free ends, joined by springs and dampers (the longitudinal and transverse stiffness of the tread rods) to the wheel disc. The viscous friction acts at the contact points of the rods with the road. The equations of motion of the wheel in the vertical plane are obtained, taking into account the impact phenomena at the boundary points of the contact area. The shape of the deformed periphery, the contact area, the frequencies of rods vibrations in steady-state regime are found. The value of external forces power required to existence of a steady-state regime is determined when wheel translational motion speed and its angular velocity are constant. The wheel vibrations in the vertical plane about the equilibrium position of the loaded wheel are also studied.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224602510","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a model of a wheel consisting of a disc and a continuous set of rods joined to the disc. The rods are replaced by a continuous set of masses at free ends, joined by springs and dampers (the longitudinal and transverse stiffness of the tread rods) to the wheel disc. The viscous friction acts at the contact points of the rods with the road. The equations of motion of the wheel in the vertical plane are obtained, taking into account the impact phenomena at the boundary points of the contact area. The shape of the deformed periphery, the contact area, the frequencies of rods vibrations in steady-state regime are found. The value of external forces power required to existence of a steady-state regime is determined when wheel translational motion speed and its angular velocity are constant. The wheel vibrations in the vertical plane about the equilibrium position of the loaded wheel are also studied.
期刊介绍：
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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