Modelling of Mobile Nonlinear Frictional Systems

  • V. V. ShapovalovEmail author
  • V. B. Mishchinenko
  • G. A. Areshjan
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


The article describes modelling of mobile frictional systems which allows real estimation of values of required parameters taking into account dynamic characteristics of definite mechanical systems, definite friction units and materials of friction surfaces. It allows considering complex nonlinear interrelation of dynamic processes that occur in frictional contact area and in a mechanical subsystem. The construction of a mechanical subsystem model on the basis of its mathematical model allows investigating interrelation and interference of dynamic processes occurring in a definite friction unit and a definite mechanical subsystem in modelling and natural conditions. Maintaining equal identical conditions of interaction contacting micro- and macroroughnesses provides identical kinds of wear-out and its intensity, current values of a friction factor in natural and modelling conditions. On the basis of a method of the analysis of the differential equations of the object and its model, there have been chosen two equations corresponding to rotary (longitudinal rolling of a body) and forward (to vertical offsets of the first wheelset) oscillations.


Frictional systems Dynamic model Cargo tank Physical and mathematical modelling Frictional contact area Friction surfaces Similarity scales Dynamic processes 


  1. 1.
    Wiener N (1949) Extrapolation, interpolation and smoothing of stationary time series. New YorkGoogle Scholar
  2. 2.
    Khinchin AJa (1953) Theory of correlation of stationary stochastic processes. Success Math Sci VIII, Iss. 3(55)Google Scholar
  3. 3.
    Kolmogorov AN (1941) Interpolating and extrapolating of stationary random sequence. Bull Acad Sci USSR Ser Math V, 5, No. 1Google Scholar
  4. 4.
    Shapovalov VV, Sladkowski A, Erkenov ACh (2015) Topical problems of modern tribotechnics and ways of their solution. J High Educ Inst (Mach Build) 1:64–75Google Scholar
  5. 5.
    Shapovalov VV, Chelokhyan AV, Ozjabkin AL et al (2010) Amplitude and phase-frequency analysis of frictional systems critical condition: monography. UMTC ZHDT Publish House, Moscow, p 383Google Scholar
  6. 6.
    Shapovalov VV (1985) Complex modelling of dynamically loaded friction units of machines. Friction Wear-Out 3:451–457Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • V. V. Shapovalov
    • 1
    Email author
  • V. B. Mishchinenko
    • 1
  • G. A. Areshjan
    • 1
  1. 1.Rostov State Transport UniversityRostov-on-DonRussia

Personalised recommendations