Two Models for Hydraulic Cylinders in Flexible Multibody Simulations

  • Antti YlinenEmail author
  • Jari Mäkinen
  • Reijo Kouhia
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 41)


In modelling hydraulic cylinders interaction between the structural response and the hydraulic system needs to be taken into account. In this chapter two approaches for modelling flexible multibody systems coupled with hydraulic actuators i.e. cylinders are presented and compared. These models are the truss-element-like cylinder and bending flexible cylinder models. The bending flexible cylinder element is a super-element combining the geometrically exact Reissner-beam element, the \(C^1\)-continuous slide-spring element needed for the telescopc movement and the hydraulic fluid field. Both models are embeded with a friction model based on a bristle approach. The models are implemented in a finite element enviroment. In time the coupled stiff differential equation system is integrated using the L-stable Rosenbrock method.


Friction Force Friction Model Jacobian Matrice Hydraulic Cylinder Cylinder Lining 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Bathe KJ (1996) Finite Element Procedures. Prentice HallGoogle Scholar
  2. 2.
    Bauchau O, Liu H (2006) On The Modeling of Hydraulic Components in Rotorcraft Systems. Journal of the American Helicopter Society 51(2):175–184Google Scholar
  3. 3.
    Cardona A, Géradin M (1990) Modeling of a hydraulic actuator in flexible machine dynamics simulation. Mechanism and Machine Theory 25(2):193–207Google Scholar
  4. 4.
    Ellman A, Piché R (1999) A two regime orifice flow formula for numerical simulation. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME 121(4):721–724Google Scholar
  5. 5.
    Géradin M, Cardona A (2001) Flexible Multibody Dynamics: A Finite Element Approach. J. Wiley & SonsGoogle Scholar
  6. 6.
    Hairer E, Wanner G (1991) Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems. Springer Series in Computational Mathematics 14, SpringerGoogle Scholar
  7. 7.
    Holzapfel GA (2000) Nonlinear Solid Mechanics - A Continuum Approach for Engineering, 1st edn. John Wiley & SonsGoogle Scholar
  8. 8.
    Ibrahimbegović A, Mamouri S (1999) Nonlinear dynamics of flexible beams in planar motion: Formulation and time-stepping scheme for stiff problems. Computers & Structures 70(1):1–22Google Scholar
  9. 9.
    Ibrahimbegović A, Mamouri S (2002) Energy conserving/decaying implicit time-stepping scheme for nonlinear dynamics of three-dimensional beams undergoing finite rotations. Computer Methods in Applied Mechanics and Engineering 191(37–38):4241–4258Google Scholar
  10. 10.
    Mäkinen J (2007) Total Lagrangian Reissner’s geometrically exact beam element without singularities. International journal for numerical methods in engineering 70(9):1009–1048Google Scholar
  11. 11.
    Marjamäki H, Mäkinen J (2003) Modelling telescopic boom - the plane case: Part I. Computers & Structures 81(16):1597–1609Google Scholar
  12. 12.
    Marjamäki H, Mäkinen J (2006) Modelling a telescopic boom - the 3D case: Part II. Computers & Structures 84(29-30):2001–2015Google Scholar
  13. 13.
    Marjamäki H, Mäkinen J (2009) Total Lagrangian beam element with C\(^1\)-continuous slide-spring. Computers & Structures 87:534–542Google Scholar
  14. 14.
    Naya M, Cuadrado J, Dopico D, Lugris U (2011) An efficient unified method for the combined simulation of multibody and hydraulic dynamics: Comparison with simplified and co-integration approaches. Archive of Mechanical Engineering 58(2):223–243Google Scholar
  15. 15.
    Piché R (1995) An L-stable Rosenbrock method for step-by-step time integration in structural dynamics. Computer Methods in Applied Mechanics and Engineering 126(3–4):343–354Google Scholar
  16. 16.
    Shampine L, Reichelt M (1997) The MATLAB ode suite. SIAM Journal on Scientific Computing 18(1):1–22Google Scholar
  17. 17.
    Viersma TJ (1980) Analysis, Synthesis, and Design of Hydraulic Servosystems and Pipelines. Elsevier Scientific Publishing CompanyGoogle Scholar
  18. 18.
    Canudas de Wit C, Olsson H, Astrom K, Lischinsky P (1995) New model for control of systems with friction. IEEE Transactions on Automatic Control 40(3):419–425Google Scholar
  19. 19.
    Ylinen A (2015) Hydraulic cylinder models for flexible multibody system simulation. PhD thesis, Department of Mechanical Engineering and Industrial Systems, Tampere University of TechnoogyGoogle Scholar
  20. 20.
    Ylinen A, Marjamäki H, Mäkinen J (2014) A hydraulic cylinder model for multibody simulations. Computers & Structures 138:62–72Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.FS Dynamics Finland Oy AbTampereFinland
  2. 2.Department of Civil EngineeringTampere University of TechnologyTampereFinland
  3. 3.Department of Mechanical Engineering and Industrial SystemsTampere University of TechnologyTampereFinland

Personalised recommendations