Skip to main content
SpringerLink
Log in

Non-linear parametric modelling of a high-speed rail hydraulic yaw damper with series clearance and stiffness

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

At high operational speeds, the train system becomes very sensitive to parameter variations of components. Therefore, it is imperative to incorporate more accurate component models in the vehicle dynamics studies. This study addresses a more subtle and comprehensive non-linear parametric model of a high-speed rail hydraulic yaw damper. A new concept of a hydraulic yaw damper model is suggested, in which the small mounting clearance, the series stiffness, and the viscous damping are built in. The series stiffness is the tandem result of the dynamic oil stiffness, the rubber attachment stiffness, and the mounting seat stiffness. A dynamic oil property model is established and coupled to the entire modelling process, in which the density, the dynamic viscosity, the volumetric elastic modulus, and the stiffness of the oil are all changeable in terms of the instantaneous working pressure, the oil temperature, and the entrapped air ratio of the oil. The dynamic flow loss and the valve system dynamics are also incorporated. Experiments validated that the established non-linear parametric model is accurate and robust in predicting the damping characteristics within an extremely wide speed range. The validated damper model was then successfully applied to a thorough parameter sensitivity analysis and damping nature prediction under practical, in-service conditions. The established damper model couples all the main influential factors that are not or are insufficiently considered in normal-speed problems; thus, it will be more accurate and appropriate for furthering high-speed problem studies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

Ae (m2):

equivalent action area on the valve seat

B (N s/m):

viscous damping coefficient of the piston-and-rod assembly

C (N s/m):

damping coefficient

C d :

discharge coefficient

Ce (N s/m):

effective damping coefficient

D (m):

piston diameter

E r :

set-pressure deviation rate of the relief valve

F (N):

damping force at a typical stroke speed

F(t), Fr(t) (N):

nominal and initial instantaneous damping force

H, Hp (m):

height of the inner tube and the piston

K (N/m):

spring stiffness of the relief valve

Ke (N/m):

series stiffness of the damper

Kleak (m3 Pa−1 s−1):

pressure leakage coefficient

Koil (N/m):

dynamic oil stiffness

Kq (Pa−1 s−1):

flow coefficient of the relief valve

Krubber (N/m):

rubber attachment stiffness

Kseat (N/m):

mounting seat stiffness

L (m):

piston seal width

Lgap (m):

accumulated clearance at the ends of the damper

Lt (m):

piston sweep distance

P, P0 (Pa):

instantaneous and the reference working pressure

Pb (Pa):

instantaneous back pressure

Pb0 (Pa):

back pressure when piston is in the neutral position

Pt (Pa):

set pressure of the relief valve

Q (m3/s):

instantaneous flow

Qleak (m3/s):

pressure leakage flow

Qloss (m3/s):

total flow loss

Qvalve (m3/s):

flow forced through the complete valve system

T, T0 (°C ):

instantaneous and the reference oil temperature

Vgas,0 (m3):

enclosed air volume when piston is in the neutral position

Voil (m3):

instantaneous oil volume in the pressure chamber

X0 (m):

initial length reduction of the relief valve spring

d (m):

piston rod diameter

d1, d3 (m):

constant orifice diameters

f (Hz):

excitation frequency

fc (N):

sliding friction force of the rod

h (m):

opening height of the valve rod

i :

index number

l (m):

rod seal width

m (kg):

mass of the piston-and-rod assembly

moil (kg):

mass of the oil in the pressure chamber

r1, r2 (m):

inner and outer radius of the inner tube port restriction

rn, rw (m):

inner and outer radius of the seal land on the valve seat

v (m/s):

typical stroke speed

x(t), xr(t) (m):

nominal and actual instantaneous displacement

αP (Pa−1):

oil viscosity-pressure coefficient

αT (°C−1):

oil volumetric thermal expansion coefficient

β (Pa−1):

oil compressibility coefficient

βe (Pa):

instantaneous oil elastic modulus

βe0 (Pa):

pure oil elastic modulus at T 0

δ (m):

seal or restriction clearance

ε :

entrapped air ratio of the oil

λ :

oil viscosity-temperature coefficient

μ (Pa s):

instantaneous oil dynamic viscosity

μ0 (Pa s):

oil dynamic viscosity at P 0 and T 0

ρ (kg/m3):

instantaneous oil density

ρ0 (kg/m3):

oil density at P 0 and T 0

References

  1. Miyamoto, M., Suda, Y.: Recent research and development on advanced technologies of high-speed railways in Japan. Veh. Syst. Dyn. 40(1–3), 55–99 (2003)

    Article  Google Scholar 

  2. European Standard: Railway Applications—Suspension Components—Hydraulic Dampers, CEN EN 13802 (2004)

  3. Wrang, M.: Instability phenomena of a passenger coach, caused by internal yaw damper flexibility. Veh. Syst. Dyn. 33, 406–417 (1999)

    Google Scholar 

  4. Wang, W.L.: Design theory and practices on an adjustable linear hydraulic damper for high-speed railway vehicles. Ph.D. thesis, Zhejiang University (2001)

  5. Eyres, R.D., Champneys, A.R., Lieven, N.A.J.: Modelling and dynamics response of a damper with relief valve. Nonlinear Dyn. 40(2), 119–147 (2005)

    Article  MATH  Google Scholar 

  6. Wang, W.L., Xu, G.X.: Fluid formulea for damping changeability conceptual design of railway semi-active hydraulic dampers. Int. J. Non-Linear Mech. 44(7), 809–819 (2009)

    Article  Google Scholar 

  7. Simms, A., Crolla, D.: The influence of damper properties on vehicle dynamic behavior. SAE Paper: 2002–01–0319 (2002)

  8. Alexander, L., Swenja, L.: A thermo-mechanically coupled model for automotive shock absorbers: Theory, experiments and vehicle simulations on test tracks. Veh. Syst. Dyn. 37(4), 241–261 (2002)

    Article  Google Scholar 

  9. Richard, V.K., Wang, C.G., Qian, L.X., Liu, J.Z., Ye, G.H.: A new shock absorber model for use in vehicle dynamics studies. Veh. Syst. Dyn. 43(9), 613–631 (2005)

    Article  Google Scholar 

  10. Shieh, N.C., Lin, C.L., Lin, Y.C., Liang, K.Z.: Optimal design for passive suspension of a light rail vehicle using constrained multi-objective evolutionary search. J. Sound Vib. 285(1–2), 407–424 (2005)

    Article  Google Scholar 

  11. He, Y.P., Mcphee, J.: Multidisciplinary optimization of multi-body systems with application to the design of rail vehicles. Multibody Syst. Dyn. 14(2), 111–135 (2005)

    Article  MATH  Google Scholar 

  12. Kowalski, D., Rao, M.D., Blough, J., Gruenberg, S.: Dynamic testing of shock absorbers under non-sinusoidal conditions. IMechE, Part D: J. Automob. Eng. 216(5), 373–384 (2002)

    Article  Google Scholar 

  13. Schiehlen, W., Hu, B.: Spectral simulation and shock absorber identification. Int. J. Non-Linear Mech. 38(2), 161–171 (2003)

    Article  MATH  Google Scholar 

  14. Calvo, J.A., López-Boada, B., San Román, J.L., Gauchía, A.: Influence of a shock absorber model on vehicle dynamic simulation. IMechE, Part D: J. Automob. Eng. 223(2), 189–202 (2009)

    Article  Google Scholar 

  15. Richard, V.K.: A new numerical damper model based on the magic formula with an application in railway vehicle dynamics. Ph.D. thesis, Beijing JiaoTong University (2005)

  16. Weigel, M., Mack, W., Riepl, A.: Nonparametric shock absorber modelling based on standard test data. Veh. Syst. Dyn. 38(6), 415–432 (2002)

    Article  Google Scholar 

  17. Witters, M., Swevers, J.: Black-box identification of a continuously variable semi-active damper. In: Proceeding of the IEEE Multi-Conference on Systems and Control, pp. 19–24, Texas, San Antonio (2008)

    Google Scholar 

  18. Codecà, F., Savaresi, S.M., Spelta, C., Montiglio, M., Ieluzzi, M.: Identification of an electro-hydraulic controllable shock absorber using black-block non-linear models. In: Proceeding of the IEEE Multi-Conference on Systems and Control, pp. 462–467, Texas, San Antonio (2008)

    Google Scholar 

  19. Yang, G.Z., Wang, F.T.: Hydraulic Dampers for Railway Rolling Stock. China Railway Publishing House, Beijing (2003)

    Google Scholar 

  20. Dixon, J.C.: The Shock Absorber Handbook. Wiley, New York (2007)

    Book  Google Scholar 

  21. George, E.T.: Handbook of Hydraulic Fluid Technology. Marcel Dekker, New York (2000)

    Google Scholar 

  22. Alonso, M., Comas, Á.: Thermal model of a twin-tube cavitating shock absorber. IMechE, Part D: J. Automob. Eng. 222(11), 1955–1964 (2008)

    Article  Google Scholar 

  23. Alonso, M., Comas, Á.: Modelling a twin tube cavitating shock absorber. IMechE, Part D: J. Automob. Eng. 220(8), 1031–1040 (2006)

    Article  Google Scholar 

  24. Ramos, J.C., Rivas, A., Biera, J., Sacramento, G., Sala, J.A.: Development of a thermal model for automotive twin-tube shock absorbers. Appl. Therm. Eng. 25(11–12), 1836–1853 (2005)

    Article  Google Scholar 

  25. Stefaan, W.D.: Simulation tools, modelling and identification, for an automotive shock absorber in the context of vehicle dynamics. Veh. Syst. Dyn. 33(6), 261–285 (2000)

    Google Scholar 

  26. Wang, W.L., Yang, X.J., Xu, G.X.: Computer package for the optimal design and simulation of railway hydraulic dampers. In: Proceeding of the International Conference on Information Engineering and Computer Science, Wuhan, China, pp. 578–582 (2009)

    Google Scholar 

  27. Rabie, M.G.: Fluid Power Engineering. McGraw-Hill, New York (2009)

    Google Scholar 

  28. Javier, L., Jorge, B., José, A.S.: Modelling of friction phenomena in sliding conditions in suspension shock absorbers. Veh. Syst. Dyn. 46(suppl), 751–764 (2008)

    Google Scholar 

  29. Wang, W.L., Xia, X.F., Xu, G.X.: A Dynamic fluid property model for the engineering design of hydraulic dampers. Key Eng. Mater. 450, 35–38 (2011)

    Article  Google Scholar 

  30. Fujimoto, H., Miyamoto, M.: Lateral vibration and its decreasing measure of a Shinkansen train. Veh. Syst. Dyn. 25(suppl), 188–199 (1996)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Vehicle Engineering Laboratory, School of Mechanical and Electrical Engineering, Nanchang University, Nanchang, Jiangxi Province, 330031, People’s Republic of China

    W. L. Wang, Y. Huang, X. J. Yang & G. X. Xu

Authors
  1. W. L. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. X. J. Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. G. X. Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to W. L. Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, W.L., Huang, Y., Yang, X.J. et al. Non-linear parametric modelling of a high-speed rail hydraulic yaw damper with series clearance and stiffness. Nonlinear Dyn 65, 13–34 (2011). https://doi.org/10.1007/s11071-010-9871-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-010-9871-7

Keywords

Search

Navigation