Audible-frequency stiffness of a primary suspension isolator on a high-speed tilting bogie

Abstract

The preload-dependent dynamic stiffness of a primary suspension isolator on a high-speed tilting bogie is examined via measurements and modelling within an audible frequency range. The stiffness is found to depend strongly on both frequency and preload. The former displays some resonance phenomena, such as stiffness peaks and troughs, while the latter exhibits a steep low-frequency stiffness increase in addition to an anti-resonance peak shifting to a higher frequency with increased preload. The problems of simultaneously modelling the preload and frequency dependence are removed by adopting a frequency-dependent waveguide approach, assuming incompressible rubber with an Abel operator kernel as its shear relaxation function. The preload dependence is modelled by a non-linear shape factor based approach, using a globally equivalent preload configuration. All the translational stiffnesses are modelled, including the vertical, longitudinal and lateral directions, and the vertical stiffness results are compared to those of measurements in a specially designed test rig. Good agreement is obtained for a wide frequency domain-covering 100-600 Hz-using a minimum number of parameters and for a wide preload domain-from vanishing to the maximum in service, 90 kN.

Keywords

dynamic stiffness primary suspension bogie shape factor rubber

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References

Elbeheiry

E. M.

Karnopp

D. C.

Elaraby

M. E.

Abdelraaouf

A. M.

Advanced ground vehicle suspension systems-a classified bibliography

Veh. System Dynamics, 1995, 24, 231–258.

Ferguson

N. S.

Modelling the vibrational characteristics and radiated sound power for a Y25-type bogie and wagon

J. Sound Vibr., 2000, 231, 791–803.

Kari

Modelling the audible stiffness of preloaded vibration isolators. In Proceedings of Conference on

Constitutive Models for Rubber II, Hannover, Germany, 2001, pp. 285–295.

Lindley

P. B.

Load-compression relationships of rubber units

J. Strain Analysis, 1966, 1, 190–195.

Gent

A. N.

Meinecke

E. A.

Compression, bending, and shear of bonded rubber blocks

Polym. Engng Sci., 1970, 10, 48–53.

Dai

H.-H.

Exact solutions for the large axially symmetric deformations of a neo-Hookean rod subjected to static loads

Q. J. Mech. Appl. Math., 2001, 54, 39–56.

Hill

J. M.

A review of partial solutions of finite elasticity and their applications

Int. J. Non-linear Mechanics, 2001, 36, 447–463.

Gent

A. N.

Engineering with Rubber, 1992 (Carl Hansen Verlag, Munich).

Lindley

P. B.

Engineering Design with Natural Rubber, 1992 (The Malaysian Rubber Producers’ Research Association, Brickendonbury).

10.

Göbel

E. F.

Rubber Springs Design, 1974 (Newnes-Butterworths, London).

11.

Payne

A. R.

Scott

J. R.

Engineering Design with Rubber, 1960 (Interscience Publishers, New York).

12.

Kari

Eriksson

Stenberg

Dynamic stiffness of natural rubber cylinders in the audible frequency range using wave guides

Kautsch. Gummi Kunstst., 2001, 54, 106–113.

13.

Payne

A. R.

Whittaker

R. E.

Low strain dynamic properties of filled rubbers

Rubber Chem. Technol., 1971, 44, 440–478.

14.

Bagley

R. L.

Torvik

P. J.

Fractional calculus-a different approach to the analysis of viscoelastically damped structures

Am. Inst. Aeronaut. Astronaut. J., 1983, 21, 741–748.

15.

Koeller

R. C.

Applications of fractional calculus to the theory of viscoelasticity

J. Appl. Mechanics, 1984, 51, 299–307.

16.

Lapčík

Jr Augustin

Píštěk

Bujnoch

Measurement of the dynamic stiffness of recycled rubber based railway track mats according to the DB-TL 918.071 standard

Appl. Acoust., 2001, 62, 1123–1128.

17.

Thompson

D. J.

Verheij

J. W.

The dynamic behaviour of rail fasteners at high frequencies

Appl. Acoust., 1997, 52, 1–17.

18.

Bruni

Collina

Modelling the viscoelastic behaviour of elastomeric components: An application to the simultion of train-track interaction

Veh. System Dynamics, 2000, 34, 283–301.

19.

Kari

On the waveguide modelling of dynamic stiffness of cylindrical vibration isolators. Part I: The model, solution and experimental comparison

J. Sound Vibr., 2001, 244, 211–233.

20.

Dickens

J. D.

Norwood

C. J.

Universal method to measure dynamic performance of vibration isolators under static load

J. Sound Vibr., 2001, 244, 685–696.

21.

ISO 10846 Acoustics and Vibration-Laboratory Measurement of the Vibro-acoustic Transfer Properties of Resilient Elements, 1997 (International Standardization Organization, Geneva).

22.

Eickhoff

B. M.

Evans

J. R.

Minnis

A. J.

A review of modelling methods for railway vehicle suspension components

Veh. System Dynamics, 1995, 24, 469–496.

23.

Snowdon

J. C.

Vibration isolation: Use and characterization

J. Acoust. Soc. Am., 1979, 54, 1245–1274.

24.

Kari

Dynamic transfer stiffness measurements of vibration isolators in the audible frequency range

Noise Control Engng J., 2001, 49, 88–102.

25.

Sjöberg

Kari

Non-linear behavior of a rubber isolator system using fractional derivatives

Veh. System Dynamics, 2002, 37, 217–236.

26.

Kari

Stiffness scaling laws and vibration isolators

Appl. Acoust., 2002, 63, 583–594.

27.

Freakley

P. K.

Payne

A. R.

Theory and Practice of Engineering with Rubber, 1978 (Applied Science Publishers, London).

28.

Fenander

Å.

Frequency dependent stiffness and damping of railpads

Proc. Instn Mech. Engrs, Part F: J. Rail and Rapid Transit, 1997, 211 (F1), 51–62.

29.

Kim

Singh

Multi-dimensional characterization of vibration isolators over a wide range of frequencies

J. Sound Vibr., 2001, 245, 877–913.

30.

Abramowitz

Stegun

I. A.

Handbook of Mathematical Functions, 1972 (Dover Publications, New York).