Skip to main content
SpringerLink
Log in

The improvement of scientific foundations for the technical theory of pneumatic elements with rubber-cord membranes: thermo-dynamic model of force and geometric characteristics of air springs

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

Air springs have many advantages; besides, air spring dampers hold much promise for application in car suspension systems. A thermodynamic model of pneumatic elements is proposed in this study. Unlike the standard model generally accepted at present, this one does not imply that the rubber-cord membrane is absolutely flexible, and its middle surface is inextensible. The force and geometric characteristics of pneumatic elements not depending on the temperature are considered. Two examples of mathematical modeling of force and geometric characteristics of Firestone pneumatic springs with rubber-cord membranes of bellow and rolling-lobe types illustrate the proposed method. Compared to the standard model, the accuracy of coincidence with the experimental data has increased significantly.

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

A e :

Effective area

A ext :

Work of external forces

A int :

Work of internal forces

a int :

Specific work of internal forces

β :

Specific heat sources external

C x,p :

Isobaric heat capacity at constant height

c E, c ε :

Specific heat capacity without deformation

d :

Differential with respect to space

d :

Differential with respect to time

E :

Total energy

E :

The green-St. venant strain tensor

ε :

The infinitesimal strain tensor

F :

Free energy (helmholtz potential)

F :

Deformation gradient tensor

G :

Free enthalpy (gibbs potential)

I :

Unit tensor

I E :

Enthalpy of deformation

K :

Kinetic energy

L E, L ε :

Latent heat tensor of deformation

m :

Mass

n :

Polytropic coefficient

n :

Unit vector of the outer normal

P :

Force

p :

Absolute pressure

p u :

Overpressure

p atm :

Atmospheric pressure

P E :

Reduced stress tensor (second piola-kirchhoff stress tensor)

Q ext :

Heat from external sources

q ext :

Specific heat from external sources

q V :

Specific heat sources internal

q :

Heat flux vector

ρ :

Density

S :

Entropy

Σ :

Volume boundary

T, θ :

Absolute temperature

T :

Stress tensor

t :

Time

U :

Internal energy

U E :

Deformation energy

U θ :

Thermal energy

u :

Specific internal energy

u E :

Specific deformation energy

u θ :

Specific thermal energy

V :

Volume

v :

Velocity

x :

Height of pneumatic element

References

  1. Firestone Industrial Products Company, Airstroke Actuators, Airmount Isolators, Engineering Manual and Design Guide, Firestone Industrial Products Company, Available at http://www.firestoneip.com/content/dam/fsip/pdfs/airstroke/Actuators-and-Isolators-Metric-Design-Guide.pdf (Accessed 14, August, 2020).

  2. C. Erin et al., An improved model of a pneumatic vibration isolator: theory and experiment, Journal of Sound and Vibration, 218 (1) (1998) 81–101.

    Article  Google Scholar 

  3. G. Quaglia and M. Sorli, Air suspension dimensionless analysis and design procedure, Vehicle System Dynamics, 35 (6) (2001) 443–475.

    Article  Google Scholar 

  4. S. Zhu et al., Research on theoretical calculation model for dynamic stiffness of air spring with auxiliary chamber, IEEE Vehicle Power and Propulsion Conference, Harbin, China (2008).

  5. H. Liu and J. C. Lee, Model development and experimental research on an air spring with auxiliary reservoir, International Journal of Automotive Technology, 12 (6) (2011) 839–847.

    Article  Google Scholar 

  6. E. Zheng et al., Prediction of the vibration characteristics for wheeled tractor with suspended driver seat including air spring and MR damper, Journal of Mechanical Science and Technology, 30 (9) (2016) 4143–4156.

    Article  Google Scholar 

  7. P. Hedrich and P. F. Pelz, Luftfederdämpfung als zukunftsweisende Technologie im Nutzfahrzeugbereich, Optimale Auslegung eines Luftfederdäfmpfers, 2261 (2015) 145–153.

    Google Scholar 

  8. N. Bruno et al., Development of a piezoelectric high speed on/off valve and its application to pneumatic closed-loop position control system, Journal of Mechanical Science and Technology, 33 (6) (2019) 2747–2759.

    Article  Google Scholar 

  9. R. A. Akopyan, Theory and Practice Questions, Vyshcha shkola Publ., Izdatel’stvo pri L’vovskom universitete Publ., Lviv, Ukraine (1979) (in Russ.).

    Google Scholar 

  10. A. V. Pozdeyev et al., Adjustable Air and Pneumohydraulic Springs of Vehicle Suspensions, VSTU Publ., Volgograd, Russia (2014) (in Russ.).

    Google Scholar 

  11. S. A. Korneyev et al., Fundamentals of the Technical Theory of Air Springs Dampers, Omsk State Technical University, Omsk, Russia (2016) (in Russ.).

    Google Scholar 

  12. V. L. Biderman, Calculations of rubber and rubber-cord parts, S. D. Ponomarev et al. (Ed.), Strength Calculations in Mechanical Engineering, Mashgiz Publ., Moscow, Russia, 2 (1958) 487–591 (in Russ.).

    Google Scholar 

  13. V. L. Biderman et al., Automobile Tires, Construction, Design, Testing and Operation, NASA Technical Translation, NASA, USA (1969) NASA TT F-12,382.

  14. J. F. Purdy, Mathematics Underlying Design of Pneumatic Tires, Edwards Brothers Inc., Ann Arbor, USA (1963).

    Google Scholar 

  15. W. Hoferberth, Zur festigkeit des luftreifens, Kautschuk und Gummi, Kunststofe, 9 (1956) 225–231.

    Google Scholar 

  16. R. Hadekel, Some notes of pneumatic tires, Aircraft Engineering and Aerospace Technology, 16 (1) (1944) 11–13.

    Article  Google Scholar 

  17. R. S. Rivlin, The deformation of a membrane formed by Inextensible cords, Archive for Rational Mechanics and Analysis, 2 (1959) 447–476.

    Article  MathSciNet  Google Scholar 

  18. S. K. Clark, Mechanics of Pneumatic Tires, U.S. Department of Transportation, National Highway Traffic Safety Administration, Washington, D. C., USA (1981).

    Google Scholar 

  19. A. E. Belkin et al., On models and methods of mechanics of pneumatic tires and rubber-cord shells. Development of the ideas due to Professor V. L. Biderman, Mechanics of Solids, 52 (3) (2017) 233–242.

    Article  Google Scholar 

  20. G. O. Ravkin, Air Suspension Car, Mashgiz Publ., Moscow, Russia (1962) (in Russ.).

    Google Scholar 

  21. Y. M. Pevzner and A. M. Gorelik, Pneumatic and Hydropneumatic Suspensions, Mashgiz Publ., Moscow, Russia (1963) (in Russ.).

    Google Scholar 

  22. X. Li and T. Li, Research on vertical stiffness of belted air springs, Vehicle System Dynamics, 51 (11) (2013) 1655–1673.

    Article  Google Scholar 

  23. P. K. Wong et al., Analysis of automotive rolling lobe air spring under alternative factors with finite element model, Journal of Mechanical Science and Technology, 28 (12) (2014) 5069–5081.

    Article  Google Scholar 

  24. J. Ye et al., Analysis of vertical stiffness of air spring based on finite element method, MATEC Web of Conferences, 153 (2018) 06006.

    Article  Google Scholar 

  25. G. Quaglia and A. Guala, Evaluation and validation of an air springs analytical model, International Journal of Fluid Power, 4 (2) (2003) 43–54.

    Article  Google Scholar 

  26. M. N. Fox, R. L. Roebuck and D. Cebon, Modelling rolling-lobe air springs, Int. J. Heavy Vehicle Systems, 14 (3) (2007) 254–270.

    Article  Google Scholar 

  27. Z. Xie et al., A noise-insensitive semi-active air suspension for heavy-duty vehicles with an integrated fuzzy-wheelbase preview control, Mathematical Problems in Engineering, 2013 (2013) 1–12.

    Google Scholar 

  28. P. Sathishkumar et al., Reducing the seat vibration of vehicle by semi active force control technique, Journal of Mechanical Science and Technology, 28 (2) (2014) 473–479.

    Article  Google Scholar 

  29. V. A. Galashin, Determination of air spring stiffness taking into account heat transfer, Automotive Industry (1965) 21–23 (in Russ.).

  30. S. J. Lee, Development and analysis of an air spring model, International Journal of Automotive Technology, 11 (4) (2010) 471–479.

    Article  Google Scholar 

  31. R. Kubo, Thermodynamics: an Advanced Course with Problems and Solutions, North Holland Publishing Co., Amsterdam, Holland (1968).

    Google Scholar 

  32. C. Truesdell, Rational Thermodynamics, Springer-Verlag, New York, USA (1984).

    Book  Google Scholar 

  33. C. Truesdell, A First Course in Rational Continuum Mechanics, Academic Press, Boston, USA (1991).

    Google Scholar 

  34. S. A. Korneyev, Concepts and Foundations of Locally Non-equilibrium Thermodynamics of a Continuous Medium, Om-STU Publ., Omsk, Russia (2009) (in Russ.).

    Google Scholar 

  35. V. S. Korneyev et al., On the issue of classical heat transfer equation applicability to highly elastic materials at large strains, Thermal Processes in Engineering, 11 (2) (2019) 79–85. (in Russ.).

    Google Scholar 

  36. I. P. Bazarov, Thermodynamics, Vysshaya Shkola, Moscow, Russia (1991) (in Russ.).

    Google Scholar 

  37. J. Gough, A description of a property of caoutchouc or Indian rubber, Memoirs of the Literary and Philosophical Society of Manchester, Second Series, I (1805) 288–295.

    Google Scholar 

  38. J. P. Joule, On some thermo-dynamic properties of solids, Philosophical Transactions, 149 (1859) 91–131.

    Article  Google Scholar 

  39. L. Treloar, The Physics of Rubber Elasticity, Oxford, Great Britain (1949).

    Google Scholar 

  40. A. A. Il’yushin, Continuum Mechanics, Moscow State Iniversity, Moscow, Russia (1978) (in Russ.).

    Google Scholar 

  41. J. S. Sneddon and D. S. Berry, The Classical Theory of Elasticity, Springer, Berlin, Germany (1958).

    Google Scholar 

  42. I. S. Grigor’eva and E. Z. Mejlihova, Physical Quantities: A Reference Book, Energoatomizdat, Moscow, Russia (1991) (in Russ.).

    Google Scholar 

  43. I. N. Francevich, Elastic Constants and Elastic Moduls of Metals and Non-Metals, Naukova Dumka, Kiev, Ukraine (1982) (in Russ.).

    Google Scholar 

  44. V. S. Korneyev et al., The approximate analytic solution of non-stationary heat conduction problem of a deformable plate with time-dependent boundary conditions, Thermal Processes in Engineering, 11 (9) (2019) 417–425 (in Russ.).

    Google Scholar 

Download references

Acknowledgments

The work was completed in Omsk State Technical University, Russia, Omsk.

Author information

Authors and Affiliations

  1. Faculty of Transport, Oil and Gas, Omsk State Technical University, Omsk, 644050, Russian Federation

    Vladimir Sergeyevich Korneyev, Sergey Alexandrovich Korneyev & Viktor Vladimirovich Shalay

Authors
  1. Vladimir Sergeyevich Korneyev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sergey Alexandrovich Korneyev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Viktor Vladimirovich Shalay
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir Sergeyevich Korneyev.

Additional information

Korneyev Vladimir Sergeyevich is a Doctor of Science (Eng.) and Associate Professor at the Department of Foundations of the Theory of Mechanics and Automatic Control, Omsk State Technical University.

Korneyev Sergey Alexandrovich is a Doctor of Science (Eng.). He is a Professor at the Department of Foundations of the Theory of Mechanics and Automatic Control, Omsk State Technical University.

Shalay Viktor Vladimirovich is a Doctor of Science (Eng.). He is a Professor, an Honorary Worker of the Higher School of Russia, a President of Omsk State Technical University, and a Head of Transport, Oil and Gas Storage, Standardization, and Certification Department, Omsk State Technical University.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Korneyev, V.S., Korneyev, S.A. & Shalay, V.V. The improvement of scientific foundations for the technical theory of pneumatic elements with rubber-cord membranes: thermo-dynamic model of force and geometric characteristics of air springs. J Mech Sci Technol 38, 49–65 (2024). https://doi.org/10.1007/s12206-023-1205-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-023-1205-z

Keywords

Search

Navigation