A novel air spring dynamic model with pneumatic thermodynamics, effective friction and viscoelastic damping

Hengjia Zhu, James Yang, Yunqing Zhang, Xingxing Feng

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


An accurate air spring model is critical for vehicle design equipped with air spring pneumatic systems to provide a better performance. However, it is particularly difficult to establish a generalized analytical model to predict the amplitude- and frequency-dependent behaviors of an air spring resulting from many factors such as thermodynamics, friction, and damping. In this paper, an air spring dynamic model is developed by considering the thermodynamics of the bellow-pipe-tank pneumatic system, the effective friction, and viscoelastic damping of the bellow rubber. It is worth mentioning that parameters in the friction model depend on the standard deviation of the displacement excitation through a statistics method rather than constant values in the classic Berg's friction model. The bellow rubber viscoelastic property is modeled by a fractional calculus element with only two parameters. The proposed model parameters are identified and further validated by conducting bench tests of the stand-alone air spring component and the bellow-pipe-tank system, separately. Several models for the air spring are compared with the proposed model and the measurements in harmonic excitations with different amplitudes and frequencies, and random excitations with both large and small displacement cases. The results of comparison show that the proposed model can accurately predict the dynamic characteristics of the air spring in an acceptable computation time.

Original languageEnglish
Pages (from-to)87-104
Number of pages18
JournalJournal of Sound and Vibration
StatePublished - Nov 10 2017


  • Air spring
  • Fractional derivative
  • Friction
  • Nonlinear dynamics


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