Abstract
Not only has the dynamic stiffness of a rubber air spring been inherited by effects of the compressed air, but it has also been affected by hysteresis behaviors caused by the friction, viscoelasticity of bellow material. Hence, this paper will analyze comprehensively the stiffness model of a commercial rubber air spring. One of the first works is to predict the structure parameters including effective area, volume and their change rate. Then, the restoring force generated by compressed air will be analyzed and built through the theory of thermodynamics. The hysteresis model of the rubber bellow will be obtained based on the Berg’s frictional model connecting in parallel with fractional Kelvin-Voigt model. Next, an experimental apparatus is set up to identify the parameters of this model as well as evaluate the proposed restoring force model of the rubber air spring. The study results show that the analysis model of the rubber air spring matches well the measured data. This work will offer a helpful insight in the design of the vibration isolation system using rubber air springs as elastic elements.
Highlights
As known, mechanical springs including coil spring [1,2,3], Euler column spring [4,5,6] have been widely employed in the vibration isolation systems to suppress the unwanted vibrations transmitted from source to the isolated object
The resultant force generated by the rubber air spring is contributed by the thermodynamic force of the compressed air, the frictional force contributed by the relative motion the between the rubber and fabric as well as rubber bellow and the surface of the piston, and the viscoelastic force of the rubber material
Assuming that the heat exchange in the rubber bellow as well as air leakage is ignored, according to the thermodynamic theories and ideal air state equation, the mathematical model of the pressure (P) in air spring is determined as follows: dP dx where, V is the effective volume of the inflated bellow, n is the polytropic exponent which depends on the thermodynamic state of the compressed air including n = 1 for the isothermal state, n = 1.4 for the adiabatic state and 1 < n < 1.4 for the polytropic process
Summary
Mechanical springs including coil spring [1,2,3], Euler column spring [4,5,6] have been widely employed in the vibration isolation systems to suppress the unwanted vibrations transmitted from source to the isolated object. Magnetic springs have been studied and applied widely in vibration isolation systems [7,8]. Application limitation of the magnetic spring is inevitable Another type of elastic elements, which can overcome problems mentioned above, is air spring due to easy control of the spring coefficient and high bearing capacity. The dynamic model of air spring for reducing the vibration transmissibility was developed and experimented by Gavriloski et al [18]. Motivated by attractive merits of air springs for isolating vibration, the present paper will establish a restoring force model of a commercial rubber air spring including the effects of compressed air inside bellow and the hysteresis of the rubber material.
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