The dynamic stiffness of an air-spring

The measurement of the dynamic stiffness of an air spring identifies a behaviour which up until now is not fully understood. Depending on whether the compression is isothermal or adiabatic the dynamic stiffness differs by a factor of 1.4 for a perfect diatomic gas. The frequency band in which the stiffness increase takes place is determined by the heat conduction from the compressed air to the air-spring wall. Since the heat transport is diffusive, the change of stiffness happens to be in a surprisingly low frequency band, ranging between 0.001 Hz and 0.1 Hz for a typical vehicle air spring. To understand this dynamic behaviour in detail, i.e. to find the temperature distribution within the spring, the energy equation must be solved using the momentum and mass balance simultaneously. This is done in an analytic manner by considering only small disturbances from the initial pressure, temperature, and density, when the air is at rest. The results show that an oscillating temperature boundary layer is formed in which the heat conduction takes places. With increasing dimensionless frequency, i.e. Peclet number, the boundary-layer thickness decreases and the stiffness approaches its adiabatic value. In theory there is no need to use a heat transfer coefficient. Furthermore the theory serves as a way to determine the heat transfer coefficient. The dimensionless transfer coefficient, i.e. the Nusselt number, is useful when only the average temperature and pressure are of interest. This is usually the case when the air spring is considered as a connecting part between different masses in a dynamic system. It is found that the Nusselt number for the heat conduction inside the air spring is a constant ( 0.3≈Nu )