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 isotherma l o 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 compr essed air to the air-spring wall. Since the heat transport is diffusive, the change of stiffness happens t o be in a surprisingly low frequency band, ranging between 0.001 Hz and 0.1 Hz for a typical vehicle air s pr ng. To understand this dynamic behaviour in detail, i.e. to find the temperature distribut ion 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, t emperature, 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 freque ncy, i.e. Peclet number, the boundary-layer thickness decreases and the stiffness approaches its adiabati c v lue. 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 numb er, is useful when only the average temperature and pressure are of interest. This is usually the case w hen the air spring is considered as a connecting part between different masses in a dynamic system. It is found t hat the Nusselt number for the heat conduction inside the air spring is a constant ( 0 . 3 ≈ Nu ). 1 Boundary conditions for the simplified geometry The one dimensional problem the most simple geometric model of a n air spring is considered: two, plane, infinite plates with the initial separation dista nce 0 h , one of which (the upper) is set into harmonic oscillation perpendicular to its plane at frequen cy /(2 ) f ω π = and amplitude h ∆ (see figure 1). Since the plates are infinite large (or the l at ral extension is much greater than 0 h ) only the velocity component υ in the normal y -direction must be considered.