We present an analytical model of air spring suspensions that is based on an experimental characterization. The suspension consists of three principal parts: the air spring, an auxiliary tank, and a pipe connecting the two. An analytical nonlinear fluid dynamics model is first analyzed, modeling the suspension stiffness, damping factor, and transmissibility. The model is then linearized and this linear version is studied in depth, finding that the behaviour of the suspension as reflected in the aforementioned three characteristics is strongly dependent on the size of the three suspension parts. The analysis allows us to propose a practical strategy for the operation of the suspension. NOMENCLATUREA s Spring effective area [m 2 ] C r The pipe restriction coefficient [N 5 /m/s] D p The pipe's cross section diameter [m] F Force exerted at the air spring [N] g Acceleration due to gravity [m/s 2 ] k Pneumatic suspension total stiffness [N/m] k as Air spring effective area stiffness [N/m] k s Air spring stiffness [N/m] k vs Air spring volume stiffness [N/m] k vsr Pneumatic suspension volume stiffness [N/m] l p The pipe length [m] M Sprung mass [kg] n Polytropic coefficient P r Relative pressure at the reservoir [bar] P s Relative pressure at the air spring [bar] R Gas constant for air [J/kg/K] T Air suspension temperature [K] V r Reservoir volume [m 3 ] V s Air spring volume [m 3 ] V sr Reservoir plus spring volume [m 3 ] x Absolute response [m] y Excitation [m] z Suspension height [m] z 0 Initial height for the air spring [m] γ Specific heat ratio ε Dimensionless parameter θ Dimensionless parameter µ Dynamic viscosity of air [Pa·s] ρ Density of air [kg/m 3 ] ω tr Transition frequency [rad/s] m Mass flow rate [kg/s]

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The paper describes an adaptive pneumatic suspension system that can improve both comfort and handling. Each air spring in the vehicle is connected to an auxiliary tank via two connecting pipes of different sizes. Choosing the connecting pipe with larger diameter and shorter length renders a compliant suspension which improves comfort. Conversely, choosing the connecting pipe with smaller diameter and longer length makes the suspension stiffer which favors handling. Toggling between configurations is fast, efficient, and easily done by simply opening or closing the corresponding electrovalves. The proposed adaptive system requires a GPS receiver and access to two pieces of information regarding the road at every location: the International Roughness Index and the curve radius (if not infinite). This information is used to predict road-induced vibrations and evaluate comfort with the ISO 2631 standard, as well as forecast roll angles and settling times for handling assessment. These predictions are used to select the most appropriate configuration.

Semi-active and active suspensions can improve both ride comfort and handling compared to passive suspensions. The authors have proposed a suspension comprising a pneumatic system capable of changing the stiffness of the suspension and a semi-active magnetorheological damper capable of controlling the suspension damping. Eight configurations of this magnetorheological/pneumatic suspension result from combining two possible stiffnesses (compliant and stiff) and four possible means of producing damping (constant low, constant high, on-off skyhook control and on-off balance control). The minimization of a cost function, which considers both ride comfort and handling, leads to decision maps which indicate the most appropriate configuration depending on vehicle velocity and two pieces of information about the road: the international roughness index and the curve radius. All this information can be gathered from a GPS system and toggling between set-ups is fast, efficient, and easily done by simply opening or closing pipes in the pneumatic system and modifying the current supply in the magnetorheological dampers. The proposed magnetorheological/pneumatic suspension achieves the same roll angle levels as in a comparable passive vehicle while improving ride comfort by reducing acceleration by up to 30%.

The problem of unbalanced machinery isolation is tackled in this paper. The proposed solution incorporates an air suspension that can be adapted depending on the turning frequency. The system is built with three main parts: an air spring, a reservoir and a connecting pipe. A model of the suspension excited by the unbalanced rotor is also shown in this paper. The properties of the system make it possible to use a configuration of the suspension (one pipe size) over a bandwidth range and another configuration (another pipe size) over the remaining bandwidth range. This idea is implemented with solenoid controlled valves and the results show significant improvements with respect to completely passive configurations.