An analytical model of pneumatic suspensions based on an experimental characterization

Abstract

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]

Dynamic Characteristics Analysis of Vehicle Incorporating Hydraulically Interconnected Suspension System with Dual Accumulators

“…However, they are too expensive for ordinary passenger cars. erefore, some inexpensive passive suspension systems, which can also benefit vehicle dynamic performance, have been widely studied, such as hydraulic suspension subsystems, to investigate their effects on vehicle dynamics [17,18].…”

Performance analysis of semi-active suspensions with control of variable damping and stiffness

“…It is well known that classical load-levelling or slow-active suspensions based on hydro-pneumatic or pneumatic technologies are subject to spring-stiffness variations, but the stiffness change is more a side-effect than a real control variable [9,35,55]. A variation of the spring coefficient can be achieved in active suspension (see, e.g.…”

“…The research area of variable-damping-and-stiffness suspensions in a semi-active framework is still largely unexplored; a few works have been proposed on this topic [34,35], mainly focused on the description of variable-damping architectures capable of approximating an ideal variable-stiffness suspension.…”

“…• Two different suspension architectures are presented, capable of reproducing a variabledamping-and-stiffness suspension system, based on the contributions in [34,35]. • A detailed analysis on the advantages and trade-offs of the two variable-damping-andstiffness suspension systems is developed.…”

Modeling and sensitivity analysis of a pneumatic vibration isolation system with two air chambers

“…Some studies pointed out that the diaphragm has an important role in the elastic and damping characteristic of a PVIS [4,12,13]. However, its nonlinear properties have been thus far neglected in Mechanism [14][15][16][17] or the properties of the diaphragm have taken the form of lookup table even in some studies that regarded it as a nonlinear element [12,13]. The mathematical modeling of the diaphragm is essential since it makes transfer functions to be analytic so that the transfer functions might be used not only for transmissibility calculation but also for sensitivity analysis and performance optimization.…”