Bond graph modeling and optimization for small scale, demand driven pneumatic circuits

Abstract

A medical device currently in the market that could have benefited from this modeling approach is the Novamedix A-V Impulse device used to provide Deep Vein Thrombosis prophylaxis therapy. This device is comprised of standard components that are typically used in compressed gas devices like valves and storage volumes. These components comprise a general system bond graph model. Fluid flow is computed based on Fanno flow and orifice flow equations for compressible fluids. Numerical methods are applied to allow the model to account for both subcritical and critical flow in the same simulation. The numerical methods used for calculation of fluid flow require a large number of iterations to achieve a low residual solution. The method of steepest descent is applied to accelerate convergence. This technique permits greater model resolution. Furthermore, regression techniques are applied to the output valuues and residuals to minimize error. The model and numerical techniques are validated by building and testing eight different component geometric configurations. The model and experiment show how configuration and initial condition changes to a compressed gas system affect the system’s behavior, for both critical and subcritical flows. The hybrid modeling method presented in this paper is best suited to show how prospective system changes will affect system behavior in conjunction with limited empirical testing instead of relying solely on bond graph modeling or physical testing.

Pneumatic medical and consumer devices that use compressed gas are designed using standardized components with many possible variations. A typical development project includes lengthy empirical testing to optimize component selections. Tools that can be used outside a lab to model these systems are either slow or unable to handle fluid compressibility effects at both sonic (critical) and subsonic (subcritical) flow conditions simultaneously. The modeling approach in this thesis is original because there is a lack of existing studies using bond graphs to model compressed gas medical devices in both critical and subcritical states. This research shows that using bond graphs and numerical methods is possible for a simple model to quickly approximate the dynamic response of a pneumatic system and facilitate an engineer’s ability to optimize component selection.