Normal Modes in Hydraulic Lines

In this article, we use bond graph techniques to model hydraulic lines in high-pressurehydraulic control systems. We shall present different models obtained from modal analysis of the wave equation which is done in two dual forms. It is combined with the causal information obtained from the bong graph. The models have the following causalities: pressure input, flow input or mixed. This allows an interconnection with other sub-systems. They can either have lumped or distributed parameters without algebraic problems. Furthermore, we show that the models which have a residual element-either capacitive or inertial-lead to a very good approximation of steady state and dynamic behaviour. This remains true even if only one mode is included. After writing different forms of the state equations of the line, we demonstrate the power of the method on two examples; the study of the transient response of a line and the study of the behavior of a diesel engine fuel injection system.