Bond graph representations of hydraulic pipelines using normal modes with dissipative friction
The one-dimensional (1-D) unsteady-pressure-flow equations of hydraulic pipeline can be approximated and solved numerically using a finite-mode approach. This paper deals with constructing bond graph representations for the hydraulic pipelines with laminar flow by using the previously established 1-D linear-friction bond graph structures and modal approximation techniques when 2-D frequency-dependent friction is taken into account. To model hydraulic pipelines as components in different systems using bond graphs, there are four possible input-output causalities: pressure inputs at both ends, flow rate input at both ends and the two cases of mixed inputs. In this paper, all four configurations are considered. The developed bond graph structures together with their corresponding modal parameters are presented. A comparison is made for three models, namely lossless, 1-D linear fluid friction and 2-D fluid friction. Simulation results show that the modified bond graph models studied in this work can give more satisfactory results.
bond graphs hydraulic pipeline normal mode dissipative model