Analytical Modeling and Simulation of Machinery Containing Hydraulic Lines with Fluid Transients

In industrial equipment containing hydraulic lines for power transmission, the lines have boundary conditions defined by components such as pumps, valves, and actuators located at the ends of the lines. Sudden changes in any of the boundary conditions may result in significant pressure/flow dynamics (fluid transients) in the lines that may be detrimental or favorable to the performance of the equipment. Accurate models for line transients are defined by the exact solution to a set of simultaneous partial differential equations. In this paper, analytical solutions to the partial differential equations provide Laplace transform transfer functions applicable to any set of boundary conditions yet to be specified that satisfy the requirements of causality. Analytical solutions of these partial differential equations from previous publications are reviewed for cases of laminar and turbulent flow for Newtonian and a class of non-Newtonian fluids. This paper focuses on a method for obtaining total system analytical models and time domain solutions for cases in which the end-of-line components can be modeled with linear equations for perturbations relative to pre-transient flow conditions. Examples with pumps, valves, and actuators demonstrate the process of coupling equations for components at the ends of a line to obtain total system transfer functions and then obtain time domain solutions for outputs of interest associated with system inputs and load variations.