Analysis of dynamic properties of hydraulic lines for fluid power transmission

This paper presents the results of a hydraulic line dynamic properties analysis taking into account inertia of the fluid flowing in rigid and flexible lines, the compressibility effect for this fluid and the viscous friction effect. The following are described and analyzed: solution of the wave equation in the form binding four variables: pressure and flow rate at the line input, and pressure and flow rate and the line output; two of the above-mentioned variables should be regarded as independent (input) and the other two as dependent (output), the accuracy comparison of distributed parameters model to lumped parameters model with regard to applicability range in hydraulic systems analysis, pressure value at given installation points as a response to rapid valve closing (transient response) or to valve opening (waterhammer effect). In these considerations the hydraulic line is regarded as a two-port with two inputs and two outputs with a definite transmittance matrix. Main considerations concern the variable resistance model. A general solution is given as a function of the Laplace operator. Introducing appropriate simplifications into the variable resistance model, the constant resistance model and lossless line model is obtained. Also, general solutions for three different lump parameter models are presented. For the lumped parameters lin presents three equivalent models possible, i.e. as: a symmetrical two-port, a two-port with shared resistance and a two-port with capacitance at the output.