This paper is directed toward a comprehensive nonlinear modeling and simulation of the performance of a class of a pilot operated relief valves. A mathematical model is deduced to predict the performance of the valve in the steady state and transient modes of operations. The developed model takes into consideration most nonlinearities of the valve and is studied within the MATLAB-SIMULINK environment. The validity of the proposed model is assessed experimentally in the steady state and transient modes of operations. The detailed modeling has resulted in a good agreement between simulation and experimental results. During the simulation studied, it was found that, nonlinearity occurs due to three factors: the pressure changes cause nonlinear velocity changes of the flow rate, the throttling area of the valve restriction usually changes nonlinearly, and the discharge coefficient of the throttling area of the valve restriction does not remain constant. In the transient mode of operation, the simulation studied identified some critical parameters which have a significant effect on the transient response of the valve. Most of the model’s parameters can be evaluated readily by direct measurement of the valve components dimensions thought the Coulomb friction factor and bulk modulus are tuned to match the model to the measurements.
This paper deals with modeling and simulation of a class of three-way pressure reducing valves. The study aims to point out the peculiarities of function and operation of this class of valves in the steady-state and transient modes of operation. A comprehensive nonlinear mathematical model is deduced in order to predict the performance of the studied valve in both modes. The proposed model takes into consideration most nonlinearities of the studied valve. A computer simulation, based on the proposed model, is performed to predict the steady-state and transient performance. During the simulation study, it was found that nonlinearity occurs due to the following factors: the transient change in the valve operating pressures and the change in the throttling areas of the valve restrictions and their discharge coefficients. The transient change in the valve operating pressures causes nonlinear velocity changes of the fluid flow passing through the throttling areas of the valve restrictions. These throttling areas usually have nonlinear mathematical formulas. The discharge coefficients of these throttling areas are assumed constant independent of the flow rates, Reynolds number, and dimensions of these areas. However, these parameters affect the discharge coefficient in a complicated manner. The validity of the proposed model is assessed experimentally in the steady-state and transient modes of operation. The results show good agreement between simulation and experiment in both modes. The study shows that the geometry of the throttling orifice, which connects the upstream port to the downstream port, plays an important role in the studied valve steady-state and transient performance. This result implies the need for further investigation of the effect of the dimensions of the throttling orifices on the steady-state and transient performance of hydraulic control valves.
This study examined the use of bond graphs for the modeling and simulation of a fluid power system component. A new method is presented for creating the bond graph model, based upon a previously developed mathematical model. A nonlinear dynamic bond graph model for a two-stage pressure relief valve has been developed in this paper. Bond graph submodels were constructed considering each element of the studied valve assembly. The overall bond graph model of the valve was developed by combining these submodels using junction structures. Causality was then assigned in order to obtain a computational model, which could be simulated. The simulation results of the causal bond graph model were compared with those of a mathematical model, which had been also developed in this paper based on the same assumptions. The results were found to correlate very well both in the shape of the curves, magnitude, and response times. The causal bond graph model was verified experimentally in the dynamic mode of operation. As a result of comparison, bond graphs can quickly and accurately model the dynamics in a fluid power control system component. During the simulation study, it was found that nonlinearity occur due to three factors: changes in pressure, which cause nonlinear velocity changes of the flow rate; changes in the throttling area of the valve restriction, which usually changes nonlinearly; and changes in the discharge coefficient of the throttling area of the valve restriction, which does not remain constant.
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