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FLUIDA library examples
Hydraulic actuator
In this example, some FLUIDA components are arranged to simulate the behaviour of an actuator commanded by a signal applied to a 4-way valve.
Depending on the working fluid selected, this model represents a hydraulic or pneumatic actuator (component "Actuator_2C") controlled by means of a four-way valve (component "Ev_4w").
The actuator contains two chambers separated by a piston. This piston moves according to the chamber pressures, the spring and Coulomb friction forces, and the external forces. The 4-way valve connects the actuator chambers to the low and high-pressure tanks. When the valve has no signal, actuator "Volume1" is set to atmospheric conditions and actuator "Volume2" is connected to the high-pressure tank. These connections are reversed when a signal is applied to the valve. Some other elements are used to connect all the parts of the circuit, such as pipes and junctions. The diameter considered in all these items is 0.006 metres.
The mass of the piston is 6.4 kg, its effective area on its two sides is 0.001963 m2 and the length of stroke is 0.051 metres. Chambers dead volumes are 6.1 · 10-5 m3 and 2.5 · 10-5 m3 for "Volume1" and "Volume2", respectively. The equivalent throat diameters (0.96 mm) depend on the direction of flow (different coefficients for direct and reverse pressure losses). The effective EV throat diameter of the valve is 0.00357 metres.
In this model, the spring and Coulomb friction data are set to zero, but the following specific equations are written in the continuous block of the model defining the piston-chamber interaction as shown in the figure below:
Spring force = 0.5 · (fic1 + fic2 / (rpiston · cos(ø))
Coulomb force = 0.5 · (fic1 - fic2) * tanh(1000 · vpiston) / (rpiston · cos(ø))
The use of the hyperbolic tangent gives zero Coulomb forces at zero speed. "fic1" and "fic2" are the interpolation results in the data tables of measured torque (at positive speed "f1_theta" and negative speed "f2_theta"):
fic1 = linearInterp1D(f1_theta, ø)
fic2 = linearInterp1D(f2_theta, ø)
ø = ø1 + asin(xpiston + x0) / rpiston
x0 = rpiston · sin(ø1);
Finally, the environmental conditions are set by the components "Bound_PT_atm" and "Bound_PT_HP". The pressure is set to 0.1 MPa and 7.0 MPa, respectively. Additionally, the temperature is set to 300K in both elements.
In the first stage of the simulation, the 4-way valve signal is set to 0. That means that chamber 1 of the actuator is set to atmospheric conditions and chamber 2 is connected to the high-pressure tank. After a brief stabilisation period of less than 0.25 seconds, this chamber reaches high-pressure conditions. The piston remains motionless throughout the process.
After 1 second, the chambers flow paths are reversed when the valve signal changes to 1. Then the pressure in chamber 1 starts growing while the pressure in chamber 2 drops. Soon after the pressure in both chambers crosses, the piston starts moving once the pressure difference is enough to overcome the friction forces. Pressure oscillation can be seen in both chambers while the piston is moving. This oscillation disappears when the piston reaches its end stop.
In the last part of the simulation, a 0 signal is again applied to the valve after 3 seconds, the pressure in the chambers is then reversed and the piston moves backwards. As in the previous phase, some pressure oscillatory phenomena are also seen, but they are different because of the faster movement of the piston. The different orifice area in each chamber causes this asymmetry. Finally, the simulation stops after 6 seconds.
The following plots illustrate the actuator behaviour using Helium gas as the working fluid: Actuator piston position, pressure evolution in the actuator chambers, temperature evolution in tanks walls, and actuator chamber incoming mass flow.
The following plots illustrate the actuator behaviour using liquid water as the working fluid: Actuator piston position, pressure evolution in the actuator chambers, and actuator chamber incoming mass flow. The movement is slower because of the greater orifice resistance (pressure drop) with water for the same orifice area.
