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# Hydraulics

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# Hydraulics

The 20-sim Hydraulics library contains components to model the dynamic behavior of hydraulic circuits. Most components have lumped volumes to ensure a seamless connection with other components. Therefore almost all components can be connected arbitrarily. Care has to be taken that physically relevant circuits are created.

The elementary components (without lumped volumes) are stored in the basic libraries. These models should only be used by experienced modelers who want to create their own library components.

Hydraulic components can easily be coupled to other library models. The pumps and motors have a rotation port that can be coupled to models of the Rotation library. The cylinder models have a translation port that can be coupled to models of the Translation library. Some models have a variable input that can be coupled to models of the Signal library.

To get a good impression of the use the components of this library, have a look at the example circuits.

## Ports

Every library component has one or more hydraulic connectors, which are called ports in 20-sim. Ports always have two variables: pressure [Pa] and volume flow [m3/s]. The following ports a and b are usually provided:

 a a.p Pressure in [Pa] with respect to atmospheric pressure (p stands for pressure). a.phi Volume flow [m3/s], positive if oil is entering the component at port a (phi stands for flow).

 b b.p Pressure in [Pa] with respect to atmospheric pressure (p stands for pressure). b.phi Volume flow [m3/s], negative if oil is entering the component at port b (phi stands for flow).

## Pressure

The 20-sim hydraulics library uses the common definition of pressure in Pa:

1 Pa = 1 N/m2 = 1e-5 bar

The air pressure at sea level is taken as the zero value:

0 Pa = air pressure

Consequently the pressure for liquid oil that starts to vaporize is negative. In 20-sim the default value of the vapour pressure is:

p_vapour = -0.999e5 Pa

The vapour pressure is the minimum pressure. Some models have a safeguard on the pressure to prevent it to become smaller. You can change the value of the vapour pressure but take care that always a value is chosen that is smaller than zero. Otherwise some of the models will not work correctly.

## Bulk modulus

No liquid is fully incompressible. The compliance characteristics of the oil in a hydraulic system is a vital parameters affecting the response. The effect of compressibility is incorporated by entering the bulk modulus of the fluid:

dp = -B*dV/V

Here dp is the pressure , V the volume and B the bulk modulus. For small pressure variations the compressibility effect my be rewritten as:

p = B/V*int(flow)

The bulk modulus is a very uncertain parameter. It depends on the percentage of air dissolved in the fluid, the pressure and the temperature. In most textbooks a values of 1.5 to 1.75 [GPa] is used. 20-sim uses a default value of 1.6 [GPa]. If fluid should be simulated at elevated temperatures or with a high percentage or air dissolved, you should use a smaller value for the bulk modulus.

## Units

20-sim uses SI-units for the hydraulic components. If you want to use other units select them in the Parameters Editor or the Variables Chooser.

## Laminar flow

Many hydraulic models have a laminar (leakage) flow:

flow = G * dp

with G the flow conductance and dp the pressure difference. The table below shows the flow rates for various conductance values and pressure differences of 10 [bar] and 400 [bar].

 G m3/s.Pa P Pa P bar flow m3/s flow l/min 1.0e-14 1.0e6 10 2.89e-8 0.002 1.0e-14 4.0e7 400 1.82e-7 0.01 1.0e-12 1.0e6 10 1.44e-6 0.09 1.0e-12 4.0e7 400 9.12e-6 0.6 1.0e-10 1.0e6 10 1.44e-4 9 1.0e-10 4.0e7 400 9.12e-4 55 1.0e-8 1.0e6 10 2.89e-3 173 1.0e-8 4.0e7 400 1.82e-2 1095

If the flow rate is very small (leakage flow), choose G below 1.0e-14 [m3/s.Pa]. If the flow rate is very large (open connection to a tank), choose G 1.0e-9 or higher if desired.

## Turbulent flow

Some hydraulic models have a turbulent (orifice) flow described by:

flow = Cd * A * sqrt( 2/ rho * dp)

with Cd the discharge coefficient, A the orifice area, rho the fluid density and dp the pressure difference. Except for small pressure around zero, the discharge coefficient is constant. In most textbooks a value of 0.6 is recommended. The table below shows the flow rates for various orifice areas and pressure differences of 10 [bar] and 400 [bar].

 Cd m3/s.Pa A m2 rho kg/m3 dp Pa dp bar flow m3/s flow l/min 0.6 1.0e-9 865 1.0e6 10 1.0e-8 0.0006 0.6 1.0e-9 865 4.0e7 400 4.0e-7 0.024 0.6 5.0e-8 865 1.0e6 10 1.0e-6 0.06 0.6 5.0e-8 865 4.0e7 400 4.0e-5 2.4 0.6 5.0e-6 865 1.0e6 10 1.0e-4 6 0.6 5.0e-6 865 4.0e7 400 4.0e-3 240 0.6 1.0e-4 865 1.0e6 10 1.0e-2 600 0.6 1.0e-4 865 4.0e7 400 4.0e-1 24000

If the flow rate is very small (leakage flow) choose A smaller than 1.0e-9 [m2]. If the flow rate should be very large (open connection) choose A equal to 1.0e-4 or higher if desired. For very small pressure differences the flow will become laminar and the discharge coefficient will drop. For such cases, specialized models should be applied. If they are not available, use a laminar flow model with a small conductance value.

## Simulation

Hydraulic circuits can be simulated with all the available integration methods. In practice the default integration method (BDF) will give the most accurate and quickest response. Take care with hydraulic circuits that will give high pressure peaks and small flow rates. These circuits are sometimes hard to simulate. In practice high pressure peaks should be reduced with pressure relief valves to avoid damage. Fortunately adding pressure relief valves will in most cases improve the simulation response.

## Disclaimer

All models have been tested with standard configurations. This will however not ensure that valid results will be found at all times. For example temperature effects are not included and certain parameter values will lead to unstable simulations. Therefore any application of the library without validation of the user is at its own risk!

## Literature

The 20-sim hydraulic library has been based on the following literature:

P. Dransfield, Hydraulic Control Systems - Design and Analysisi of Their Dynamics, Springer 1981,ISBN 3-540-10890-4.

P. Beater, Entwurf Hydraulischer Maschinen, Modelbildung, Stabilitätsanalyse und Simulation hydrostatischer Antriebe und Steurungen, Springer 1999, ISBN 3-540-65444-5.

The models have been designed as close as possible to the Modelica hydraulic library (www.modelica.org). To compare both libraries the example model Closed Circuit Drive Train.emx has been added.