Translational Mechanical Converter (IL)

Interface between isothermal liquid and mechanical translational networks

Since R2020a

• 

Libraries:
Simscape / Foundation Library / Isothermal Liquid / Elements

Description

The Translational Mechanical Converter (IL) block models an interface between an isothermal liquid network and a mechanical translational network. The block converts isothermal liquid pressure into mechanical force and vice versa. It can be used as a building block for linear actuators.

The converter contains a variable volume of liquid. If the Fluid dynamic compressibility check box is selected, then the pressure evolves based on the dynamic compressibility of the liquid volume. The Mechanical orientation parameter lets you specify whether an increase in pressure moves port R away from or towards port C.

Port A is the isothermal liquid conserving port associated with the converter inlet. Ports R and C are the mechanical translational conserving ports associated with the moving interface and converter casing, respectively.

Mass Balance

The mass conservation equations in the mechanical converter volume are

$$\begin{array}{l}{\dot{m}}_{\text{A}}=\{\begin{array}{cc}\epsilon {\rho }_{I}Sv,& \text{if}\text{fluid}\text{dynamic}\text{compressibility}\text{is}\text{off}\\ \epsilon {\rho }_{I}Sv+\frac{1}{{\beta }_I}\frac{d{p}_I}{dt}{\rho }_{I}V,& \text{if}\text{fluid}\text{dynamic}\text{compressibility}\text{is}\text{on}\end{array}\\ v=\frac{dx}{dt}\\ v=v_R-v_C\\ V=V_{dead}+\epsilon Sx\end{array}$$

where:

• $${\dot{m}}_{\text{A}}$$ is the mass flow rate into the converter through port A.

• ε is the mechanical orientation of the converter (1 if increase in fluid pressure causes positive displacement of R relative to C, -1 if increase in fluid pressure causes negative displacement of R relative to C).

• ρ_I is the fluid density inside the converter.

• β_I is the fluid bulk modulus inside the converter.

• S is the cross-sectional area of the converter interface.

• v is the translational velocity of the converter interface.

• v_R and v_C are the translational velocities of ports R and C, respectively.

• x is the displacement of the converter interface.

• V is the liquid volume inside the converter.

• V_dead is the dead volume, that is, volume of liquid when the interface displacement is 0.

• p_I is the pressure inside the converter.

If you connect the converter to a Multibody joint, use the physical signal input port p to specify the displacement of port R relative to port C. Otherwise, the block calculates the interface displacement from relative port velocities, according to the equations above. The interface displacement is zero when the liquid volume is equal to the dead volume. Then, depending on the Mechanical orientation parameter value:

• If Pressure at A causes positive displacement of R relative to C, the interface displacement increases when the liquid volume increases from dead volume.

• If Pressure at A causes negative displacement of R relative to C, the interface displacement decreases when the liquid volume increases from dead volume.

Equations used to compute the fluid mixture density and bulk modulus depend on the selected isothermal liquid model. For detailed information, see Isothermal Liquid Modeling Options.

Momentum Balance

The momentum conservation equation in the mechanical converter volume is

$$F=\epsilon \left(p_{\text{env}}-p\right)S,$$

where:

• F is the force the liquid exerts on the converter interface.

• p_env is the environment pressure outside the converter.

Assumptions and Limitations

• Converter walls are perfectly rigid.

• The converter contains no mechanical hard stops. To include hard stops, use the Translational Hard Stop block.

• The flow resistance between the inlet and the interior of the converter is negligible.

• The kinetic energy of the fluid in the converter is negligible.

Examples

Hydraulic Actuator with Analog Position Controller

How the Foundation library can be used to model systems that span electrical, mechanical and isothermal liquid domains. In the model, a hydraulic system implemented in the isothermal liquid domain controls the mechanical load position in response to a voltage reference demand. If the reference demand is zero, then the hydraulic actuator (and load) displacement is zero, and if the reference is +5 volts, then the displacement is 100 mm.

• Open Model

Ports

Input

p — Displacement of port R relative to port C, m

physical signal

Input physical signal that passes the position information from a Simscape™ Multibody™ joint. Connect this port to the position sensing port p of the joint. For more information, see Connecting Simscape Networks to Simscape Multibody Joints.

Dependencies

To enable this port, set the Interface displacement parameter to Provide input signal from Multibody joint.

Conserving

A — Converter inlet

isothermal liquid

Isothermal liquid conserving port associated with the converter inlet.

R — Rod

mechanical translational

Mechanical translational conserving port associated with the moving interface.

C — Case

mechanical translational

Mechanical translational conserving port associated with the converter casing.

Parameters

Mechanical orientation — Select the converter orientation

Pressure at A causes positive displacement of R relative to C (default) | Pressure at A causes negative displacement of R relative to C

Select the alignment of moving interface with respect to fluid pressure:

• Pressure at A causes positive displacement of R relative to C — Increase in the fluid pressure results in a positive displacement of port R relative to port C.

• Pressure at A causes negative displacement of R relative to C — Increase in the fluid pressure results in a negative displacement of port R relative to port C.

Interface displacement — Select method to determine relative port positions

Calculate from velocity of port R relative to port C (default) | Provide input signal from Multibody joint

Select method to determine displacement of port R relative to port C:

• Calculate from velocity of port R relative to port C — Calculate displacement from relative port velocities, based on the mass balance equations. This is the default method.

• Provide input signal from Multibody joint — Enable the input physical signal port p to pass the displacement information from a Multibody joint. Use this method only when you connect the converter to a Multibody joint by using a Translational Multibody Interface block. For more information, see How to Pass Position Information.

Initial interface displacement — Translational offset of port R relative to port C at the start of simulation

0 m (default) | scalar

Translational offset of port R relative to port C at the start of simulation. A value of 0 corresponds to an initial liquid volume equal to Dead volume.

Dependencies

Enabled when the Interface displacement parameter is set to Calculate from velocity of port R relative to port C.

• If Mechanical orientation is Pressure at A causes positive displacement of R relative to C, the parameter value must be greater than or equal to 0.

• If Mechanical orientation is Pressure at A causes negative displacement of R relative to C, the parameter value must be less than or equal to 0.

Interface cross-sectional area — The area on which the liquid exerts pressure to generate the translational force

0.01 m^2 (default) | positive scalar

The area on which the liquid exerts pressure to generate the translational force.

Dead volume — Volume of liquid when the interface displacement is 0

1e-5 m^3 (default) | positive scalar

Volume of liquid when the interface displacement is 0.

Environment pressure specification — Select a specification method for the environment pressure

Atmospheric pressure (default) | Specified pressure

Select a specification method for the pressure outside the converter:

• Atmospheric pressure — Use the atmospheric pressure, specified by the Isothermal Liquid Properties (IL) block connected to the circuit.

• Specified pressure — Specify a value by using the Environment pressure parameter.

Environment pressure — Pressure outside the converter

0.101325 MPa (default) | positive scalar

Pressure outside the converter acting against the pressure of the converter liquid volume. A value of 0 indicates that the converter expands into vacuum.

Dependencies

Enabled when the Environment pressure specification parameter is set to Specified pressure.

Fluid dynamic compressibility — Select whether to model fluid dynamic compressibility

On (default) | Off

Select whether to account for the dynamic compressibility of the liquid. Dynamic compressibility gives the liquid density a dependence on pressure and temperature, impacting the transient response of the system at small time scales.

Initial liquid pressure — Liquid pressure at time zero

0.101325 MPa (default) | positive scalar

Liquid pressure in the converter at the start of simulation.

Dependencies

To enable this parameter, select the Fluid dynamic compressibility check box.

References

[1] Gholizadeh, Hossein, Richard Burton, and Greg Schoenau. “Fluid Bulk Modulus: Comparison of Low Pressure Models.” International Journal of Fluid Power 13, no. 1 (January 2012): 7–16. https://doi.org/10.1080/14399776.2012.10781042.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2020a