# Translational Mechanical Converter (TL)

Interface between thermal liquid and mechanical translational networks

Libraries:
Simscape / Foundation Library / Thermal Liquid / Elements

## Description

The Translational Mechanical Converter (TL) block models an interface between a thermal liquid network and a mechanical rotational network. The block converts thermal 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. The temperature evolves based on the thermal capacity of this volume. If the Fluid dynamic compressibility check box is selected, then the pressure also 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 thermal liquid conserving port associated with the converter inlet. Port H is the thermal conserving port associated with the temperature of the liquid inside the converter. Ports R and C are the mechanical translational conserving ports associated with the moving interface and converter casing, respectively.

### Mass Balance

The mass conservation equation in the mechanical converter volume is

${\stackrel{˙}{m}}_{\text{A}}=\epsilon \text{\hspace{0.17em}}\rho S\text{\hspace{0.17em}}v+\left\{\begin{array}{cc}0,& \text{if}\text{\hspace{0.17em}}\text{fluid}\text{\hspace{0.17em}}\text{dynamic}\text{\hspace{0.17em}}\text{compressibility}\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{off}\\ V\rho \left(\frac{1}{\beta }\frac{dp}{dt}+\alpha \frac{dT}{dt}\right),& \text{if}\text{\hspace{0.17em}}\text{fluid}\text{\hspace{0.17em}}\text{dynamic}\text{\hspace{0.17em}}\text{compressibility}\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{on}\end{array}$

where:

• ${\stackrel{˙}{m}}_{\text{A}}$ is the liquid 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 is the liquid mass density.

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

• v is the translational velocity of the converter interface.

• V is the liquid volume inside the converter.

• β is the liquid bulk modulus inside the converter.

• α is the coefficient of thermal expansion of the liquid.

• p is the liquid pressure inside the converter.

• T is the liquid temperature 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 block equations. 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.

### Momentum Balance

The momentum conservation equation in the mechanical converter volume is

$F=-\epsilon \left(p-{p}_{\text{Atm}}\right)S$

where:

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

• pAtm is the atmospheric pressure.

### Energy Balance

The energy conservation equation in the mechanical converter volume is

$\frac{d\left(\rho uV\right)}{dt}={\varphi }_{\text{A}}+{Q}_{H}-pS\epsilon v,$

where:

• u is the liquid internal energy.

• ϕA is the total energy flow rate into the mechanical converter volume through port A.

• QH is the heat flow rate into the mechanical converter volume.

### Assumptions and Limitations

• Converter walls are not compliant. They cannot deform regardless of internal pressure and temperature.

• 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 thermal resistance between the thermal port and the interior of the converter is negligible.

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

## Ports

### Input

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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

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Thermal liquid conserving port associated with the converter inlet.

Thermal conserving port associated with the temperature of the liquid inside the converter.

Mechanical translational conserving port associated with the moving interface.

Mechanical translational conserving port associated with the converter casing.

## Parameters

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### Main

Select the alignment of moving interface with respect to the converter liquid volume:

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

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.

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.

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

Volume of liquid when the interface displacement is 0.

Select a specification method for the pressure outside the converter:

• Atmospheric pressure — Use the atmospheric pressure, specified by the Thermal Liquid Settings (TL) or Thermal Liquid Properties (TL) block connected to the circuit.

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

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.

### Effects and Initial Conditions

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.

Liquid pressure in the converter at the start of simulation.

#### Dependencies

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

Liquid temperature in the converter at the start of simulation.

## Version History

Introduced in R2013b