# Translational Mechanical Converter (TL)

Interface between thermal liquid and mechanical translational networks

• Library:
• 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 Model dynamic compressibility is set to `On`, then the pressure also evolves based on the dynamic compressibility of the liquid volume. If Mechanical orientation is set to `Positive`, then an increase in the liquid volume results in a positive displacement of port R relative to port C. If Mechanical orientation is set to `Negative`, then an increase in the liquid volume results in a negative displacement of port R relative to 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 positive, `-1` if negative).

• 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.

### 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

### 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:

• `Positive` — Increase in the liquid volume results in a positive displacement of port R relative to port C.

• `Negative` — Increase in the liquid volume results in a negative displacement of port R relative to port C.

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

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

• If Mechanical orientation is `Positive`, the parameter value must be greater than or equal to 0.

• If Mechanical orientation is `Negative`, the parameter value must be less than or equal to 0.

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

Enabled when the Fluid dynamic compressibility parameter is set to `On`.

Liquid temperature in the converter at the start of simulation.