# Translational Mechanical Converter (TL)

Interface between thermal liquid and mechanical translational networks

## Library

Thermal Liquid/Elements

## Description

The Translational Mechanical Converter (TL) block represents the liquid side of a translational mechanical interface. This interface converts liquid pressure into force and vice versa. The output force acts in a single direction, set using a Mechanical orientation parameter.

The translational mechanical interface contains no hard stops. To include hard stops, use the Simscape™ Translational Hard Stop block. A model of a translational hydraulic actuator, for example, requires both blocks.

Port A is a thermal liquid conserving port corresponding to the converter inlet. The liquid pressure in the converter equals that at port A. Port Q is a thermal conserving port for modeling heat exchange between the converter liquid and the converter housing. The liquid temperature in the converter equals that at port Q.

### Mass Balance

The mass conservation equation in the mechanical converter volume is

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

• 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.

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

• v is the translational velocity of the converter interface (positive for converter expansion, negative for converter contraction).

• 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

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

`$\frac{d\left(\rho uV\right)}{dt}={\varphi }_{\text{A}}+{Q}_{H}-pA\epsilon v,$`
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 through the converter wall.

### Block Source Code

The block dialog box does not have a Source code link. To view the underlying component source, open the following files in the MATLAB® editor:

• For the code corresponding to fluid dynamic compressibility `Off``translational_converter.ssc`

• For the code corresponding to fluid dynamic compressibility `On``translational_converter_compressibility.ssc`

## Assumptions and Limitations

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

• The converter contains no mechanical hard stop.

## Parameters

Mechanical orientation

Select the relative orientation of the converter with respect to the thermal liquid system. The relative orientation determines the translation direction associated with positive flow into the converter. That direction is positive if the mechanical orientation of the converter is positive. It is negative if the mechanical orientation of the converter is negative. The default setting is `Positive`.

Interface cross-sectional area

Enter the cross-sectional area of the converter interface. This is the area the liquid must push to generate a force. The default value is `0.01` m^2.

Interface initial displacement

Enter the offset distance between the translating converter interface and the converter cap at time zero. The displacement should be positive for positive mechanical orientations and negative for negative mechanical orientations. The default value is `0` m.

Enter the liquid volume remaining in the converter at a zero offset distance. The default value is `1e-5` m^3.

Environment pressure specification

Select a specification method for the environment pressure. Options include `Specified pressure` and ```Atmospheric pressure```. The default setting is ```Atmospheric pressure```.

Environment pressure

Enter the environment pressure for the component. This parameter is active only when the Environment pressure specification parameter is set to `Specified pressure`. The default value is `0.101325` MPa.

Fluid dynamic compressibility

Select whether to include the effect of fluid dynamic compressibility on the transient response of the converter model. Selecting `On` exposes an additional parameter. The default setting is `Off`.

Initial liquid temperature

Enter the liquid temperature in the converter at time zero. The default value is `293.15` K.

Initial liquid pressure

Enter the liquid pressure in the converter at time zero. This parameter is visible only if Fluid dynamic compressibility is `On`. The default value is `1` atm.

## Ports

This block has the following ports.

 A Thermal liquid conserving port H Thermal conserving port R Translational mechanical conserving port associated with the moving interface C Translational mechanical conserving port associated with the converter casing