# Rotational Mechanical Converter (TL)

Interface between thermal liquid and mechanical rotational networks

## Library

Thermal Liquid/Elements

## Description

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

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

Port A is a thermal liquid conserving port corresponding to the converter inlet. 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. Liquid temperature in the converter equals that at port Q.

### Mass Balance

The mass conservation equation in the mechanical converter volume is

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

• D is the converter displacement.

• Ω is the angular 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

`$\tau =-\epsilon \left(p-{p}_{\text{Atm}}\right)D,$`
where:

• τ is the torque the liquid exerts on the converter interface.

• pAtm is the atmospheric pressure.

### Energy Balance

The energy conservation equation in the mechanical converter volume is

`$\frac{d\left(\rho uV\right)}{dt}={\varphi }_{\text{A}}+{Q}_{H}-pD\epsilon \Omega ,$`
where:

• u is the liquid internal energy in the converter.

• 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``rotational_converter.ssc`

• For the code corresponding to fluid dynamic compressibility `On``rotational_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 rotation 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 volume displacement

Enter the displaced liquid volume corresponding to a unit rotation angle of the spinning converter interface. The default value is `1.2e-4` m^3/rad.

Interface initial rotation

Enter the rotation angle between the spinning converter interface and the clamping structure at time zero. The angle should be positive for positive mechanical orientations and negative for negative mechanical orientations. The default value is `0` rad.

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

Cross-sectional area at port A

Enter the flow cross-sectional area at the converter inlet. The block uses this parameter for thermal conduction calculations. The default value is `0.01` m^2.

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 four ports.

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