# Rotational Mechanical Converter (TL)

Interface between thermal liquid and mechanical rotational networks

**Libraries:**

Simscape /
Foundation Library /
Thermal Liquid /
Elements

## Description

The Rotational 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 torque and vice versa. It can be used as a building block for rotary 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. The **Mechanical orientation**
parameter lets you specify whether an increase in the liquid volume results in a positive or
negative rotation 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 rotational conserving ports associated with the
moving interface and converter casing, respectively.

### Mass Balance

The mass conservation equation in the mechanical converter volume is

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

where:

$${\dot{m}}_{\text{A}}$$ 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 rotation of R relative to C,`-1`

if increase in fluid pressure causes negative rotation of R relative to C).*ρ*is the liquid mass density.*D*is the converter displacement.*Ω*is the angular 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
**q** to specify the rotation of port **R** relative to
port **C**. Otherwise, the block calculates the interface rotation from
relative port angular velocities, according to the block equations. The interface rotation
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 rotation of R relative to C`

, the interface rotation increases when the liquid volume increases from dead volume.If

`Pressure at A causes negative rotation of R relative to C`

, the interface rotation decreases when the liquid volume increases from dead volume.

### 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.*p*_{Atm}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.*ϕ*_{A}is the total energy flow rate into the mechanical converter volume through port A.*Q*_{H}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 Rotational 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

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2013b**