# Rotational Mechanical Converter (TL)

Interface between thermal liquid and mechanical rotational networks

• Library:
• 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

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

where:

• ${\stackrel{˙}{m}}_{\text{A}}$ 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 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.

• 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.

### 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

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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 q of the joint. For more information, see Connecting Simscape Networks to Simscape Multibody Joints.

#### Dependencies

To enable this port, set the Interface rotation 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 rotational conserving port associated with the moving interface.

Mechanical rotational 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 rotation of R relative to C``` — Increase in the liquid volume results in a positive rotation of port R relative to port C.

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

Select method to determine rotation of port R relative to port C:

• ```Calculate from angular velocity of port R relative to port C``` — Calculate rotation from relative port angular velocities, based on the block equations. This is the default method.

• `Provide input signal from Multibody joint` — Enable the input physical signal port q to pass the rotation information from a Multibody joint. Use this method only when you connect the converter to a Multibody joint by using a Rotational Multibody Interface block. For more information, see How to Pass Position Information.

Rotational 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 rotation parameter is set to ```Calculate from angular velocity of port R relative to port C```.

• If Mechanical orientation is ```Pressure at A causes positive rotation 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 rotation of R relative to C```, the parameter value must be less than or equal to 0.

Displaced liquid volume per unit rotation of the moving interface.

Volume of liquid when the interface rotation is 0.

The cross-sectional area of the converter inlet, in the direction normal to the flow path.

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.

## Version History

Introduced in R2013b