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Interface between isothermal liquid and mechanical rotational networks

**Library:**Simscape / Foundation Library / Isothermal Liquid / Elements

The Rotational Mechanical Converter (IL) block models an interface between an isothermal liquid network and a mechanical rotational network. The block converts isothermal 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. If **Model dynamic
compressibility** is set to `On`

, then the pressure
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 isothermal liquid conserving port associated with the
converter inlet. Ports **R** and **C** are the mechanical
rotational conserving ports associated with the moving interface and converter casing,
respectively.

The mass conservation equations in the mechanical converter volume are

$$\begin{array}{l}{\dot{m}}_{\text{A}}=\{\begin{array}{cc}\epsilon \text{\hspace{0.17em}}{\rho}_{I}D\text{\hspace{0.17em}}\omega ,& \text{if}\text{\hspace{0.17em}}\text{fluid}\text{\hspace{0.17em}}\text{dynamic}\text{\hspace{0.17em}}\text{compressibility}\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{off}\\ \epsilon \text{\hspace{0.17em}}{\rho}_{I}D\text{\hspace{0.17em}}\omega +\frac{1}{{\beta}_{I}}\frac{d{p}_{I}}{dt}{\rho}_{I}V,& \text{if}\text{\hspace{0.17em}}\text{fluid}\text{\hspace{0.17em}}\text{dynamic}\text{\hspace{0.17em}}\text{compressibility}\text{\hspace{0.17em}}\text{is}\text{\hspace{0.17em}}\text{on}\end{array}\\ \omega =\frac{d\theta}{dt}\\ \omega ={\omega}_{R}-{\omega}_{C}\\ V={V}_{dead}+\epsilon D\theta \end{array}$$

where:

$${\dot{m}}_{\text{A}}$$ is the 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*_{I}is the fluid density inside the converter.*β*_{I}is the fluid bulk modulus inside the converter.*D*is the converter volume displacement, that is, fluid volume needed to rotate the shaft per angle unit.*ω*is the angular velocity of the converter interface.*ω*_{R}and*ω*_{C}are the angular velocities of ports**R**and**C**, respectively.*θ*is the converter interface rotation.*V*is the liquid volume inside the converter.*V*_{dead}is the dead volume, that is, volume of liquid when the interface rotation is 0.*p*_{I}is the pressure 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 equations above. 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.

Equations used to compute the fluid mixture density and bulk modulus depend on the selected isothermal liquid model. For detailed information, see Isothermal Liquid Modeling Options.

The momentum conservation equation in the mechanical converter volume is

$$\tau =\epsilon \left({p}_{\text{env}}-p\right)D,$$

where:

*τ*is the torque the liquid exerts on the converter interface.*p*_{env}is the environment pressure outside the converter.

Converter walls are perfectly rigid.

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 kinetic energy of the fluid in the converter is negligible.