# Translational Mechanical Converter (IL)

Interface between isothermal liquid and mechanical translational networks

*Since R2020a*

**Libraries:**

Simscape /
Foundation Library /
Isothermal Liquid /
Elements

## Description

The Translational Mechanical Converter (IL) block models an interface between an isothermal liquid network and a mechanical translational network. The block converts isothermal liquid pressure into mechanical force and vice versa. It can be used as a building block for linear actuators.

The converter contains a variable volume of liquid. If the **Fluid dynamic
compressibility** check box is selected, then the pressure evolves based on the
dynamic compressibility of the liquid volume. The **Mechanical orientation**
parameter lets you specify whether an increase in pressure moves port **R**
away from or towards port **C**.

Port **A** is the isothermal liquid conserving port associated with the
converter inlet. Ports **R** and **C** are the mechanical
translational conserving ports associated with the moving interface and converter casing,
respectively.

### Mass Balance

The mass conservation equations in the mechanical converter volume are

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

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 displacement of R relative to C,`-1`

if increase in fluid pressure causes negative displacement of R relative to C).*ρ*_{I}is the fluid density inside the converter.*β*_{I}is the fluid bulk modulus inside the converter.*S*is the cross-sectional area of the converter interface.*v*is the translational velocity of the converter interface.*v*_{R}and*v*_{C}are the translational velocities of ports**R**and**C**, respectively.*x*is the displacement of the converter interface.*V*is the liquid volume inside the converter.*V*_{dead}is the dead volume, that is, volume of liquid when the interface displacement 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
**p** to specify the displacement of port **R** relative
to port **C**. Otherwise, the block calculates the interface displacement
from relative port velocities, according to the equations above. The interface displacement
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 displacement of R relative to C`

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

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

, the interface displacement 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.

### Momentum Balance

The momentum conservation equation in the mechanical converter volume is

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

where:

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

### Assumptions and Limitations

Converter walls are perfectly rigid.

The converter contains no mechanical hard stops. To include hard stops, use the Translational 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.

## Ports

### Input

### Conserving

## Parameters

## References

[1] Gholizadeh, Hossein, Richard
Burton, and Greg Schoenau. “Fluid Bulk Modulus: Comparison of Low Pressure Models.” *International Journal of Fluid Power* 13, no. 1 (January 2012):
7–16. https://doi.org/10.1080/14399776.2012.10781042.

## Extended Capabilities

## Version History

**Introduced in R2020a**