# Rotary Pneumatic Piston Chamber

Rotational pneumatic piston chamber based on ideal gas law

## Library

Pneumatic Elements

## Description

The Rotary Pneumatic Piston Chamber block models a pneumatic rotary piston chamber based on the ideal gas law and assuming constant specific heats. Use this model as a building block for pneumatic rotational actuators. The piston can generate torque in one direction only, and the direction is set by the Chamber orientation parameter.

The continuity equation for the network representation of the piston chamber is

`$G=\frac{{V}_{0}+D·\theta }{RT}\left(\frac{dp}{dt}-\frac{p}{T}\frac{dT}{dt}\right)+\frac{D}{RT}·p·\frac{d\theta }{dt}$`

where

 G Mass flow rate at input port V0 Initial chamber volume D Piston displacement (volume per unit angle) Θ Piston angle p Absolute pressure in the chamber R Specific gas constant T Absolute gas temperature t Time

The energy equation is

`$q=\frac{{c}_{v}}{R}\left({V}_{0}+D·\theta \right)\frac{dp}{dt}+\frac{{c}_{p}·D}{R}p\frac{d\theta }{dt}-{q}_{w}$`

where

 q Heat flow due to gas inflow in the chamber (through the pneumatic port) qw Heat flow through the chamber walls (through the thermal port) cv Specific heat at constant volume cp Specific heat at constant pressure

The torque equation is

`$\tau =p·D$`

Port A is the pneumatic conserving port associated with the chamber inlet. Port H is a thermal conserving port through which heat exchange with the environment takes place. Ports C and R are mechanical rotational conserving ports associated with the piston case and rod, respectively. The gas flow and the heat flow are considered positive if they flow into the chamber.

## Basic Assumptions and Limitations

• The gas is ideal.

• Specific heats at constant pressure and constant volume, cp and cv, are constant.

## Dialog Box and Parameters

### Parameters Tab

Displacement

Specify the effective piston displacement, as volume per unit angle. The default value is `.001` m^3/rad.

Initial angle

Specify the initial piston angle. The default value is `0`.

Specify the volume of gas in the chamber at zero piston position. The default value is `1e-5` m^3.

Chamber orientation

Specify the direction of torque generation. The piston generates torque in a positive direction if this parameter is set to `1` (the default). If you set this parameter to `2`, the piston generates torque in a negative direction.

### Variables Tab

Use the Variables tab in the block dialog box (or the Variables section in the block Property Inspector) to set the priority and initial target values for the block variables prior to simulation. For more information, see Set Priority and Initial Target for Block Variables.

## Ports

The block has the following ports:

`A`

Pneumatic conserving port associated with the chamber inlet.

`H`

Thermal conserving port through which heat exchange with the environment takes place.

`R`

Mechanical rotational conserving port associated with the piston (rod).

`C`

Mechanical rotational conserving port associated with the reference (case).