Rotary Pneumatic Piston Chamber

Rotational pneumatic piston chamber based on ideal gas law

Library

None (example custom library)

Description

Note

As of Release R2016b, the Gas block library replaces the Pneumatic library as the recommended way of modeling pneumatic systems. The former Pneumatic library is now included in the product installation as an example custom library. The pneumatic domain definition is still provided with the software, and all the pneumatic blocks in your legacy models continue to work as before. However, these blocks no longer receive full production support and can be removed in a future release.

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

$G = \frac{V_{0} + D \cdot θ}{R T} (\frac{d p}{d t} - \frac{p}{T} \frac{d T}{d t}) + \frac{D}{R T} \cdot p \cdot \frac{d θ}{d t}$

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

$q = \frac{c_{v}}{R} (V_{0} + D \cdot θ) \frac{d p}{d t} + \frac{c_{p} \cdot D}{R} p \frac{d θ}{d t} - q_{w}$

where

q	Heat flow due to gas inflow in the chamber (through the pneumatic port)
q_w	Heat flow through the chamber walls (through the thermal port)
c_v	Specific heat at constant volume
c_p	Specific heat at constant pressure

The torque equation is

$τ = p \cdot D$

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.

Variables

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

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

Basic Assumptions and Limitations

The gas is ideal.
Specific heats at constant pressure and constant volume, c_p and c_v, are constant.

Parameters

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.
Dead volume: 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.

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).

Version History

Introduced in R2009b