Two chamber pneumatic cylinder (P)#

The Two chamber pneumatic cylinder (P) block models a pneumatic cylinder controlled by two gas chambers. The force generated depends on the pressure difference between the media in the chambers.

1. Mass conservation equations for the chamber (1) :

(1)#\[\dot{m}=\rho \cdot S \cdot ϑ +(\frac{1}{\beta}\cdot \frac{dp}{dt}-\alpha\cdot \frac{dT}{dt})\cdot \rho \cdot V\]

where:

\( ho\) - gas density, [kg/m\(^3\)];

ϑ - piston speed, [m/s];

S - piston area, [m\(^2\)];

\(\beta\) - gas elastic modulus, [Pa];

\(\alpha\) - coefficient of isobaric thermal expansion, [1/K];

p - gas pressure inside the chamber, [Pa];

V - volume of the pneumatic chamber, [m\(^3\)].

2. Energy balance for the chamber

Law of conservation of energy (2):

(2)#\[\phi+Q-p\cdot S \cdot ϑ =\frac{\delta E}{\delta t}\]

where:

Q - heat flow through the heat port, [W];

\(\phi\) - energy flow through the input port of the chamber, [W].

Piston speed (3):

(3)#\[ϑ=\frac{dx}{dt}\]

Chamber volume (4):

(4)#\[V=V_{dead}+S\cdot x\]

where:

\(V_{dead}\) - dead volume, [m\(^3\)];

x - piston position.

Force equation (5):

(5)#\[F=S\cdot (p_1-p_2)\]

where:

\(p_1\) - pressure in chamber 1, [Pa];

\(p_2\) - pressure in chamber 2, [Pa].

Important

The Two chamber pneumatic cylinder (P) block does not have mechanical stops; to limit the piston movement, they must be installed in the Mass block, connected to the piston output port.

1. Properties#

Property	Default Value	Description	Units of measurement
Piston stroke	0.1	-	m
Initial piston displacement relative to chamber 1	0.1	-	m
Chamber 1 piston area	0.015	-	m\(^2\)
Chamber 1 dead volume	1.0E-6	-	m\(^3\)
Chamber 1 initial gas gauge pressure	15000.0	-	Pa
Chamber 1 port cross-sectional area	0.01	-	m\(^2\)
Chamber 1 initial gas temperature	20.0	-	°С
Chamber 2 piston area	0.015	-	m\(^2\)
Chamber 2 dead volume	1.0E-6	-	m\(^3\)
Chamber 2 initial gas gauge pressure	15000.0	-	Pa
Chamber 2 initial gas temperature	20.0	-	°С
Chamber 2 port cross-sectional area	0.01	-	m\(^2\)

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Input chamber 1	Input	-	-	Pneumatics
Heat port chamber 1	Input	-	-	Heat exchange
Input chamber 2	Input	-	-	Pneumatics
Heat port chamber 2	Input	-	-	Heat exchange
Force	Output	-	N	Translational motion

In order to see the connection capabilities of the block, you need to go to page Description of block ports