Two chamber rotary pneumatic cylinder (P)#

The Two chamber rotary pneumatic cylinder (P) block models a rotary actuator in a pneumatic network that converts the pressure difference between two cylinder chambers into torque.

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

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

where:

\(\dot{m}\) – gas consumption, [kg/s];

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

\(\omega\) - angular velocity of piston movement, [rad/s];

D - volumetric displacement of the piston, [m\(^3\)/rad];

\(\beta\) - 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)#\[\phi+Q-p\cdot D \cdot \omega =\frac{\delta E}{\delta t}\]

where:

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

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

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

D - volumetric displacement of the piston, [m\(^3\)/rad];

\(\omega\) - angular velocity of piston movement, [rad/s];

E - gas energy, [J].

Piston angular velocity (3):

(3)#\[\omega=\frac{d\theta}{dt}\]

where:

\(\omega\) - angular velocity of the piston, [rad/s];

\( heta\) - angular displacement of the piston, [rad].

Chamber volume (4):

(4)#\[V=V_{dead}+D\cdot \theta\]

where:

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

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

D - volumetric displacement of the piston, [m\(^3\)/rad];

\( heta\) - angular displacement of the piston, [rad].

Torque equation (5):

(5)#\[M=D\cdot (p_1-p_2)\]

where:

M - torque, [N\(\cdot\)m];

D - volumetric displacement of the piston, [m\(^3\)/rad];

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

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

1. Properties#

Property	Default Value	Description	Units of measurement
Rotary piston stroke	0.1	-	rad
Initial interface rotation from chamber 1	0.05	-	rad
Chamber 1 interface volume displacement	0.015	-	m\(^3\)/rad
Chamber 1 dead volume	1.0E-6	-	m\(^3\)
Chamber 1 initial gas pressure	15000.0	-	Pa
Chamber 1 port area	0.01	-	m\(^2\)
Chamber 1 initial gas temperature	20.0	-	°С
Chamber 2 interface volume displacement	0.015	-	m\(^3\)/rad
Chamber 2 dead volume	1.0E-6	-	m\(^3\)
Chamber 2 initial gas pressure	15000.0	-	Pa
Chamber 2 port area	0.01	-	m\(^2\)
Chamber 2 initial gas temperature	20.0	-	°С

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
Torque	Output	-	N\(\cdot\)m	Rotational motion

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