Two chamber hydraulic cylinder (TL)#

The Two chamber hydraulic cylinder (TL) block simulates a hydraulic cylinder controlled by two liquid chambers. The force created depends on the pressure difference of the media in the chambers.

1. Mass conservation equations for 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:

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

ϑ - piston speed, [m/s];

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

\(\beta\) - liquid modulus of elasticity, [Pa];

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

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

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

2. Energy balance for the chamber

Energy conservation law (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 inlet 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 hydraulic cylinder (TL) block does not have mechanical stops, in order to limit the piston movement, it is required to install them in the block Mass 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\(^3\)
Initial chamber 1 gauge pressure	15000.0	-	Pa
Chamber 1 port cross-sectional area	0.01	-	m\(^2\)
Chamber 1 initial liquid temperature	20.0	-	°С
Chamber 2 piston area	0.015	-	m\(^2\)
Chamber 2 dead volume	1.0E-6	-	m\(^3\)
Initial chamber 2 gauge pressure	15000.0	-	Pa
Chamber 2 initial liquid 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
Chamber 1 in	Input	-	-	Thermohydraulics
Chamber 2 in	Input	-	-	Thermohydraulics
Chamber 1 heat port	Input	-	-	Heat exchange
Chamber 2 heat port	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