Mechanical converter (translational motion) (TL)#

The Mechanical converter (translational motion) (TL) block simulates the conversion of gas pressure to mechanical force and vice versa for translational motion systems.

Equations of mass conservation

Without compression (1) :

(1)#\[ \frac{dm}{dt} = \rho \cdot S \cdot \vartheta ; \]

With compression (2) :

(2)#\[ \frac{dm}{dt} = \rho \cdot S \cdot \vartheta + \frac{1}{\beta}\cdot \frac{dp}{dt}\cdot \rho \cdot V, \]

where:

\(dm/dt\) - mass flow rate of liquid, [kg/s];

\(ρ\) - fluid density, [kg/m\(^3\)];

\(ϑ\) - piston movement speed, [m/s];

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

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

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

Piston velocity (3) :

(3)#\[ \vartheta =\frac{dx}{dt}. \]

Hydraulic chamber volume (4):

(4)#\[ V = V_{dead} + Sx, \]

where:

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

\(x\) - piston position, [m].

Force equation (5) :

(5)#\[ F = S\cdot (p - p_{env}), \]

where:

\(p\) - pressure in the hydraulic chamber, [Pa];

\(p_{env}\) - ambient pressure, [Pa].

The Mechanical converter (translational motion) (TL) block has no mechanical stops, to limit the piston movement it is required to install them in the block Mass connected to the piston output port.

Law of conservation of mass (6):

(6)#\[\dot m_A+\dot m_B=0\]

Law of conservation of energy (7):

(7)#\[\phi_A+\phi_B=0\]

where:

\(\phi_A\) - energy flow at the input, [W];

\(\phi_B\) - energy flow at the output, [W].

1. Properties#

Property	Default Value	Description	Units of measurement
Initial piston displacement	0.1	-	m
Piston area	0.015	-	m\(^2\)
Dead volume	1e-6	-	m\(^3\)
Environment gauge pressure specification: Atmospheric Pressure; User Pressure	Atmospheric Pressure	-	-
Initial liquid pressure	15000	-	Pa
Initial liquid temperature	20	-	℃
Port cross-sectional area	0.01	-	m\(^2\)

Parameters	Input\Output	Description	Units of measurement	Port type
Mass Flow	Input	-	kg/s	Thermohydraulics
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