Mechanical converter (translational motion) (IH)#

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

Equations of mass conservation

Uncompressed (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];

\(ρ\) - liquid density, [kg/m\(^3\)];

\(ϑ\) - piston speed, [m/s];

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

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

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

Piston Speed (3) :

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

Volume of hydraulic chamber (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) (IH) block does not have mechanical stops; to limit the piston movement, it is required to install them in Mass block connected to the piston output port.

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: Atmosphere Pressure; User Pressure	Atmosphere Pressure	-	-
Environment gauge pressure, available when `Environment gauge pressure specification` - `User Pressure`	10000	-	Pa
Initial liquid gauge pressure	15000	-	Pa

Parameters	Input/output	Description	Units of measurement	Port type
Mass Flow	Input	-	kg/s	Isothermal hydraulics
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