Mechanical converter (rotational motion) (TL)#

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

Equations of mass conservation

Without compression (1) :

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

With compression (2) :

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

where:

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

\(ρ\) - fluid density, [kg/m\(^3\)];

\(ω\) - angular velocity, [rad/s];

\(D\) - volume displacement, [m\(^3\)/rad];

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

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

Piston angular velocity (3):

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

Hydraulic chamber volume (4):

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

where:

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

\(θ\) - turning angle, [rad].

Torque equation (5) :

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

where:

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

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

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 interface rotation	0.1	-	rad
Interface volume displacement	0.001	-	m\(^3\)/rad
Dead volume	1e-6	-	m\(^3\)
Environment pressure specification: Atmosphere Pressure; Specified Pressure	Atmosphere 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
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