Fixed displacement pump (TL)#

The unit describes operation of the fixed displacement hydraulic pump.

The mass flow rate of liquid through the hydraulic pump is described by the ratio (1):

(1)#\[\dot{m} = \dot{m}_{ideal} - \dot{m}_{leak}\]

where:

\(\dot{m}_{ideal}\) – ideal mass flow rate, [kg/s];

\(\dot{m}_{leak}\) – leakage mass flow rate, [kg/s].

(2)#\[\dot{m}_{ideal} = \rho_{avg}\cdot \frac{\Delta V}{2\pi} \cdot \omega\]

where:

\( ho_{avg}\) – average density of liquid, [kg/m\(^3\)];

\(\Delta V\) – volume of moved fluid per one revolution, [m\(^3\)];

\(\omega\) – shaft angular speed, [rad/s].

(3)#\[\dot{m}_{leak} = K\cdot \rho_{avg}\cdot \Delta p\]

where:

\(\Delta p\) – pressure differential across the pump, [kg/m\(^3\)];

The Hagen-Poiseuille coefficient is defined as (4):

(4)#\[K = \frac{\Delta V \omega_{nom} (1 - \zeta_{\nu,nom})}{\Delta p_{nom}}\]

where:

\(\Delta p\) – nominal pressure drop, [kg/m\(^3\)];

\(\zeta_{ u,nom}\) – volumetric efficiency;

\(\omega_{nom}\) – nominal angular speed of the shaft, [rad/s].

Force torque on the shaft is defined as the ideal moment of the pump plus friction torque (5):

(5)#\[\tau = \tau_{ideal} + \tau_{fric}\]

\(\tau_{ideal} = \Delta V \cdot \Delta p\);

\(\tau_{fric} = (\tau_0 + k \mid\Delta p \mid) tanh(\frac{4\omega}{5\times 10^{-5} \omega_{nom}})\);

where:

\( au_0\) – no-load torque;

\(k = (\frac{1}{\zeta_{m,nom}} - 1)\cdot \Delta V - \frac{\tau_0}{\Delta p_{nom}}\) ;

\(\zeta_{m,nom}\) – mechanical efficiency;

\(\Delta p_{nom}\) – nominal pressure drop.

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

(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
Nominal pressure gain	300000.0	-	Pa
Nominal angular velocity	30.0	-	rps
Volumetric efficiency	0.92	-	-
Displacement	3.0e-5	-	m\(^3\)/rev
No load torque	0.0	-	N \(\cdot\) m
Mechanical efficiency	0.88	-	-
Nominal dynamic viscosity	9.0E-4	-	Pa \(\cdot\) s
Ports cross sectional area	0.1	-	m\(^2\)

Parameters	Input/Output	Description	Units of measurement	Port type
Input	Input	-	-	Thermohydraulics
Angular velocity	Input	-	rad/s	Rotational motion
Output	Output	-	-	Thermohydraulics

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