Fixed-Displacement Pump (IH)#

block — Block appearance in REPEAT VISION#

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].

Ideal mass flow rate (2):

(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].

Leakage mass flow rate (3) :

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

where:

\(\Delta p\) – pressure differential across the pump, [Pa];

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

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

where:

\(\Delta p\) – nominal pressure drop, [Pa];

\(\zeta_{\nu,nom}\) – 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)#\[\begin{split}\tau = \tau_{ideal} + \tau_{fric} \\ \tau_{ideal} = \Delta V \cdot \Delta p \\ \tau_{fric} = (\tau_0 + k \cdot \mid\Delta p \mid) \cdot tanh(\frac{4 \cdot \omega}{5 \cdot 10^{-5} \cdot \omega_{nom}})\end{split}\]

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, [Pa].

1. Properties#

Property	Default value	Description	Units of measurement
Nominal pressure drop	3.0e5	-	Pa
Nominal shaft angular velocity	30	-	rps
Volumetric efficiency	0.92	-	-
Displacement	3.0e-5	-	m\(^3\)/rev
No-load torque	0	-	N \(\cdot\) m
Mechanical efficiency	0.88	-	-

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Input	Input	-	-	Isothermal hydraulics
Shaft angular speed	Input	-	-	Rotational motion
Output	Output	-	-	Isothermal hydraulics

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