Fixed-Displacement Motor (IH)#

The unit describes operation of a hydraulic motor with a fixed displacement.

The mass flow rate of liquid through the hydraulic motor 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 (2):

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

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].

Lookup Mass Flow (3) :

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

where:

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

К - the Hagen-Poiseuille coefficient is defined as (4) :

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

\(\Delta p_{nom}\) - nominal pressure differential across the motor, [Pa];

\(\zeta_{ u,nom}\) – 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 motor minus the moment of friction forces (5) :

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

where:

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

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

\( au_0\) – rated torque on the shaft without load;

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

where:

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

\(\Delta p_{nom}\) - nominal pressure differential across the motor.

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	-	-

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

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