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MapleSim Hydraulics Library from Modelon

Id Var Mot  Ideal variable displacement motor

This component describes an ideal motor with variable displacement.

Implementation

The torque, tau, is given by:

tau = Dmotor  factor  sig  (port_A.p - port_B.p) / (2  π)

The flow rate, q, is given by:

q = Dmotor  factor  sig  w / (2  π)

The commanded relative displacement volume of the motor is input at commandSignal, [-1 ... 1]. If the inlet pressure is lower than the atmospheric pressure, the delivered flow rate becomes smaller (that is, the value of factor decreases). Flow from port_A to port_B is considered positive.

Variables used in the above equations

tau

Torque Nm.

q

Flow rate at the outlet port m3s.

sig

−1commandSignal<−11commandSignal>1commandSignalotherwise

Dmotor

Displacement per revolution m3.

w

Angular velocity rads.

factor

Pressure dependent variable. Equals 1 at normal running conditions and 0 at vapor pressure.

Assumptions

Ideal motor (that is, no losses).

 

Equations

Variables

Connections

Parameters

Equations

T&equals;T0oil&plus;&Delta;Tsystem

factor&equals;00<sigwandpAabs<pvapourg11+pAabspvapourg2`port_A.p`<0<sigw0sigw<0andpBabs<pvapourg11+pBabspvapourg2sigw<0and`port_B.p`<01otherwiseotherwiseotherwiseotherwise

q&equals;mflowAρoilpAabs&comma;T&comma;vair&equals;vgasoil&comma;psat&equals;psat

q&equals;12Dmotorwsigfactorπ

sig&equals;−1commandSignal<−111<commandSignalcommandSignalotherwiseotherwise

w&equals;tφa

&Delta;p&equals;pAlimitedpBlimited

φa&equals;φb

pAabs&equals;pA&plus;patmoil

pAlimited&equals;maxpA&comma;pvapouroilpatmoil

pBabs&equals;pB&plus;patmoil

pBlimited&equals;maxpB&comma;pvapouroilpatmoil

12&Delta;pDmotorfactorsigπ&equals;flange_a.tau&plus;flange_b.tau

mflowA&plus;mflowB&equals;0

Variables

Name

Value

Units

Description

Modelica ID

&Delta;p

 

Pa

Pressure drop

dp

pAlimited

 

Pa

Limited gauge pressure

pA_limited

pBlimited

 

Pa

Limited gauge pressure

pB_limited

pAabs

 

Pa

Absolute pressure

pA_abs

pBabs

 

Pa

Absolute pressure

pB_abs

q

 

m3s

Flow rate at connector A

q

w

 

rads

Angular velocity of pump shaft

w

T

 

K

Local temperature

T

pAsummary

pA

Pa

Pressure at port A

summary_pA

pBsummary

pB

Pa

Pressure at port B

summary_pB

&Delta;psummary

&Delta;p

Pa

Pressure drop

summary_dp

qsummary

q

m3s

Flow rate flowing into port_A

summary_q

Pmechsummary

[1]

W

Mechanical Rotational Power

summary_MP

Phydsummary

&Delta;pq

W

Hydraulic Power

summary_HP

psat

[2]

Pa

Gas saturation pressure

p_sat

pvapourg

[3]

Pa

Vapour pressure as gauge pressure

pvapour_g

factor

 

 

 

factor

sig

 

 

 

sig

[1] ϕ.aτa&plus;ϕ.bτb

[2] oil.gasSaturationPressureT&comma;oil.vgas

[3] oil.pvapouroil.patm

Connections

Name

Description

Modelica ID

portA

Port A, where oil flows into the component (0<q, pB<pA means 0<&Delta;p)

port_A

portB

Port B, where oil leaves the component (q<0, pB<pA means 0<&Delta;p)

port_B

flangea

 

flange_a

flangeb

 

flange_b

oil

 

oil

commandSignal

Input signal commands relative displacement volume

commandSignal

Parameters

Name

Default

Units

Description

Modelica ID

&Delta;Tsystem

0

K

Temperature offset from system temperature

dT_system

Dmotor

10-4

m3

Maximum displacement per revolution

Dmotor

See Also

Pumps

MapleSim Hydraulics Library from Modelon Overview

 


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