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MapleSim Hydraulics Library from Modelon

Servo Valve  Servovalve with second-order spool dynamics and nonlinearities

The Servo Valve component describes a servovalve with second-order spool dynamics and nonlinearities.

Implementation

Valve

The qnom parameter gives the nominal flow rate of the fully opened valve at the pressure drop Δpnom. The dleak parameter gives the equivalent diameter of an orifice to describe the leakage flow if the valve is closed.

Amax=qnom12ρk2Δpnom

Aleak=14πdleak2

Spool

Input signal: command

Output signal: position

The position of the spool is modeled as a second-order system with natural frequency ω0, damping damp, limits for the velocity, and hysteresis for the position. The flow area depends linearly on the spool position.

The position of the spool is normalized in the interval:

1<position < 1

and the parameter vmax is the maximum value that the normalized speed, tposition, can obtain. If the physical position of the spool is used (denoted here by x), we have:

0<x < L

where L is the maximum distance the spool can move (in m).

The relationship between the normalized position and speed is then:

position&equals;2xL1

tposition&equals;2txL

This can be used to express the maximum speed as:

vmax&equals;2vxmaxL

where vxmax is the maximum velocity of the spool in ms.

Assumptions

The laminar/turbulent flow through the valve is modeled as flow through orifices without cavitation. Flow forces are not modeled.

Flow scheme

See component Servo Valve No States.

Connections

Name

Description

Modelica ID

portA

Port A, one of valve connections to actuator or motor

port_A

portB

Port B, one of valve connections to actuator or motor

port_B

portP

Port P, where oil enters the component from the pump

port_P

portT

Port T, where oil flows to the tank

port_T

command

Command signal for valve position

command

oil

 

oil

Parameters

General Parameters

Name

Default

Units

Description

Modelica ID

use volume A

true

 

If true, a volume is present at port_A

useVolumeA

use volume B

true

 

If true, a volume is present at port_B

useVolumeB

use volume P

true

 

If true, a volume is present at port_P

useVolumeP

use volume T

true

 

If true, a volume is present at port_T

useVolumeT

VA

10-6

m3

Geometric volume at port A

volumeA

VB

10-6

m3

Geometric volume at port B

volumeB

VP

10-6

m3

Geometric volume at port P

volumeP

VT

10-6

m3

Geometric volume at port T

volumeT

&Delta;Tsystem

0

K

Temperature offset from system temperature

dT_system

Actuation Parameters

Name

Default

Units

Description

Modelica ID

ω0

500

rads

Natural frequency of spool

omega0

damp

710

 

Damping coefficient of spool

damp

overlap

0.02

 

Overlap relative to max. displacement = 1

overlap

hyst

0.005

 

Half of hysteresis width

hyst

vmax

100

 

Max. spool velocity [1/s]

vmax

Flow Parameters

Name

Default

Units

Description

Modelica ID

qnomPA

8.33·10-4

m3s

Nominal flow rate

qnompa

&Delta;pnomPA

1.5·106

Pa

Pressure drop at qnom

dpnompa

qnomBT

8.33·10-4

m3s

Nominal flow rate

qnombt

&Delta;pnomBT

1.5·106

Pa

Pressure drop at qnom

dpnombt

qnomPB

8.33·10-4

m3s

Nominal flow rate

qnompb

&Delta;pnomPB

1.5·106

Pa

Pressure drop at qnom

dpnompb

qnomAT

8.33·10-4

m3s

Nominal flow rate

qnomat

&Delta;pnomAT

1.5·106

Pa

Pressure drop at qnom

dpnomat

k1PA

10

 

Laminar part of orifice model

k1pa

k2PA

2

 

Turbulent part of orifice model, k2&equals;1Cd2

k2pa

CdPA

1k2PA

 

Max discharge coefficient

C_dpa

λcPA

2k1PAk2PA

 

Critical flow number

lambdacpa

k1PB

10

 

Laminar part of orifice model

k1pb

k2PB

2

 

Turbulent part of orifice model, k2&equals;1Cd2

k2pb

CdPB

1k2PB

 

Max discharge coefficient

C_dpb

λcPB

2k1PBk2PB

 

Critical flow number

lambdacpb

k1BT

10

 

Laminar part of orifice model

k1bt

k2BT

2

 

Turbulent part of orifice model, k2&equals;1Cd2

k2bt

CdBT

1k2BT

 

Max discharge coefficient

C_dbt

λcBT

2k1BTk2BT

 

Critical flow number

lambdacbt

k1AT

10

 

Laminar part of orifice model

k1at

k2AT

2

 

Turbulent part of orifice model, k2&equals;1Cd2

k2at

CdAT

1k2AT

 

Max discharge coefficient

C_dat

λcAT

2k1ATk2AT

 

Critical flow number

lambdacat

ρnom

865

kgm3

Nominal density

rhonom

dleak

1.67·10-5

m

Diameter of equivalent orifice to model leakage of closed valve

dleak

Transition

1

 

Transition model

Transition

See Also

Servo Valve No States, Valves, MapleSim Hydraulics Library from Modelon Overview


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