Piloted Relief Valve - MapleSim Help
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Piloted Relief Valve

Piloted spring-loaded relief valve

 

Description

Equations

Variables

Connections

Parameters

Description

The Piloted Relief Valve component is a relief valve with a pilot pressure that can be used to assist in opening or closing the valve.

The valve orifice area is assumed to be a piecewise linear function of the pressure difference between port A and port B.

Based on the orifice area, the pressure vs. flow rate relationship is calculated by the formulation used in the Orifice component.

Formulation Approaches

One of two approaches can be selected for modeling the flow in the device. When the boolean parameter Use constant Cd is true, a constant coefficient of discharge (Cd) is used, otherwise a variable coefficient of discharge with maximum value (Cdmax) and a critical flow number (Critno) are used.

Optional Volumes

The boolean parameters Use volume A and Use volume B, when true, add optional volumes VA  and VB to ports A and B, respectively. See Port Volumes for details.

If two orifices or valves are connected, enabling a volume at the common port reduces the stiffness of the system and improves the solvability.

Equations

p=pApB

Orifice Fluid Equations

{p=π4ρνqCd2AcsπAcs16q4π2Acs2ν4+ReCr414Use constant Cd=trueq=Cdmaxtanh4Acsπ2pρνCritnoAcs2pρsignpotherwise

Pilot Equations

{Acs=Ai=AtExactAcs=minAopen,maxAclose,Ai,tcdAidt+Ai=Atotherwise

ptot=p+{kppCdir=1kppCotherwise

S={smoothnesssmoothTransition0otherwise

qC=0

At&equals;{AcloseptotpcloseAclose&plus;AopenAcloseSmoothTransS&comma;ptotpclosepopenpcloseptot<popenAopenotherwise

Optional Volume Equations

VfA&equals;{Va1&plus;pAElUse volume A&equals;true0otherwiseVfB&equals;{Vb1&plus;pBElUse volume B&equals;true0otherwise

q&equals;qAqVA&equals;qBqVB

qVA&equals;{dVfAdtUse volume A&equals;true0otherwiseqVB&equals;{dVfBdtUse volume B&equals;true0otherwise

Variables

Name

Units

Description

Modelica ID

p

Pa

Pressure drop from A to B

p

pX

Pa

Pressure at port X

pX

q

m3s

Flow rate from A to B

q

qX

m3s

Flow into port X

qX

qVX

m3s

Flow rate into port X's optional volume

qVX

VfX

m3

Effective volume at port X

VfX

Connections

Name

Description

Modelica ID

portA

Hydraulic port on left side

portA

portB

Hydraulic port on right side

portB

portC

Hydraulic port on the bottom (no volume, used as pilot)

portC

Parameters

General Parameters

Name

Default

Units

Description

Modelica ID

pclose

1.9·107

Pa

Pressure at which valve is fully closed (A = Aclose)

pclose

popen

2.05·107

Pa

Pressure at which valve is fully open (A = Aopen)

popen

Aclose

1·10−12

m2

Valve area when closed (leakage)

Aclose

Aopen

1·10−5

m2

Valve area when fully open

Aopen

Pilot action

1

 

Select whether the pilot operates to open or close the valve

dir

kpilot

3

 

Pilot ratio

kp

Exact

false

 

When true (checked) first-order dynamics are used for the valve area

Exact

tc

0.1

s

Time constant

tc

Smooth Transition

false

 

True (checked) means enable the smoothness factor

smoothTransition

smoothness

0.5

 

Smoothness factor (0: sharpest, 1: smoothest); used when Smooth Transition is enabled

smoothness

Orifice

Name

Default

Units

Description

Modelica ID

Use constant Cd

true

 

True (checked) means a constant coefficient of discharge is implemented, otherwise a variable Cd is used in flow calculations

UseConstantCd

Cd

0.7

 

Flow-discharge coefficient; used when Use constant Cd is true

Cd

ReCr

12

 

Reynolds number at critical flow; used when Use constant Cd is true

ReCr

Cdmax

0.7

 

Maximum flow-discharge coefficient; used when Use constant Cd is false

Cd_max

Critno

1000

 

Critical flow number; used when Use constant Cd is false

Crit_no

Optional Volumes

Name

Default

Units

Description

Modelica ID

Use volume A

false

 

True (checked) means a hydraulic volume chamber is added to portA

useVolumeA

VA

1·10−6

m3

Volume of chamber A

Va

Use volume B

false

 

True (checked) means a hydraulic volume chamber is added to portB

useVolumeB

VB

1·10−6

m3

Volume of chamber B

Vb

For more information see Port Volumes.

Fluid Parameters

The following parameters, used in the equations, are properties of the Hydraulic Fluid component used in the model.

Name

Units

Description

Modelica ID

ν

m2s

Kinematic viscosity of fluid

nu

ρ

kgm3

Density of fluid

rho

El

Pa

Bulk modulus of fluid

El

See Also

Hydraulics Library

Valves