WOLFRAM SYSTEMMODELER

SimpleSolenoid

Simple network model of a lifting magnet with planar armature end face

Diagram

Wolfram Language

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SystemModel["Modelica.Magnetic.FluxTubes.Examples.SolenoidActuator.Components.SimpleSolenoid"]
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Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

Please refer to the Parameters section for a schematic drawing of this axisymmetric lifting magnet. In the half-section below, the flux tube elements of the actuator's magnetic circuit are superimposed on a field plot obtained with FEA. The magnetomotive force imposed by the coil is modelled as one lumped element. As a result, the radial leakage flux between armature and yoke that occurs especially at large working air gaps can not be considered properly. This leads to a a higher total reluctance and lower inductance respectively compared to FEA for large working air gaps (i.e., armature close to x_max). Please have a look at the comments associated with the individual model components for a short explanation of their purpose in the model.

Field lines and assigned flux tubes of the simple solenoid model

The coupling coefficient c_coupl in the coil is set to 1 in this example, since leakage flux is accounted for explicitly with the flux tube element G_mLeakWork. Although this leakage model is rather simple, it describes the reluctance force due to the leakage field sufficiently, especially at large air gaps. With decreasing air gap length, the influence of the leakage flux on the actuator's net reluctance force decreases due to the increasing influence of the main working air gap G_mAirWork.

During model-based actuator design, the radii and lengths of the flux tube elements (and hence their cross-sectional areas and flux densities) should be assigned with parametric equations so that common design rules are met (e.g., allowed flux density in ferromagnetic parts, allowed current density and required cross-sectional area of winding). For simplicity, those equations are omitted in the example. Instead, the found values are assigned to the model elements directly.

Connectors (3)

p

Type: PositivePin

Description: Electrical connector

n

Type: NegativePin

Description: Electrical connector

flange

Type: Flange_b

Description: Flange of component

Parameters (17)

R

Value: 10

Type: Resistance (Ω)

Description: Armature coil resistance

N

Value: 957

Type: Real

Description: Number of turns

r_yokeOut

Value: 15e-3

Type: Radius (m)

Description: Outer yoke radius

r_yokeIn

Value: 13.5e-3

Type: Radius (m)

Description: Inner yoke radius

l_yoke

Value: 35e-3

Type: Length (m)

Description: Axial yoke length

t_yokeBot

Value: 3.5e-3

Type: Length (m)

Description: Axial thickness of yoke bottom

l_pole

Value: 6.5e-3

Type: Length (m)

Description: Axial length of pole

t_poleBot

Value: 3.5e-3

Type: Length (m)

Description: Axial thickness of bottom at pole side

t_airPar

Value: 0.65e-3

Type: Length (m)

Description: Radial thickness of parasitic air gap due to slide guiding

material

Value: Material.SoftMagnetic.Steel.Steel_9SMnPb28()

Type: BaseData

Description: Ferromagnetic material characteristics

r_arm

Value: 5e-3

Type: Radius (m)

Description: Armature radius = pole radius

l_arm

Value: 26e-3

Type: Length (m)

Description: Armature length

c

Value: 1e11

Type: TranslationalSpringConstant (N/m)

Description: Spring stiffness between impact partners

d

Value: 400

Type: TranslationalDampingConstant (N·s/m)

Description: Damping coefficient between impact partners

x_min

Value: 0.25e-3

Type: Position (m)

Description: Stopper at minimum armature position

x_max

Value: 5e-3

Type: Position (m)

Description: Stopper at maximum armature position

rho_steel

Value: 7853

Type: Density (kg/m³)

Description: Density for calculation of armature mass from geometry

Components (15)

material

Type: BaseData

Description: Ferromagnetic material characteristics

ground

Type: Ground

Description:

coil

Type: ElectroMagneticConverter

Description: Electro-magnetic converter

r

Type: Resistor

Description: Coil resistance

g_mFeYokeSide

Type: HollowCylinderAxialFlux

Description: Permeance of of hollow cylindric section of ferromagnetic yoke

g_mFeArm

Type: HollowCylinderAxialFlux

Description: Permeance of ferromagnetic armature

g_mAirWork

Type: HollowCylinderAxialFlux

Description: Permeance of working air gap (between armature and pole end faces)

g_mFeYokeBot

Type: HollowCylinderRadialFlux

Description: Permeance of bottom side of ferromagnetic yoke

g_mAirPar

Type: HollowCylinderRadialFlux

Description: Permeance of parasitic radial air gap due to slide guiding

g_mFePoleBot

Type: HollowCylinderRadialFlux

Description: Permeance of bottom side of pole

g_mFePole

Type: HollowCylinderAxialFlux

Description: Permeance of ferromagnetic pole

armature

Type: TranslatoryArmatureAndStopper

Description: Inertia of armature and stoppers at end of stroke range

g_mLeak1

Type: QuarterCylinder

Description: Leakage permeance between inner edge of yoke bore and armature side face

g_mLeak2

Type: QuarterHollowCylinder

Description: Leakage permeance between inner side of yoke bottom and armature side (r_i = t_airPar)

g_mLeakWork

Type: LeakageAroundPoles

Description: Permeance of leakage air gap around working air gap (between armature and pole side faces)

Used in Examples (2)

ComparisonQuasiStationary

Slow forced armature motion of both solenoid models so that electromagnetic field and current are quasi-stationary

ComparisonPullInStroke

Pull-in stroke of both solenoid models after a voltage step at time t=0