WOLFRAM SYSTEMMODELER

PermeanceActuator

Detailed actuator model for rough magnetic design of actuator and system simulation

Diagram

Wolfram Language

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SystemModel["Modelica.Magnetic.FluxTubes.Examples.MovingCoilActuator.Components.PermeanceActuator"]
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Information

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

In the ConstantActuator model the force F is strictly proportional to the current i as indicated by the converter constant c. However, there is an additional non-linear force component in such an actuator that is due to the dependency of the coil inductance L on the armature position x. The inductance increases as the armature moves into the stator. The total force is

        1  2 dL
    F = - i  --  + c i
        2    dx

Both force components are properly considered with a simple permeance model as shown in the figures below. Figure (a) illustrates the dimensions of the axisymmetric moving coil actuator that are needed in the permeance model. Figure (b) shows partitioning into flux tubes and the permanent magnetic field without current. G_ma and G_mb both are the permeances resulting from a series connection of the permanent magnet and air gap sections. The field plot of the coil-imposed mmf is shown in figure (c) without the permanent magnetic mmf (H_cB=0). The placement of the magnetic network components in figure (d) retains the geometric structure of the actuator. In figure (e), the permeance model is restructured and thus simplified.

Structure, assigned flux tubes and field plots of the moving coil actuator

Connectors (3)

p

Type: PositivePin

Description: Electrical connector

n

Type: NegativePin

Description: Electrical connector

flange

Type: Flange_b

Description: Flange of component

Parameters (13)

N

Value: 140

Type: Real

Description: Number of turns

R

Value: 2.86

Type: Resistance (Ω)

Description: Coil resistance

r_core

Value: 12.5e-3

Type: Radius (m)

Description: Radius of ferromagnetic stator core

l_PM

Value: 3.5e-3

Type: Length (m)

Description: Radial thickness of permanent magnet ring

t

Value: 0.02

Type: Length (m)

Description: Axial length of permanent magnet ring and air gap respectively

l_air

Value: 3e-3

Type: Length (m)

Description: Total radial length of armature air gap

l_FeOut

Value: 4e-3

Type: Length (m)

Description: Radial thickness of outer back iron (for estimation of leakage permeance)

material

Value: Material.HardMagnetic.BaseData()

Type: BaseData

Description: Ferromagnetic material characteristics

m_a

Value: 0.012

Type: Mass (kg)

Description: Mass of armature

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: -4e-3

Type: Position (m)

Description: Position of stopper at minimum armature position

x_max

Value: 4e-3

Type: Position (m)

Description: Position of stopper at maximum armature position

Components (10)

material

Type: BaseData

Description: Ferromagnetic material characteristics

mmf_PM

Type: ConstantMagneticPotentialDifference

Description: Permanent magnet's magnetomotive force

armature

Type: TranslatoryArmatureAndStopper

Description: Inertia of moving coil + coil carrier; stoppers at end of stroke range

r

Type: Resistor

Description:

ground

Type: Ground

Description:

coil

Type: ElectroMagneticConverter

Description:

g_ma

Type: HollowCylinderRadialFlux

Description:

g_mb

Type: HollowCylinderRadialFlux

Description:

g_mLeak1

Type: CoaxCylindersEndFaces

Description: Leakage between coaxial end planes of ferromagnetic stator core and outer back iron

g_mLeak2

Type: HalfCylinder

Description: Leakage between edges of ferromagnetic stator core and outer back iron

Used in Examples (3)

ForceCurrentBehaviour

Comparison of the force-current characteristics of both converter models with armature blocked at mid-position

ForceStrokeBehaviour

Force-stroke characteristic of the permeance model at constant current

ArmatureStroke

Armature stroke of both moving coil actuator models after a voltage step at time t=0