modelPermeanceActuator

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

Information

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 axis-symmetric 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

Parameters

TypeNameDefaultDescription
SI.ResistanceR2.86Coil resistance
SI.Radiusr_core12.5e-3Radius of ferromagnetic stator core
SI.Lengthl_PM3.5e-3Radial thickness of permanent magnet ring
SI.Lengtht0.02Axial length of permanent magnet ring and air gap respectively
SI.Lengthl_air3e-3Total radial length of armature air gap
SI.Lengthl_FeOut4e-3Radial thickness of outer back iron (for estimation of leakage permeance)
Parameters
RealN140Number of turns
Material
FluxTubes.Material.HardMagnetic.BaseDatamaterialMaterial.HardMagnetic.BaseData()Ferromagnetic material characteristics
Armature and stopper
SI.Massm_a0.012Mass of armature
SI.TranslationalSpringConstantc1e11Spring stiffness between impact partners
SI.TranslationalDampingConstantd400Damping coefficient between impact partners
SI.Positionx_min-4e-3Position of stopper at minimum armature position
SI.Positionx_max4e-3Position of stopper at maximum armature position

Connectors

TypeNameDefaultDescription
Modelica.Electrical.Analog.Interfaces.PositivePinpElectrical connector
Modelica.Electrical.Analog.Interfaces.NegativePinnElectrical connector
Modelica.Mechanics.Translational.Interfaces.Flange_bflangeFlange of component

Components

TypeNameDefaultDescription
SI.PositionxArmature position, alias for flange position
SI.InductanceLCoil inductance
FluxTubes.Sources.ConstantMagneticPotentialDifferencemmf_PMPermanent magnet's magnetomotive force
FluxTubes.Examples.Utilities.TranslatoryArmatureAndStopperarmatureInertia of moving coil + coil carrier; stoppers at end of stroke range
Modelica.Electrical.Analog.Basic.Resistorr
Basic.Groundground
FluxTubes.Basic.ElectroMagneticConvertercoil
FluxTubes.Shapes.Force.HollowCylinderRadialFluxg_ma
FluxTubes.Shapes.Force.HollowCylinderRadialFluxg_mb
FluxTubes.Shapes.Leakage.CoaxCylindersEndFacesg_mLeak1Leakage between coaxial end planes of ferromagnetic stator core and outer back iron
FluxTubes.Shapes.Leakage.HalfCylinderg_mLeak2Leakage between edges of ferromagnetic stator core and outer back iron