WOLFRAM SYSTEM MODELER

PermeanceActuator

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

Diagram

Wolfram Language

In[1]:=

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

Out[1]:=

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 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 (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

Connectors (3)

	p	Type: PositivePin Description: Electrical connector
	n	Type: NegativePin Description: Electrical connector
	flange	Type: Flange_b Description: Flange of component

Type: PositivePin

Description: Electrical connector

Type: NegativePin

Description: Electrical connector

flange

Type: Flange_b

Description: Flange of component

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: Ideal linear electrical resistor
	ground	Type: Ground Description: Zero magnetic potential
	coil	Type: ElectroMagneticConverter Description: Ideal electromagnetic energy conversion
	g_ma	Type: HollowCylinderRadialFlux Description: Hollow cylinder with radial flux; constant permeability
	g_mb	Type: HollowCylinderRadialFlux Description: Hollow cylinder with radial flux; constant permeability
	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