COMSOL 6.4 - Magnetic–Structure Interaction in a Permanent Magnet Motor

Magnetic–Structure Interaction in a Permanent Magnet Motor

Permanent Magnet (PM) motors are widely used in a variety of domestic and industrial applications including electric vehicles, high speed railways, aerospace and HVAC applications. Though high in initial cost, PM motors provide high efficiency over a large operational speed and power range, which make them suitable for many of these robust machineries.

In this example, the coupling between the Multibody Dynamics interface and the Rotating Machinery, Magnetic interface for performing mechanical and electromagnetic analysis is demonstrated. A permanent magnet motor with surface mounted magnets is modeled in 2D. To model magnetic–structure coupling integrated with moving mesh, the electromagnetic force is transferred to the rotor, and the rotor motion is transferred to the moving mesh. A time-dependent problem, computing the magnetic flux density and displacement, is solved for three electrical periods.

This model requires the AC/DC Module and the Multibody Dynamics Module.

Model Definition

The main parts of an electric motor are a moving rotor, housed in a stationary stator, separated by an air gap to enable the rotation. In a PM motor, magnets are attached either to the surface of the rotor or embedded inside them.

In this example, a PM motor with 10 rotor poles and 12 stator slots is modeled in 2D. The diameter of rotor and stator are 150 mm 250 mm respectively. The axial length of the motor is 300 mm. As shown in Figure 1, the magnets are mounted on the surface of the rotor. The interaction between the magnetic field of the rotor and the magnetic field generated by stator currents produces the driving torque. To reduce the weight and minimize material usage, there are five air channels in the rotor.

Figure 1: Geometry of the motor.

Magnetic–Structure Interaction

The interaction between electromagnetic and structural domains is modeled using a Magnetic–Rigid Body Interaction in Rotating Machinery interface. This interface consists of a Rotating Machinery, Magnetic interface, a Multibody Dynamics interface, and a node with a and a subnodes. In addition, a node is added. It contains the multiphysics coupling . Using this functionality, the electromagnetic forces generated during the rotation of the motor is transferred to the structural domains.

Additional details about the interface can be found in the documentation for Multiphysics Couplings in the Multibody Dynamics Module User’s Guide.

Rotating Machinery, Magnetic

Rotating Machinery, Magnetic interface is used to solve the electromagnetic field equations in a transverse section of the PM motor. The stator and rotor iron are made of silicon steel with zero conductivity. The permanent magnets are made of NdFeB, creating a strong magnetic field. The center shaft is made of high strength alloy steel. The rotational speed is taken as 700 rpm. The stator coil is excited with a peak current of 10 A, with an initial current angle for peak torque set as 198°.

Multibody Dynamics

The Multibody Dynamics interface is used to model the rotor and permanent magnets. For mechanical analysis, they are considered as elastic with properties as shown in Table 1.

Table 1: Mechanical properties of rotor iron and Magnets.
Property	Symbol	Unit	Silicon steel	NdFeB
Young’s modulus	E	GPa	195	160
Poisson’s ratio	ν	1	0.25	0.24
Mass density	ρ	kg/m3	7700	7600

The effect of centrifugal force generated by the rotation of the rotor is modeled using a node.

Moving Mesh

A deforming domain condition is assigned to the rotor air gap and other rotor air channel domains, which experience significant deformation due to the rotation of adjacent structural domains. The shape of these domains is controlled by the moving boundaries and a smoothing equation in the interior. On the external boundaries of the rotor air gap, a condition is used to enable the sliding of the mesh.

Results and Discussion

A time-dependent problem is solved for three electrical periods.

Figure 2 displays the total displacement of rotor, with arrows showing the direction of displacement at the end of three electrical periods. In Figure 3, the displacement of a sample point on the rotor core is plotted as a function of time.

Figure 2: Displacement of rotor at the end of three electrical periods. The arrows show the direction of displacements relative to a corotating frame.

Figure 3: Displacement of a sample point on rotor iron as a function of time for three electrical periods.

Figure 4 and Figure 5 show plots from the electromagnetic analysis. In Figure 4, the norm of the magnetic flux density and field lines are shown. Figure 5 plots the rotor torque ripple as a function of time for three electrical periods.

Figure 4: The norm and field lines of magnetic flux density at the end of three electrical periods.

Figure 5: Rotor torque plotted as a function of time for three complete electrical periods.

Notes About the COMSOL Implementation

In order to get appropriate initial conditions for the time-dependent analysis, a stationary solution is run first. This will establish a state of initial deformations and strains, caused by the magnetic field and centrifugal forces.

Multibody_Dynamics_Module/Electrical_Machinery/pm_motor_2d_structure_interaction

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > > > > .

Click .

Click

In the tree, select > .

Click

Geometry 1

Change the units to mm.

In the window, under click .

In the window for , locate the section.

From the list, choose .

Begin by specifying a number of general parameters that will be used in the model.

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file pm_motor_2d_structure_interaction_parameters.txt.

Next, build the motor using rotor and stator parts from the geometry part library. Initialize the parts, and tick the selections that are predefined to make it convenient to assign material properties and magnetization direction.

Part Libraries

In the toolbar, click

and choose .

In the window, under click .

In the window, select > > > > in the tree.

Click

Geometry 1

Internal Rotor – Surface Mounted Magnets 1 (pi1)

In the window, under > click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
number_of_poles	Np	10	Number of magnetic poles in rotor
number_of_modeled_poles	Np	10	Number of magnetic poles included in the geometry
magnet_h	1.5[mm]	1.5 mm	Height of the magnets
magnet_w	7[mm]	7 mm	Width of the magnets (set to 0 to use all available space)

Click to expand the section. In the table, select the checkboxes for , , and .

Click

Circle 1 (c1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 11.8.

In the text field, type 360/APnr*APfct.

Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (mm)
Layer 1	4.8

Extract 1 (extract1)

In the toolbar, click

In the window for , locate the section.

From the list, choose .

On the object , select Domain 2 only.

From the list, choose .

Fillet 1 (fil1)

In the toolbar, click

On the object , select Points 1–4 only.

In the window for , locate the section.

In the text field, type 2/APnr.

Rotate: Rotor Air Channels

In the toolbar, click

and choose .

Select the object only.

In the window for , type Rotate: Rotor Air Channels in the text field.

Locate the section. In the text field, type range((360/APnr-360/APnr*APfct)/2,360/APnr,360).

Locate the section. Select the checkbox.

Rotating Boundaries

In the toolbar, click

and choose .

In the window for , type Rotating Boundaries in the text field.

Locate the section. From the list, choose .

Locate the section. In the text field, type inf.

In the text field, type 30.5/2*0.99.

Extract 2 (extract2)

In the toolbar, click

In the window for , locate the section.

From the list, choose .

On the object , select Domain 12 only.

From the list, choose .

Difference: Rotor Core

In the toolbar, click

and choose .

In the window for , type Difference: Rotor Core in the text field.

Select the object only.

Locate the section. From the list, choose .

Select the checkbox.

Locate the section. Select the checkbox.

Union: Rotor

In the toolbar, click

and choose .

In the window for , type Union: Rotor in the text field.

Click the

button in the toolbar.

Locate the section. Select the checkbox.

Click

Circle 1 (c1), Difference: Rotor Core (dif1), Extract 1 (extract1), Extract 2 (extract2), Fillet 1 (fil1), Internal Rotor – Surface Mounted Magnets 1 (pi1), Rotate: Rotor Air Channels (rot1), Rotating Boundaries (disksel1), Union: Rotor (uni1)

In the window, under > , Ctrl-click to select , , , , , , , , and .

Right-click and choose .

Stator

In the window for , type Stator in the text field.

Part Libraries

In the toolbar, click

In the window, click .

In the window, select > > > > in the tree.

Click

Geometry 1

External Stator – Slotted 1 (pi2)

Specify number of slots and select a radial partition for the slot winding type.

In the window, under > click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
number_of_slots	Ns	12	Number of slots in stator
number_of_modeled_slots	Ns	12	Number of slots included in the geometry
slot_winding_type	2	2	Slot winding type: 1-No partition, 2-Radial partition, 3-Azimuthal partition, 4-Radial and azimuthal partition.
Arkkio_toggle	1	1	Toggle Arkkio air gap - (1/0) (on/off)

Locate the section. In the table, select the checkboxes for , , and .

Click

Scale 1 (sca1)

In the toolbar, click

and choose .

Click in the window and then press Ctrl+A to select both objects.

In the window for , locate the section.

In the text field, type geom_scale.

Create an assembly from the two geometry objects, connected by a pair boundary.

Form Union (fin)

In the window, under > click .

In the window for , locate the section.

From the list, choose .

In the toolbar, click

Click the

button in the toolbar.

Definitions

Ramp 1 (rm1)

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type 1/t_ramp.

Select the checkbox.

Next, add selections to assign materials and physics features.

Structural Domains

In the toolbar, click

In the window for , type Structural Domains in the text field.

Locate the section. Under , click

In the dialog, in the list, choose and .

Click .

Deforming Domains

Right-click and choose .

In the window for , type Deforming Domains in the text field.

Locate the section. In the list box, select .

Under , click

In the dialog, in the list, choose and .

Click .

Shaft Boundaries

In the toolbar, click

In the window for , type Shaft Boundaries in the text field.

Locate the section. Under , click

In the dialog, select in the list.

Click .

Next, add materials and assign them to their appropriate domain selections.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > .

Click the button in the window toolbar.

In the tree, select > > .

Click the button in the window toolbar.

In the tree, select > ®) > > .

Click the button in the window toolbar.

In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Materials

Silicon Steel NGO 35PN440 (mat2)

Select Domains 2 and 35 only.

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Young’s modulus	E	195[GPa]	Pa	Young’s modulus and Poisson’s ratio
Poisson’s ratio	nu	0.25	1	Young’s modulus and Poisson’s ratio
Density	rho	7700	kg/m³	Basic
Electric conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	0	S/m	Basic

BMN-42 (mat3)

In the window, click .

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Young’s modulus	E	160[GPa]	Pa	Young’s modulus and Poisson’s ratio
Poisson’s ratio	nu	0.24	1	Young’s modulus and Poisson’s ratio
Density	rho	7600	kg/m³	Basic

High-strength alloy steel (mat4)

In the window, click .

In the window for , locate the section.

From the list, choose .

Multibody Dynamics (mbd)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Locate the section. In the d text field, type L.

Rotating Frame 1

In the window, under > click .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

In the Ωr text field, type w_rot*rm1(t[1/s]).

Fixed Constraint 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Rotating Machinery, Magnetic (rmm)

In the window, under click .

In the window for , locate the section.

In the d text field, type L.

Ampère’s Law 2

In the toolbar, click

and choose .

Select Domains 2 and 35 only.

In the window for , locate the section.

From the list, choose .

Conducting Magnet 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

From the list, choose .

North 1

In the window, click .

Select Boundary 314 only.

South 1

In the window, click .

Select Boundary 311 only.

The feature simplifies excitation of stator coils of electrical machines. For three-phase systems, an automatic ordering of coil domains into a balanced stator winding is supported, provided that the electrical machine topology in terms of number of poles and slots can accommodate it. In the following steps, use a feature to automatically populate the selections of three subnodes with coil domains representing each phase.

Multiphase Winding 1

In the toolbar, click