Permanent Magnets

In this tutorial, the magnetic fields and magnetic forces resulting from a pair of small permanent magnets is simulated.

Model definition

The model consists of two cylindrical 2 mm permanent magnets separated by a distance of 1.2 mm and an air box surrounding them.

A constant magnetic flux density is applied to the magnets. The resulting magnetic forces are determined with the Magnetism-φ formulation.

Additional cylindrical force domain volumes are created around the magnets, so that the magnetic fields around the magnets can be integrated.

Element	Geometric details
Magnet 1	Cylinder of 2 mm radius and 2 mm height centered at $(0, 0.0025, 0)$
Magnet 2	Cylinder of 2 mm radius and 2 mm height centered at $(0, -0.0025, 0)$
Force domain 1	Cylinder of 3 mm radius and 3 mm height centered at $(0, 0.0025, 0)$
Force domain 2	Cylinder of 3 mm radius and 3 mm height centered at $(0, -0.0025, 0)$
Air box	Box of size 50 mm $\times$ 50 mm $\times$ 50 mm

Output Results

1. Magnetic field distribution.
2. Magnetic forces between the magnets.

Material Data

• Air

Property	Value
Magnetic permeability	$\mu_0 = 4 \pi \times 10^{-7} ~ \rm H/m$

Boundary conditions

Type	Value	Target volume
Remanence	[0, 1.35, 0]	Magnet 1
Remanence	[0,-1.35, 0]	Magnet 2

Step-by-step guide

Here you’ll find a detailed step-by-step tutorial on how to simulate a pair of permanent magnets and the resulting forces in Quanscient Allsolve.

Step 1 - Build the geometry

Geometric entity tags

Geometric entities (volumes, surfaces, curves and points) are referenced using tags throughout this tutorial.

Carefully replicate the geometry construction steps below in order to have correct tags. Incorrect entity tags can lead to errors or unexpected behavior during simulations.

1. Create a new project and name it Permanent magnets.

2. Start off with a cylinder element.

   Name	Element type	Center point [m]	Size [m]	Rotation [deg]
   magnet 1	Cylinder	X: 0	Radius: 2e-3	X: 0
   		Y: 2.5e-3	Height: 2e-3	Y: 0
   		Z: 0		Z: 0

   Note, that rotation in the X-direction is 0.

3. Reset view after building magnet 1 to bring the small magnet cylinder back into view.

4. Copy magnet 1 to build magnet 2.

   Name	Element type	Center point [m]	Size [m]	Rotation [deg]
   magnet 2	Cylinder	X: 0	Radius: 2e-3	X: 0
   		Y: -2.5e-3	Height: 2e-3	Y: 0
   		Z: 0		Z: 0

5. Copy magnet 1 to build force domain 1.

   Name	Element type	Center point [m]	Size [m]	Rotation [deg]
   force domain 1	Cylinder	X: 0	Radius: 3e-3	X: 0
   		Y: 2.5e-3	Height: 3e-3	Y: 0
   		Z: 0		Z: 0

6. Copy force domain 1 to build force domain 2.

   Name	Element type	Center point [m]	Size [m]	Rotation [deg]
   force domain 2	Cylinder	X: 0	Radius: 3e-3	X: 0
   		Y: -2.5e-3	Height: 3e-3	Y: 0
   		Z: 0		Z: 0

   At this point, there are 4 cylinders in the model, so that the force domains envelop the magnets that are facing each other.

   

7. Build the air box.

   Name	Element type	Center point [m]	Size [m]	Rotation [deg]
   box	Box	X: 0	X: 50e-3	X: 0
   		Y: 0	Y: 50e-3	Y: 0
   		Z: 0	Z: 50e-3	Z: 0

   

Step 2 - Define materials

1. Go to the Properties section.

2. tosign the Air material to all volumes.

   

Step 3 - Define the physics and apply boundary conditions

1. Go to the Physics section.

2. Add the Magnetism ϕ physics. Let the target default to all volumes.

   Physics	Target
   Magnetism φ	All volumes

3. Add a Remanence interaction to Magnetism φ. Remanence introduces a B-field to a volume.

   Interaction name	Interaction type	Target	Value
   Remanence left	Remanence	magnet 2 (volume 4)	[0; 1.35; 0]

   

4. Add another Remanence interaction to Magnetism φ.

   Interaction name	Interaction type	Target	Value
   Remanence right	Remanence	magnet 1 (volume 1)	[0; -1.35; 0]

   

Step 4 - Generate the mesh

1. Go to the Simulations section.

2. Create a new mesh.

3. Set Mesh quality to Expert Settings.

4. Set the mesh element Max size to 0.05.

5. Scroll down to Mesh Refinement and create a Volume mesh refinement entity.

6. Select all cylindrical volumes to target and set Max size to 0.0001.

   

7. Generate the mesh and check the preview.

   

Step 5 - Apply simulation settings

1. Create a new simulation.

   Simulation name	Analysis type	Node count	Node type
   Simulation 1	Steady state	5	1 CPU, 16 GB

2. Select Mesh 1 as the mesh for your simulation.

3. Add a B field output.

   Output name	Output type	Target	Output expression
   B magnets	Magnetic flux density (B) field output	magnets 1 and 2 (volumes 1, 4)	B

4. Add another B field output.

   Output name	Output type	Target	Output expression
   B air	Magnetic flux density (B) field output	Force domains 1 and 2, air box (volumes 5, 6, 7)	B

5. Add a Magnetic force value output.

   Output name	Output type	Target
   Magnetic force left	Magnetic force value output	magnet 2 and force domain 2 (volumes 4, 6)

6. Add another Magnetic force value output.

   Output name	Output type	Target
   Magnetic force right	Magnetic force value output	magnet 1 and force domain 1 (volumes 1, 5)

7. Run the simulation.

Step 6 - See results

1. Check Summary for the magnetic force value outputs.

   

2. Add a visualization to see field output results:

   Visualization name	Fields	Filters
   Visualization 1	B magnets
   	B air	Glyph

3. Edit the Glyph settings:

   Filter	Max sample points	Scale factor
   Glyph	50000	0.001

4. Render the visualization.

   

5. The Glyph scale factor is reduced to 0.0005 here for a closer look: