Problem Description

Solution

1. Lorentz's force computations
2. Method of virtual displacement
3. Maxwell stress tensor

Whenever you have a current-carrying conductor, the forces in that domain can be computed by taking the cross product of the current density vector and the magnetic flux density vector (J x B). The result is the force density, which can be integrated using the integration functions of COMSOL Multiphysics to get the total force on the domains. These forces are known as Lorentz forces.

This Lorenz forces method cannot be used when you want to consider magnetic dipole contributions. Instead, use the method of virtual displacement. This can be used for computing forces on a set of objects surrounded by air. The cemforce and cemtorque routines in the AC/DC Module use this method. In this method the force is given from the effect of a small displacement of a domain on the total amount of stored energy in the system. Note that cemforce and cemtorque only work with linear Lagrange elements. It does not work for vector elements of any order.

The Maxwell stress tensor is a way of replacing the forces on a body by equipollent surface pressure, that is, surface forces which produce the same resultant force and torque as the volume force distribution.

• For an example of how to use the Lorentz forces method, see the model "Linear Electric Motor" in the AC/DC Module Model Library.
• For an example of how to use "cemforce", see the model "Linear Electric Motor of Moving Coil Type" in the AC/DC Module Model Library.
• For an example of how to use Maxwell's stress tensor, see the models "Permanent Magnet" and "Electromagnetic Forces on Parallel Current Carrying Wires" in the AC/DC Module Model Library.

Torque 

For torque calculations, you can use the Forces tab of the Subdomain Settings dialog box. You must specify a center point of rotation, around which you get the three axis components of the torque. As an extra option, you can also compute the torque around an arbitrary axis.

• For an example of how to use torque computation with the Maxwell's stress tensor, see the model "Generator with Mechanical Dynamics and Symmetry" in the AC/DC Module Model Library.

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