Re: [femm] Different methods for calculating force

[David Meeker <dmeeker@xxxxxxxx>]

dfj_stevenson wrote:

> Dear all,
>
> Can someone please comment on the usage of
> 1) Field Energy
> 2) Coenergy
> 3) Maxwells Stress Tensor
>
> When calculating force in Magnetostatic problems in FEMM. In
> particular what are the differences the three methods and when is it
> most appropriate to utilise a particular method. I am particularly
> interested in the basic mathematics and the numerical methods eg mesh
> density, precision that are involved.
>
> Thank-you

Generally, I like to use differentiation of energy/coenergy methods when 
I'm evaluating force for a device over a stroke, like with solenoids. 
There is an example of a solenoid that computes force in this way. This 
method is also really good if you want the average force over some range 
of displacements. Generally, you'd hold current constant and evaluate 
the change in coenergy versus position to infer force. If you hold flux 
constant, you'd differentiate energy, rather than coenergy, However, 
hardly any of the problems that you'd typically solve in femm are 
constant flux--I've only run across constant flux problems in a few real 
oddball applications that I've looked at. If all materials in a problem 
are linear, energy and conenergy are the same value.

If you are evaluating differences in coenergy at discrete points along a 
trajectory, I'd suggest making the mesh size around the moving object 
smaller than the distance between points on the trajectory. Otherwise, 
the force results can be noisy.

Stress tensor is good for things like torque on rotating machines. 
There are some guidelines in section 4.10 of the manual for getting OK 
force & torque results via stress tensor.

In some situations, one is just interested in the force on a coil (or 
set of coils). In that case, the Lorentz force or Lorentz torque can be 
evaluated. These are both volume integrals, and they tend to be an 
order more accurate than stress tensor, which is a line integral. A 
typical application for this method of force computation is voice coil 
actuators. The last message, which considered a motor with 
surface-mounted coils is also amenable to Lorentz torque, since all the 
torque is created by the magnet acting directly on the coils.

A good reference for the rationale behind energy/coenergy methods is 
Slemon's "Electric Machines and Drives," specifically section 7.8. 
There are also some papers about force computation online--try 
http://www.vtt.fi/val/val3/projects/Masi/Tulokset/raportit/MagenVoimat.pdf 
for example.

There are also a lot of papers in Transactions on Magnetics about this 
subject, some describing the methods implemented in commercial codes.

Dave.
--
David Meeker <http://femm.berlios.de/dmeeker>