# Permanent Magnet Mistakes, Part Six

Stan Trout, Spontaneous Materials

We continue with the sixth blog in this series, describing the many types of mistakes made with permanent magnets. Again, my intent is to help engineers in the future avoid mistakes made in the past, and not to embarrass anyone. Everyone’s experience is different, so please feel free to add your insights in the comments section below.
The sixth group of mistakes on my list are:
13. Assuming that large magnetized parts are easy and safe to handle
14. Failing to consider natural product variations in both magnetic properties and dimensions
15. Assuming that the attractive and repulsive forces are equivalent and can be precisely calculated

Spoiler alert: In items 13 and 15, force is the important parameter.
Of all the steps in the process of making a magnet, magnetizing is the quickest and perhaps the most dramatic. A piece of metal or ceramic is transformed from an unassuming lump of material into a fully charged magnet in less than a second. After all the work that goes into making magnets, we finally get a first glimpse of what makes them unique and interesting as they come out of the magnetizer. You might say this is where the fun begins.

Early in my career we made a sensor magnet for Hall Effect devices. The magnet was SmCo5 and the approximate dimensions were 2 mm by 2 mm by 1 mm. An entire day’s production fit in several drinking straws, was magnetized with a couple of pulses on the magnetizer, and was shipped off to the customer. These small magnets were very easy to handle.

Soon thereafter I was introduced to the Halbach array.[1] While there are several variants of the basic design, a Halbach array looks like a sliced pie with a hole at the center, with each piece having a different magnetic direction, see the figure below. I saw my first Halbach array around 1980 and they are still used today for several applications, including controlling beams of charged particles in high energy physics. Halbach arrays are easy to draw, but challenging to assemble. The problem is that as each magnet is added to the array, it interacts with all the magnets already in the array. As the magnet is moved into position, the magnitude of the forces can be large and the direction of the force can change abruptly. Even a small magnet can be easily ripped out of your hand by these forces, an extremely dangerous situation. This assembly problem becomes more serious as the size of the array increases. I haven’t tried to write an equation to describe this situation, but my impression is that the force go up by at least the square of the overall dimensions. Because of the danger, the largest arrays need to be assembled without humans nearby. Hydraulic systems are often employed for this purpose and the entire process needs to be well choreographed in advance to avoid unpleasant surprises. This warning is something that Halbach himself advised in his 1979 paper.

Large magnets frequently have handling issues once they are magnetized, so a thorough analysis of what happens to them once they come out of the magnetizer is imperative.
All magnets come with tolerances, both mechanical and magnetic. In the early stages of design, engineers pour over drawings of the magnets and other components. They discuss the stack up of all the tolerances, mostly to understand how the components physically fit together. Besides their mechanical tolerances, permanent magnets also come with tolerances on their magnetic properties. Most magnetic properties typically have a tolerance of ± 5 percent. A notable exception is (BH)max which has roughly double the tolerance, or ± 10 percent. (Graduates of my Magnetic Bootcamps may recall why this is so.)

The problem is that the magnetic and mechanical tolerances are not independent. We call on magnets to produce magnetic flux. If we want a little more flux, we can increase the magnetic properties of the material slightly or we can make the magnet just a little bit bigger. Both changes have the same effect on flux. In real magnets where both the magnetic properties and the dimensions experience normal process variations, we should be aware of how the variations interplay.

When flux output of a magnet is the key consideration, both magnetic and mechanical tolerances must be considered.

As children, one of the first things we notice about magnets is that they can attract and repel each other, depending on how we configure the poles of the magnets. It is a cause for great fascination. What we see is one of the fundamental forces of nature, like gravity, but with two magnets in our hands, we can feel this unique force. A comparable demonstration with gravity would be vastly larger, to say the least.

Sometime later we may learn about Coulomb’s Law. An equation which describes the attractive and repulsive forces between two charged particles. We may see a connection between Coulomb’s Law and the attractive and repulsive forces we observe between magnets. They certainly appear to be similar in nature, and it would seem that there should be a very nice equation that describes both the attractive and the repulsive forces between magnets. But the truth is not that simple.

First, we find that there is a noticeable difference in magnitude between the attractive force and the repulsive force, something that Coulomb’s Law does not predict. Further we find the agreement between theory and experiment is at times OK, and at other times awful. Over the years, people have asked me how this can happen. My impression is that the assumptions built into the equations we might consider to describe this force are sometimes obeyed well and other times, not so well. This is the reason for the varying quality of the agreement. This is a conundrum I would like to study in the future.
Consequently, when knowing the forces between magnets is a very important in an application, typically finite element analysis or experimental data are the preferred tools to find good answers.

Fifteen down, two to go.

Reference
[1] Klaus Halbach, Strong Rare Earth Cobalt Quadrupoles, IEEE Transactions on Nuclear Science NS-26, 3882 (1979) DOI: 10.1109/TNS.1979.4330638