# How to Design a Donut Electromagnet

• Tim in NY
In summary: Hello,In summary, the problem is that the electromagnet does not have the desired effect because the field inside the coil is too weak. The solution is to use a stronger coil.
Tim in NY
I have an electromagnet device that I am designing and need a bit of help from some of the brilliant people on this site. Here's the problem:

I have a disk attached to the end of a shaft and the shaft/disk assembly can move radially (via a spring loaded mechanism). This shaft/disk fits within the inside diameter of a donut shaped electromagnet consisting of a coil surrounded by an iron armature. The electromagnet is stationary.

When the shaft moves radially over to the side of the ID of the magnet, the magnet is then energized to temporarily to hold the shaft/disk against the ID (the magnet does not cause the movement). After a set amount of time the magnet is de-energized releasing the shaft/disk which returns back to center. The radial movement can happen in any direction (0 to 360°) and

Here's a sectional image:

Here's very preliminary data just to get an idea of sizes: Magnet Iron Armature OD = 10" ID=5". Disk OD= 4", Shaft=1.5", and a force of around approx 8 lbs.

So here are my questions:

1) I've been looking but have not been able to find any physics papers on this type of magnet. I'm trying to find formulas and some theory for optimum dimensions, coil sizes, wire sizes etc. (it's been 40 years since I had this type of physics in college...ugh) Any links that you can provide would be great!
2) What is the best orientation of the coil's winding to create a radial force?

Any help would be appreciated! ...and thank you in advance!

Tim

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Tim in NY said:
I'm trying to find formulas and some theory for optimum dimensions, coil sizes, wire sizes etc.
Welcome to PF.

What DC voltage and current is available to drive the coil. How long in seconds does the field have to latch on, and to release the disk.

What do you mean by “magnet iron”? You must use something like common mild steel if you want the field to turn off. You may need to use a special circuit to turn the field off quickly and then stop with very low or zero magnetic field.

Have you considered using a permanent magnet for the disk. That way, momentarily reversing the electromagnet field might repel the disk from the gap. What will stop the disk swinging like a pendulum?

Why reinvent the wheel? What is the purpose of this device?

Hi and thanks for a quick response!

I haven't designed the power supply yet, but was thinking 24vdc and sized to provide whatever current I need to get the forces I need.
I didn't really mean "magnet iron", I'm going to use mild steel(A36) or ductile iron...any suitable, easy to machine material.
Latching on-off times of the PS would be controlled via a programmable microcontroller, so I can do anything in terms of timing.
I hadn't thought about using a permanent magnet for the disk (nice idea), but since the shaft/disk assembly is on a damped spring loaded mechanism, I'm not sure that's necessary.

Can't disclose the device because I signed a NDA but it is for a new type of 3D printer that will print a heavy thick material.

Thanks again!

Baluncore said:
How long in seconds does the field have to latch on, and to release the disk.
Tim in NY said:
Latching on-off times of the PS would be controlled via a programmable microcontroller, so I can do anything in terms of timing.
The time it takes to switch the magnetic field on or off is decided by the inductance, supply voltage and demagnetisation circuit. You will need to specify the time that is available in seconds for the turn-on, and for the turn-off transition. Would you be happy to wait for 10 seconds ?

10 seconds would be too long...I would need something around ±2 seconds. Does the demagnetization circuit simply switch polarity?

Tim in NY said:
Does the demagnetization circuit simply switch polarity?
It could if you used a permanent magnet for the disk. But with an on/off electromagnet it would reduce the current flow as quickly as possible to zero, then it would “ring” the magnet current either side of zero so as to kill the remnant magnetism in the iron.

I guess you could make the donut as two circular halves. Glue a wrapped circular coil into one half before putting the other half on as a lid.

Yes, the donut steel or iron armature would have to be in two circular halves (that would be the only way to machine it) and the coil would be wound onto a separate round donut which would be glued into the half and then the two halves bolted together.

The problem I'm having is that the field inside a coil is easily predicted and I can calculate that, but in this application I need the concentrated field to to be in the plane of the donut. It seems i can't use the right-hand rule because of cancelling fields? I am unsure as to what the best configuration of the coil would be to achieve this effect. In order to orient the fields, should there be two coils sitting on top of each other, or side-by-side? Or just a single coil? Should the coil(s) be wound around a nonferrous core...such as a plastic donut? .

I was hoping there would be some published data, or someone can provide technical guidelines for this type of electromagnet in order to be able to create the most efficient configuration.

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Tim in NY said:
I was hoping there would be some published data, or someone can provide technical guidelines for this type of electromagnet in order to be able to create the most efficient configuration.
With a prototype it is only necessary for it to work. There is no requirement that it be optimum. It is usually the case that a novel geometry will not be optimum and that there will be another geometry that uses less copper wire, more efficiently, and that can be built for less. How will you keep stray nuts and magnetic grit out of the pole gap? Why hold the disk magnetically when it could be latched mechanically, or the mounting bearings could be clamped with a band or sealed magnetic clutch?

The design of this device has been fixed by someone without experience in electromagnet design. There is a strong probability that the design will be inverted to a more efficient and lower cost design, or completely replaced, later in the prototyping process. Without mass or force specifications it is impossible to engineer a solution. This device cannot be engineered or optimised behind a NDA. You must build one and get it to work before you will realize the elegant design that eliminates the unforeseen problems, complexity and cost.

The position locking effect is not likely to be stable . Magnetic force might hold armature off centre but there is no component of that force preventing the armature from orbiting around .

I agree with @Baluncore that there must be better ways of doing this .

I understand about the instability and that's okay. I found something that is very very close in principal to what I need. It is the type of magnet used to keep Foucault Pendulum displays moving. It consists of a disk attached to the cable (near the cable's attachment at top), and a stationary ring magnet surrounding the cable/disk which is energized when the pendulum nears the apex of each swing. This pulls the disk into the magnet with enough force to overcome air friction and gravity to keep the pendulum moving.

Here's a link to a paper by the Physics Dept at The University of Louisville: http://www.astro.louisville.edu/foucault/pendulum.pdf

So back to my question: Page 31 of the paper is a drawing of the armature, and the schematic on page 21 provides the resistance and inductance of the coil, but that isn't enough info to determine the type of coil. Is it one big round coil with the windings wound in a diameter of the inner coil area within the armature, or is it a toroidal coil that is set within the armature? And exactly how does the iron armature direct the fields so that there is a strong effect in the plane of the ring?

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Let's start by setting the DC voltage to 24 volt and the current to 1 amp.

After the voltage has been turned on for some time, the current will have risen to 1 amp, it will be limited by ohms law and coil resistance. The DC resistance of the coil will be R = 24 / 1 = 24 ohms. The magnetic field will be proportional to the product; amp * turns. We must work out how many turns of how thick a wire to use.

The mean diameter of the coil will come from specified armature OD = 10" ID=5" and disk OD= 4", Shaft=1.5". Using diameters throughout, the disk projects 4” - 1.5” = 2.5” from shaft, add 1” to keep coil clear of disk gives a penetration of 3.5”. The ID=5”, penetrated by 3.5” gives a coil ID=8.5”. The OD of coil will be restricted by the outer wall to about 10” - 1” = 9”. So the coil lies between 8.5” and 9”. The mean diameter will be about 8.75”. Multiply by Pi to get circumference of coil = 27.5” = 0.70 metre of wire per turn.

Now examine the wire tables at; https://en.wikipedia.org/wiki/American_wire_gauge and you will see that ampacity = 1 amp at 75°C occurs for 26 awg, which has a copper area of 0.13mm2 and resistance of 133.9 ohm per km. We know R must be 24 ohms so we have 24 / 133.9 = 0.1792km or 179.2m to play with. Circumference is 0.70 metre so we can wind only 179.2 / 0.70 = 256 turns.

0.13 mm2 will not pack that well so each turn will need about 0.2mm2. 256 turns will be 51mm2 which will need a space of about 51 = pi * r2. So r = sqrt( 51 / pi ) = 4.03mm, or diam of bundle = 8.1mm. So you will need to drop the coil into a circular groove of at least 9mm or 3/8” diameter.

The ampere * turns will be 256. If that does not work you will need to use more current = thicker wire = bigger bundle = greater heat.So much for the steady state. Looking at the switching times. For the rise time of a current in the inductance V = L · di / dt. We start by guessing an initial minimum current rise-time of 1 amp per second. This makes the maximum L = V · dt / di, so Lmax = 24 henry.

Now see; https://en.wikipedia.org/wiki/Inductor#Inductance_formulas
The inductance of a coil bundle having 256 turns with a diameter 8.75”, (r = 4.375”), will be about;
L in uH = ( r2 * N2 ) / ( 9 * r + 10 * x ), where r and x are in inches. x = 0.375”
L = (19.14 * 65536 ) / ( 39.375 + 3.75 )
L = 1254400 / 43.125 = 29087.5 uH = 29 mH in free space.
An iron core with a relative permeability ur = 1000 will lift that to about 29H, so you might just get away with switching in a second or two.
Give it a try.

Thank you Baluncore! Your coil design process was really well written and right on target.

You confirmed what I already knew about designing a coil, however my questions are regarding how to design the outer iron 'shield', in conjunction with the coil, to optimize the magnetic field strength in the plane of the slot of the shield, thereby maximizing the resulting radial force on the armature (disk). When I started this project, my thinking was that an iron shield surrounding the coil with a single open slot around the ID, would 'redirect' and focus the field radially within the slot of the iron. This is the same methodology used with the University of Louisville's Foucault pendulum magnet, so I believe I'm on the right track with the shape of the iron.

I've also been trying to determine if a toroidal type of coil would be better than one wound into the diameter of the coil chamber in the iron (as the one you detailed). Intuitively this doesn't seem to work, but I did see a toroidal electromagnet on a site that was used as an magnetic bearing for an axle. I know that with a toroidal coil, the maximum field strength is within the coil, whereas a coil wound to the diameter of the chamber, the maximum field strength would be somewhere around the center of the coil which is the center of the iron ID. Of course without the iron, this field would be normal to the plane of the slot which is 90° to the direction of field/force that I need. I've looked up methods to calculate fields outside a coil (Biot -Savart for one), but I have been unable to find analysis methods for approximating shielding to redirect fields . I know it can be modeled in magnetostatics software, but is there a simple way to approximate it?

BTW, the lowest carbon content iron I could find in the size I need is actually steel SAE1018 with 0.15% carbon...although this isn't the best, I'm hoping it has enough high susceptibility and low retentivity for my application.

Thanks again!

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Tim in NY said:
This is the same methodology used with the University of Louisville's Foucault pendulum magnet, so I believe I'm on the right track with the shape of the iron.
We had a Foucault pendulum at a University where I worked in the Geophysics Electronics Lab. It used a completely different magnet system. A university does not often build an optimum solution. The design is usually done by an academic without experience, or as an exercise by a student. The fact that it was the first one that actually worked is the reason that it is still there and has not been changed since. Optimum design is only needed for mass production.
See yet another example here; https://www.physics.uoguelph.ca/foucault/F14.html

Tim in NY said:
I know it can be modeled in magnetostatics software, but is there a simple way to approximate it?
Design of the magnetic circuit is difficult because the disk only intrudes into part of the internal anular gap. So just make sure that the magnetic path has the same minimum wall thickness as the pole area, and is no where excessively thick which would slow down the magnetic transition. Like in your drawing, but replace the sharp corners with radius bends.

As I wrote earlier, your design is not yet optimum, you will have to stop procrastinating and build the prototype. If it fails, modify it to make it work. If it works, expect to replace it with an engineered solution later, optimised for the quantity that will be built.

## 1. How does an electromagnet work?

An electromagnet works by using electricity to create a magnetic field. When an electric current flows through a wire, it creates a magnetic field around the wire. By coiling the wire and increasing the current, the magnetic field becomes stronger.

## 2. How do you design an electromagnet to look like a donut?

To design an electromagnet in the shape of a donut, you will need to use a toroidal (donut-shaped) core. The core can be made of iron or another ferromagnetic material. Then, you will need to wrap the core with an insulated wire, creating multiple layers. The more layers you have, the stronger the magnetic field will be.

## 3. What materials do I need to create a donut electromagnet?

You will need a toroidal core, an insulated wire, a power source, and a switch. The core can be made of iron, steel, or other ferromagnetic materials. The wire should be insulated to prevent short circuits. The power source can be a battery or a power supply, and the switch will allow you to turn the electromagnet on and off.

## 4. How do you control the strength of the donut electromagnet?

The strength of the donut electromagnet can be controlled by adjusting the number of wire turns, the amount of current flowing through the wire, and the type of core material. Increasing the number of turns or the current will make the magnetic field stronger, while using a different core material may also affect the strength of the magnet.

## 5. What are the practical applications of a donut electromagnet?

A donut electromagnet has various practical applications, such as in electric motors, generators, and MRI machines. It can also be used in magnetic levitation trains, speakers, and particle accelerators. Additionally, donut electromagnets are commonly used in experiments and demonstrations to study the properties of magnetism and electricity.

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