# Trying to achieve at least 1 Tesla for a solenoid

1. Mar 4, 2009

### shotgunshogun

I am trying to produce a magnetic field with a flux density of 1 Tesla through a solenoid with an iron core and im having trouble crunching the numbers. I may also be doing the wrong computations. I am not too sure of the permeability of the iron core, i've seen different values, one being the permeability compared to air is 200 times greater ( someone can double check to verify). Im limited to the number of turns available. The length of the solenoid cannot exceed 5 cm and the gauge of wire is between 32-36. So theres a lmit on what the current going through the wires can be, otherwise a burn out. I believe these are the amp limits for each set of wire:

32 : 0.53 A
34 : 0.33 A
36 : 0.21 A

If anyone could suggest a possible configuration for this solenoid I would be glad to use. Also, if anyone sees something i can improve on to make this as small as possible, be my guest. This is planned to be incorperated into a compact DC brushless motor design, so other considerations can be taken into account ( such as copper loss or any other significant factors). Thanks a lot

2. Mar 4, 2009

### Nabeshin

Relative permeability of iron is around 200, yeah.

Umm, good luck getting up to 1T, though. The magnetic field strength is given by:
$$B=\mu_{0}kNI$$ where N is the turn density in turns/length. For I=.5A I get a coil density of 8000 turns per meter, or 400 turns in 5cm.

That's about gauge 32 wire, which can do 50 turns per cm, so your first layer of coiling would contain ~250 turns. So you'd have to do a second layer as well which (I think) in some way decreases the effect but shouldn't be that great.

However, this is all from a theoretical point of view, and there are a few complications:

First, your ferromagnetic constant isn't likely going to be 200, so you're probably going to get something significantly less than that.
Second, passing .5A of current through a 32 gauge wire is going to make it very very hot. This temperature increase increases the resistivity of the copper and may cause a problem in maintaining a .5A current (depending on what you have available for a power source).
Third, your magnetic field will drop off very quickly as you move away from the iron, so don't expect 1T measurements even under ideal circumstances anywhere but exactly at the iron core.
Fourth, depending on what type of iron you are using you might actually saturate it before you reach 1T. In this case, you're going to have a lower limit on the magnetic field you can possibly attain using that type of a core.

All in all, my experiences show it's quite difficult to get a homemade electromagnet up to 1T, especially if you want it to be so tiny. My advice for now is to use what you have and try to see what kind of a field you can get.

Cheers!

3. Mar 4, 2009

### Bob S

First, you need to plan the overall brushless motor design geometry. In cylindrical coordinates with z along the armature axis, the torque on the rotor requires forces along theta, so the relevant B fields and current conductors have to be along z and r, or vice versa (remember the Lorentz force law (F = I X B). Second, since this is a brushless motor, the rotor is a permanent magnet, and the "stator" is an AC magnet (commutated current). The current carrying conductors should be as close to the rotor as possible. Third, this motor will be either a sensor type (Hall effect) or sensorless design to commutate the curent. Fourth, the iron in the coil design has to be laminated to minimize eddy currents.

Last edited: Mar 4, 2009
4. Mar 4, 2009

### shotgunshogun

Bob S :
- I have planned out my geometry, It will be a 9 coil stator with a 12 magnet rotor.
- I also plan to use Hall sensors in my motor
- DO you think you can elaborate a little bit on the lamination and eddy currents, do you mean the iron will need a laminate coating?

Nabeshin:
- The magnetic field will decrease the wider the radius is around the iron core, but with this distance, I believe it would be minimal
- How significant do you think the decrease would be, and if so I would definatly look into considering other alternative cores to use ( possibly permalloy or some other cores with a higher permeability)
- I know temperature will be a significant issue and I'm trying to compensate for it in order to have a long lasting motor design, would you have suggestions on the gauge and possible amp value? ( i would perfer to exclude a cooling fan, but if it is neccesary, then so be it)
- I know about the air gap and reduction in tesla, so I would like to consider a tesla value of at least .5 at the face of the magnet of the rotor after air gap reduction
- I've looked up the saturation levels of iron alloy cores and such, and the saturation level is between 1.6 and 1.8 Tesla before reluctance increases rapidly, so Im not too worried ( source is Electric Motor and Drives: Fundamentals, Types, and Applications)

Thanks!

5. Mar 4, 2009

### Nabeshin

Which decrease are you talking about? I'm assuming a decrease in the relative permeability of the core, because you mention cores. After looking into it a little more some kind of "soft" iron should give you a high relative permeability and won't saturate anywhere near the levels you're looking at.

Well the higher gauge wire you use the higher the resistance and thus more temperature increase which leads to more resistance and can become a problem for the current. The higher gauge wire obviously the more compact you're going to be able to make your design though, but your amp limit will be lower, so I'd say the 32 or even 30 sounds like a good bet, if you can afford the space. It solves both the amp limit and temperature problems in one fell swoop.

I can crunch some more numbers to get a more realistic idea of what we're looking at if I knew how large the core is, so I knew how much wire is being used.

As far as the magnetic field decreasing with radius... I haven't bothered to calculate it but I'm not happy with just saying it's "minimal". I might work on this problem later but I don't feel like tackling it at the moment, so if anyone has an equation for this I'd appreciate it.

6. Mar 5, 2009

### shotgunshogun

The soft iron soulds good... I'll see what i can find. What I'll be doing today is actually drawing out the motor design using AutoCAD so ill post the basic design of the motor, and then I can adjust accordingly to what needs are to be met. Ill post dimensions.

$$\frac {\mu I\ }{2R}$$ Is the field at the center of a current Loop, and $$\mu\ = \mu_{o}\ k$$

I got this from hyperphysics, so there may be other equations there.

7. Mar 5, 2009

Staff Emeritus
Those are the current limits for chassis wiring, whose definition includes "not in a bundle" and "wiring in air", neither of which is true if it's coiled around a piece of iron.

8. Mar 5, 2009

### shotgunshogun

yea i wasn't too sure of which limit to use... so im gonna guess the limit is gonna be based on power transmission? If so then the new set of limits would be:

34 gauge: 0.056 A
32 gauge: 0.091 A
30 gauge: 0.142 A

Unless someone has another source for these numbers...

9. Mar 5, 2009

### Nabeshin

Those are really small... I don't think you'll be able to get 1T with only .15A of current, tops.

10. Mar 5, 2009

### shotgunshogun

Here are 2 diagrams

And dimensions:
Rotor
Outside Diameter: 3"
Inner Diameter: 2.25"
12 magnets embedded into Stator 0.125"
Stator Axle
Inner Diameter: .25" ;
2 Inner Diameter: .5"
Outer Diameter: 0.75"
Length: 2" ( to allgin with magnets)

Stator
length of Armature: 0.675" ( can be adjusted slightly if neccesary)
Thickness of plate at end of the Armature: 1 mm ( might need to correct)
core thickness: square crosssectional: (.2" x .2" )
Round Crosssectional ( radius .15")( not sure which core shape id want, most likey the round cross section

Magnets embedded into the Rotor ( l*w*h) : 2" x .5" x .125") N40 grade Neodymium magnets

I actually had an realization last night. Instead of trying to get 1 Tesla in one solenoid, I can always try to get a fracton of it and acheive it within 3 or 4 solenoids. So I think a third or a quarter of a Tesla is acheiveable depending on the core, gauge wire, amperes, and length. There is only one issue, I needed to reduce the length of the solenoid signifcantly. Instead of the original 5 cm, it needs to be at most 1.7 cm. I screwed up when i first posted the thread so im terribly sorry =/ I am eager to construct this motor, so im grateful for everyone contributing.

The one consideration I'm really gonna take into account is to change the core to a higher grade in order to compensate for both the size reduction as well as the current through the magnet wire. If anyone has some figures they can throw in, then by all means. I'm really interested in a type of material called permalloy, which has a much higher relative permability (8000). Ill be continuing research on the permalloy as well as anything else i may be able to do with the design, so I'll be updating.

Last edited: Mar 6, 2009