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Step 7Magnet Layout and 2D Design
What were we talking about? Oh, yeah, hub motors. With a preliminary electrical specification for your motor, you can now proceed onto the early stages of mechanical work.
By now, you should have stator dimensions available to you. The goal of magnet rotor layout is to size 14 magnet poles to fit around the stator until you have enough information to spec out or purchase magnets.
The process is constrained bidirectionally. The minimum diameter of your circle of magnets clearly has to be larger than the stator. However, you may find yourself additionally constrained if you have already picked a wheel. Then, the maximum inner diameter you can use on your wheel & tire becomes the other mechanical constraint: your magnet circle's outer diameter plus a certain can thickness is limited by the wheel.
Using online tools
It used to be that you had to whip out a calculator and a pencil and hash out some serious trigonometry to lay out the magnets, or use a 2D computer aided design program... or, if you have machine shop access, just making the motor can bigger until it fits. Below is an image of my initial layout for Razer's motor in Autodesk Inventor's sketch environment.
Rotor design tools have now emerged on the Intergoogles. The most prominent of these is the GoBrushless rotor calculator, which conveniently packages all the layout into a form. Heck, it even draws what your rotor will look like. Let's go over what the terms on the page mean. All dimensions are millimeters:
Stator Diameter: The maximum outer diameter of your stator.
Rotor Diameter: The minimum INNER diameter of your rotor
Magnet Width: Assuming square magnets, how wide your magnet is.
Magnet Thickness: How thick your magnet is. A magnet you would select for your motor is almost always going to be magnetized through its thickness.
Magnet Poles: How many magnets there are in total. There are going to be a multiple of 14.
The Air Gap (Updated 28 March 2012 to include air gap factor for the magnets)
The one thing I left out of the above list is Air gap, because the subject warrants its own discussion.
The tightness of your air gap determines how much of the magnetic field is linked to your stator. The E&M term is coupling. A tighter airgap yields better coupling between magnet and stator. You know why the B rating of the magnet is called remnance? Because that's how much field remains at its surface if the magnet is in open air, with no magnetic materials to surround itself.
A motor is a magnetic circuit, and there are a whole set of laws that govern them. For practical purposes, it boils down to the more coupling you can ensure in your magnetic circuit, the stronger the field in your airgap. The "Gap Factor" equation is:
Ba = B0 * (t / (t + g))
where t is the thickness of the magnet, g is the radial thickness of the airgap, and Ba is the flux density at the surface of your stator. This is the flux that will actually generate torque, so really it is the value that should be used in the NIBLR equation! B0 is the surface remnance rating of your magnets - for high N grades like N48 and N50, this could be as high as 1.3 to 1.4. But if your airgap is loose, or the thickness of the magnet is small compared to the gap, then you will lose a substantial fraction of it before the stator radius.
For example, if you have type N42, 3mm magnets but a 1mm airgap, the multiplier is 0.75! That means the B value you thought was close to 1 (since N42 magnets have roughly 1 Tesla of remnance) is more like 0.75. This can really throw your motor design and make it clock high speeds (thus less torque) than you expected.
Now you see why you can't just glean the first torque equation off the intro page and be done. The updated torque equation is:
T = 4 * m * N * B0 * (t / t + g) * L * R.
So, the tighter the airgap the better - to a limit, as with everything. If you are running tenths of millimeter airgaps, you had better be well-versed in machining, or have a computer controlled machine do it for you. Wobble in your can from machining tolerances and irregularities can throw off your airgap measure and could cause your magnets to collide with your stator!
I try to shoot for an airgap of 0.5mm or thereabouts. 0.4, 0.6, whatever. The wide the airgap, the more "fiddle space" I have if something turns out to not fit correctly.
Magnet fill percentage
This describes the fraction of the rotor circumference on the inside of the magnet ring that is occupied by the magnets. This number should be somewhere between 75% and 95%, generally. Square magnets can never achieve 100% fill unless you are truly lucky. Numbers below 75% will hurt torque and efficiency because the B-field in the airgap becomes irregular.
Oddly enough, very high fill percentages actually have a slightly negative effect towards motor performance, because the magnets become so close together they "leak" to eachother. The effect is minimally noticeable for low speed hub motors, however.
While fill percentage isn't calculated on the GoBrushless rotor designer, you can easily calculate it by
Fill = (14 * k * Magnet Width) / (pi * Rotor Diameter) using consistent units, like millimeters.
Metamagnets
What's that k I stuck in the equation there? Another random constant to keep track of? AAAAHHH
Not really. Let's say you can't get good fill and an acceptable airgap number using single-piece square magnets, and you can't change the rotor diameter.
It is allowed to use two smaller magnets side-by-side to emulate a single large magnet. This also has the advantage of better conformity to the round walls of the rotor. Smaller magnets are a better approximation to the game of squaring the circle. The less your airgap deviates from the average, the less torque ripple your motor will exhibit.
Hence my reference to multiples of 14 earlier. GoBrushless' rotor designer will space all the magnets out evenly, but as long as they fit evenly, there is no reason you can't group them into larger metamagnets, as seen in Figure 3 below.
In the extreme case of RazEr, I used four mini magnets to make one magnet pole. Two side by side, and two rows deep. The fill factor was incredibly close to 100%!
That brings me to...
Magnet Length
Up until this point, your design has been exclusively 2D. Once you get the profile of the magnets right, you need to make sure they are available in the correct length.
The magnet length can be fudged a little. Optimally, the magnet length is equal to the stator length (L). That is because the steel in the stator is what focuses the magnetic field generated by the motor windings into the magnets. Shorter magnets will result in suboptimal performance - try to avoid this, because part of the stator field will be essentially shooting off into empty space.
It is also not advisable to spec out magnets which are too much longer than the stator. This causes interaction with the end turns of your windings, which is undesirable. A small amount longer, such as the next millimeter or two up in order to achieve a stock magnet size, is fully acceptable.
In RazEr's motor, I had a 35mm wide stator, but no 35mm magnets. I thus spec'd out for twin 20mm magnet stacks, which brought the magnet width to 40mm. I decided to live with the "stickout", so to speak.
Rotor Thickness
One of the constraints you will face is the OD of the rotor. In the best possible situation, the ID is set by the magnets and you have free reign over the outside. However, if you already have your prospective wheel and tire picked out, you might face limits here.
This is problematic because you cannot make the rotor can too thin in the walls. Not only does structural strength suffer, but the magnetic field of your permanent magnets won't be properly contained. If it leaks out, then the airgap field strength B will suffer, because what goes out of the motor doesn't come back in, so to speak.
The rule of thumb is to make can more than one half the magnet thickness. Going under this will cause quick flux containment loss. It does not hurt to go over - in fact, if your rotor is very thick, it can actually be part of the motor structure. Most commercial hub motors for bikes and large (road-legal) scooters and mopeds are made in this way. The only potential downside to a massive rotor is weight.
By now, you should have stator dimensions available to you. The goal of magnet rotor layout is to size 14 magnet poles to fit around the stator until you have enough information to spec out or purchase magnets.
The process is constrained bidirectionally. The minimum diameter of your circle of magnets clearly has to be larger than the stator. However, you may find yourself additionally constrained if you have already picked a wheel. Then, the maximum inner diameter you can use on your wheel & tire becomes the other mechanical constraint: your magnet circle's outer diameter plus a certain can thickness is limited by the wheel.
Using online tools
It used to be that you had to whip out a calculator and a pencil and hash out some serious trigonometry to lay out the magnets, or use a 2D computer aided design program... or, if you have machine shop access, just making the motor can bigger until it fits. Below is an image of my initial layout for Razer's motor in Autodesk Inventor's sketch environment.
Rotor design tools have now emerged on the Intergoogles. The most prominent of these is the GoBrushless rotor calculator, which conveniently packages all the layout into a form. Heck, it even draws what your rotor will look like. Let's go over what the terms on the page mean. All dimensions are millimeters:
Stator Diameter: The maximum outer diameter of your stator.
Rotor Diameter: The minimum INNER diameter of your rotor
Magnet Width: Assuming square magnets, how wide your magnet is.
Magnet Thickness: How thick your magnet is. A magnet you would select for your motor is almost always going to be magnetized through its thickness.
Magnet Poles: How many magnets there are in total. There are going to be a multiple of 14.
The Air Gap (Updated 28 March 2012 to include air gap factor for the magnets)
The one thing I left out of the above list is Air gap, because the subject warrants its own discussion.
The tightness of your air gap determines how much of the magnetic field is linked to your stator. The E&M term is coupling. A tighter airgap yields better coupling between magnet and stator. You know why the B rating of the magnet is called remnance? Because that's how much field remains at its surface if the magnet is in open air, with no magnetic materials to surround itself.
A motor is a magnetic circuit, and there are a whole set of laws that govern them. For practical purposes, it boils down to the more coupling you can ensure in your magnetic circuit, the stronger the field in your airgap. The "Gap Factor" equation is:
Ba = B0 * (t / (t + g))
where t is the thickness of the magnet, g is the radial thickness of the airgap, and Ba is the flux density at the surface of your stator. This is the flux that will actually generate torque, so really it is the value that should be used in the NIBLR equation! B0 is the surface remnance rating of your magnets - for high N grades like N48 and N50, this could be as high as 1.3 to 1.4. But if your airgap is loose, or the thickness of the magnet is small compared to the gap, then you will lose a substantial fraction of it before the stator radius.
For example, if you have type N42, 3mm magnets but a 1mm airgap, the multiplier is 0.75! That means the B value you thought was close to 1 (since N42 magnets have roughly 1 Tesla of remnance) is more like 0.75. This can really throw your motor design and make it clock high speeds (thus less torque) than you expected.
Now you see why you can't just glean the first torque equation off the intro page and be done. The updated torque equation is:
T = 4 * m * N * B0 * (t / t + g) * L * R.
So, the tighter the airgap the better - to a limit, as with everything. If you are running tenths of millimeter airgaps, you had better be well-versed in machining, or have a computer controlled machine do it for you. Wobble in your can from machining tolerances and irregularities can throw off your airgap measure and could cause your magnets to collide with your stator!
I try to shoot for an airgap of 0.5mm or thereabouts. 0.4, 0.6, whatever. The wide the airgap, the more "fiddle space" I have if something turns out to not fit correctly.
Magnet fill percentage
This describes the fraction of the rotor circumference on the inside of the magnet ring that is occupied by the magnets. This number should be somewhere between 75% and 95%, generally. Square magnets can never achieve 100% fill unless you are truly lucky. Numbers below 75% will hurt torque and efficiency because the B-field in the airgap becomes irregular.
Oddly enough, very high fill percentages actually have a slightly negative effect towards motor performance, because the magnets become so close together they "leak" to eachother. The effect is minimally noticeable for low speed hub motors, however.
While fill percentage isn't calculated on the GoBrushless rotor designer, you can easily calculate it by
Fill = (14 * k * Magnet Width) / (pi * Rotor Diameter) using consistent units, like millimeters.
Metamagnets
What's that k I stuck in the equation there? Another random constant to keep track of? AAAAHHH
Not really. Let's say you can't get good fill and an acceptable airgap number using single-piece square magnets, and you can't change the rotor diameter.
It is allowed to use two smaller magnets side-by-side to emulate a single large magnet. This also has the advantage of better conformity to the round walls of the rotor. Smaller magnets are a better approximation to the game of squaring the circle. The less your airgap deviates from the average, the less torque ripple your motor will exhibit.
Hence my reference to multiples of 14 earlier. GoBrushless' rotor designer will space all the magnets out evenly, but as long as they fit evenly, there is no reason you can't group them into larger metamagnets, as seen in Figure 3 below.
In the extreme case of RazEr, I used four mini magnets to make one magnet pole. Two side by side, and two rows deep. The fill factor was incredibly close to 100%!
That brings me to...
Magnet Length
Up until this point, your design has been exclusively 2D. Once you get the profile of the magnets right, you need to make sure they are available in the correct length.
The magnet length can be fudged a little. Optimally, the magnet length is equal to the stator length (L). That is because the steel in the stator is what focuses the magnetic field generated by the motor windings into the magnets. Shorter magnets will result in suboptimal performance - try to avoid this, because part of the stator field will be essentially shooting off into empty space.
It is also not advisable to spec out magnets which are too much longer than the stator. This causes interaction with the end turns of your windings, which is undesirable. A small amount longer, such as the next millimeter or two up in order to achieve a stock magnet size, is fully acceptable.
In RazEr's motor, I had a 35mm wide stator, but no 35mm magnets. I thus spec'd out for twin 20mm magnet stacks, which brought the magnet width to 40mm. I decided to live with the "stickout", so to speak.
Rotor Thickness
One of the constraints you will face is the OD of the rotor. In the best possible situation, the ID is set by the magnets and you have free reign over the outside. However, if you already have your prospective wheel and tire picked out, you might face limits here.
This is problematic because you cannot make the rotor can too thin in the walls. Not only does structural strength suffer, but the magnetic field of your permanent magnets won't be properly contained. If it leaks out, then the airgap field strength B will suffer, because what goes out of the motor doesn't come back in, so to speak.
The rule of thumb is to make can more than one half the magnet thickness. Going under this will cause quick flux containment loss. It does not hurt to go over - in fact, if your rotor is very thick, it can actually be part of the motor structure. Most commercial hub motors for bikes and large (road-legal) scooters and mopeds are made in this way. The only potential downside to a massive rotor is weight.
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I think 29mm is too much but why 29mm I found several Magnets with a length of 20mm:
http://www.supermagnetman.net/index.php?cPath=37&page=3