Fly Electric!

Winding Density

One of the objectives in winding brushless motors is to make the windings as dense as possible. Put another way, you want as much copper around the teeth as possible. This allows you to improve power and efficiency.

I discuss two main themes in describing how to achieve this. The first is whether to use one thick strand or a number of thinner strands. Provided the strand is not too difficult to bend around the stator, my findings are that you will almost always achieve the greatest density with a single strand. Its also usually quicker & easier to wind. There may be circumstances where multiple thinner strands are better but you will usually only use multiple thinner strands where a single thick strand is too difficult to wind and you accept slightly lower efficiency.

The other theme presented is to do with technique and here is what I recommend:
1.1 Concentrate hard and be very NEAT
1.2 Try to wind strands so that they lie in the hollows between other strands (of the previous layer)
1.3 Avoid crossing over strands as much as possible
1.4 Use new wire and make sure it does not get kinks in it
1.5 Flatten strands between the teeth after each layer
1.6 'Overflow' onto the heads to gain an extra turn or two (as shown on my CDRom page)
1.7 Check for shorts between each phase and the stator before running the motor.


These 'rules' apply mainly to the sections between teeth of the stator. However, note that the gap between the stator and rotor is small on many motors so you may need to keep the 'inside' head neat as well.

This somewhat lengthy page now explains the reasons for the views expressed above and provides more practical advice. Please let me know if you have any comments or better techniques. I have some comments on Star vs Delta at the bottom of the page. Other pages relating to motors are as follows:

* Summary page (small and large motors)
* CD-Rom motors (easy construction) and Crocodile motors (high efficiency)
* Machining tips (more advanced advice)



First some important questions:

Why is winding density important?

Our motors have permament and electro-magnets which use attraction and repulsion to create motion. The electro-magnet is created by the copper wound around the teeth of the stators. The more 'winding' there is, the stronger is the electro-magnet and therefore the motor.

How does winding density affect efficiency?

All wire has resistance which impedes the flow of electrons. The thicker the wire, the bigger the 'pipe' and smaller the resistance. This has to be good.

As a result of the smaller resistance, there will be a smaller voltage drop across the windings. The motor will therefore 'see' a higher voltage which means the RPM will increase (speed is always proportional to the voltage). The greater the RPM, the better the performance.

Ohms Law dictates that for a fixed resistance, that current will rise when voltage rises. This means that a side effect of increasing the thickness of the wire will be that the current will also increase. Bundle all this together and the thicker wire has yielded a more powerful motor.

You may have been seeking greater efficiency rather than more power. You can either achieve this by flying at a lower throttle setting (remember you have more revs now) or by increasing the number of turns. Increasing the number of turns will reduce RPM and increase torque. If you reduced RPM back to what it was (with thinner wire) you would now have a motor which achieves the same RPM but with more torque. More torque makes it is easier for the motor to turn the prop which will manifest itself as lower current. Voila!

And now onto the mystries of achieving this...



'Square' patterns

Round wires take up the area of a square if laid 'on top' of each other in a rectangular pattern (ie: if they are not wound into the hollows formed by the previous layer). For a 1mm wire the area of the imaginary square is 1 mm2 and the area of the wire is 0.786 mm2. The unfilled portion is therefore 0.214 mm2 (ie: 21.4%).

Regardless of the thickness of the wire the percentage of the unfilled space using this pattern remains the same. A 0.5mm wire has an area of 0.196 mm2. Four would be needed to fill the same space as one 1mm wire. 4 x 0.196 = 0.786 - the same as one 1mm wire.



'Honeycomb' patterns

When layers of a winding are offset in a honeycomb or diamond pattern, the 'last' wire wound will typically lie in the hollow between two wires in the previous layer. If you continue to imagine that each wire has a square box around it, there will be four overlapping 'corners' for each new winding (a corner from each of the bottom wires and two corners from the top wire). Again using the 1mm example, the area of wire now filling a corner which would otherwise have been empty is about 0.0313 mm2. Four overlapping corners will therefore recover 0.125 mm2 of empty space. This has the potential to halve the loss in the 'square' winding pattern (irrespective of whether the strands are thick or thin).



'Spiral' effects

A tooth of a stator is normally rectangular in shape. Each turn will therefore have four 'legs'. The first leg of the first turn is likely to start perpendicular / 90 degrees to the tooth (eg: going downwards on the far side of the tooth). The second leg will come back towards you, again at 90' to the tooth. The third and fourth legs will usually be at a bit of an angle so that they end up to the right of the first leg ready for the next turn. It takes two legs to achieve this offset because the top of the tooth (4th leg) is usually too thin to achieve it on its own. To summarise, each full turn is part of a spiral and it is reasonable to expect (with one strand) two sides may be roughly at 90' to the tooth and the other two to both 'lean' slightly. You may be able to see what I mean in the following photo.



It is normal to wind successive layers in opposite directions. This creates spirals which lean in opposing directions. This means that every turn has to cross over another. These crossings effectively take the form of the 'square' winding described above (ie: large unfilled spaces). The 'square' sections are likely to comprise most of the two 'angled legs' described above (legs 3 and 4) and the goal will be to wind the other two in the 'honeycomb' fashion to reduce unfilled gaps. Using this approach the best one can hope to achieve is therefore about 50% of the optimum.

'Same direction' winding

An alternative approach is to wind all the layers in the same direction. The advantage is that most strands will be wound in the honeycomb pattern and achieve maximum density. However, it has some serious disadvantages which limit it effectiveness. Here are two approaches:

1. Return the wire back down the length of the tooth after every layer (along a dead head side). The next layer will be in the same direction as the first and go over the 'return leg' of the previous layer. Not only is this quite hard to do but it impairs performance. This is because magnet flux circles a wire. These forces will be down the length of the tooth for normal winds, but at right-angles for the return leg. Clearly this will disrupt the flow of flux and my tests have revealed that these inefficiencies outweight the benefits of improved density. Here is a motor with the first layer wound and ready for the second, and the finished article.



2. 'Sputnik': This approach is to wind each layer of each tooth with its own length of wire. This overcomes the main disadvantage above but has its own challenges:
* it's only practical when the number of turns required fills most of a single layer (ie: you need to select appropriate wire thicknesses to achieve this).
* the first layer is significantly shorter than the last which results in it having a lower resistance and carrying a higher portion of the current. This is bad for cooling and increases the risk of wire failure.
* the beginning and end of the winding around every tooth have to be soldered to the next tooth's winding. This is quite difficult and increases the risk of shorts. It also tends to increase the length of wire and together with all the joins makes the resistance similar to a more conventional less dense winding.
Some motors wound with this technique have yielded better results but others have been similar to simpler motors with thinner wire. They take two to four times longer to wind and I'm not convinced its worth the hastle.



Winding against 'flats'

The first layer is wound against the flat sides of the stator tooth so unfilled sections are inevitable. One unfilled corner of our imaginary 1mm square is 0.0536 mm2 (0.214/4) and 0.0134 mm2 for a 0.5mm wire. A tooth 8mm long which is wound with 8 strands of 1mm wire would therefore have 0.857 mm2 of unfilled space against the tooth (0.0536 x 8 strands x 2 corners each). 16 strands of 0.5mm wire would also cover the first layer fully and would have only 0.429 mm2 of unfilled space against the tooth (0.0134 x 16 x 2). By halving the wire diameter we have reduced the losses against the flat side by a half. This is consistent the principles described under 'square pattern' winding and thinner wire creates an opportunity for improvement which would be nice to try to exploit.

Battle of the Bulge!

The teeth of a stator are rectangular and wire wound around them tends to take an oval shape. Tests have shown that the thicker the stator, the greater the effect. This explains why I can only fit 24 strands onto a stator which will 'take' 35 when drawn perfectly in a CAD program. The solution is to flatten the wires between each tooth with a non-abbrasive tool such as a wooden wedge or (carefully) with the side of a penknife. Here are some photos to demonstrate the 'bow' effect. The third photo reveals the extent of the 'bow' because you can see how the corners are deformed at an 'angle'.



Thick vs Thin wire

I have demonstrated so far:
(i) that 'honeycomb' type winding can halve the unfilled area compared to 'square';
(ii) that unless you follow the 'same direction' winding approach you are unlikely to achieve much better than a 50:50 mix;
(iii) that thinner wires reduces unfilled spaces against flat surfaces;
(iv) that the winding takes the shape of an oval and wastes considerable space.
I will now describe some benefits of thinner wire.

It is clearly easier to get thin wires into little nooks and crannies than thick wires. Gaps between stator teeth are usually wedge-shaped. This means that there will be some small gaps where only thinner wires will fit. It difficult to predict the 'perfect' wire thickness to exactly fill the opening so again, thin wires will be an advantage over thick.

There is benefit in using the honeycomb pattern but it does mean that there might be gaps at each end of each layer (because the wires overlap by 50%). Once again thinner wires are better than thick because there these gaps will be smaller and with the wedge shape between the teeth there is more opportunity to fill some of them.

A theoretical motor

To demonstrate that thin wire should be better than thick, 15 x 1mm strands completely fill a 8 x 1.86mm rectangle in a honeycomb pattern (8 wires on the base and 7 on top). The total area of wire is 11.79 mm2 (0.786 x 15).



If you halve the diameter of the wire to 0.5mm you should get four times the number of strands which you do. However, in reality you can fit 2 more strands, 62 in total. The filled area becomes 12.17 mm2 which is a 3% improvement in filled volume due to the extra 2 strands. This is using a 50/50 honeycomb/square pattern.



If you halve the diameter again to 0.25mm the quantity should increase fourfold to 248 strands. In reality you can fit another 8 strands, 256 in total (again 50/50 honeycomb/square). The filled area increases to 12.57 mm2 (another 3% denser than the 0.5mm wire). Clearly, the smaller the wire, the greater the density (so far...).



Multiple strands

I have demonstrated that thinner strands of wire have some potential to be denser than fewer thick wires. However, a major issue with winding multiple strands together, even just two, is that the spiral around the tooth is likely to become even and continuous (instead of having one or two legs perpendicular to the tooth). This means that when you return to make subsequent layers in the opposite direction, most of them will lie on top of the previous layer ('square' pattern) and not many will lie in the hollows ('honeycomb'). As indicated right in the beginning, whether you use thick or thin wire in the square pattern, both produce the same density.

Another problem with multiple strands is that they can become twisted. You can prevent this with two, three or perhaps even four strands by pre-winding them onto a dowel neatly and then winding from there onto the stator. However, as the number of strands increase, it become impractical to wind each strand neatly side by side. You have more problems when you reach the end of the tooth and need to get the spiral to change direction back the other way. The first two photos below show three 0.375mm strands are being wound together.



What is likely to happen when many strands are wound is they 'bunch' up and spread out in a random fashion. Clearly this will result in no better than a 'square' pattern and quite probably worse. You may be able to see this from the third photo above where many 0.375mm strands are being wound in a 'bunch'.

Going back to my theoretical motor, sixteen 0.25mm strands have the same cross-section as one 1mm wire. If bunching them produces a 'square' pattern, you will only fit 217 strands into the imaginary 8 x 1.86mm rectangle. This is just a 10.66 mm2 coverage which is almost 10% worse than the 1mm honeycomb and more than 12% worse than the 0.5mm example.



So, I think I have demonstrated that thinner wire has some advantages but only if we can find the technique to exploit it. It is likely to result in a worse density in most other situations. Windings done with the 'same direction' approach helps improve density with thick and thin wire but this approach too has negative implications.

Flat wire

Part of the challenge we face is because wire is round. By squashing some wire between a disc and my lathe's face plate I have been able to make some 'flat' wire. I had high expectations but found that because it is wider than round wire, the 'spiral effect' is greater and it wastes space at each end of the tooth. It also tries to stand up on its narrow end on subsequent layers, and this together with its propensity to twist results in no discenable advantange over round wire.



Tests

There is benefit in increasing winding density. This is evident in the chart that follows. For example, going from 0.375mm wire to 0.45mm with the same number of turns reduced current by 13% with little effect on RPM. However, it is worth noting that the benefits diminish as you approach the maximum density (eg: only 3.8 and 5.1% improvement on some other tests). For more info take a look at this thread: Ezone



Conclusion

Multiple strands of thinner wire may have some advantages over fewer thicker strands on some motors. However you are likely to struggle to achieve these benefits. Even where you do they are likely to be smaller than you might be seeking and may result in inner strands being overworked on high power motors. So, use one thicker strand and seek improvements in density from the various techniques described. Other pages related to motors are as follows:

* Summary page (small and large motors)
* CD-Rom motors (easy construction)
* Machining tips (more advanced advice)

Delta vs Star This seems to be the subject of huge debate. Technically, the main concern appears to be that there can be recirculating currents flowing through the delta circuit which leads to higher temperature and lower efficiency. However, these are said to be hardly measureable in 7-10" OD motors and can be ignored in our small outrunners.

The conversion factor between the two is 1.732 (10 turns star = 17.32 turns delta and visa versa). I use both to fine-tune the number of turns and winding style. For instance, on a CDRom motor with 23 turns star this is much easier to wind than 40 turns delta. However, on a Croc motor which has very few turns, 6 turns delta can be easier to wind than 3 or 4 star because you can use thinner wire. Also, 3 star may be too 'hot' and 4 star may be too mild.



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