## Friday, November 23, 2018

### Why you don't see tape wound foil conductors used on electric motors

2019 update: Induced eddy currents also contribute significant losses to tape wound motors. This argument has now also been added.

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Most electric motors are wound using circular conductors. Some motors are wound using square or rectangular shaped conductors. However, I have never seen a motor with conductors that have a flat, tape-like cross section made from thin foils which are then wound onto a tooth like a roll of sticky tape.

 A comparison of the different winding topologies on a stator (black)
That was until this blog post by Shane Colton come to my attention.

This raised a question: Why is it that this style of winding is not used for electric motors?

The short answer: If you wind a thick (i.e. mm) tape wound conductor then you will likely see very large induced eddy current losses in your conductors due to the changing flux they are exposed to. If you use very thin tape wound conductors (i.e. < 0.1 mm thickness) then your copper fill factor will be very poor and you would be better off using a more typical stranded conductor.

### Potential benefits for using a tape wound foil conductor

First, why use this style of conductors? The benefits may include:
1. A high copper fill factor. Perfectly stacked round conductors will have a maximum fill factor of ~0.9. Tape wound conductors may improve on this. (This turns out to not be true in most cases)
2. Ease of winding. A single wide tape may be easier to stack than many small conductors.
3. High conductor cross section while maintaining a small minimum bend radius. For an equal conductor area, a flat foil will have a much smaller minimum bend radius than a round conductor.
4. Improved conductor utilisation at high frequency. Due to the skin effect, the centre of a round conductor will carry little current when operating at high electrical frequencies.
5. The possibility of improved cooling capacity. The large uniform area of a tape wound conductor may prevent hot spot formation and facilitate better heat conduction to the surface of a winding stack when compared to round wires.

### Potential negative consequences for using a tape wound foil conductor

Potential drawbacks to this style of conductors include:
1. Difficulty in winding a tape wound foil conductor due to the surrounding stator teeth getting in the way.
2. Stray flux crossing the conductor at right angles (normal to the flat surface of the foil) may significantly increase eddy current losses in a motor.
3. A high aspect ratio may mean that the electrical insulation occupies a significant fraction of the available area, reducing the copper fill factor.
4. Due to the proximity effect and the difference in inductance seen by different parts of a tape wound conductor embedded in the slot of a motor, a larger AC current will tend to flow in the region of a conductor closer to the top of a stator slot than the bottom. This will cause a larger than expected AC resistance. See chapter 3.6.7.4 of this book for further details.
Let's look at each of these drawbacks one by one:

### 1. Difficulty in winding around stator teeth

For small radial flux motors, it may be difficult to automate the winding process. However, segmented radial flux motors or yokeless and segmented armature (YASA) axial flux motors, such as those made by Magnax, Emrax and Yasa, and used by Shane in his blog post, are becoming increasingly common.

 A YASA motor with segmented stator teeth.
A YASA axial flux motor has a stator constructed from individual core sections which can each be wound separately before final assembly of the motor. These motors could, therefore, be easily wound with a tape-style conductor.

 Stator segments wound and ready for assembly of a Magnax motor
Therefore for segmented core motors winding a tape wound foil should pose no problem.

### 2. Induced eddy current losses

Let's consider the worst-case scenario. Below is a 2D FEMM simulation of an open-ended 30 mm diameter, 80 mm long mild steel rod with 10 turns of conductors added to one end with a current of 6A. Side note: Drawing lines in FEMM is a pain. I recommend using a dedicated CAD program like F360 and then just exporting your model as a DXF and importing that into FEMM

It's quite clear that a large portion of the flux is crossing the windings placed at one end and so it would be expected that a foil conductor would have large induced eddy currents. To test if this is really a problem when operating at electrical typical electrical frequencies you would find in an electric motor I wound two rods with the same dimensions as mentioned above. One with round conductors and one with a foil conductor. The foil was cur to a width such that its CSA was the same as the round conductor and both had ten turns applied.

Using an AC BH tracer I thin applied a 1 kHz and 10 kHz sinusoidal current to the windings. The result:
 AC BH loops
It's clear that at 1 kHz there is little difference in the shape of the BH loop while at 10 kHz they are quite distinct. This indicates that even under this worst-case scenario a 10 kHz frequency, which is well above the typical electrical frequency used by electric motors, is required to produce significant eddy currents in the foil conductors.

This suggests that for an electric motor, which will likely operate at a lower frequency and has less stray flux than this example, will not suffer from significant eddy currents in the conductors.

For a real BLDC electric motor, the flux crossing the conductors due to the relative movement of the magnets on the rotor must also be considered. This flux can be considerably larger than that induced by the stator windings alone. You can use this sheet to estimate the expected eddy current losses in a tape wound conductor. To edit the sheet just make a copy using the 'file -> make a copy' option.

### 3. Copper fill factor

It is desirable to have as high a copper fill factor as possible when constructing an electric motor so as to reduce the current density in the conductors so as to minimise I^2R losses. The copper fill factor is impacted by:
• The stacking factor ( P_{d}): How efficiently a conductor is arranged in the slot.
• The copper to insulation area ratio: A thick layer of insulation gives a low area ratio and a low fill factor.
As previously mentioned, round conductors have a fundamental stacking factor limit of ~0.9. Square and tape conductors can have a theoretical 100% stacking factor.

I imagine that it is this desire for a high stacking factor without the need to purchase expensive square conductors that convinced Shane to use tape wound conductors.

Even though square and tape wound conductors can have a theoretical 100% fill factor, the copper fill factor (ratio of copper to total area) can never be 100% due to the need for an insulation layer in-between each winding. The thicker this insulation layer, the lower the copper (Cu) fill factor. Therefore the copper stacking factor is given by:

Cu fill factor =\frac{CSA_{Cu}}{(CSA_{Cu}+CSA_{Ins})}\times Stacking factor

According to this site, a typical 24 gauge magnet wire has an insulation layer thickness of ~0.025 mm. For Shane's motor, he used a single polyimide (Kapton) tape, which has a typical thickness of 0.03mm, to insulate just one side of his copper foil.

Using this information I have estimated the copper fill factor when winding a conductor with a cross sectional area of 13.1 mm^2 which is 2.54 mm wide, like that used by Shane's design. The spreadsheet can be found here.

Here are the results:
• Round conductor: 88.5 % Copper fill factor
• Square conductor: 97.3 % Copper fill factor
• Tape conductor: 94.5 % Copper fill factor
This is quite a respectable copper fill factor and would only be superseded by the use of square conductors. Shane is therefore justified in his choice of a tape wound conductor.

However, one thing to note here is that the currents used by Shane's motor are unusually high, and his winding turn number is quite low. You will more typically encounter motors that have dozens to hundreds of turns and that operate at well less than 50 A. In this situation, a tape wound conductor may make less sense.

 A more typical motor that operates at < 50A with many turns per tooth

For example, if you wound a small motor with a tape conductor that has a cross-section equal to a 24 gauge conductor (0.5 mm diameter, 0.205mm^2) onto a 10 mm stator tooth your fill factor is as follows:
• Round conductor: 75 % Copper fill factor
• Square conductor: 80.8 % Copper fill factor
• Tape conductor: 40.6 % Copper fill factor
All of the fill factors listed above are relatively low since the insulation layer is fixed while the motor size is reduced. The tape fill factor is also unacceptably small since the area per turn of the insulating Kapton layer at ~0.1 mm^2 is now comparable to that of the copper foil itself at 0.2 mm^2.

To really drive this point home lets consider the copper fill factor of Shane's motor if he were to use lower currents and a higher number of turns, and therefore smaller cross section conductors.

If you were to halve the peak current of Shane's motor while maintaining the same current density (i.e. also halve the copper cross section) then it no longer makes sense to use a tape wound conductor. At this point, you are probably better off purchasing flat magnet wire or just sticking with round wire.

User Kindiana over on the Odrive Robotics discord channel also pointed out that motor manufacturers are even less likely to be interested in tape wound conductors for the following reasons:
• The extra weight and cost of copper is likely not worth the efficiency improvements at low torque for RC applications and is likely also why they don't stack windings closer together.
• The tooling for machine winding foil may be far more complicated for a one piece stator compared to round wires or bundles of round wires.
• There may be no readily available source of pre-insulated copper foils with custom dimensions, so manufacturers may need to do their own insulation.

## Conclusion

At first glance, a tape wound conductor may appear as an attractive means to increase your electric motors copper fill factor without the need for expensive square conductors. However, when you look at the numbers more closely it becomes apparent that the high aspect ratio of a tape wound conductor will likely result in a worse fill factor for most applications. Furthermore, when a tape wound conductor is made quite thick then you will likely encounter considerable induced eddy currents in the conductor itself. Therefore careful consideration is required before you decide on a conductor geometry for your electric motor.

Equations were produced in this post with the help of arachnoid.com. If you have noticed any errors in the above article then please let me know.