Make Your Own Miniature Electric Hub Motor
14 Steps

## Step 3: The Brushless DC Motor and You

So how does

T = 4 * m * N * B * L * R * i , otherwise known as T = Km * i

affect your motor design, and why am I viciously pounding on torque so much? Because torque is ultimately what hauls you around, and is one of the components of mechanical power Pm. Once you determine roughly how much mechanical power you will need, you can size wires and components appropriately.

Notice some key characteristics of the equation and how they affect motor performance:

� Torque increases with number of turns N
� ...and radius of the stator R
� ...and strength of the magnetic field B
� ...
and length of the stator L
� ...and winding current i.

What we observe here is that to a degree, you can linear scale motor characteristics to estimate the performance of another motor.

This is "R/C Hobby Industry Hand Wave" number one. The concept of turns and motor sizes.

A 100mm diameter motor will, all else being equal, produce twice as much torque as a 50mm diameter motor.

A motor with 1.2T permanent magnetic field will likely be 20% more torquey than a 1T motor. And so on.

This has its limits - you cannot reasonably assume that you can quintuple your windings and get 5 times the torque - other magnetic characteristics of motors, such as saturation come into play. But, as will be shown, it is not unreasonable to extrapolate the performance of a 25 turn-per-stator-tooth motor from a 20 turn one, and such.

The LRK Winding

At the bottom of it all, what I am designing and making is a fractional-slot permanent magnet three phase motor. What the frunk does that mean? The fractional slot just means that (magnet pole pairs * phases) / (number of teeth on the stator) is not an integer. If you understood that, you know it more than I do.

A brief explanation is that the ratio of "number of stator teeth" to "number of magnet pairs" strongly affects the physical characteristics of the motor. A "magnet pole pair" is defined as two magnets, one with the North pole facing radially inwards, the other with the N pole facing outwards.

This ratio, commonly called T : 2P (for teeth to 2 * total poles), affects the cogging of the motor, i.e. its smoothness.

Get a DC brush motor and twirl the shaft - there is a minimum amount of torque required to 'click' it over to the next stable position. This is cogging. It causes undesirable vibrations and high-order electrical system effects, and we don't like it.

A type of motor winding with T : 2P close to 1 (but not 1 exactly - that results in a motor which doesn't want to move) substantially reduces cogging (to near zero) and is the most popular "small BLDC motor" winding around. It is called the LRK winding, after Messrs. Lucas, Retzbach, and Kuhlfuss, who documented the use of this winding for model airplane builders in 2001. Not only does it offer low cogging, but also ease of winding and scalability.

Here are figures of the basic LRK winding and a variant called the DLRK (Distributed LRK).

The takeaway here is that using a stator with 12 teeth (or slots, the area between the teeth) and 14 magnets (that is, 7 pole pairs) will give you a pretty decent motor to start with and use in your fledgling motor engineering career.

The difference between the two winding styles is subtle. The distributed LRK winding has a smaller end-turn effect. An end turn is the wire that has to wrap around outside of the magnetic field in order to close the loop. It contributes no torque, but does have a resistance (all wires have nonzero resistance - we're not talking superconductors here). The dLRK avoids bunching the end turns up excessively, which results in a slightly more efficient motor. Slightly as in one or two percentage points - nothing to win a Nobel Prize over.

Below is a picture of Razer's motor core with a full dLRK winding.

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