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Influence of Motor Winding End Turns On Torque

  1. Jun 14, 2015 #1
    What is the effect of motor winding end turns on torque for small DC brushless motors.? end 5.jpg end 3.jpg pancake.jpg
    Many state that end turns have no effect on torque and that the only influence is from the winding portion in the stator slots.

    My belief is that because the end turns on small brushless motors are still within the influence of the stator flux, they still play a role.

    Others use the Lorenz force on a rectangular conducting current loop to demonstrate that there is no net force on a conducting current loop from its end turns, only the outer ends of the loop, but fail to realize that force isn't torque. Torque requires a moment arm which in the case of brushless motors is equivalent to the end turn length. Since torque is proportional to the winding area which is equal to

    Area = slot length X slot width = slot length X end turn length

    this demonstrates that end turns are a factor in creating torque.

    From many sites, torque on a conducting loop in a constant magnetic field


    Torque = NIAB where N is the number of turns, I is the current, A is the Area, B is the magnetic flux.

    Since Area equals Stator Tooth Length X End Turn Length

    Torque = N X I X Stator Tooth Length X End Turn Length X B

    which clearly demonstrates that Torque is also dependent on the end turns and could contribute as much as the slot turns.

    Many disagree, but my feeling is that they have been conditioned to this because of the stacking of end turns on large industrial motors which have end turns outside the influence of the magnetic core flux unlike small brushless motors the end turns of which are still under the influence of the stator's flux.

    From a purely empirical approach, if the end turns are not involved, then motor efficiency would fall drastically if half the windings were not contributing. Many brushless motors have maximum efficiencies approaching 90% and if the end turns were not contributing, the I squared R losses would be very large.

    All DC brushless motors would be designed with extremely long stator teeth to minimize the percentage contribution made by end turns, yet pancake motors with 1:1 slot to end ratios can have extremely high efficiencies.

    My question is, who is correct, those who feel that stator end turns on these small motors do not contribute to motor torque or those who do?

    Attached Files:

    Last edited: Jun 14, 2015
  2. jcsd
  3. Jun 14, 2015 #2
    I'm not sure what you mean by "end turn". Initially I thought you meant the bits past the coils. Later you seemed to be referring to the sides of each turn. Anyway, it's not clear to me which you mean.

    I was under the impression the rotor was on the outside on these motors. As such shouldn't the torque be the vector cross product of the magnetic force and the radius? Thus any wire part that adds to the magnetic force would seem to be relevant. (Of course some parts might subtract as well...)

    The bits on the end seem to be partly in phase and partly out of phase in your picture. In other words, for each bit adding to a relevant core field, it seems to be adding to the core next to it (which likely is the opposite of what we want depending on the core/magnet aliasing). Thus I would guess they make no difference as they cancel.

    The ends of each turn add directly to the core flux and thus the torque.

    That's my opinion and I'm sticking to it -- until someone smarter comes along anyway.
  4. Jun 14, 2015 #3
    end turns.jpg
    Thanks for your response. The end turns are the portion of the windings that go around the end of the stator tooth. To my surprise, from an analysis of a rectangular loop using Lorentz force analysis there is apparently no contribution to torque from the wires at the end, only the wires in the slots.

    In many larger motors, the end turns are outside the magnetic flux of the stator core material and I understand that they would make no contribution to torque. I have included a photo.

    I am having a hard time accepting that the same exists for these little BLDC motors because of their physical construction.

    All the math and my own conclusions are included in the original post.
    Last edited: Jun 14, 2015
  5. Jun 14, 2015 #4
    I think "end terns" is a confusing designator. Perhaps it's a corruption of "turn ends" with the noun and adjective transposed.

    Any iron residing out of the slot, for which the wire is in proximity, will be influenced by the current in the conductor. This could produce some parasitic back EMF that is out of phase. [It looks like I'm pretty much agreeing with Jeff, here.]

    Instead of the confusing multitooth armature of 12+ you might look at a simplified linear motor model and see what happens when an extraneous turn is added to an intervening tooth.
    Last edited: Jun 14, 2015
  6. Jun 15, 2015 #5
    "end terns" would be a confusing designator but end turns is commonly used in the business.

    I first became involved with this after reading a comment in another thread that stated that only the windings in the stator slots had an effect on the motor and the end turns had no effect.

    I think I have it figured out. Many use the Lorentz force to analyze the torque effects on a rectangular current loop. This reveals that it is only the slot windings that generate a force and not the ends.

    Force is not torque, however. Torque requires a moment arm and in this case the moment arm is equal to the end turn length. At some level it would appear that semantics are at play in determining whether the end turns are involved or not.


    The formula for torque Torque = NIAB includes the area of the loop.

    Torque = N x I x slot length x end turn length X B

    There is another way of analyzing this system based on the flux in the stator tooth and its interaction with the permanent magnets in the motor. Using this technique, the end turns have to be considered as contributors to the flux in the stator tooth.
    Last edited: Jun 15, 2015
  7. Jun 15, 2015 #6


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    @Voltage_drop : Another confusing designator:

    Do you mean "shading coil" / "shading ring"?

    Last edited: Jun 15, 2015
  8. Jun 15, 2015 #7
    No, the common term is end turns. In many larger motors, the end turns are outside the influence of the magnetic core and have little influence on the total flux.

    I have resolved my disagreement with the statement that it is only the slot turns that influence the motor operation. Using the Lorentz method of force analysis, the end turns do not contribute to the rotational force.

    There are other methods of analysis using the interaction between the flux from the stator windings and the magnets. The Ampere method and the Gilbert method of using magnetomotive force to analyze the motor operation require the use of the total flux including the flux from the end turns.

    My view is that the interpretation of the influence of the end turns is somewhat dependent on the analysis technique. You say Lorentz, I say Ampere or Gilbert.
    Last edited: Jun 15, 2015
  9. Jun 15, 2015 #8
    Hmmm.. In an "air core" motor I would use the Lorenz sine the coil is the only physical structure - but in an Iron core the primary torque would be purely magnetic.i.e. - the torque does not come from Lorentz. Lorentz is the force on the wire ( charges in it) in a magnetic field - for example how a e-beam is bent in one axis my a mag field.

    The current in the coil makes the Mag field - then the end winding would count - and they ensure as much flux as possible exits the outer edge. ( similar to leakage in a transformer)
  10. Jun 15, 2015 #9


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    Each coil has two end connections. Those links between coils all carry currents between poles along parallel paths in the same direction.
    For a three phase motor, the currents in the bundle of end connections will cancel, as will the resulting field.
  11. Jun 17, 2015 #10
    Windadct: I really like your response. It agrees with my way of thinking.

    Baluncore: Your comments appear to me to apply only to large motors in which the end turns are stacked outside the magnetic influence of the core. On these little motors, the windings are still under the influence of the core and would contribute flux to the core. Since torque is proportional to flux, it appears to me that on these small motors, the end turns would contribute to the flux and therefore torque.

    If end turns don't contribute, why aren't all motors made with the longest slots possible? I understand that this is practiced in larger AC motors, but in these cases the end turns are stacked outside the influence of the magnetic core.

    For wire loops, the torque is proportional to the area. Rectangular loops of 1x1 cm, 2x0.5cm and 4x0.25cm all have the same area and the same torque, yet the side turns are all different lengths.

    For a wire loop, the Lorentz force is commonly used to analyze the circuit. There are other ways. For iron cores, the interaction of the magnet flux and winding flux may be analyzed using the Ampere of Gilbert analysis techniques. One source that I came across suggested that a text by Jim Ireland existed in which an end turn correction factor could be introduced which effectively increased the length of the slot windings.

    The bottom line is that I still don't have an explanation of the effects of the end turns on these small motors that I am comfortable with.
    Last edited: Jun 17, 2015
  12. Jun 17, 2015 #11


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    You assume that scale is so important that it overrides symmetry and construction practices.
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