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Today, I've decided to observe my PC fan as I shut the computer down. The fan slowly lost angular momentum over time. What I've found really interesting is the fact that the momentum vector change did not stop at the zero vector, but instead flipped its orientation and "went to the negatives", albeit very small in the absolute value compared to the powered spin; this caused the fan's angle to deviate by a few degrees (opposite to the powered spin rotation) compared to the observed angle when momentum was equal to the zero vector.

If I let $\overrightarrow{L}$ be the momentum vector, $\overrightarrow{L}_0$ be the momentum vector at $t_0$ (= poweroff time), and $\overrightarrow{L}(t) = y(t) * \overrightarrow{L}_0$ (with $y_0 = y(t_0) = 1$), then these are the plots of $y$ through the course of time.

Expected fan poweroff behavior:

enter image description here

Observed fan poweroff behavior:

enter image description here

Can anyone explain why may this happen?

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8 Answers 8

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The overshoot behavior you noticed is called cogging and occurs when the magnet arrangement in the motor "catches" the rotating magnetic core of the motor during shutdown and jerks it back to one of the local strong spots in the field.

You can demonstrate this yourself by carefully rotating the fan blade around with your finger when the motor is off. You will notice there are certain rotation angles where the fan wants to come to rest and others which it wants to avoid. If the motor passes one of the preferred spots but fails to rotate far enough to "climb the hill" and snap forward into the next cog spot, the motor will very briefly rotate backwards a fraction of a turn and go "boing-oing-oing-oing" as it settles into that cog position.

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    $\begingroup$ If you spend as much time as I have playing around with permanent magnet motors, you'll learn all sorts of weird and useful things about them. they really are quite remarkable devices. $\endgroup$ Feb 17, 2021 at 7:40
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    $\begingroup$ @nick012000 If you are proposing that the fan blades act as springs, I think you will find that they are too rigid for that to be a significant factor. Indeed, fan manufacturers try to make the blades stiff so that they do not hit the frame with as small a tip clearance as possible, e.g. using Sterrox. $\endgroup$ Feb 17, 2021 at 10:47
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    $\begingroup$ @nick012000 A car doesn't do that though. You perceive that because your senses can only detect changes of acceleration (and, mildly, the actual acceleration). What you perceive as going backwards is actually just a change of deceleration whilst you're still going forwards. Unless you mean the car dipping on its suspension under braking, which has nothing to do with distribution of momentum, and indeed does not involve the car going backwards at all. $\endgroup$
    – Graham
    Feb 17, 2021 at 12:21
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    $\begingroup$ @Graham: But a car does jerk backwards when you hit the brakes. The wheels stop first; the chassis still has momentum. The chassis overshoots and is pulled back. $\endgroup$ Feb 17, 2021 at 19:28
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    $\begingroup$ And by releasing the brakes at the right time, you can even start rolling backwards using the energy stored in the suspension. $\endgroup$ Feb 17, 2021 at 20:46
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Your PC is a box with limited vents for air to enter/exit. Especially if these clog up with dust, the fan could create a noticeable pressure differential between inside and outside of the box. After the fan turns off, that equalizes, forcing some air backward through the fan, and causing it to rotate backward. Maybe.

Another possibly, as pointed out in comments, and since you report much less than a full rotation backward, is that the DC motor running the fan likes to be in certain orientations and not others when it is unpowered, due to alignment of the permanent magnet with other motor parts. As the fan slows down, at some point it passes one of these preferred orientations but lacks the momentum to make it over the hump to the next one, and rotates back.

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    $\begingroup$ Negative pressure seems unlikely, as most electronics ventilation systems operate with internal neutral or positive pressure. To get to negative pressure, you'd have to run the exhaust fan faster than the intake fan. I'm not sure how you'd get negative pressure inside the case if the exhaust fan is stopped - once it spins down, there's nothing else that would create negative pressure to make it spin backwards. $\endgroup$ Feb 16, 2021 at 15:44
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    $\begingroup$ With some fans, you can feel the latter effect if you spin the unpowered fan slowly by hand. $\endgroup$
    – user253751
    Feb 16, 2021 at 16:18
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    $\begingroup$ Negative pressure is also unwanted in computers since it lets them suck in dust from everywhere, instead of only sucking in dust from where the fan is. $\endgroup$
    – user253751
    Feb 17, 2021 at 11:26
  • $\begingroup$ @NuclearHoagie that assumes there is an intake fan. Often it's the CPU fan and a duct of course, but some low-spec corporate desktops are back to the old configuration of intake vents, CPU fan, and outlet only through the PSU $\endgroup$
    – Chris H
    Feb 17, 2021 at 12:31
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On balance, I think @nielsneilsen's answer is likely the correct one. But there is another possibility.

Is there a control loop in play?

Almost universally, practical control systems for hitting a desired position, velocity, flow rate or whatever use a PID control loop, sometimes omitting the P or D element depending on the application. Other control techniques exist, but a PID controller has a number of advantages.

  • It's very well understood.
  • It's very simple to configure.
  • It hits the target value without much error.
  • It doesn't need a particularly complicated implementation, and can even be built with old-school analogue electronics if you want.
  • It remains stable over a fairly wide range of actuator/sensor tolerances, so you don't need to tune each widget individually, making production easy.
  • The ramp-up/down time is easily configurable, which can be useful where (as with a motor) a rapid change of output produces a current spike.

One standard feature of a PID controller though is that in order to get the position/velocity/whatever to settle rapidly to where you want, you have some overshoot.

PID examples from Wikipedia

If you have a speed controller on the motor, and it uses a PID loop to govern speed, then stopping the motor will naturally give a small speed in the opposite direction before it comes back to zero.

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    $\begingroup$ I'd argue that while this might apply to running the fan at any given speed, I'm fairly certain that when the PC is turned off, the PSU simply stops providing any current to the motor/controller, allowing it to coast to zero, as opposed to actively setting a speed of zero to stop the fan rapidly. $\endgroup$ Feb 17, 2021 at 22:58
  • $\begingroup$ @DanHenderson Quite likely, yes. But it may depend on timings, whether there are chunky capacitors in the motor-controller supply (which there often are, to decouple noisy motors from the more sensitive supplies), and anything like that. It's worth including as a possibility, even if perhaps (as I said) it's not the most likely possibility. $\endgroup$
    – Graham
    Feb 18, 2021 at 14:55
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Did the fan really rotate backwards, or merely appear to? You may be looking at a Wagon-Wheel Effect. Basically, when a wheel or propeller rotates at a certain speed, particularly if you're using fluorescent lighting, which has a natural flicker to it that isn't always obvious, the object can appear to stop or rotate in the opposite direction. All the blades of the fan are basically indistinguishable, so between one flicker of the light and the next, one blade has taken the position of the previous, or slightly behind it, making it appear that the blades are moving backwards. When the fan is at full speed, you can't really see much more than a blur, but as it gets slower, it hits these "wagon-wheel" speeds that coincide with the frequency of your flickering fluorescent lights, and appears to spin in reverse for a bit.

You can also get the effect by filming the wheel/propeller with a camera, since the frame rate of the camera will produce the same effect as a flickering fluorescent does to the naked eye (at different speeds obviously.)

You might be able to tell the difference by using a sharpie to make a mark on one blade, and watching the mark as it spins down. However, this can still display the effect at certain speeds if the fan makes a complete almost-360° rotation between one flicker and the next, but obviously the fan must be moving much faster for this than it does to get the effect between just one blade and the next.

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    $\begingroup$ No, no sir, I am perfectly positive that is not the case. I believe the flickering lights are a necessity for the wagon-wheel effect (from what I've gathered from the link you posted) and my lightning was natural (a transparent window in afternoon sun). Also, the reverse motion happened when the fan was already moving too slowly to produce the effect (it would have to rotate $2\pi - \epsilon$ radians in a flicker tick). $\endgroup$ Feb 17, 2021 at 22:11
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    $\begingroup$ @CaptainTrojan Flickering lights are not necessary for the wagon-wheel effect; it can happen under continuous illumination. I agree that this case wasn't caused by the wagon-wheel effect though. $\endgroup$
    – Altay_H
    Feb 18, 2021 at 22:11
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    $\begingroup$ @Altay_H True, but according to Schouten(1967), the minimum spin speed required for this effect under continuous illumination is 8 revolutions per second, which is nowhere near the observed speed close to zero. $\endgroup$ Feb 19, 2021 at 11:04
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I also think the effect is cogging. This torque is position dependent and its periodicity per revolution depends on the number of magnetic poles and the number of teeth on the stator. Cogging torque is an undesirable component for the operation of such a motor. It is especially prominent at lower speeds, with the symptom of jerkiness. Cogging torque results in torque as well as speed ripple; however, at high speed the motor moment of inertia filters out the effect of cogging torque.

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Hi Reading this is interesting. The reason that the fan goes backwards is simple. It is a Direct Current motor which has a capacitor across the power terminals to keep the power factor near to unity. A motor is a wound component which will produce a lagging current so a capacitor is added to bring that current nearer to unity (A capacitor creates leading current). When the power is switched off, the capacitor will discharge through the motor in reverse polarity, making it run backwards for a short while..

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  • $\begingroup$ Yeah, that would make sense, but the motor is turned off many seconds (like 15) before the fan stops spinning (which happens right before backward motion). So yes, probably there is a force applied to the fan opposite to its momentum, but that force would quicky deplete without stopping the fan. $\endgroup$ Feb 18, 2021 at 21:21
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I just have guesses.

Is there any sort of spring in the motor, or anything spring like? For example a fan belt could stretch if it was trying to turn a stiff bearing. You might discover this by trying to spin the fan by hand and seeing if it turns the other way when it stops.

Another source of springiness could be electrical. A power smooths variations in input power. When you turn off the power, the power supply uses energy in an inductor or capacitor to keep going for a bit.

The fan is controlled by a feedback system. When the power is turned off, perhaps the input to the feedback system drops to $0$, telling the feedback system to set the fan speed to $0$. The fan is still spinning, so perhaps the feedback system uses the last bit of power from the power supply to slow the fan. Perhaps it overshoots. You might see this with an oscilloscope.

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(Answering for completeness, although this isn't the specific case that you observed where the fan only spins less than one rotation.)

It's possible that it does it deliberately. In 2011 MSI released a graphics card which automatically "de-dusted" its fan to improve cooling. It did that by spinning backwards at full power for about 30 seconds on start-up. It's possible that this idea has made its way into other parts of computer hardware or other fans, and it would functionally work to do the de-dusting on/after shutdown (although startup or intermittently during normal running are better ideas and more likely). However, this would result in certainly more than 1 full rotation, since the de-dust spin should be fast enough to dislodge dust.

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