question: Why a wobbling ceiling fan never balances itself
comment: It wobbles because it is out of balance. That won't change without human intervention. You can tape a penny to the top of a blade to fix it. Some trial & error will be needed.
passages: Contrary to popular misconception, wobbling alone will not cause a ceiling fan to fall. Ceiling fans are secured by clevis pins locked with either split pins or R-clips, so wobbling won't have an effect on the fan's security, unless of course, the pins/clips were not secured. To date, there are no reports of a fan wobbling itself off the ceiling and falling. However, a severe wobble can cause light fixture shades or covers to gradually loosen over time and potentially fall, posing a risk of injury to anyone under the fan, and also from any resulting broken glass. When the MythBusters were designing a fan with the goal of chopping off someone's head, Scottie used an edge finder to find the exact center of their blades with the aim of eliminating potentially very dangerous wobbling of their steel blades.
   Wobbling is usually caused by the weight of fan blades being out of balance with each other. This can happen due to a variety of factors, including blades being warped, blade irons being bent, blades or blade irons not being screwed on straight, or blades being different weights or shapes or sizes. Also, if all the blades do not exert an equal force on the air (because they have different angles, for instance), the vertical reaction forces can cause wobbling. Wobble can also be caused by a motor flaw, but that very rarely occurs. Wobbling is not affected by the way in which the fan is mounted or the mounting surface.
   Imagine putting a marble in a ladle. It will settle itself into the lowest point of the ladle and, unless disturbed, will stay there. Now imagine giving the ball a push, which is an approximation to a Dirac delta impulse. The marble will roll back and forth but eventually resettle in the bottom of the ladle. Drawing the horizontal position of the marble over time would give a gradually diminishing sinusoid rather like the blue curve in the image above.
   Section::::Rotor Instability Phenomena.:Transient Stability.
   BULLET::::- The upper pivot point of the central supporting column is prevented from moving left–right and front–back by the fulcrum itself; it is prevented from moving up–down by gravitational pull. The lower pivot point of this column must be held in place so that it cannot sway left–right and, to a lesser extent, front–back as the arms move, but it experiences no up–down movement forces — in this arrangement, the entire pivot process takes place on the upper central pivot point, which acts as the single fulcrum for the entire balance; it is possible to reverse this, so that the lower pivot point acts as the fulcrum and the upper is only held in place so that it cannot sway left–right or front/back.
   Section::::Safety concerns with installation.:Wobble.
   Section::::Structure.
  
  The user stands on a board or other platform which is on top of an unstable ground-contacting member, the fulcrum. The height of the fulcrum of most models is between 3 and 6 inches (i.e., the top of the fulcrum is that distance above the ground). Due to the fulcrum's instability, the user must remain balanced and coordinated in order to prevent the board from touching the ground.
   Section::::Rotor Instability Phenomena.
   Section::::Theory.
  
  Sustained oscillation has two necessary components: an underdamped second- or higher-order system and a positive feedback mechanism. An example of an underdamped second order system is a spring and mass system, where the mass can bob up and down (oscillate) when hanging from a spring.
  
  If shimmy cannot be designed out of the system, a device known as a steering damper may be used, which is essentially a notch filter designed to damp the shimmy at its known natural frequency.
   BULLET::::- If the weight of the pan above either vertical column is itself greater than zero and any weight placed on that pan is off-center then that pan's tendency to "tilt" will cause the balance to exist in a state of "tension" at the pivot points below that pan. This tension will manifest as an increase in static friction.
  
  BULLET::::- The longer the arms generally, the more sensitive the balance, though longer arms usually entail greater arm weight, which tends to decrease sensitivity
  
  BULLET::::- Heavier pans and vertical columns also tend to decrease sensitivity
   Under conditions where rotating speed is very high even though the mass is low, as in gas turbines or jet engines, or under conditions where rotating speed is low but the mass is high, as in ship propellers, balance of the rotating system should be highly considered, because it may generate large vibrations and cause failure of the whole system.
   The same phenomenon is sometimes labelled as "maintained", "sustained", "self-exciting", "self-induced", "spontaneous", or "autonomous" oscillation. Unwanted self-oscillations are known in the mechanical engineering literature as hunting, and in electronics as parasitic oscillations. Important early studied examples of self-oscillation include the centrifugal governor and railroad wheels.
  
  Section::::Mathematical basis.
   Rotating unbalance
  
  Rotating unbalance is the uneven distribution of mass around an axis of rotation. A rotating mass, or rotor, is said to be out of balance when its center of mass (inertia axis) is out of alignment with the center of rotation (geometric axis). Unbalance causes a moment which gives the rotor a wobbling movement characteristic of vibration of rotating structures.
  
  Section::::Causes of unbalance.
  
  BULLET::::- Distortion from stress: Routine manufacturing processes can cause stress on metal components. Without stress relief, the rotor will distort itself to adjust.
   A continuous system having imaginary poles, i.e. having zero real part in the pole(s), will produce sustained oscillations in the output. For example, an undamped second-order system such as the suspension system in an automobile (a mass–spring–damper system), from which the damper has been removed and spring is ideal, i.e. no friction is there, will in theory oscillate forever once disturbed. Another example is a frictionless pendulum. A system with a pole at the origin is also marginally stable but in this case there will be no oscillation in the response as the imaginary part is also zero ("jw" = 0 means "w" = 0 rad/sec). An example of such a system is a mass on a surface with friction. When a sidewards impulse is applied, the mass will move and never returns to zero. The mass will come to rest due to friction however, and the sidewards movement will remain bounded.
   Humans can sense head tilting and linear acceleration even in dark environments because of the orientation of two groups of hair cell bundles on either side of the striola. Hair cells on opposite sides move with mirror symmetry, so when one side is moved, the other is inhibited. The opposing effects caused by a tilt of the head cause differential sensory inputs from the hair cell bundles allow humans to tell which way the head is tilting, Sensory information is then sent to the brain, which can respond with appropriate corrective actions to the nervous and muscular systems to ensure that balance and awareness are maintained.
   A step input in this case requires supporting the marble away from the bottom of the ladle, so that it cannot roll back. It will stay in the same position and will not, as would be the case if the system were only marginally stable or entirely unstable, continue to move away from the bottom of the ladle under this constant force equal to its weight.
   When in flight the rocking wing functions in the following manner, "when the rocking aeroplane...is tilted out of the horizontal...by moving the lever...to one side, the normal pressure of the rocking aeroplane...is inclined out of the vertical and gives rise to a horizontal component pulling its axle...to one side relative to the line of flight."
   BULLET::::- In an inclined plane, a load can be pulled up the plane by a sideways input force, but if the plane is not too steep and there is enough friction between load and plane, when the input force is removed the load will remain motionless and will not slide down the plane, regardless of its weight.
   The senses must detect changes of spatial orientation with respect to the base of support, regardless of whether the body moves or the base is altered. There are environmental factors that can affect balance such as light conditions, floor surface changes, alcohol, drugs, and ear infection.
   A problem with the motor shown above is that when the plane of the coil is parallel to the magnetic field—i.e. when the rotor poles are 90 degrees from the stator poles—the torque is zero. In the pictures above, this occurs when the core of the coil is horizontal—the position it is just about to reach in the last picture on the right. The motor would not be able to start in this position. However, once it was started, it would continue to rotate through this position by momentum.
   When the transient torque ends, the control program will stop the gimbal movement, and the rotors will be left pointing more forward than before. The inflow of unwanted forward angular momentum has been routed through the CMGs and dumped into the rotors; the forward component of their total angular momentum vector is now greater than before.
   BULLET::::- U-bolt system. Similar to J-hook system, except that the hook on the ceiling is U-shaped and is being held by screws. One advantage of U-bolt system as opposed to J-hook system is that it wouldn't unscrew itself by the fan's torque in either direction. J-hook can be unscrewed by the fan torque when spinning clockwise (or counterclockwise if J-hook is left-hand threaded).
   In a non-rotating fluid the fluid parts above the rising ball and closes in underneath it, offering relatively little resistance to the ball. In a rotating fluid, the ball needs to push up a whole column of fluid above it, and it needs to drag a whole column of fluid along beneath it in order to rise to the surface.
  
  A rotating fluid thus displays some degree of rigidity.
  
  Section::::History.
   BULLET::::- Lamprey
  
  The lamprey moves using lateral undulation and consequently left and right motor hemisegments are active 180 degrees out of phase. Also, it has been found that the endogenous frequency of the more anterior oscillators is higher than that of the more posterior ganglia. In addition, inhibitory interneurons in the lamprey project 14-20 segments caudally but have short rostral projections. Sensory feedback may be important for appropriately responding to perturbations, but seems to be less important for maintaince of appropriate phase relations.
  
  Section::::Robotics.
   Initially, however, there is no precession, and the top falls straight downward. This gives rise to an imbalance in torques that starts the precession. In falling, the top overshoots the level at which it would precess steadily and then oscillates about this level. This oscillation is called "nutation". If the motion is damped, the oscillations will die down until the motion is a steady precession.
  