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Going through some theory about epicyclic gears I came accross a comment that says that the spin velocity of the gear irrelevant if perfectly balanced, I don't understand why this might be true, is it because it would be constant and thus can be measured without variations?

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  • $\begingroup$ If the gear is perfectly balanced and rotating at constant angular velocity, what effect could it have on the dynamics of the system? Answer: none! $\endgroup$ – alephzero Jul 3 '17 at 15:32
  • $\begingroup$ @alephzero and how would it affect if it was not balanced? $\endgroup$ – spe4ker Jul 3 '17 at 15:43
  • $\begingroup$ I think this questions needs to clarify in what ways it is irrelevant. Clearly a faster rotational speed has some relevance in the system. The question is tagged vibration; so I assume the relevance has to do with that; but it is not explicit in the question and therefore unclear IMO. $\endgroup$ – JMac Jul 4 '17 at 11:53
  • $\begingroup$ I think this is an oversimplification assuming the gear a rigid unbreakable body. Given enough RPM centrifugal force will rip the gear apart. $\endgroup$ – SF. Jul 4 '17 at 13:03
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This depends greatly on the context. Here is a counter-example, a situation in which the spin velocity of the gear is relevant to the dynamics of the overall system, even if that velocity is constant. That situation is high speed gears on aircraft (e.g. in the engines). At sufficiently high speed, the gear will exhibit the gyroscopic effect. Then when the plane executes a maneuver angular velocity (e.g. nose pitch up on takeoff), there is a gyroscopic reaction moment on the gear, which change the loading on the bearings, and possibly shift the gear off center a little. Of course, this is probably a rare example. Most gears do not get fast enough to have significant gyroscopic moment, and most gearboxes are not rotated like in an aircraft.

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If the gear is not balanced then the center of mass will oscillate as it spins which will induce additional load on the shaft and create vibrations. This effect greatly depends on the speed of the imbalanced gear.

If the gear is perfectly balanced then there will be no oscillations.

However at extremely high speeds you will need to ensure that the tensile strength of the material is enough to keep the gear together. By the time you get to those speeds however you will have to deal with similar issues elsewhere.

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