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Power-User

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Does Coriolis Force Act On A Planetary Gear?

02/14/2017 12:49 AM

The axis of a planet gear on a rotating arm has a tangential velocity besides its own angular velocity, both absolute and relative to the arm. I am unable to find any proper (intuitive) explanation of whether a coriolis force acts on the planet in such a case. I suspect that the effect may be small compared to tooth forces, or even centrifugal effects, but it may influence the bearing loads for the planet shaft. I'd be grateful for any insight into this problem.

The texts I have seen mostly talk of particles moving in a rotating frame, and it's not clear how that concept can be extended. Frankly I've never dealt with coriolis effects in a long career as a design engineer, and my theory is now quite rusty!

My real problem is not regarding gears, but concerns the force analysis of a vertical roller mill (for grinding of raw minerals in a chamber having a cylindrical grinding track and multiple roller assemblies suspended from a rotating spider). The order of magnitude of forces will be much greater, and I would naturally like to ensure that I don't make any blunder in estimating the bearing loads!

Thanks =TeeSquare=

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Guru
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#1

Re: Does coriolis force act on a planetary gear?

02/14/2017 1:15 AM

All other forces x (1.000 ± 0.001) [WAG]

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Guru

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#2

Re: Does coriolis force act on a planetary gear?

02/14/2017 1:28 AM

You probably can't find anything because the force is negligible...

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Guru

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#3

Re: Does coriolis force act on a planetary gear?

02/14/2017 2:53 AM

You're exerting enough force to grind minerals (not to mention the vibration from that) and you're concerned about the addition of comparatively microscopic coriolis forces on top of that?

Why would you be operating a bearing so close to its limits that coriolis forces would even make a difference?

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Guru

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#16
In reply to #3

Re: Does coriolis force act on a planetary gear?

02/14/2017 9:27 PM

I wonder how much magnitude would coriolis force have compared to gravity and why it affects water flushing to some point?

Is there any place coriolis wont effect.

I reckon, the farther you are in the center or axis of revolution the greater is the force. Is the force more significant enough in ISS?

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Guru

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#17
In reply to #16

Re: Does coriolis force act on a planetary gear?

02/14/2017 9:38 PM

In a 30-35 cm toilet bowl the magnitude of the effect is about 10 million times less than the force of gravity.

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Guru

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#4

Re: Does coriolis force act on a planetary gear?

02/14/2017 7:52 AM

Do your calculations with respect to a non-rotating frame of reference. Calculate force = mass x change of velocity, where, of course, velocity is a vector. You can determine the velocity of each piece by vector summing the components of its motion.

Centrifugal and Coriolis forces are only fictional forces that appear when your frame of reference is rotating. A good example is the surface of the earth. Air masses appear to deviate to the right in the northern hemisphere due to "Coriolis force", but in fact, it is the earth's surface that is rotating counter-clockwise.

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Guru

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#5

Re: Does coriolis force act on a planetary gear?

02/14/2017 8:27 AM

If this is a large concern, move your grinding mill to the equator.

Otherwise ignore it.

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Guru

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#6
In reply to #5

Re: Does coriolis force act on a planetary gear?

02/14/2017 1:24 PM

Coriolis forces due to Earth's rotation certainly contribute to cyclonic weather systems and must be accounted-for in aircraft navigation, but in this case the machine's latitude has nothing to do with it, actually - you can observe coriolis forces on a merry-go-round

or even in a spinning bowl, regardless of its latitude:

Object moving frictionlessly over the surface of a very shallow parabolic dish. The object has been released in such a way that it follows an elliptical trajectory.
Left: The inertial point of view.
Right: The co-rotating point of view.

source

In the OP's case the frame-of-reference is co-rotating with the system of planetary gears.

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Guru

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#7
In reply to #6

Re: Does coriolis force act on a planetary gear?

02/14/2017 3:47 PM

I might be inclined to agree with you, if the gears 1. are free floating, 2. are rotating and 3. if the rotation is perpendicular to the rotation of the earth's.

In any case, immeasurable on practically any scale..

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Guru

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#8
In reply to #7

Re: Does coriolis force act on a planetary gear?

02/14/2017 5:09 PM

Okay, if you eliminated any possibility of the Earth's rotation contributing to the motion, that is, if you placed either one of the above examples at the equator, would you still see the same behaviour? Yes you would. That behaviour is what the OP is asking about.

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Guru

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#9
In reply to #8

Re: Does coriolis force act on a planetary gear?

02/14/2017 5:20 PM

OK, but I see the effect as being equivalent to scooping a bucket of sand from an Atlantic Ocean beach and dumping it onto a Pacific Ocean beach.

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Guru

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#10
In reply to #9

Re: Does coriolis force act on a planetary gear?

02/14/2017 5:30 PM

I know, right? If the OP is looking for piece-of-mind, he should simply specify a heftier bearing and go get some sleep.

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Guru
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#11
In reply to #10

Re: Does coriolis force act on a planetary gear?

02/14/2017 7:23 PM

The comments might be called piece-of-mind, and hopefully peace-of-mind too.

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Guru

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#12
In reply to #11

Re: Does coriolis force act on a planetary gear?

02/14/2017 7:42 PM

It became misspelt only after the 15-minute grace period had elapsed. It was just fine until then.

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Guru

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#13
In reply to #8

Re: Does coriolis force act on a planetary gear?

02/14/2017 7:53 PM

If you think the earth's rotation has any effect, you might believe that it causes the circulation in the toilet to rotate counter-clockwise (which it doesn't).

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Guru

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#14
In reply to #13

Re: Does coriolis force act on a planetary gear?

02/14/2017 8:33 PM

It doesn't. The effect is swamped by other variables on these scales and only becomes signifant at much larger scales (weather systems) and speeds (aircraft).

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Guru

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#15
In reply to #13

Re: Does coriolis force act on a planetary gear?

02/14/2017 9:01 PM

Well, yes it actually does.

Not in an ordinary toilet, bathtub or kiddie pool.

However the effect is real, if miniscule as it is in the OP's gear train.

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Guru

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#19
In reply to #15

Re: Does coriolis force act on a planetary gear?

02/15/2017 11:34 PM

Over 50 years ago, I spent many hours, over a period of several months, leaving water sitting in a bathtub all day long until it was very still, carefully pulling the rubber plug as straight up as possible, and observing the direction of flow rotation. I did this both in California, and in Chile, and in both locations, was unable to observe a statistical difference in the directions of swirl.

In other words, the way the plug happened to come out was more important than the Coriolis force.

It takes large distances (much larger than a bathtub) for the Coriolis force to be significant.

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Power-User

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#18

Re: Does coriolis force act on a planetary gear?

02/15/2017 6:39 AM

The short answer is no force worth talking about.

Let me explain.

Coriolis force is that force which is needed to (say) increase the "sideways" velocity of body that arises as a consequence of it moving outward along the radius of a rotating plane. The classic model is of (say) a person walking towards the outer edge of a spinning disc - as the person's distance from the centre of rotation increases, so also does their velocity in the tangential direction, and clearly a side force is needed to make this happen (Newtons first law). This is the coriolis force.

In the your planatery gear case, there is no mass that is moving outward along a radius - so no coriolis - unless you want to consider minute forces that arise out of the movement of some of the orbiting components in combination with that of the rotation of the earth.

Those forces could hardly be measured, and their value would depend on where the unit was on earth, and its orientation in relation to the axis of spin of the earth.

Unless you are designing something to detect gravitational waves or space time drag - ignore it!

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Power-User

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#22
In reply to #18

Re: Does coriolis force act on a planetary gear?

02/16/2017 11:47 PM

Your reply has given me a clue! (... mass that is moving outward along a radius ...). In the spinning roller for every element which has an outward radial velocity there is a diametrically opposite element with an inward velocity, but these two elements are located at different distances from the central axis. Maybe they will all cancel out in some way (or maybe not) and the effect is negligible in all likelihood.

The nature of my doubt is getting clearer though, and I'll have to think over it. I'll be travelling and without internet access for a few days -- will see if there are iny more inputs when I return. Thanks =TeeSquare=

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#20

Re: Does Coriolis Force Act On A Planetary Gear?

02/16/2017 7:47 PM

Thanks to all those who replied. Sorry my internet access is irregular, hence delay. Now I have both piece(s) of mind and peace of mind!

It's clear that the effect is going to be negligible compared to other forces. However my question is really about understanding the concept. I'm not concerned with the earth's rotation, but with the fact that a spinning planet or roller having some angular velocity is independently orbiting around another axis. Is there a coriolis component to the forces which keep the planet/roller in equilibrium? I could not find an answer to this in the references I tried!

=TeeSquare=

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#21

Re: Does Coriolis Force Act On A Planetary Gear?

02/16/2017 11:21 PM

Further to my last, since the two rotation axes are parallel in my case there should be no gyroscopic effect (which could perhaps be very significant). In the roller mills with inclined or horizontal axes it is only the track which rotates. There could be other machines like mixers where both coriolis and gyroscopic effects are not negligible.

I have attended lectures on these topics (and other exotic stuff like Lagrange equations) and maybe even answered some exam questions on them, but that was some fifty years ago and I've never had to use any of that stuff during my working career. Anyway I could never make much sense of vector equations which are far from intuitive, and continue to be wary of people who produce impressive-looking computer results because I don't know if they used the right concepts! =TeeSquare=

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