Variables Related to High RPM Vibrations

Your running into what is called the 'Critical Speed', that's the speed where the natural frequency matches the RPM.

To answer your question, yes you can change the critical speed in one of two ways.

Not knowing your set up, I don't know which is the best solution for you, but here goes.

In no particular order, you can 'adjust' your critical speed by either changing the center of gravity or the mass of the spindle. To keep the vibration down, you'll want the critical speed to be more then 10% different from your running speed.

Good luck and let us know how it works out.

Laby

Thank you... Yes, but can I know if reducing the mass will raise the critical speed? Or will in lower the critical speed? Is there a predictable relationship that will tell me what will happen if I remove material or add material?

The set-up is rather complex and time consuming, so I'd like to be able to make some reasonable predictions, as opposed to just removing material, then putting it back together and seeing what happens. And then finding out I should have removed much less than I did .. or finding out I should have added to the mass instead.

Sorry, I didn't see your second half of the question...

if you make the chuck bigger, the mass (weight) will increase and the first critical speed will also increase.

As to the runout... that is a contributer through centrifugal force, and that will always be there and will get worse as the speed increases. So keep runout to a min.

You mention deformation, keep this in mind, vibration is caused when the center of gravity tries to become the center of rotation, and it always will, so if you have your spindle balances, you should avoid, or minimize it.

if you can't balance it, then holding as tight a tolerance on runout between the OD and the ID will help a lot.

Laby

Are you saying that if I add mass, it will not begin to vibrate until it reaches a higher speed? And a lower mass will reach critical speed, and vibrate, at lower RPM?

That sounds backwards somehow.

I agree - IMHO, the assembly with the heavier chuck will probably have a lower resonant frequency - though the critical thing is balance. The nearer the C of G of the system to the axis of rotation, the higher the resonant frequency will be.

A few years ago I had this same problem, we fixed the problem by moving shorting the shaft, or moving the center of gravity. we move it 3" and that changed the critical speed from 3,600 to 3,900.. and we running at 3,600 so problem was solved.

Back then adding weight was not an option. Sense then, I found this chart used by a balance machine manufacture and when I reference this chart, it show that an increase in outside diameter will increase the first critical speed. (that is if the length of the shaft remains the same)

They provide this formula:

CS = D/L^2 * 4.75 * 10^6

(note: I tried this and it didn't work for me, if I used 10^4 it came alot closer.)

Where:

CS = Critical Speed

D = Diameter of shaft

L = Length of Shaft

here's my suggestion, put in all your variables and if you come up with the first critical that matches where your seeing it, then let me know.. I don't think this formula works that's why I didn't offer it at first. .. but if you use this and it does match what your seeing, you can use it to predict where to put your O.D.

Hope this helps..

hi everyone,

what about this, the natural frequency depends on stiffness of the structure (k) and the mass (m). circular natural freq = sqrt ( k / m ),

could increase in stiffness (k) resulting higher natural freq? thus increasing rpm limit

however, i think its a bit hard to find the stiffness (k), maybe you could do a "bump test" to get the approx. natural freq ( call somebody in university)

i hope that helps, be well

Critical frequency in a system as you describe is no function of COG but only of bending stiffness of the shaft and mass of the "chuck". The position of the COG (radial) influences the amplitude of the vibration but not the frequency.

As mentioned by an other comment shortening the shaft increased the frequency via increase of stiffness.

A mass reduction has same effect since f≈ sqrt( C/M) with C= stiffness and M = mass.

Your chuck is on the motor shaft which reduces your possibilities to influence the behaviour. If you can accelerate fast to your working frequency you can work in overcritical range.

What you have to do is to increase the mass which will decrease the critical frequency and your system will work quite at your required speed. This approach is often used in high speed turbines. But as mentioned you should pass fast through the critical speed range.

It is only by trial that you can get the optimal mass to add. It can be also computed but for it you need a lot of data about the motor, bearings, support, aso. It can also be possible to use a bigger motor ( shaft stiffness increases wit d^4) and have stiffer bearings to reduce angular deformation of shaft under radial loads.

So you're suggesting that I would get better results by decreasing the frequency, and passing quickly thru it... rather than increasing the frequency beyond my working frequency?

Work above the critical frequency, rather than below?

That is how most high speed rotating machinery works, you run through the critical speed and operate well above it. This usually gives a much wider operating range with low vibration. The only danger is if you begin into a second mode (second critical speed) at the top of your operating range.

I would try to make your rig more flexible (less stiff) and reduce the critical that way. If you can add damping that will also help.

Okay, sounds good on the low frequency and the damping.

But you say that stiffer will lower the critical frequency?

So as I understand it...

- stiffer and more mass will move the critical frequency into a lower range

- more flexible and less mass will move the critical frequency into a higher range

The spinning chuck that I'm speaking of is roughly mushroom shaped and sized. It has a slender portion, into which fits the shaft of the motor. It is mounted vertically. It is made of plastic (actually PVDF, not teflon.. I misspoke), so there is a lack of stiffness that is inherent in the material... particularly since it has that slender portion, and it is top-heavy.

Oh hell, I'll just send a photo of it...

No I said less stiff (more flexible) will lower the critical frequency, holding mass the same.

Critical frequency is the square root of stiffness divided by mass. If you wish to reduce the critical then you either reduce the stiffness or increase the mass holding the stiffness the same (which is often hard to do as increasing mass often increases stiffness also).

To reduce the critical frequency here you could reduced the cross sectional area of the shaft a bit, or make the shaft longer.

Adding damping to the system will be very difficult to do, so I would suggest that you balance the rotating element as precisely as possible to reduce the forcing function.

Yes, of course you did! My apologies for my dyslexic-esque error in reading your reply. Now it makes more sense to me.

I'm going to point out the fact that you, Steve S, and the comment below by Nickname, are heading in two opposing directions with your suggestions. Your method suggests lowering the critical frequency below my working speed, and Nickname I believe is suggesting a method to increase stiffness to bring the critical above my working speed. This is what I asked for... a way to either lower or raise the critical. Now to choose between the two.

I see that more details are needed, so I will continue below, in respose to Nickname, and give additional design requirements. Thank you to you both for your sage advice. Mechanical frequencies are an area I'm unfamilar with.

Now that I have the image I think that your first problem is the connection between the upper more massive part and the one put on the shaft as well as the connection to the shaft it self.

What I mentioned about bearings can be forgotten since the parts over the motor are in fact the problem.

First step should be to shorten the "shaft" between motor and upper part. Bending stiffness is proportional to 1/L^3 so that you could this way increase rapidly the stiffness. Second step should be to reduce compliance at the connection between your parts and motor shaft. Combining the 2 there is a chance that you still work in the sub-critical speed at your working rpm.

I would suggest a flange fastened on the motor shaft and a broad connection (with several screws) of your upper part on this flange.

Flange of aluminum for instance will drastically increase stiffness at motor shaft connection level.

If you want you can use the PM channel to send a drawing and I shall make the recommendations on it. With dimensions.

Nickname, thank you for your suggestions. If you will read my reply to Steve S., above, you will see an alternative train of thought that I am also following with him.

I will disclose additional design requirements. I hadn't anticipated such detail in all these suggestions. Given that, here goes...

The larger massive portion of the plastic chuck is actually umbrella shaped. Like an inverted cup. Together, the two profiles are forming a labyrinth seal. There is a collar that is mounted around a hole in a table-top which is between the bottom of the inverted cup and the top of the motor. This collar fits up into the inside of the cup. This labyrinth protects the motor from the corrosive chemical that is being sprayed in the area above the table top.

The next detail you need to know is that this entire motor/chuck assembly moves up and down about 1". That 1" is the height of the collar. It is also the depth of the cup. The collar is fixed (on the table top), the motor/chuck moves up and down during two steps of the process, all the while maintaining an effective seal between the area above, and below, the table top. This is the reason for these shapes. It is a non-contact seal, but the inside surface of the cup rides very close to the outside surface of the collar. The vibration is causing the two to rub against each other, which I can't have.

This situation also makes it impossible to either lengthen of shorten the plastic shaft length. And also prevents changing the top-heavy aspect of the chuck itself. The chuck shaft and the cup are machined out of a single piece of plastic.

One thing that I believe we will do is to send the assembly off to be balanced. Unanticipated added cost on our part, but it seems necessary.

There is also an air hole going thru the motor shaft and all the way thru the chuck shaft that I need to maintain.

Also, I can't introduce any metal into the area above the table top due to a corrosive chemical spray.

We have several plastic chucks to experiment with. Currently we are using one of them and trying to reduce the mass of the chuck by removing every bit of extraneous plastic that isn't critical to maintaining our labyrinth. Beyond that, I'm still open to suggestions.

Thanx again to all of you for your ongoing suggestions.

Hi sorry but I was busy with other things.

Does your assembly looks as the sketch?

It shows the two position (extreme) you describe and a solution to obtain better results.

If yes you are confronted in the actual situation with several problems:

1- being a soft material you cannot guarantee a Coaxiality between the motor shaft and the rest of the part.

2- the shaft is long and has a very low stiffness since plastics have very low Young modulus even if glass filled

3- the mass is relatively large and will be as under #1 mentioned not coaxial so that centrifugal forces will increase the flexure and the amplitude.

You have several possibilities to correct it:

- as sketched you can make the shaft of a stiffer material since it is in the protected zone (aluminum for instance) and obtain at same time :

an increase of the own frequency due to the higher modulus

a better centering of the upper more massive part

This will not modify your dimensions.

If I misunderstood your explanation (English is not my first language) please correct the figure.

The balance has as only effect a reduction of the centrifugal load but has NO impact on the critical frequency. If you have a system stiff enough the forces generated by the upper part will not lead to too high deformations and amplitudes. their only effect will be a lower bearing life due to the rotating load but nothing else. I would suggest you try first an amplification of the stiffness and only if the amplitudes are still too high you make the balance. A metallic connection shaft will lead to a better Coaxiality and may be you do not need to make the balance.

Oh, I suppose I'll have to forgive you for being busy with other things. But just this once! :)

Ok, evidently I descibed it pretty well, because you have drawn a 97% perfect replica of the actual assembly. Amazingly accurate. Dang! You're good!

I understand everything you just explained and suggested. Makes perfect sense. I feel I should have thought of replacing the inner shaft with a metal. It seems obvious now. But that's always how it goes, isn't it. It can be right under your nose, and all it takes is a fresh set of eyes.

Yes, yes... all very good. I believe that is the solution, in combination with a couple other small things that have been discussed here these past couple days. Thank you once again, for all your efforts, everyone. I believe this case is closed.

Hi have you considered taking the armature out of the motor reattaching the Teflon module and have it dynamically balanced, it is possible that the motor {but not usual} could have a slight miss balance. If the whole assy is done this way it should run true. assuming you have machined your module accurately.

Do you mean removing the metal shaft entirely, and replacing it directly with an extended plastic shaft on the chuck? Interesting thought. The motor is of the type that has an airline running thru the center of it and out the end of the motor shaft. The motor appears to run true to the eye, although we haven't checked it with instruments at this point.

Getting the chuck dynamically balanced is likely my next step. I don't know the exact set-up that is used to do that. I'm wondering if it is possible to dynamically balance the plastic chuck/motor assembly while they are attached to each other. That probably would make sense, if possible.

Hi no what I meant is remove the armature out of the motor casing just leave bearings on the motor shaft, remount your teflon thingamabob on the armature shaft as it would be in the finished unit and then have it balanced at the speeds to which you will use it. This is a specialised thing to do possibly some motor Rewinders will have the correct gear. Just let them know where they can add or remove material to your teflon unit

I'm hoping I'm understanding you... So you're suggesting that in order to dynamically balance the plastic chuck on the motor shaft, I should first take off the armature... and then replace it after the balancing process is complete? I apologize for my confusion.

That is exactly what he is suggesting...

BTW Nickname makes a very good case, especially given that I now know how this gizmo is going to be used.

The bottom line is that either approach is valid, however given the brittle nature of the material you are using, and given the forces associated with the movement and the sealing, I concede my approach and will take up his.

Get rid of the shaft entirely, so there is just the umbrella on the end of the motor shaft (make the rotating assembly as short and fat as possible), then have the assembly high speed balanced. If you can remove the motor rotor as suggested above and have it balanced with the teflon element so much the better.

Short fat and stiff is the ticket, but precision balance will make the difference.

Like this...

Yeah, what garth said. Thanks Garth.