I am trying to do a guestimate of a rotor design before first prototype to see if there may be any problem that can be "guessed" using the venerable Critspeed. So if anyone would have a estimated, suggested or tested bearing stiffness for a bearing with seismic mount on rubber isolation (in both ends) I would be grateful. Bearings are in one end a normal electrical motor and in the other end a single standard bearing. I can likely verify it in a few months but I would like to have a look in the crystal ball to make the designer aware of eventual problems. Olov

What is a standard bearing?

Found an old version of Crtspd? There are several versions. If you have a version that supports a dual level system, you might be able to make a simple model of the foundation, which might help with the seismic mount.

The seismic mount manufacturer should be able to provide stiffness for the isolators.

Thank´s Bill,
Yes I have used a DOS version of Crtspeed for many years. Standardbearing to me is the antifriction type bearing found in a typical electrical motor. Since this is a prototype stage and there is no prototype to calibrate simulation against the precision may only be like 50% or worse but I would like to have a hint on if we are facing a resonance in operational range btw. a few 100 RPM and 3000 RPM that I find likely, and if so in the upper or the lower end of that speed range. My gut guess is somewhere in the middle. Naturally, the rubber mounting is not yet selected so I was just looking for a rough number to get in the range at all. Olov

I suspect that the model you will end up using is a rotor with bearing stiffnesses, and you intend to lump the support stiffnesses lumped into the bearing stiffnesses. There is no support mass modeled, only the rotor mass (correct?)

This is a simple model that I often use. But I don't think it is good for this situation. I think this model loses accuracy when you have large mass of the support structure that is moving as is the situation for a machine mounted on rubber isolators.

OLI,

These guys use 200,000 lbf/in for ball bearing stiffness

http://istrdyn.com/includes/PT%20Example%20Analysis.pdf (page 10)

Pete has a point. Although my opinion is that the rotor model without all the support stucture considerations will at least give you a ballpark figure...

Hope this helps.

Well it´s a 25 Kg rotor with a lump of 5 Kg in the middle and a length of like 1 meter or so, I don´t think the antifriction bearings will make a major difference compared to the influence of the rubber mount that maybe will make it close to "free floating" and that is the number I am not so sure about or am I wrong? I will try some crude variations and see where it will end up. I basically would like to give the designer a input so he may see what problems there may or may not be when it´s still cheap to modify the design. Normally I have had a real thing to calibrate against that makes it easier. I have rarely tried a guess from a drawing only and then it´s been cases with more or less "normal" bearing stiff fittings where a input like Elias suggested is reasonably near. Olov

The series combination of the bearing stiffness and mount stiffness will be very close to the mount stiffness as you say.

In the limit where the bearing is completely rigid and assuming your rotor were rigid in the frequency range of interest, we would have in the vertical direction a simple SDOF mass spring system. The spring is the stiffness of parallel combination of your rubber mounts. The mass is the TOTAL mass supported on the rubber springs (both rotor, stator, and the entire structure that is mounted on top of the rubber mounts).

So if you were using only rotor mass, you would compute w=sqrt(K/Mrotor) when the real answer should be w=sqrt(K/Mtotal). Your system may not be exactly like this in terms of rigid rotor, but it is an example that illustrates that if you have substantial support mass moving, you need to model the effects of that mass or your result will be inaccurate.

This message has been edited. Last edited by: electricpete,

You can find formula for rolling element bearings. The Vibration Institute includes this in some of their literature.

Thank´s guys, I am not looking for a number on the antifriction bearing but a rough number on the rubber part. 1/100 of the bearing k or 1/400 or even more? I strongly suspect that the rotor is not a stiff rotor over the operational speed range so that is the reason for having a go on Crtspeed. I am trying to guesstimate if there will be a rotor resonance in the lower speed range or in the upper, that is the accuracy I am trying for. Olov

Hey Oli, can you get a sample of the rubber? If so you could do an experiment applying known weight to the rubber and measure deflection. That would at least give you a ball park number..

You may be going down the wrong path for this model. If the machine has rolling element bearings, and the case/support structure is isolated on rubber then just using a spring in series with the bearings to calculate an undamped critical speed is not correct.

If the support structure is stiff enough then it will act like a mass supported by the rubber isolators. To this the rotor is connected by presumably much stiffer bearings.

If one simply puts two springs in series, one may get an approximation to the free-free modes of the rotor, which is not what you want.

Where did you find a copy of critspd? The manual may be of help.

Sorry to beat a dead horse. I would like to take another attempt at explaining it to the best of my understanding (of course I am by no means any expert... I welcome corrections if I am off-base). This is a subject of interest to me, because I have the same model you are talking about available to me (I don't have the ability to model support mass), so I like to understand the limiations.

First, the fact that I assumed rigid rotor above does not mean the conclusion is limited to a rigid rotor. I only made that assumption because it results in a solution that is easy enough to visualize without computer solution.

So let's start again without that assumption.

System A: Ground === Kb == Mr
Kb is sort of stiffness of bearing and Mr is sort of mass rotor... except that I am going to declare that Kb and Mr are the MODAL stiffness and mass associated with the first critical speed of your flexible rotor, IF the bearings were on firm ground. The point is that we can reasonably represent your bearing/rotor as a SDOF system for purposes of determining first critical, even though you have a flexible rotor. It is certainly true if your system resembles a massless shaft with disk in the center.

System B: Ground === Krubber === Mskid === Kb === Mr
This is the real world system you are trying to model. Mskid is the mass of machine stator and everything (other than rotor) that sits on the plate or skid which is mounted on top of the rubber mounts. Krubber is the stiffness of the rubber mounts

System C: Ground === Krubber === Kb === Mr
System Cequivalent Ground === Kequivalent === Mr
This is your critspd model. Kequivalent = (Krubber + Kb)/(Krubber*Kb) ~ Krubber

So now the question, is: When can we replace the 2DOF system B with the SDOF system C? The answer is when the resonant frequency sqrt(Krubber/Mskid) is much higher than the frequency range of interest which will include the operating range and the sqrt(Kb/Mr). In that case, the subsystem Krubber == Mskid is "spring-controlled" and it's mass does not have much effect on the system dynamics, and we can discard Mskid without much loss of accuracy.

So, the simple Critspd model system C would be appropriate (we could neglect the skid mass) IF we can demonstrate that the frequency range of interest is far below sqrt(Mskid/Krubber). It could be a valid model if Krubber was describing a sturdy base support as many machine, but I don't think it would be a valid assumption when Krubber represents rubber isolators. I think if you bump the skid (minus rotor) on it's mounts you would likely still see a frequency below operating speed.

Another very loose way to look at it would be Raleigh analysis. The first resonant speed will be determined at the frequency/modeshape where the kinetic energies are equal to the potential energies. If the mass Mskid is small or is not moving very much, then it doesn't contribute much to the PE. In the flexibly supported system, it will probably alter the PE quite a bit and it's presence cannot be neglected.

This message has been edited. Last edited by: electricpete,

Well, we did buy it from the manufacturer long time ago and manual say version 1.02 1987, software say ver 1.04, what is the newest version known?
My problem is that I don´t have a rubber to check, the thingy is drawing only. So I will look in a catalog and get a reasonable number.
Mskid is likely to be less than 10% of Mr and Kb surely is a lot higher than Krubber so it comes down to be a play btw. Mr and krubber and the geometrics of the rotor in my simplified world?
Maybe a wise selection of Krubber will make the crit speed to be as low as a few 100RPM, my gut says that I would like to see that IRL before believing, but that is part of the reason for this exercise. Setup basically look like the 1 mass Bently rotor example but at a scale so I will start just entering the proper dimensions and material. Olov

This message has been edited. Last edited by: OLI,

Do you really mean that Mskid < 0.1 Mrotor?

As I know, there are two groups that have put out Crtspd (with possibly different spellings), Rodyn and UVA. Rodyn's proprietor is E. J. Gunter, and he directed the development of the early version of Crtspd on a desktop computer (HP 9845), while a professor at UVA.

UVA still has versions of Crtspd. This was developed as a transfer matrix program often calculating undamped modes with circular whirl.

You should be able to get forward whirl, backwards whirl, and order tracking modes. People still view undamped critical speed analysis in the design and review of rotors.

I almost forgot, Concepts ETI may be able to sell a version as well. It used to be on their web site. They have their own user interface.

Thank´s Bill, this is a Rodyn version. I tried to search for them a year ago or so but had no luck. I will look for the others. This is not something we use every day but from time to time it´s very handy. This old version still runs with XP. Yes this case is not a industrial rotor thingy but a more home appliance that will be made in 10 000´s per year they say. So there will be samples later this year but that is a bit late in my taste and a lot of work that still may be required. So yes the "sturdy" mount btw. the antifriction bearings and rubber mount will surely be less than 2kg.
Seems like Romac of UVA have CRTSP2 and some other nice things but you need to be a member. Concepts ETI have the DyRoBeS and that have a hefty price tag last time I asked. I actually now found Rodyn and it´s DyRoBeS that is promoted, wonder if they accept upgrade discount from 1987?
I have now made a couple of runs and to my surprise I can´t make the first critical go much lower than about 6000RPM even when fiddling with bearing stiffness real much. So maybe this is a lucky design. Time will tell. Thank´s. Olov

This message has been edited. Last edited by: OLI,

OLI,
Your calculated first critical of 6000 cpm appears to be a bending mode. The bending modes aren't going to change much at all with a resilient mount. The two modes you need to worry about are the rigid body modes (shaft straight, bouncing in it's bearings, first mode ends in phase, second mode ends out of phase).
The rigid body modes are highly dependent on support stiffness (your rubber mounts). In order to calculate where these will end up, you only need have the weight of your motor and get with the manufacturer of the rubber supports. Where a good number for estimated equivalent support stiffness for a motor on steel in concrete is 200,000 lb/in, on rubber this number could easily drop to 2,000 lb/in.

Ron,
Well, shafts are thin aluminium tubes so they seem to be pretty stiff compared to weight. I did start at a stiffness of normal but not rock solid bearings that I used before that has been working and that gave about 40000 RPM, reduced stiffness by a factor 10 that gave around 17000 RPM and than again to reach about what you suggested as at the bottom reasonable estimate another 10 times. So I also did think that a factor of 100 would be reasonable as an estimate. Whatever I did also trying to adjust weight distribution estimate at the most unfavourable I could make, still not getting lower than 5500 RPM. Yes you can clearly see the modes changing from the classic banana bending mode to rigid body motion dominating as you predicted. There are always a lot of unknown factors when comparing to the reality as connections between rotorparts etc. but anyway my suggestion to the designers can be to go for a as stiff design as possible to make it never reach the critical in operation and that was the question that was pestering me. I did think it would end up being at 1500 RPM by the looks but I am more used to steelworks and the drawing is one thing, all kinds of estimate can be wrong and we will eventually see by how much. Thank´s for thinking, and it feels good that we had some similar estimate of a factor 100 btw. normal and soft mount. I normally try to follow the rule of thumb that the mounting resonance using seismic mount would be 0.1x(the lowest machine speed) to get maximum isolation, in this case that would be less than 1Hz and will maybe be to flimsy, so it will likely be some compromise. Thank´s again for the input. Olov

Have you looked at what the static sag would be that would cause a 0.1 Hz resonance? 977.7 inches (24.8 m) - I would think that would be flimsy.

Bill,
Lowest speed is 400 RPM so it would be 0.7 Hz,
still flimsy. Olov

OLI,
Does the software you are using calculate the rigid body modes and does it give you a critical speed map (nat. freq vs equivalent support stiffness)?
With this type of output, it should be very easy to see the results based on choosing different resilient mounting types.
The attached file is an example critical speed map. The two bottom traces are the rigid body modes. As you can see, they are highly dependent on the support below the motor. The next line up is the first bending mode and the next line after that is the second bending mode. Does your software have this ability? If so, the answer to your problem should lie within it.