I am not able to understand why a flexible rotor flexes in the vicinity of 1st critical and then the flexure decreases,where as a rigid rotor does not flex at 1st critcal speed.My be it will sound like a silly question,but please explain to me ,why it flexes becasues the stiffness is less and what makes the flexure to decrease after 1st critical.Can any of the readers explain in the most simple manner psooble.Any power point presenation about critcal speed?
In my world there is no rotor that is stiff around itÂ´s 1 critical and no more after that. I define a stiff rotor as being stiff reasonably lower in speed than the first critical, when itÂ´s getting closer to the critical itÂ´s flexible and it will remain so at all higher speeds, to simple view? Olov
olov dot li at vtab dot se
www.vtab.se Good Vibrations for 40 years and first vibrometer patented 60 years ago 2012
As long as this isn't too philisophical of a discussion, here goes.
It's a natural frequency.
Ok, what is a natural frequency but a frequency where the subject likes to deform.
If we look at how one calculates and defines a natural frequency, that might help. To find a natural frequency one writes the equations of motion with no force, an unforced problem. A non-trivial solution to the unforced (0 forces) equations of motion is a natural frequency, i.e. the object likes to vibrate at that frequency - it has a mode shape and frequency that solves the equations of motion with no force; it is very happy at these frequencies.
Ok, typically these frequencies and modeshapes (for rotors, particularly) are complex - that is a story for another day.
A critical speed is when the rotor operates at (actually, near the complex frequency) a natural frequency.
I do not believe that there exist any rigid rotor design.
If one was able to rotate a typical rotor at an infinite variety of speeds, sure enough the natural frequency/critical speed of the rotor would manifest itself at a certain speed by vibrating to a more or less degree of vibration, depending on the amplitude of the exciting force such as the tiniest amount of residual unbalance, as an example.
Look at natural frequency or critical speed if you like, as you would for a tuning fork.
Give the tuning fork a slight tap and it will vibrate at a certain frequency depending on its size. The same goes for a rotor. That is its natural frequency.
If we change a feature of that same tuning fork, by either shortening it or grinding off some weight off it, then the frequency will change.
If a rotor is of a design that allows it to bend when supported between 2 supports/bearings, that deflection will act as an unbalance when being rotated.
Then, it will vibrate to a certain degree at some rotational speed. Unfortunately, that speed may be the operating speed for which it has been designed.
Or, it may run thru its critical speed while being accelerated to its operating speed; that is not an ideal situation if that equipment is subjected to a lot of stop and start cycles.
Experienced rotor equipment designers will always attempt to have the rotor critical speed to be beyond operating speed. That is quite a feat to perform for high speed rotating machinery.
Hoping that I was some help.
If you will send me your email address, I will send you a paper/case history on flexible rotors and balancing. email@example.com.
The Balancing Systems Group, Inc.
1706 Sabine Lane
Richmond, TX 77469
Are you saying that if a rotor has sag while not rotating that this will act as imbalance?
Not all rotors are designed to operate below a bending critical. In my industry almost all (if not all) centrifugal compressors operate above the first critical speed. Turbine generators operate above 1 or several. Washing machines have a soft support and operate above the critical.
Reply to Bill :
Yes, I am sure of it... the rotor mass will be rotating about a false axis. Now... I'm not talking about a lot of deflection.
And the worst of it, if that rotor is balanced at a speed lower than its operating speed which is the case for shop balancing most of the time, it may not show due to the parasitic mass of the rotor and of course, lesser centrifugal force trying to move that rotor.
Therefore, when the rotor operates at full design speed, it will likely show still some unbalance.
Yes, I agree that most rotating equipments operate above their natural frequency, and that is OK for machines that do not always have to be stopped and started often.
I've seen some generator rotors shake like the dickens, almost to destruction, when passing thru 1st critical and then, purr like a kitten at operating RPM.
The draw back with that approach is that every time a rotor goes thru a lot of shaking, parts get loose, motor rotor bars crack, rotor pole windings get loose, etc. etc.
I believe that you will be in accord with this.
As I've said, designers hope and try to design rotating equipments whose rotors are 'rigid' rotors, but it is dangerous to do that because one may bring the 1st critical too close to operating RPM.
Sometimes... it is better to run thru it.
Reply to Earl : Is your message directed to me ?
MarkoLeoThis message has been edited. Last edited by: Markoleo,
Thank you Mr.Earl Halfen.My e-mail address is<firstname.lastname@example.org>
Thanks for the replies from all of you.I hope more experts will write.
This would imply that a vertical rotor of the same dimensions would not be imbalanced whereas a horizontal version would be. I think if you check the facts/research regarding this you will find it not so. Hysteresis is required to couple the gravity force to rotational stuff. The gravity sag does result in alternating stress to what ever degree present; this should be benign – otherwise there is a design/life issue – of course misalignment could cause a problem like this.
Again, many rotors are ˜designed' to run above the first critical. These are designed for this; there is no mistake by the designers. API speaks extensively on this. Washing machines aren't meant to be rigid during the spin cycle; otherwise, that misplaced towel would create havoc.
Good morning Bill,
In fact, we are saying the same thing but in a different way.
A small question, Bill.
What is your opinion regarding a possible installation of Vertical Pump Assemblies at an incline from the vertical, say... 20 to 30 degrees.
Just wondering if that would not resolve some of the vibratory problems caused by lateral instability of the rotating elements due to minute bearing clearances vs gyroscopic phenomena ?
Installing a vertical machine with a large tilt would be interesting, but you would probably just be looking for trouble.
If one has a lateral instability in a vertical machine with fluid film bearings, look for a bearing change (complete analysis recommended prior to design change) - this may be an easy fix. If it has rolling element bearings, time to investigate, and squeeze film dampers may be an option. Supports conditions need to be reviewed (resonances).
I guess you have a good point, Bill.
You could not have a Kingsbury type bearing at the top, that is for sure.
Any kind of thrust bearing for that matter would be a problem.
Although, two bearings could be used at the top; one for the thrust and a guide bearing, either roller or ball, for radial loads.
Still, lubrication would present a problem.
Interesting thought tho.
Have a good day,
Can I have this paper/case history please.
My e-mail is email@example.com
I'll appreciate if you can email me the paper
Ditto on the paper, shoot me one too!!
I am not sure where this thread was headed, but back to your original question, "why does the flexure decrease after going through the first critical?" Rotors operating below or near the first critical have a "first mode shape" which exaggerated looks like a U or a jump rope. If there is static imbalance in the rotor, it will be magnified as the rotor approaches the first critical. Static imbalance is most effectively balanced by placing a weight in the mid-span. It is often impossible to put enough weight in the end planes to balance a first critical vibration.
Once the rotor has passed through the first critical, the rotor begins to move from the "first mode shape" to the "second mode shape" that exaggerated would look like an S. As the rotor moves away from the first critical toward the second critical, the mid-span of the rotor is pulled back toward the center of rotation. The vibration levels seen at the first critical decrease as the effect of the first mode shape decreases. That is why a rotor may shake going through the first critical and be relatively smooth at running speed.
There may still be static imbalance present, but its effect is not magnified.
Low speed balancing is usually effective at reducing vibration at the first critical, because the rotor is in the first mode.
All rotors sag. The amount of sag depends on the rotor geometry, material and construction. The shape the rotor takes is that of a catenari, most commonly seen is sagging transmission lines. The rotor center of rotation maintains the catenari during operation. The rotor must be flexible to do this. Rotor that have been sitting still will take a temporary set, where the flexibility is lost until it rotated sufficently on turning gear to reestablish it. Operators monitor rotor eccentricity to make sure the rotor does not vibrate excessively on start up.
I hope this helps.
John B. Lovelace
Simon, let me take a "shot" at this. It's not the simplest theory to explain on a forum.
First, by definition, a rigid rotor is just a rotor that operates below the 1st critical. If that rigid rotor is operated at sufficient speed, it will pass through a resonance. See response after next quote for second part of the question.
Don't think of it as the stiffness changes; it's related to the forces due to the square of the angular velocity and stiffness cancel each other at the resonance, leaving only the damping force to control the amplitude.
The square of angular velocity (acceleration) leads displacement by 180 degrees. Before the resonance the dominating force is due to the stiffness component (stiffness * displacment). Above the resonance the dominating force is due to the square of the angular velocity (angular velocity ^2 * mass). At resonance the 90 degree phase change is seen since the damping term (angular velocity * damping coefficient) is a function of angular velocity, and velocity leads displacement by 90 degrees and lags acceleration by 90 degrees. Below the resonance the rotor tends to rotate about its geometric center, while well above the resonance, the rotor tends to rotate about its mass center. Since the angular acceleration is the dominant factor, we see a 180 degree phase shift from the original response.
I believe that 'flexible' and 'rigid' are shorthand for the design of the equipment. A 'rigid' machine had a natural frequency, but the equipment is not designed to reach a speed which will be affected by it. e.g. a machine which shows change of phase in getting to running speed will not be 'rigid'.
Please refer to the attached definitions from international standards for both rigid and flexible rotors.
Regarding the original question (explanation of why vibration increase till rotor reaches the critical speed then it decreases) first, usually rigid rotors run below their critical speeds and hence they do not experience the condition of resonance.
Second, rigid rotors are designed to have less elasticity compared to flexible rotors. So, when if both undergo the critical speed, the rigid rotor will be less affected.
Third, for both rigid and flexible rotors, the rotor internal resistance to vibrate due to an external force changes with speed. At low speed, the stiffness is the main resistance; around the resonance, the damping is the main resistance; above the resonance, the mass is the main resistance. If the damping is low, high vibration will be encountered while passing the critical speed; otherwise the vibration could be smaller than that generated by a small unbalance at higher speeds.
Hope this helps a little and this is only MHO.
Thx- Ali M. Al-Shurafa
Doc1.doc (102 Kb, 55 downloads) Definitions
Would you please send me the case history you cited to Simon. I would be very interested in reading it also.
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