Vibration modes of rotating shafts

[UKpete]

In simple terms (!) what is the difference between a forwards mode and a backwards mode, and why do the vibration mode frequencies change as the rotor speed changes? I'm referring particularly to small v.high-speed machine rotors that operate above first critical speed.

 

[electricpete]

I am not sure if this is what you are referring to, but....

Let's say the support for your rotor has a different stiffness (and different resonant frequency) in the horizontal direction than in the vertical direction.

Start off at a speed below both H and V resonant frequencies. Both vibration displacements are in-phase with the forcing function. So there will be 90 degree difference between H and V.

Now increase speed until you are above one resonance and below the other. One of your two vibrations has now flipped it's phase 180 degrees with respect to forcing function. It can be shown by simple trig that this will be a reversal of rotation from the previous case.

Now when you increase speed past the other resonance you will flip the other, reverse direction of rotation of the vibration and be back where you started from (same direction of vibratio rotation as shaft rotation).

I think this would apply more to housing vib than shaft vib, I'm not sure.

There is a lot of discussion of reverse and forward orbit significance in Bently Nevada's literatue which is available on-line.

 

[electricpete]

Here is one article on the effect I was trying to describe:

http://www.bently.com/articles/articlepdf/695don.pdf

You will likely find quite a bit more among these articles:

http://www.bently.com/search/Search.asp?q1=reverse&ct=BNCArticles&so=Rank[d],DocTitle

Another cause of reverse orbit can be a severe rub (full annular rub?)

 

[vanstoja]

A good basic(though not certainly simple) discussion of forward and backward rotor whirling in a rotor-bearing system can be found in the following:
Nelson,F.C.(2002a), "Rotor Dynamics - Critical Speeds, Sound and Vibration, May,2002, pp.6-8
Nelson,F.C.(2002b), "Rotor Dynamics - Instabilities, Sound and Vibration, Sept.2002, pp.8-11
Nelson essentially says that if one element of a rotor system has a large polar moment of inertia (eg., a disk) it produces an inward, stiffening effect for forward whirl and an outward softening effect for backward whirl which raises forward whirl frequencies and lowers backward whirl frequencies as rotational speed is increased.

 

[UKpete]

electricpete, thanks for the links. I think the Bently tech note is referring to a different phenomena namely forwards and backwards orbits rather than forwards and backwards bending modes.

vanstoja thanks also for the references, but what is meant by forward whirl and backward whirl, is this also talking about the direction of the orbits? The way I remember bending modes being described, the first bending mode was referred to as a forwards mode (a simple bow shape), the second mode (typically the rotor taking up an 's' shape) was referred to as a backwards mode.

 

[vanstoja]

To UKPete
I never heard of forward and backward bending modes. Forward and backward whirl modes in rotordynamics refer to rotor orbit precessions which are co-rotational and counter-rotational with respect to shaft direction of rotation.

 

[UKpete]

I got it wrong actually - I have been receiving some training on the subject today. As you both say, the forwards and backwards modes refer to the direction of the whirl (i.e. orbits) relative to shaft rotation direction. I understand that each bending mode (0,1,2 etc.) typically has both a forwards and backwards mode, the backwards mode is usually not excited by out-of-balance forces but by gyroscopic forces and as such is not usually as dangerous.

 

[vanstoja]

Further insight into forward and backward whirling can be found in:
R.Gordon Kirk(2003),"Lund's Elliptic Orbit Forced Response Analysis: The Keystone of Modern Rotating Machinery Analysis", ASME, J.Vibration and Acoustics, Vol.125, Oct. pp.455-461
In a discussion of elliptical orbits, Kirk says, "A major basic understanding required in the study of dynamics of rotors is the concept of forward and backward whirl. Elliptic motion may in fact be whirling in one of two directions. A flexible rotor can have stations that whirl either forward or backward along the rotor, at the same time. Lund denoted a backward whirl by making the semi-minor axis value a negative value...[Shaft motion] amplitudes and phase angles can be obtained from experimental results(see Fig.5)if the direction of whirl is known. This type synchronous orbit and timing mark can be shown on a dual axis scope with z-axis input of the one per rev timing mark. The phase angles are dependent on whether the whirl is forward or backward...from (x,y) probes at 90 degrees, the whirl is backward if the phase lag difference for the y-phase minus x-phase lies between 180 and 360 degrees. For a symmetric system the phase lag difference will produce round forward/straight line/round backward/straight line for phase lag difference of 90/180/270/360 degrees respectively. The experimental result from the early 1970's for a test rig rotor is shown in Fig.6. This figure shows a strong backward mode and then a forward mode [at higher RPM] excited by very small imbalance levels. The rotor was operating on hard mount precision ball bearings. Numerous other whirl orbits are also visible in the attached scope
photo."
The last paragraph indicates that rotor unbalance, not just gyroscopic effects, can produce backward whirls.

 

[UKpete]

vanstoja thanks again, I'm slowly getting there. I will look up these refs.