To all,

I plan to perform an experimental modal analysis test (using an instrumented hammer and accel) on a 6' long 12" dia hollow roll situated in its antifriction bearings secured to a frame of machine. Unfortunately no animation software is available, but I think Excel will do the job by having relative amplitude-phase data at various points on the roll.

The suspicion is that one of the mode shapes is being excited, thus affecting thickness of the paper between the rolls.

Had anybody done something like that for product quality troubleshooting?

Thanks,
Dave

Dave,

If you measure the Transfer Function with accel/force, then plot the imaginary (IMAG) response where peaks are at natural frequencies and +/- amplitudes gives mode shape when plotted versus scaled distance along roll. Be careful about choice of impact or response locations to avoid a node point that may miss identifying a vibration mode. You should also measure in both directions (inline and perpedicular) to the bearing supports in case of different stiffness. You may also want to measure shell modes that are different from bending modes.

Walt

Any wrinkles on the paper or stretch? Does the thickness vary from side to side? Does it taper from side to side? What are the bearings clearances?

And, do you intend to secure the bearing or are you striking it hard enough to impact or ding it?

I would expect a roll of those dimensions would be pretty stiff on its own and hence high natural frequency (assuming that it has a decent bore of say 10” or more such that mass does not become the most influential factor in the natural frequency calculation w= sqrt k/m ) It could of course be vibrating as a whole body in the machine if mounting and / or frame is soft which would have lower natural frequency.

You may have already done so but I would begin with confirming (or otherwise) the pattern in your paper. Can you see the bars? If so roll out a decent length, count the bars and measure spacing.

How are you measuring caliper (paper thickness) at the moment? I have successfully used a micrometer in a case where the cross machine “bars” of different thickness could be seen. Also plugged an analyzer into an online caliper sensor to obtain data whilst machine is running. Using bar spacing and machine speed you can calculate a frequency, then look if frequency can be traced to roll. Analyzing paper at different machine speeds (if possible) will tell you more. For example, does bar spacing remain constant at different machine speeds? (In which case not resonance but roll barring) If spacing changes and frequency is constant you could be looking at a resonance. Rgds.

Sam, Vibe-rater,

This is actually a corrugated roll, so all it does is corrugating paper. Two rolls are engaged as in a gear set and are separated by paper.

I don't know in details as to what exactly gets messed up in the corrugated paper but it occurs only at a certain speed of the web. At that speed vibration on the roll's bearing housing is at maximum and process can not be sustained for more then a few seconds.

It has been determined that frequency of vibration ( and apparently the forcing frequency ) is Roll Mesh Frequency (RMF= Roll_RPM * #_of_teeth ) with harmonics. Preliminary bump testing showed no structural resonances at that frequency. The rolls (there are some other rolls involved, all pressed together ) are the only elements that may go into resonance and one of their resonance frequency with its associated mode shape may councide with RMF.

Walt,

I'm thinking to myself whether it is worth of trouble to acquire the Transfer Function and to costruct bending mode shapes? After all it is a beam clamped at both ends. The mode shapes for a beam are well known. So the only thing that may be necessary are only the resonance frequencies.

On another hand, assume that a Mode shape is determined and is being excited. In this case how does one determine from the Transfer function the actual deflection of a roll in thousands of an inch provided that values in the mode shape plot are all relative ???

Dave

Dave,

What is the roll speed and tooth mesh frequency?

You can do a simple impact test with a single channel analyzer to identify the presence of a natural frequency. It is far better to test with an impact hammer and 2-channel analyzer, because of the force-response values, Coherence to test data quality, mode shape (if needed), and damping (if needed). Obviously the roll is not a fixed-fixed beam, since the bearing have high vibrations.

Do not rule out a shell vibration mode without testing. Do not rule out a torsional vibration resonance, if all else is checked and the cause of the fault is still unknown.

Walt

Walt,

The roll has about 156 teeth and runs at 200 RPM.

Of course, no one would argue that acquiring a Transfer Function and constructing a mode shape is far better then a single channel bump test. I just don't have the modal analysis software to animate it. As I said Excel can do a static representation at various times. This may be sufficient for bending modes but not for shell mode shapes. (BTW, torsional mode shapes would be nice to acquire, but technically it won't be easy).

Still have the same question on how to determine from the Transfer function actual deflection (in displacement units) of a roll in when machine is running, provided that values in the mode shape plot are all relative ???

Dave

Dave,

The tooth mesh frequency is 520 Hz and should be very audible. This is a high structural frequency for what I would guess would be well above the first two bending modes of the cylinder. So unless the roll speed matched a bending mode, I would not think that there is a bending mode issue. I would certainly do a simple impact test and variable speed operating test to verify this. An impact test to above 500 Hz would require a hard plastic tip on the impact hammer.

Shell modes can be plotted in Excel using the Radar (quasi polar) Plot. Think of the sound of an aluminum baseball bat (about 2.5" diameter) and compare it to what might occur with a 12" diameter roll; similar but lower frequency!

A torsional natural frequency does not have to match the TM to have a problem. A much lower torsional natural frequency can cause the gears (rolls) to chatter that produces high noise and vibs. I found this probem in a gearbox. I would measure torsional vibrations by using a magnetic sensor or an optical sensor picking up the 156 teeth. A F-V converter could detect torsional frequencies up to about 250 Hz, and should be adequate for identifying a torsional "chatter" issue.

"Still have the same question on how to determine from the Transfer function actual deflection (in displacement units) of a roll in when machine is running, provided that values in the mode shape plot are all relative ???"

I don't have an answer, but it looks like trying to compare apples and oranges.

There are a lot of possible causes of your problem, and probably more than one way to solve it when you identify the cause.

Walt

Walt,

Yes, this thing is very noisy even when not causing product quality problems. So noise is considered to be normal evil. Also, preliminary simple bump tests indicated that tooth mesh excitation frequency is above first 2 bending modes.

The teeth are small, about 1/4 " high. It is unlikely they chatter, but I can't rule it out.

I'm attaching a waterfall plot. 3 resonances could be seen there. Tooth mesh frequency dominates the plot. 2x of mesh frequency is significant. I'm not sure if this could be interpreted as rolls misalignment or due to a mode shape at resonance. I'd like to prove/disprove existance of a bending or shell mode as causing excessive vibration.

Teeth profile may not be perfect, thus, causing excessive vibration, but in this case there is clearly a resonance ( at 206 RPM ) causing quality problems. There are two more resonances not causing problems. The question is 'What is the resonating component?'

Dave

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

Waterfall.doc (52 Kb, 18 downloads)

All the corrugators I have ever worked on (BHS, Peters, Mitsubishi, Langston, Agnati and others) have shown a tight speed range where severe vibration exists. I believe this to be a torsional mode causing teeth chatter. This holds true for A, B, C, D, E & F Flute corrugator patterns. Vibration wise it shows as very high toothmesh peak (in the high 100’s, the smaller the flute, the higher the number) with harmonics – your description would suit this pattern. Your tooth count suggests a coarse flute - like "B" Flute.

In all cases the vibration is passed through quickly and machine is never run at the “critical” speed for extended periods. Not sure what effects it would have on the cardboard / end result.

If there is a variation in cardboard thickness then I would have a serious look at whether it is possible the upper and lower corrugator rolls can move with respect to one another. Rgds,
ps. I don't think the presence of harmonics of FMF necessarily indicates roll misalignment or improper tooth profile - I think it is normal and related to the impactive nature of the mesh which Fourier states will generate harmonics.

This message has been edited. Last edited by: Vibe-Rater,

Dave,

I did some impact testing recently, at a factory where they make rolls for many different corrugaters. Attached is some of the data. Note that the testing was done with the rolls hanging in a sling from an overhead crane. I have lots more if you can tell me more about your rolls and machine they are installed in.

Corrugating_Rolls_FRF_Impact_Testing.pps (30 Kb, 18 downloads) corrugating roll impact testing

Vibe-Rater,

Was teeth chattering due to torsional vibration the diagnosis or just a suspect?

Regarding 2nd order of teeth mesh frequency... There is no impacting in there as could be seen. In fact it has a classical TWF pattern distorted by 2nd harmonic even in the acceleration TWF. That is where my diagnosis of misalignment or roll's shape distortion comes from.

I am not sure about exact number of teeth, as it has been derived from my vibration data, but it is a C-flute roll.

Hydraulic cylinders press the upper and lower corrugating rolls together. I have read (without knowing details) that another company which is making corrugated cardboard machines introduced some kind of damper in order to reduce vibration. I'd guess that it works in parallel with the cylinders? Of course, it does not eliminate the cause, just reduces resonance effects.

Unfortunately I don't have coherent information on how this apparent resonance affects the product in details, but I'll try to find this out.

Bill,

I have performed just a simple bump test on the rolls in-situ as oppose to your test performed on a free hanging roll. I wonder which one provides more information in regards to the problem I am coping with.

Also, what are the mode shapes associated with the identified natural frequencies in your case? Have you done torsional modal analysis?

These are also CRC C-flute corrugating rolls installed on Mitsubishi MHM machines. What information is still needed on my behalf? I'll appreciate any additional information you can share.

All,

Detection of torsional vibrations in general requires special equipment, as Walt mentioned. I wonder whether measuring motor current can help here? Had someone ever tried it?

Also, since there are two rolls meshing via a flute, wouldn't any torsional vibration along with vibration due to variable teeth meshing forces translate into radial vibration detectable on the bearing housing, which in fact has been detected?

Thanks to all.
Dave

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

Dave,

"Also, since there are two rolls meshing via a flute, wouldn't any torsional vibration along with vibration due to variable teeth meshing forces translate into radial vibration detectable on the bearing housing, which in fact has been detected?"

That's correct, but you need to know whether it is torsional or not to fix the problem. Motor current spectrum analysis may be useful if the torsional frequency is well below 60 Hz and can be seen as a modulation side-band of 60 Hz.

Another resonance mechanism comes to mind: assume that the two rolls are nonresonant masses in a spring-mass system, and the paper (in mesh) and the hydraulic cylinders and their supports are the springs. At resonance the rolls would move in-out of mesh in a radial direction to shaft axis. An impact test with the machine off may be difficult to prove this.

Has anyone inspected or measured the corrugated paper for patterns of thickness variations? This could reveal the type of roll movement; either radial or tangential (angular).

Walt

Hi Dave_man,
The torsional chatter is a suspect, not a confirmed via testing. We did not think it worthwhile investigating further since it was not out of the ordinary out of the many corrugator roll sets monitored. (and hence considered "normal" in the design) When machine speed was increased, there seems to be an abrupt point where the severe vibration kicks in and vibration reduced enormously only small speed increase later - so very tight frequency range. In all cases operators just avoid that tight frequency range. Rgds,