http://www.unitechinc.com/pdf/...WaveformAnalysis.pdf
On page 11 of 19 he states:

quote:

Amplitude Symmetry
When observing time waveform data symmetry above and below the centerline axis is important. Symmetrical data indicates that the machine motion is even on each side of the center position. Non-symmetrical time waveform data indicates the motion is constrained possibly by misalignment, or rubs.

[shows a non-sinusoidal velocity TWF]

This waveform pattern is symmetrical above and below the zero line.

I don't understand the logic here.

First of all – what the heck is meant by "constrained". Pretty much any system is "constrained" unless it is operating far above resonance, correct?

Perhaps he meant constrained in a non-linear manner? But that doesn't really make sense... the example waveform shown is non-sinusoidal and is identified as not constrained and apparently not an example of misalignment (which he states would create the assymmetric pattern). So I presume it is a sinusoidal forcing function acting on a non-linear system.

Perhaps he meant constrained assymetrically from above/below (or from left/right). I could buy that if we were looking at a displacement TWF. But I don't think displacement being symmetric above/below zero is not the same thing as velocity being symmetric above/below zero.

Also, I'm pretty sure if I looked at some bearing impacting waveforms in velocity I could find lack of symmetry. Is that supposed to have something to do with constraint (rhetorical question)

I am not meaning to be hung up on the terminology of "constrained". I just honestly don't understand what the logic of what he is trying to say.

What is it we are supposed to learn from the fact that the velocity TWF is not symmetric with respect to zero... and why?

I do not have a clear answer but let me through my 2C.
Your argument reminds me about the topic of "velocity orbits". I guess the difficulty comes because of that the physical interpretation of velocity motion/trend is not as intuitive as displacement motion/trend.

Theoretically, the velocity of a vibrating mass is related to the damping but it is governed by all the parameters in/affecting the system (mass, accel, damping, vel, stiffness, displacement, force). The entire system could be linear but the force might not be constant which leads to impure sinusoidal response.

On the other hand, the plots that we have from the real cases can be processed from/to velocity. Some classical rub cases collected by relative probes show truncation on the peaks of the displacement waveform. This truncation when differentiated to have the velocity waveform, turns to be zero. This part of the response is sometimes explained as nonlinear and "constrained". The peaks in the velocity waveform should refer to the least resistance times in the response not the highest.

Just thoughts.

El'Pete,

I can't speak for the author, but I doubt that Symmetry means the Shape of the waveform is identical above and below the 0-amplitude axis. A Sine wave has true Symmetry, but two Sine waves with a phase relation could be assymetric yet have the same positive and negative peak amplitudes. My definition of Symmetry would mean that the positive going amplitudes are nearly equal. Asymmetry would indicate that positive going amplitudes are much higher then the negative going amplitudes or vice-versa. This would indicate that either/both the dynamic force or the structural properties were nonlinear. Typical ICP accelerometers have positive amplitude for vibration outward from surface and negative motion is inward. The waveform can indicate the direction of greater motion.

Walt

This message has been edited. Last edited by: Walt Strong,

I read it as, it could be symmetrical but not necessarily. Symmetry produces one while non-symmetry produces another ____________ set of logistical circumstances.

I think I'm more in line with Walt and Pete I don't think you are out of line with your line of thinking but merely didn't read into it what I assumed it to say or I could be wrong.

As perhaps, an aside, this leads to a larger issue: if we are using an accelerometer (90% of all analysis?), then the physical property we measure is acceleration, and the acceleration waveform is the "purest" form of data we have available (with A-D conversion). Everything else (spectra, velocity, displacement) is just math. We should be careful of how we interpret these mathematical conversions. Right?

The way I read author's intention is to show that a symmetrical TWF signifies symmetrical motion from the rest point regardless of units of measurements.

If TWF is not symmetrical then there is some sort of restriction ( constrain ) in motion in this direction. One can also call it non-linear mechanical resistance in this direction, such as due to misalignment or rub.

Again, units are irrelevant. Assymetry in TWF will show up regardless.

An interesting point shown is that when looseness is present causing impact, low harmonics are much smaller in magnitudes then that in the higher range.

quote:

Again, units are irrelevant. Assymetry in TWF will show up regardless.

Here is one example where we could say the displacement and velocity are symmetric about the horizontal axis and the velocity is not. But maybe the definition of symmetric deserves some more thought. The two half-cycles of displacement and acceleration are mirror images around a horizontal axis and around a time. This is one type of symmetry about the horiziontal axis, although it is not "half-wave symmetric". I'll think about some more examples.

DVX_DifferentWRT_Zero1.pdf (28 KB, 47 downloads)

Pete, I take my statements about units back. As you have shown same data in VEL appears to be non-symmetrical, whereas in DISPL - symmetrical. At least in some cases.

This fact adds up a whole new burden to TWF analysis: do we really want to analyze TWF asymmetry at all ? and draw conclusions based on that. Frankly, I am not sure if we do.

Another option is to analyze data in all 3 units of measurement: DISPL, VEL, ACCEL. If all 3 of them show asymmetry then there is some problem.

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

Rusty is correct with his statement or eluding into 'right?': the data integrated are only relative and not absolute and David's conclusion is correct. I never use Vel TWF from an accel; why bother - acceleration is adequate.

Here's one thing that David's comments made me realize:

look at half-wave symmetry:
y(t) = -1*y(t-T/2)
where T is fundamental period.
It means any half of a period is an inverted copy of the previous half of a period.

Odd harmonics have half-wave symmetry (based on fundamental period T). A sum of odd harmonics will have half-wave symmetry. If we differentiate or integrate it, it is still a sum of odd harmonics and therefore still has half-wave symmetry.

So, if half-wave symmetry is what is meant (I suspect it is), then any conclusions about half-wave symmetry applies the same to displacement as to velocity as to acceleration (provided the same frequencies are dominant in all three). But we could also verify the same property by looking at the spectrum and checking for only odd harmonics.

At any rate, it makes a little more sense now. Half-wave symmetry in displacement tells us something closer to physical intuition. If we see half-wave symmetry in velocity or acceleration it also applies to displacement.

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

quote:

This fact adds up a whole new burden to TWF analysis: do we really want to analyze TWF asymmetry at all ? and draw conclusions based on that.

We find that a pronounced amplitude difference one way (that is, the waveform has higher amplitude one way or the other; either positive or negative), along with a bunch of running speed harmonics in the spectrum, is a reliable indicator of bearing sleeve looseness. This seeems to be most apparent in the velocity waveform. It's not always obvious in the acceleration waveform.

quote:

Pete Quote:
Perhaps he meant constrained in a non-linear manner? But that doesn't really make sense... the example waveform shown is non-sinusoidal and is identified as not constrained and apparently not an example of misalignment (which he states would create the assymmetric pattern). So I presume it is a sinusoidal forcing function acting on a non-linear system.

Pete,
I think the waveform on page 11 is not the one the author is referring to as being "constrained", as you stated in your original opening thread,

quote:

the example waveform shown is non-sinusoidal and is identified as not constrained and apparently not an example of misalignment (which he states would create the assymmetric pattern) So I presume it is a sinusoidal forcing function acting on a non-linear system.

.
but the one on page 12. (see the attached file). Page 11 is, to me, an example of one that is not constrained. I may be wrong, but from what I read in his paper, and from my experience, this is the one, page 12, "constrained".

I can't say for sure, but he may be using the word "constrained" to simplify matters for simply-minded folks like me. Sometimes one word can say what many words stumble around and try to say. The machine is "allowed" or free to move more in one direction than the other, hence, "constrained" and exhibiting a waveform with a higher value, either in the "+" or "-" direction, in reference to the "zero" scale line, regardless of the units used, (well, "regardless", to some degree) .
(one definition for constrained is: "To inhibit or restrain; hold back")

Only my opinion and I could be totally wrong.

Author's_Opinion.doc (134 KB, 18 downloads)

In the example below, based on the spectrum pattern ( multiple 1x's and 1/2x's ) looseness can be clearly diagnosed, likely bearing-to-shaft fit.

TWF was collected in ACCEL units and integrated to VEL by the software. My question: is it worth to analyze TWF's asymmetry or other features in VEL ? Doesn't the spectrum tell us all?

TWF in g's appears to be more informative.

IMO, analysis of a TWF for asymmetry/clipping makes sense ONLY when data is taken with a displacement probe on shafts?

Velocity_TWF.doc (78 KB, 23 downloads)

Here is an example sort of like Ians is possibly referring to on sleeve bearings. The first one in the doc file is in velocity (converted from acceleration) and the second one is in acceleration (stored units). Did not convert to displacement, too ridiculous looking.

This message has been edited. Last edited by: Ralph Stewart,

waveform.doc (143 KB, 30 downloads)

quote:

Odd harmonics have half-wave symmetry (based on fundamental period T). A sum of odd harmonics will have half-wave symmetry. If we differentiate or integrate it, it is still a sum of odd harmonics and therefore still has half-wave symmetry.

What about even harmonics?

sin(2w-pi) = -sin(2w); same for cosine

Note I said "based on the fundamental period T".
i.e. the "half" in "half-wave symmetry" refers to half a period of the fundamental

Let the fundamental period be T

First harmonic: sin(2*pi*t/T). *
It does have half-wave symmetry:
Verify by substituting t = t-T/2:
sin(2*pi*<t-T/2>/T) = sin(2*pi*t/T - Pi) = - sin(2*pi*t/T) (confirms half wave symmetry)

Second harmonic: sin(2*pi*2*t/T). *
It does not have half-wave symmetry:
Verify by substituting t = t-T/2:
sin(2*pi*2*<t-T/2>/T) = sin(2*pi*2*t/T - 2*Pi) = sin(2*pi*2*t/T) (confirms no half-wave symmetry)

Third harmonic: sin(2*pi*3*t/T). *
It does have half-wave symmetry:
Verify by substituting t = t-T/2:
sin(2*pi*3<t-T/2>/T) = sin(2*pi*3*t/T - 3*Pi) = -sin(2*pi*3*t/T) (confirms half-wave symmetry)

Nth harmonic sin(2*pi*n/T)*
Check by substituting t = t-T/2:
sin(2*pi*n<t-T/2>/T) = sin(2*pi*n*t/T - n*Pi)
For n odd this is -sin(2*pi*n*t/T)
For n even this is +sin(2*pi*n*t/T)
This confirms half wave symmetry exists for only the odd harmonics.

* - Note each of the harmonics could include an arbitrary phase angle theta such as sin(2*pi*n<t-T/2>/T - theta). However theta does not affect the conclusion and was ommitted for brevity.

If you think about it, comparing half wave symmetry at the fundamental is perfectly logical. A complicated periodic waveform has half wave symmetry at it's fundamental frequency/period if and only if each harmonic has half wave symmetry at that fundamental frequency (i.e. only if all harmonics odd). In contrast, talking about half wave symmetry of a harmonic based on half the harmonic period is pointless because all sinusoids are half-wave symmetric about their own period and it does not allow us to make any conclusions about the symmetry of the composite waveofrm.

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

Ralph,
Thanks for your response.
I'm not sure if your example is of a sleeve bearing (journal)?. I was more referring to a REB with a withdrawal or adaptor sleeve.

This example also has the waveform collected in acceleration, then converted to velocity by the software. The acceleration waveform doesn't seem to me to have a particular positive or negative bias, but the velocity waveform does. We find that this helps in confirming a sleeve looseness.

looseness.doc (52 KB, 26 downloads)

Thanks for all the comments. I am still mulling over what significance to attach to these types of features of the TWF.

Attached is TWF measured on frame near top of a vertical motor (rlling beairngs). Slide 1 shows the fundamental period appears to be 0.5x however there is a gradual change in pattern over the course of 2 seconds (we routinely see the overall slowly vary during data collection).

Slide 2 is zoom in.

Slide 3 shows the same velocity TWF with superimposed computed displacement and acceleration waveforms. The displacement and velocity are clearly non-symmetric above/below zero in all senses of the term. The acceleration TWF is relatively symmetric above/below zero in the sense that the peaks above/below zero are roughly the same magnitude (however it does not have half-wave symmetry).

So, what conclusions can be drawn from symmetry/asymmetry in this case?

What conclusions can be drawn from the TWF in general. My reaction would be looseness but still thinking about it.

I am having a hard time explaining the slowly varying nature of the TWF. I would expect this if I had non-synchronous components, but everything seems to be 0.5x/1x/1.5x etc as shown in slide 4.

By the way, any comments on overall diagnosis are welcome. This is the continuing saga of the machine described here:
http://maintenanceforums.com/e...51089011/m/819106752

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

LPHD22twfpostsmall.ppt (507 KB, 19 downloads)

EP,

I just want to make a statement that symmetrical sinusoidal TWF in g's will also produce symmetrical TWF in VEL and DISPL assuming no errors occur during integration.

The opposite is also true. Therefore, the assymetry you see in VEL and DISPL is present because there is assymetry in ACCEL. In ACCEL units it is just not that noticeable visually.

I agree with your comments if you substitute the term "half-wave symmetric". As mentioned above, half-wave symmetry corresponds to a waveform which contains only odd harmonics. Differentiating/integrating don't change which harmonics are present, so the half-wave symmetry doesn't change when converting among displacement, velocity, acceleration.

There are other meanings of the term symmetric.

The articifical waveform I posted Posted 22 June 2009 01:43 PM is one type that I think most people would call symmetric, but it is not half-wave symmetric. In that case seeing symmetry in one type of waveform (displacement, velocity, acceleration) does not guarantee symmetry when converted to another type as we see in the pdf.

Some people responding in this thread use the term "symmetry" to refer to the fact that the positive peaks are the same magnitude as the negative peaks. Let's call that "equal-peak-amplitude symmetry". The ppt posted directly above is a real-world example where the acceleration has equal-peak-amplitude symmetry but the the displacement and velocity waveforms do not.

Interesting to look back at the original Dunston article example of a "symmetric" waveform. If you look closely at the spectrum, it is not half-wave symmetric. It has very large 1x, and then small harmonics with decaying magnitude but odd harmonics are not greater than even harmonics (other than 1x). The waveform closely resembles a sinusoid which is symmetric. But the small deviations from sinusoidal behavior in this twf are not at all symmetric. So it does not give any clue what type of symmetry he is refering to because it is only symmetric by virtue of being primarily sinusoidal, and a sinusoid meets all of the types of symmetry discussed.

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