Another philosphical question/comment.

Down where I live in a rural area of the Texas Gulf coast, we have large yards which require a riding lawnmower. We also don't have sidewalks - instead we have ditches along the road. As much as I hate to admit it, the climate and the little critters around here are similar to Louisiana. In particular, when it's wet outside, little critters called crawdads build little piles of dirt in the ditches. A crawdad is also called a crawfish... it looks a little bit like a lobster. People in Louisiana might even tell you it tastes like a lobster. Myself, I don't eat stuff that grows in my ditches ;-) (Just kidding you Louisiana guys)

This morning I was mowing my ditches and running over dried up piles of Texas clay/dirt that used to be crawdad piles. And I noticed (no surprise) that when I ran over them going full speed, it's a bumpy ride. If I slow way down, the bumps are tolerable. My rump-meter tells me the acceleration and force is roughly proportional to speed^2. (maybe someone can explain that with a math model?) It's the same as if you hit a pothole while driving a car. If you hit a pothole going twice as fast the acceleration and force are in the neighborhood of 4x as bad.

So let's name it the "crawdad pile effect": The force and acceleration from hitting a crawdad pile or pothole is roughly proportional to speed^2.

As I was mowing my lawn and running over crawdad piles in the Texas sun with 95 degree heat and 99% relative humidity, I naturally started wondering what the crawdad pile effect tells us about ball bearings.

What are the implications of the crawdad pile effect for estimating the life of rolling element bearings?
The classic lifetime equation assumes that each revolution contributes the same amount to lifetime, regardless of speed:

L10(revolutions) = 1E6 * (C/P)^3 revolutions.
where C = bearing load rating and P = actual load

Or considering we have 60* RPM revolutions in 1 hour, the above relationship is often expressed as:
L10 (hours) = 1E6 * (C/P)^3 / (60*RPM ) hours

The crawdad pile effect suggests two objections to this approach:
#1 - Smaller objection - A large number of defects develop through contamination. (This is sometimes captured in life-adjustment factors which are based on lubrication conditions -but not speed to the best of my knoweldge). The crawdad effect tells us that contamination will cause more severe damage to a high-speed bearing than a low-speed bearing for each impact.
#2 - Bigger objection - Regardless of how the defect originates, a defect will eventually appear. We all know there is a long time between first formation of a defect and eventual complete functional failure of the bearing (I have seen a lot of bearings with defects on the races and balls but very few bearings that actually stopped working). So once the defect develops we have a lot of life remaining. What determines how fast it degrades once that initial spall forms? The crawdad pile effect would tell us that each impact on that defect would be much more severe for a fast-speed machine and therefore it would take much fewer revolutions to completely fail. So we shouldn't just be looking at revolutions but also speed. If the impacts for the fast machine are worse by a factor of speed^2 and the number of impacts per hour is worse by a factor of speed^1, then shouldn't the degradation on the fast speed machine be worse by a factor of speed^3?

Do you guys agree it sounds like the classical approach ignores the crawdad pile effect?


What are the implications of the crawdad pile effect for analyzing rolling element defect severity based on vibration?

Let's say we see TWF pk/pk value of 3 g's on two machines - one is 3600 rpm and one is 1200 rpm. How do we interpret it?
I would say from the crawdad pile effect that the visible damage on the slow machine is worse. (Would you agree?). That seems like an important point. If you are using peak/peak acceleration TWF as a criteria, don't expect to see as much visible damage when you make a call on a high speed machine as a low speed machine.

Now even though the slow speed bearing has more damage, it's going to degrade slower (crawdad pile effect degrades the fast speed machine faster). So which is really "worse" in terms of time to failure I don't know. ... maybe the pk/pk acceleration approach as a severity criterion is just fine from this standpoint. Another complicating factor to mention in analysing time to failure - if classical fatigue life theory was used for sizing the bearings, the high-speed bearing (assuming it is the same size as the slow-speed bearing) would be limited to a lower load which favors faster degaradation of the slow-speed bearing. My gut feel is that the speed^3 increase in degradation disdcussed above is going to be the overriding factor and fast-speed bearing at 3 g's pk/pk might possibly be considered worse. But that's just a feeling...I'm not ready to change any limits based on that. And I know the peak acceleration rule is time tested.

But I still think there are two interesting results:
1 - Classical fatigue life approach seems to ignore crawdad pile effect.
2 - A slow speed bearing will likely show more visible damage than a high speed bearing when removed , given that they both had same level of pk/pk acceleration.
What do you think? Have I gone off the deep end this time? Interested to hear any comments.

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

After thinking some more, probably the first question before any of the others should be:

Do you agree that a given sized defect on a given size bearing under a given load will generate higher g's, higher force, and higher degradation rate if the bearing is rotating faster?

quote:

Do you agree that a given sized defect on a given size bearing under a given load will generate higher g's, higher force, and higher degradation rate if the bearing is rotating faster?

Yes. This is easily seen in heavy dryer cans on a paper machine, variable speed, where a can will turn between 30 and 70 rpm, depending on the desired fpm speed.

EP,

The crawdad (that's what we call them in WV too!!) pile effect beats anything I've read on this board for a long while.
One of these days I'm coming to Texas just to meet you. Any man who can turn up bearing questions from running over crawdad piles with a lawn mower I'd like to meet and shake his hand.

I do most of my "good" thinkin when I'm mowing pasture. Something about mowing and not haveing a whole lot else to do (other than stay as cool as possible) lends one to deep thought.

I have to agree with your theorum.
Dave

I don't work with slow-speed machinery much.

I did see in the excellent CSI literature, the attached graph for alarm limits for pk/pk acceleration.

The value listed would be an alert limit for inner race, ball defect or cage defect. Multiply by 2 for outer race. Multiply by 2 to convert alert limit to alarm limit.

I notice he lowers the limit below 900 rpm which may be somewhat consistent with what I said above (assuming the alarm is to be based on finding visisble damage, not on time to failure). However there is a constant limit betweeen 900 rpm and 4000 rpm. Does anyone have any explanation for the shape of that curve?

csi_pk_pk_twf_limits.ppt (95 Kb, 56 downloads)

Possible the sun effect - been out in it too long. Have a nice mow. There's also the curbing effect. It's like slagmites and slagtites in a cave - little pile protruding up from the ground; little protrusion downward onto the seat know as the hemlaroys. When the hemlaroy is equal to the dadspile the dB level is increased by ^8 but this is just a rule of thumb. When passersby stop to give assistance it's a factor of^12 and near destructive forces and definitely time for repair.

Sam - Good one. The sun was pretty bad yesterday. Don't forget the non-linear effect of preparation H.

I forgot to say that I consider Peakvue pk/pk parameter roughly the same as acceleration TWF pk/pk, only Peakvue is a little better at catching the true peak.

Regarding the speed^2 relationship:

For the lawnmower, I think I can come up with reasonable explanation that Force ~ acceleraiton ~ speed^2:
- Let's say the geometry of the bump causes me to change my velocity by an angle theta in distance L.
- The acceleration a ~ deltaV/deltaT=[V0sin(theta)]/[L/V0]
- The above result is proportional to V0 ^2

For autombiles hitting potholes, I think the shock absorbers change the picture significantly since they do not transmit high frequency forces well in either direction. (My lawnmower doesn't have shock absorbers).

For rolling bearings, I'm sure the behavior may be a lot of different for a variety of reasons which might include external loading and wide range of speed much faster than the lawnmower. But still interested to hear any comments. On variable speed machines like Ralph mentioned, how fast does peak acceleration of a defect change with speed?

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

Leave it to e-pete to take a crawdad pile and a riding lawnmower and turn it into a mathematical equation. May want to spend just a wee little bit less time in the sun .
Excellent thought provoker though.

I'm struggling, but so far I'm keeping up. Anybody got a copy of "Mechanical Engineering for Dummies?"

Pete,
There seems little doubt you are correct in this.
There's an engineering discipline called "dimensional" analysis, wherin a behaviour can be correlated in terms of "dimensionless parameters". It really helps us understand how things scale.
In this case, where you are interested in acceleration A, velocity V and a length scale L, the dimensionless parameter would be:
A*L / (V-squared).
In other words, acceleration must scale as velocity-squared divided by length. To be more complete, one could add another parameter, the "aspect ratio" of the defect, ie L / H which is also dimensionless. This second parameter would capture the scaling effect of depth and length of defect. ie shallow and long - lower acceleration ; deep and short - higher acceleration.
Also of course, velocities would scale with the "DN" of the bearing.
I hope I haven't confused anyone with this. But it's really powerful stuff, and it works.

I don't have the equation handy, but I thought it was common knowledge in the "balancing" business that force generated by an imbalance varies as the square of the rpm. I would think that by extension, this would probably apply to most forces in a piece of rotating equipment.

I once had a Toshiba motor guy tell me that motor bearing life varies inversely as the cube of the speed. So if you double the speed of a motor, bearing life is reduced by a factor of 8. Experience tells me that is about right.

As I always tell my customers, "Speed kills!" I don't have numbers to prove this, but my contention is that a 3600 rpm pump will have a life cycle cost of 10x that of a 1200 rpm pump doing the same work. I don't think that in 15 years I have ever made a "call" on a 1200 rpm pump.

In a mechanical engineering course about 45 years ago, I was told that bearing life varies as the inverse cube of belt tension for belt driven, rolling element bearings.

Rusty,

A bearing lifetime inversely proportional to speed^3 and a bearing impacting force proportional to speed^2 sound good to me based on my discussion above. But I have never heard it said before, and furthermore it seems to conflict with a lot of existing standards and practices.

AFBMA/ANSI Standard 9-1990 addresses "Load Ratings and Fatigue Life for Ball Bearings".

The basic formula from the standard is L10 = L10(revolutions) = 1E6 * (C/P)^3 revolutions.
Each revolution counts the same amount of lifetime, regardless of the speed.

If we want to express lifetime in hours instead of revolutions, then life in hours is inversely proportional to first power of speed. i.e.,
L10 (hours) = 1E6 * (C/P)^3 / (60*RPM ) hours
This does not agree with life varying with 1/speed^3.

I agree the for unbalance, Force ~ RPM^2 is common knowledge. But bearing impacting on a defect is a different problem and much more difficult to solve analytically (certainly requires more assumptions). I have never heard it stated that force is proportional to speed^2 for a given defect and given bearing and given loading. Even though Ron and I "proved it", I am still a little skeptical of this relationship as it applies to bearings.

Impact Force ~ RPM^2 would certainly seem to call into question the common practice of using a single pk/pk TWF acceleration alarm value for bearings over a broad range of speeds 900 rpm - 3600 rpm. i.e. if we assume the goal is to call a bearing when it has visible defect and force and acceleration vary as speed^2, then the same visible defect would cause 16 times as much acceleration at 3600rpm as 900 rpm assuming the same load.

OK, let's address the difference in loading. If I assume two identical bearings at different speeds were both sized using classical approach at a load which gives the same L10 life IN HOURS initially, that means
L10_hours_3600 = L10_hours_900
[Subsitute on each side L10 (hours) = 1E6 * (C/P)^3 / (60*RPM ) hours ]
1E6 * (C/P3600)^3 / (60*3600 ) = 1E6 * (C/P900)^3 / (60*900 )
Cancel out common terms 1E6 and C and 60
(1/P3600)^3 / (3600 ) = (1/P900)^3 / (900)
(P900/P3600)^3 = 3600/900 = 4
P900/P3600=4^(1/3) = 1.58
where
L10_hours_3600 = L10 life in hrs of 3600 rpm machine
P3600 = Load on 3600 rpm machine bearing.
L900, P900 = same parameters for 900 rpm machine
C = Dynamic load rating of the bearing

So the 900 rpm machine may have ~ 1.6 times the load as the 3600 rpm machine to give the same L10 life. How does that factor into our acceleration? I don't know but I would guess it might go up by 1.6.

Then the net result for two identical bearings at different speeds with the same defect and both loading selected to give the same L10 lives is that the 3600 RPM bearing has 10 times as much (16/1.6) force and acceleration.

Conclusion: If we believe all the assumptions (especially impact force ~ speed^2), then our pk/pk acceleration alarm should be 10x as high for the 3600 rpm machine as for the 900 rpm machine.

I am not ready to make that leap (to conclude the standard way of doing business is wrong) and I am waiting for someone to help understand any flaw in my logic. One thing I notice is that my "proof" deltaV/deltaT=[V0sin(theta)]/[L/V0] = V0^2 does not consider the externally applied load. It seems pretty clear that the model I proposed is a gross approximation. Any better models out there for impacting force and acceleration as a function of speed?

Back to the subject of comparing the balance problem and the impacting problem, maybe the same dimensional magic that Ron is talking about is at work in both cases. I would like to understand dimensional analysis, but it's a mystery to me. Seems like cheating to jump to the answer without solving the problem. But I realize it is a valuable technique and will try to learn some more about it.

Duncan - 45 years, wow. Your statement agrees with the classical approach described above.

On the subject of "speed kills", an interesting debate:

http://www.eng-tips.com/viewthread.cfm?qid=76076

The interesting thing in my view is that the most vocal people to argue that 3600 rpm machines are just as reliable as slower machines are the design engineers who never have to deal with the machine again after commissioning.

quote:

a single pk/pk TWF acceleration alarm value for bearings

Pete, peak-peak acceleration time waveform values don't make sense to me when setting up bearing alarms... I use "peak" time waveform values because (to me) an impact is a 'peak' event, not peak-peak like a displacement event.

Looking at the acceleration (d’Alembert’s principle and all that) in polar coordinates one has the radial component as:

d^2R/dt^2 – r(dtheta/dt)^2 if angular velocity is w then this is

d^2R/dt^2 – R w^2 – here is the speed squared, but the second derivative of radius could be a stronger influence? Notice the opposite signs. Presumably, the radial acceleration would have some negative component to it, to line up with the centripetal acceleration.

Frequency wise, the speed squared term is static in the rotating frame, constant inward acceleration. The second derivative due to the ‘bump’ only occurs due to the bump.

The tangential acceleration would be:

R d^2theta/dt^2+2*dR/dt *dtheta/dt) –

If angular velocity, dtheta/dt=w, is constant this gives

2*dR/dt*w – the Coriolis acceleration

I am not sure any of this looks exactly like speed squared.

One question, are those crawdad piles? I know in Texas there are some other piles (Who said bull?), and you may have become overwhelmed by the fumes.

Rusty
I can see some good logic for using true pk/0 acceleration vs true pk/pk:
1 - As you say the acceleration overall is expressed as pk/0. If we also express the true of TWF as pk/0, then we have an easy comparison of the ratio "true peak" / "peak" (which is sqrt[2] times the crest factor).
2 - It seems like true peak acceleration might be more directly related to true peak forces going on somewhere in the bearing. I don't see any physical significance of true peak/peak acceleration in terms of forces.
3 - If you use a demod process which includes rectification (like Entek spike energy), you can read true pk/0 from the rectified and enveloped time waveform, but you can't read true pk/pk from it.

We use true TWF pk/pk only because the CSI paper uses pk/pk. That way we can refer directly to those alarm limits Does anyone know why CSI (Robinson) does it that way?

A few thoughts about how true true pk/pk and true pk/0 compare. The ratio true pk/pk over true pk/0 has to be between 1 and 2. I notice sometimes it is close to 2. i.e. sometimes (but not always) a single impact shows equal and opposite positive and negative peaks immediately after each other (like an impact/rebound). Do other people see the same thing, and how do you interpret it?

I don't know the answer. I tend to think that the impact force is unidirectional. So what we are seeing when we see positive/negative impact/rebound peaks on accleration is an impact strongly filtered by the mass spring oscillation. Just a guess.

William

I will have to take some more time to read through your writeup.

My thinking now is maybe we can come up with two different components of the force:
#1 - A force created by acceleration of the ball which is proportional to speed^2 (assuming no load on the bearing)
#2 - A force created by static load on the bearing (i.e. rotor weight on a horizontal machine) which is also proportional to speed^2. (assuming no acceleration of the ball).

Regarding #1 - Ron and I above talked about the first item (accleration of the ball) and found speed^2 dependence of force. I think your analysis also focuses on accleration of the ball and if I look carefully I am hoping I will find that speed^2 in there somewhere. (still looking)

Regarding #2 - Let's assume we unroll the outer race so it is horizontal and straight along the x axis. The defect is a bump in the load zone at bottom of the bearing. Assume the defect is of total length L and protrudes above the race with a shape y = sin(Pi*x/L) for x from 0 to L. A portion of the rotor mass weight is pushing down on the ball. As the ball passes by the defect it is squeezed between the rotor mass above some spring action and smaller mass below. Assuming the ball doesn't compress there will be either movement of the rotor up or movement of the outer race down or some combination. The bigger the rotor mass, the more the combination shifts towards movement down. (Also, the faster the movement of the ball, the more the combination shifts towards movement down because the mass above is more effective at resisting motion at high frequency while spring force below is unaffected by frequency.. but let's neglect that for now...if we included it we would predict even higher order dependence on v)
Let's finally simplify the geometry and assume the ball exists only at a single point x (no width). As the ball moves by from from position x=0 to x=L at a speed v, we have
ball position x(t) = v*t.
downward radial displacement y(t) = sin(Pi*x(t)/L) = sin(Pi*v*t/L)
downward velcocity v(t) = dy/dt = Pi*v/L cos(Pi*v*t/L)
downward acceleration a(t) = dv/dt = - (Pi*v/L)^2 * sin(Pi*v*t/L) ~ v^2

Still a very crude model, though. Especially if I think about a pit in the outer race instead of a bump in the outer race...#2 doesn't work.... the movement is a lot more complex.

Yeah, we got a few bull piles down here where I am. It gets pretty deep sometimes ;-)

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

Ya'll got way to much time on your hands

Probably so.

There is another problem with #2 above. The variation with speed depends on what kind of shape you pick for the defect. The sinusoidal shape gave variation of acceleration as speed^2. If I pick linear increase and then decrease as the shape (ramp up and down), then acceleration is 0 while on the ramp. If I pick something that increases like x^3 on the rising edge of the defect, then I get acceleration varies with v^3.

Pete/All:

Consider this:

For a given installation if the mass (and mass unbalance) of the rotor is not known, and as an extension moment of inertia, angular momentum ... are also not known. You can waste a lot of time tinkering with this. You can make a few assumptions, but it gets dicey very fast.
Obviously RPM is directly related to acceleration.. but....

In terms of absolute acceleration alarm limits based on RPM (ala Crawdad pile) without knowing the mass unbalance of the rotor, I think you are on thin ice.
Which brings us back to basic Vibration Analysis: Trending What was your pk or pk-pk accel before the defect appeared?

In terms of judging the severity of a particularbearing defect, I would like to suggest the following, and see what you think:

A given acceleration pk in TWF is the sum of various wave components. (I hope we can all agree on THAT!)
If we identify a series of impacts in twf that match a bearing frequency, and that series of impacts modulates in amplitude, the impacts represent time when the bearing defect is in and out of phase with other components.

By extension, a series of identified bearing impacts which does not modulate (much) in amplitude indicates that a greater percentage of a given impact is in fact the bearing defect component of the impact.

Yes/no?
Soooo....

A spectrum in Acceleration can show us the distribution of acceleration across the spectrum. ie, how much impacting is coming from the defect vs other factors. Is this not indicative of the severity of a bearing defect? Or does the reduction of sensitivity of Acceleration in the lower orders skew our results too much?

Is it even relevant that acceleration is LESS sensetive in lower orders, since we are talking in relative terms anyway? This is what appeals to me about Sams arguments. Why get out of the Rolls (acceleration) and get into a volkswagon (integrated Velocity)?


Also, I'm sure most of you notice differences in the "Quality" of TWF.
Some are very orderly, and others are quite chaotic.

Do these kind of factors ever come into play when you are making a judgement on the severity of a bearing defect? ie, Early in the life of a bearing defect, the TWF will be more orderly, and later it will become more "Chaotic".
Agree or disagree?

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