# Eccentric rotor

Symptom: Pole pass sidebands around 1x N (N=running speed) and 2xLf (Lf = line frequency)

Eccentric rotors will produce a rotating variable air gap between the rotor and the stator which induces a pulsating source of vibration. We would see 2xLf. However, there will also be pole pass sidebands around the 2xLv and 1xN peaks. 1xN is expected to be high.

Note: Pole pass frequency is the slip frequency times the number of poles. The slip frequency is the difference (in terms of frequency) between the actual RPM and the synchronous speed.

Presence of pole pass sidebands around 1N and 2Lf is the key indicator of this fault. One needs sufficient resolution to see those sidebands. Else we would either miss them altogether or mistake them for resonance (a broadening of the base of the peak).

Waveform: Time waveform that covers many seconds of time will reveal the pole pass frequency modulation. Due to lack of impacting the waveform will smooth and will be a combination of the 1N and 2Lf frequencies of vibration.

Phase: Not applicable for this fault unless eccentric forces are high in magnitude.

Dibyendu De

# Eccentricity in general

Symptoms are generally 1x radial (Vertical and Horizontal for a horizontally mounted machine).

Eccentricity occurs when the centre of rotation is offset (like offset misalignment) from the geometric centreline of a gear, motor rotor or a pulley.

It would generate strong 1x radial peak — in the direction parallel to the rotor/gear/pulley. This condition is common and mimics unbalance.

For gear eccentricity we would see 1x sidebands

For motor rotor eccentricity we would see pole pass sidebands.

Time waveform would be sinusoidal when viewed in velocity. Vibration from gear will also have gear mesh vibration and modulation of the turning shaft of the offending gear.

Phase: If belt driven, phase readings taken parallel and perpendicular to belts will either be in phase or 180 degrees out of phase. For a direct driven component, vertical and horizontal readings will be 90 degrees out of phase.

# Notes on detecting Unbalance

Unbalance is a condition where a “shaft’s centreline” and mass centreline don’t coincide or when the centre of mass does not lie on the axis of rotation. This can be visualised as the a heavy spot somewhere on the shaft.

There are three types of unbalance.

1. Static
2. Couple
3. Dynamic — which is a mix of static and couple unbalance — when the rotor is not narrow compared to its diameter or in other words — when the rotor is long compared to its diameter.

With unbalance, we expect to see high amplitude of 1x (fundamental) in the signature. Usually, for horizontal machines, the vibration levels are approximately equal in the radial directions (vertical and horizontal). However, we might expect to see higher vibration in the horizontal direction, which is due to change of stiffness. It can be quite different for a vertically mounted machine where we may find the vibration in the flow direction appreciably higher than the tangential direction, which is perpendicular to the flow direction.

The time waveform should be a smooth sine or wave. If it is not, then other problems like misalignment, looseness , bearing wear might be present. It is a convention to view time waveform and signatures relating to unbalance in velocity.

Phase is a confirmatory indicator. Generally the phase difference between the vertical and horizontal directions are 90 degrees apart (+/- 30/40 degrees).

Static Unbalance

For static unbalance we expect to see large amplitude peaks at 1x in the horizontal and vertical directions with very low amplitude 1x peak in the axial direction. However, if the amplitude of 1x in the horizontal direction is more than 2 times the amplitude of 1x in the vertical direction then foundation looseness or resonance may be suspected.

For static unbalance, phase difference between vertical and horizontal would be 90 degrees and the phase difference at bearings at either end of rotor will be zero (that is “in-phase”) since forces on both bearings are always in the same direction.

Couple Unbalance

Like static unbalance, we would also expect to see large amplitude 1x peaks in the vertical and horizontal direction with a low 1x axial component. Again the phase difference between the horizontal and vertical would differ by 90 degrees +/- 30 degrees

For pure couple unbalance, phase at bearings at either end of the rotor will be 180 degrees out of phase.

However, if a rotor suffering from couple unbalance, is statically balanced it may seem to be perfectly balanced but when rotated it would produce centripetal forces on the bearings and they would be of opposite phase. In such cases a two plane balance is required to correct couple unbalance.

Dynamic Unbalance

Common form of unbalance. A combination of static and couple unbalance. Normally happens in rotors that are long compared to their diameters. Generally a two plane balancing correction is required to correct dynamic unbalance. However, in practice a single plane balance would also prove sufficient.

While phase difference between vertical and horizontal direction on any bearing would be 90 degrees out of phase, the phase difference at bearings at either end of the rotor will be between 30 to 150 degrees out of phase.

Unbalance of overhung machines

Examples — close coupled pumps, axial flow fans and small turbines.

In this case we would expect the 1x component of a signature to be high in all the three orthogonal directions — vertical, horizontal and axial. We see a high 1x axial since unbalance creates a high bending moment on the shaft that causes the bearing housing to move axially. Hence the 1x axial is generally the highest amongst the three directions.

Phase difference

As usual, the phase difference between the vertical and horizontal directions would be around 90 degrees. But axial readings on both bearings will be in phase (zero difference) — since they tend to move in the same axial direction. Similarly, phase readings on both bearings will be in phase.

Unbalance in Vertical Machines

Example: Vertical Pumps like Cooling Water Pumps in Power Plants.

Spectrum will show a high amplitude peak at 1x running speed in the radial direction — horizontal or tangential direction. This is due to variation in stiffness along the radial direction. Generally, the vibration amplitude at the top of the motor (Motor NDE) would be higher than the rest of the machine.

To distinguish motor unbalance from pump unbalance, it may be necessary to de-couple the motor and pump and run the motor solo while measuring 1x. If the 1x component is still high then unbalance exists in the motor; else it is in the pump.

Phase: Look for 90 degrees phase shift between readings taken 90 degree apart. All readings taken in the same direction should be in phase.

# External Noise in Vibration Analysis

Quite often, vibrations external to a machine (emanating from other machines or structures) can be transmitted through the foundation (from other machines) and structural supports (e.g. grinding frequencies generated from grinding of materials). It can also be transmitted through liquids (e.g. water hammer, turbulence) and air (acoustic pressures, electromagnetic radiation).

In most cases, low frequency vibrations are transmitted in this manner. This is because low frequency vibrations travel great distances.

In case such transmitted vibrations match the resonant frequency of the machine or any of its components, vibrations are greatly amplified (resonance).

Such vibrations can damage components like anti-friction bearings through a phenomenon called false brinelling if the affected machine is in the stand-by mode.

It is wise to suspect presence of such external noise if a frequency peak is found in a vibration spectrum (FFT) which can’t be identified or appears strange.

In that case we can check whether any machine near to the machine of interest exhibits that particular frequency. Or we can stop the machine to check whether the unusual or odd frequency still appears on a stationary machine. Alternatively, we can stop other local machines (usually not possible) to see whether the odd frequency disappears from the signature.

In case, the frequency happens to coincide with 2x, 3x, 8x harmonics of 1x (fundamental frequency) then we may use time synchronous averaging to see whether the amplitude contributed by the external noise averages away.

# Note on Raised “Noise Floor”

In a spectrum, if the entire noise floor is raised, it is possible that we have a situation of extreme bearing wear.

If the noise is biased towards the higher frequencies in the spectrum then we may have process or flow problem like possible cavitation, which may be further confirmed by high acceleration measurement (or filtered acceleration measurement) on the pump body on the delivery side (since high frequency waves are always localized).

Smaller “humps” may be due to resonance (possibly excited by anti-friction bearing damage, cavitation, looseness, rubs or impacts) or closely spaced sidebands arising from other defects. A high resolution measurement (or graphical zoom and a log scale) may reveal whether the source is problems that exhibit sidebands or a problem of resonance. If  machine speed can be changed, (for e.g.motor connected to VFD drives) the resonant frequency would not move – but the other peaks would. Sidebands will typically be symmetrical around a dominant peak – e.g. 1X, 2X, 2x LF (100 or 120 Hz) etc indicating different faults.

Interestingly, the time waveform would reveal the reason as to why the noise floor has been raised.

We would see signs of looseness, severe bearing wear, rubs, and other sources of impacts in the time waveform. We must make sure that there are 5 – 10 seconds of time waveform if we suspect an intermittent rub (e.g. white metal bearings of vertical pumps or loose electrical connection of motor terminals) or if we suspect flow turbulence or cavitation.

If the time waveform looks normal (making sure there is a high Fmax (following Niquist criteria) and we view the waveform in units of acceleration then increase the resolution in the spectrum to 3200 lines or higher in case we are seeing a family of sidebands (like the sidebands we find around gear mesh frequency or rotor bars).

But if a natural frequency is being excited (necessary condition for resonance) then we have to perform a bump/impact test or a run-up/coast down test to confirm the situation.

# Induced Force & Freedom for Movement

While tackling vibration problems (most machinery problems are oscillatory in nature) it is important to grasp the idea — “What causes vibration?”

The answer in its simplest form consists of two parts, which are: –

1. Induced Force
2. Freedom for Movement

We can say, that when we put these two phenomena into a relationship or when we discover a pattern involving the two phenomena, we have effectively understood the essence of a vibration problem in order to solve it or improve the situation. Without the “induced force” a piece of machinery would not continue to vibrate. And without “freedom for movement” machines would not vibrate either. Both must be present for a machine to continue to vibrate.

However, I find that students of vibration analysis often face difficulty in understanding these two related phenomenon and have a hard time linking them into a coherent pattern exhibited by a vibration problem.

So, I would first try to explain the phenomenon of “induced force.”

There are many ways of classifying vibrations. Vibrations patterns are also described depending on how they are induced. This is an important way of classifying vibration since the cause of vibration can be easily understood from such classification.

For instance, a shop floor may vibrate when a machine is switched on. Or an adjacent machine or structure may vibrate when another machine on the same floor is running. This would be called machinery induced vibration.

Similarly, a bridge or a tower may be subjected to strong winds causing those to vibrate. In that case, it would be called wind induced vibration.

Or for example, a pipe carrying fluid in a power plant or a pump may be subjected to flow induced vibration. Common problems of pumps like cavitation, re-circulation, erosion and water hammer are all examples of flow induced vibration.

Likewise, unusual vibration of an anti-friction bearing may be induced by electromagnetic forces emanating from electrical cables. We would say that the bearing is subjected to electromagnetic induced vibration.

Similarly, vibration of machines, buildings, towers, bridges can be blast induced owing to sudden application of explosive forces, like the way it happens in mining industry.

In the case of earthquakes, bridges and towers are subjected to ground induced vibrations.

We may think of “induced force” as the necessary stimulus imposed on a structure that forces it to vibrate. Structure, from the vibration point of view, may be a piece of machine, building, tower, pipe, bearings, foundation — or simply anything that has stiffness and mass.

However, a structure would only vibrate or continue to vibrate if it has freedom to move. A machine can move in many directions provided it is allowed to do so. More the number of directions a machine is allowed to move more difficult it becomes to understand a problem. However, the question is “How do we know a machine’s Freedom to move?”

One easy way to find it out is by finding the number of natural frequencies exhibited by the machine. This may be effectively found out by conducting a “bump test” on the machine where the number of natural frequencies show up on the frequency spectrum. The number of natural frequencies is just equal to the number of directions a machine is free to move. For example, if a machine has five natural frequencies within the operating range that consists of the operating speed and its harmonics then the machine is free to move in five different directions.

So, when we know the nature of the induced force and the number of directions a machine is likely to move, we may then try to find the proper relationship between the two phenomena to complete our understanding of the essence of a vibration problem. Once such relationship is understood the solution(s) to a problem is self evident.

# Learning Vibration Analysis

Every year we gather at NTPC, Noida, for our animated dialog on real life Vibration problems. This year there were 39 of us happily engaged for four fun filled days. It is a type of annual conference where engineers and practicing vibration specialists across the country come together to interact, exchange and learn from each other.

This year, the workshop was designed differently. We gently moved away from the traditional methods of vibration analysis and instead emphasized the application of complexity science in analyzing system problems through vibration patterns. I think this approach is the first of its kind in the world.

So, what was new?

First, only cases from the real world of engineering were discussed and explored. Twenty cases were discussed. Each case was unique. They were something like Zen koans waiting to be cracked for enlightenment.

Why?

There are two sides to reality. One is the phenomenal one — what we can sense. The other is the essential one — what we can’t “see” through our senses. The phenomenal side manifest as events that we experience while the essential side provides the cause that precipitates such events. Problems of vibration offer us the opportunity to explore both sides of reality. Through measurements, we can easily see the phenomenal one (the degrees of freedom, amounts of vibration and their frequencies) — that is all about sensing oscillatory movement and its nature. But to understand the cause of vibration we must be able to “see” the essential part of reality – what induces vibration?

The cases forced the participants (practicing specialists) to take multiple takes and interpretations of the cause of vibration before the reason finally clicked. Initially, each case left the participants perplexed.They sort of provided the proverbial “whack” on the head for realization to dawn.

Why is this so? Cracking one problem does not ensure that the next problem can be solved by following the same method. If one tries to use the same method that helped one to solve a problem one has to use thoughts and concepts culled through previous experiences. By trying to apply a standard method and tactic one can’t see the essential part of the reality, which often proves to be a frustrating experience. Any effort to solve a vibration problem with a standard approach ties up a practitioner in knots. Not surprisingly, even vibration specialists find vibration problems paradoxical. They are paradoxical in the sense that seemingly logical, rational and conceptual thinking held in the minds of a practitioner are challenged when dealing with vibration problems.

Therefore, for each case, the essential part — the induced cause(s) — had to be built separately — bit by bit — connecting one bit to the other till the essential nature of the problem was self evident.

At the end of the four days the participants were left smiling, relieved to know that they need not remember any standard method or approach or a formula to tackle vibration problems — more so, for the most complex ones. They only need to see through a problem with patience or perseverance to develop deep intuitive capability, which would then help them see through the essential nature of any real life vibration problem quickly and accurately.

On the whole it was great fun and we all basked in the enjoyment.

Note: In conducting this course, I was helped by Mr. Anil Sahu, my co-facilitator. He had a bunch of paradoxical cases to share.

# When Engineers fail to detect bearing failures?

It is not unusual to see condition based maintenance engineers engaged in vibration monitoring and analysis, sometimes miss detection of bearing damage. This usually happens with pumps and agitators.

Anti-friction bearings fail by fatigue. And they fail very quickly when alternating stresses approach static stress imposed on a bearing.

A German engineer named Wohler, who tested materials under conditions of rotating bending, made the first systematic study of the effect of alternating stress on fatigue.

He found that if alternating stresses were only slightly less than the static stresses which would cause breakage, only a few cycles of loading were required to cause failure.

He also found that as alternating stress was reduced in amplitude the number of cycles needed to cause a failure also increased. This tendency was maintained until the alternating stress level had been reduced to about a quarter or a third of the maximum sustainable static stress, at which level the life of the bearings or a specimen appeared to be infinitely long. This limiting stress has become known as “endurance limit” of the material.

Therefore, in many engineering applications, say anti-bearings, material is not called upon to resist alternating tension and compression (as in case of shafts and axles) but has instead to resist a fluctuating stress superimposed upon a steady stress.

Often the steady stress in a particular component is determined by the load to which it is subjected in service, while the alternating component of vibration arises from unwanted vibration in the system.

In case of anti-friction bearings, when lightness and smallness are important criteria in the design, the mean stress level in the part must approach as closely as possible to the static strength. It is therefore of great importance that the alternating component due to vibration be kept as small as possible. Hence, if the alternating component is sufficiently large the failure would take place within a few cycles, which would clearly escape the notice of a vibration analysts who chooses to monitor the bearings at regular preset intervals. In such cases, the possibility of a condition monitoring person missing out on the potential damage signal is high enough. He/she would then fail to detect a bearing failure in time for any corrective action.

Note:

Fatigue is not really a feature of vibration as there is no necessity for the stress cycles to be regularly repeated; neither is the number of stress fluctuations in a given time important — at least under normal conditions. The point is that the number of stress cycles to cause failure of a component is usually large and execution of vibration is a common way of achieving the necessary large number in a relatively short time. The other important thing is that alternating stress has to be more or less near to the static stress imposed on a material to cause rapid and sudden fatigue failure of a specimen.

# Negative Stiffness and Instability

The idea of negative stiffness might appear at first glance to be counter intuitive but that is what happens often to machinery in the real world. When such a phenomenon strikes, it triggers rapid deterioration of a machinery system.

Positive stiffness is a material property that tries to resist a force when applied on to a material, i.e. it tries to push back the force.

On the other hand, negative stiffness is a property that amplifies the deformation of a material when force is applied to a body.

Since such amplification is non-linear by nature it forces the system to go far away from its equilibrium position. When it does so, the system become unstable and as deformation quickly increases, the system fails.

The best possible way to detect the sudden appearance of negative stiffness is to monitor the displacement parameter of vibration. This is because displacement is related to stiffness. When displacement increases disproportionately without a corresponding increase in velocity parameter we would know that the phenomenon is that of negative stiffness. In addition, we might also notice a variation in the displacement readings. They don’t tend to settle to a steady state.

Negative stiffness might occur in many ways. It may happen when interference or push fitted elements come loose. It often happens to elements that are deformed over time like foundation supports or are pre-stressed like anti-friction bearings. It might happen when elements are worn out by a certain extent by different wear processes like corrosion or abrasive wear.

But in all cases, a very small change induces a system with positive stiffness to flip to negative stiffness, causing catastrophic damages and failures.

Note:

For a lucid understanding of the nature of negative stiffness you may refer to this article.

For an understanding of negative stiffness and isolation you may see this.

# Ruthless Honesty & Integrity

Excerpt from my forthcoming book — Solving Complex Problems through Vibration Analysis; An introduction to Non-linear Dynamics

One last thing before we move on to the next chapter. We have had a glimpse into the fundamental process of seeing a problem. We start with an open mind. Then we ask lots of questions out of curiosity, being mindful that we don’t know the answer. We intently observe. We then make intelligent guesses to come up with a hypothesis that relates all the problems in the system, interdependent as they are. Finally, we should still doubt as to whether we understood the system to sufficient depth. We simply can’t get rid of this nagging doubt till our solutions are proven effective through practical implementation. If proven, we learn. If not proven, we learn to unlearn our ignorance and set out to learn again. Either way we learn something useful.

This reminds me of an incident. Long back when I was studying vibration analysis under my Guru, Tim Henry of the University of Manchester, I was working on a small experiment with accelerometers. I was bit upset about the funny results I got and was ashamed about the wasted effort at the end of my week-long experiment. Tim asked me as to why I look sullen on a fine English morning.

When he came to know the reason for my long face, he just said, ‘Well, there is nothing to feel bad about. What you got is also useful knowledge. It would tell others that this method of finding out of what you wanted to find out does not work and this is why it doesn’t work and here are the results as evidence. There is no question of shame. Don’t you think it would save a lot of time and energy for other researchers who would come after you by choosing to avoid the path you just found to be incorrect? And you just learned more about the subject. Haven’t you?”

What a relief that was. Thanking him, I promptly went out to soak in the rare sun on a cold English morning. And that is where I was hit by the truth — all human search must be based on honesty – ruthless honesty — so that integrity of human learning can be preserved since quality of that integrity decides whether we survive better or not. I vowed — from now on, I must learn to take things as they are.

I also think: by learning to be honest with our failures and vulnerabilities and to resiliently respond to uncertain outcomes and situations is a vital step to get rid of fear and shame that hold us back.

Note:

This book acts as a further expansion and exploration of my previous book – Winning Anywhere – the Power of ‘See’