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.

Observing Complexity

To me, observing real life systems is something like this:

A real life System comprises of a meaningful set of objects, diverse in form, state and function but inter-related through multiple network of interdependencies through mutual feedbacks enclosed by variable space, operating far from its equilibrium conditions not only exchanging energy and matter with its environment but also generating internal entropy to undergo discrete transformation triggered by the Arrow of Time forcing it to behave in a dissipative but self organizing manner to either self destruct itself in a wide variety of ways or create new possibilities in performance and/or behaviour owing to presence of ‘attractors’ and ‘bifurcations’; thereby making it impossible to predict the future behaviour of the system in the long term or trace the previous states of the system with any high degree of accuracy other than express it in terms of probabilities since only the present state of the system might be observable to a certain extent and only a probabilistic understanding may be formulated as to how it has arrived at its present state and what would keep it going, thus triggering creative human responses to manage, maintain and enhance the system conditions, function and purpose and create superior systems of the future for the benefit of the society at large.

Such a representation of an observation looks quite involved. Perhaps it might be stated in a much simpler way. Most real life systems behave in a complex manner creating multitude of problems of performance and failures. But how do we get rid of complexity and uncertainty as exhibited by systems? We may do so by deeply observing the complex behaviour of the system to improve our perception to gain insights about the essence of the system; find out the underlying ‘imperfection’ that causes the apparent complexity and uncertainty and then find ways to improve the existing system or create new system and maintain them in the simplest possible manner. We do this by applying the principles of chaos, reliability and design. Surprisingly, the same process might be used to troubleshoot and solve problems we face on a daily basis. If done, we are no longer dominated or dictated by the ‘special whims’ of the system.

The crux of the matter is how we observe reality and understand it so as to make meaningful choices as responses to life and living.

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.

Oscillations at Severn Crossing

The important frequencies of whole structures and of machines, in general, are mostly less than 50 cycles per sec and rarely more than 500 cycles per sec.

The lowest frequencies of a system can, in fact, be quite small. A clothes line slung between two posts and having plenty of sag, for instance, may oscillate freely at only one or two cycles per sec

An oscillation of this sort was observed during the autumn of 1959 in the grid system of the Central Electricity Generating Board at the Severn Crossing.

The frequency concerned was unusually low, being of the order of 1/8th cycle per sec. The crossing has two large pylons just over a mile apart, supporting transmission cables of 1.69 in diameter. It was found that, provided it blew from the right direction, a moderate wind would make the cables sway with low frequency and large amplitude in such a violent fashion that cables normally spaced 27 feet apart actually touched, leaving broken strands and burn marks, as well as short-circuiting the electricity supply.

A probable explanation of this behavior was eventually found and a cure effected by wrapping the conductors with thin plastic tape thus altering  the geometry of the surface presented to the wind.

(Excerpt from the book – Vibration by R.E.D. Bishop, Cambridge University Press, 1965, page 29)

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.