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.

Notes on Belt problem as seen in Vibration Analysis

General Problem: Belt is worn out or is loose on the pulley. 

How to detect it in a vibration spectrum: We would find peaks at “belt frequency” (or better known as “fundamental belt pass frequency”) and its harmonics. The highest amplitude peak in the series will often be the twice the belt rate frequency.

The fundamental forcing frequency for such a problem is known as the “belt rate” or “fundamental belt pass frequency”. It is the rate at which a point on the belt passes a fixed reference point. It is always less that the speed of either pulleys (driving and driven).

Calculation of Belt Pass frequency as follows:

Driven RPM =Driving RPM x Driving sheave diameter/Driven sheave diameter

Belt freq = Pi x Sheave RPM x Sheave diameter/Belt length = PixDxN/BL

Where Pi = 3.1416

Spectrum: Look for the belt rate peak (sub-synchronous) and harmonics.  Sometimes the belt rate peak may be cut off by the high pass filter, but the harmonics will be present. Remember we are looking for the 2 times belt rate frequency to confirm the problem.

Time waveform: If the belts are simply worn then the time waveform will not be the best analysis tool.  If a belt has a distinct point of damage then there will be an event in the waveform once per belt revolution. This provides a useful distinction to discern the exact nature of the problem.

Strobe: A strobe is a very useful tool.  If you use the strobe to freeze the movement of the belts then you can inspect them without stopping the machine.  You can also detect slip on multi-belt systems.

Structure of a 2 day workshop on RCM

Day 1 
Session 1 – Introduction to RCM, History and 7 Questions
* Definition of Reliability, RCM and the 7 Vital Questions
* Maintenance Strategies
* Waddington Effect
* Nowlan & Heap’s Failure Patterns
* Inherent Reliability and its improvement strategy
Session 2 — Operating Context and Functions 
* Introduction to Operating Context
* Operating Context for a System
* Elements to be included
* Operating Context and Functions
* 5 general operating context
* Operating Context and Functional Failures
Session 3 – Failure Modes and Failure Effects  
* Introduction to Failure Modes
* Few thoughts about data
* Exploring Failure Modes
* 4 Rules for Physical Failure Modes
* Failure Effect
* Evidence that failure is occurring
Session 4 — Failure Consequence and Risk 
* Introduction to Decision Diagram
* Risk assessment — how each failure matter
* Is the function hidden or Evident
* Relation of time and Hidden vs Evident
* Safety and Environmental Consequences
* Operational and non-operational Consequences
Day 2 
Session 5 — Strategies and Proactive Tasks 
* Introduction to Proactive Tasks and PF interval
* CBM/On-condition tasks
* Scheduled Restoration and Scheduled Discard Tasks
* Determining Task Effectiveness
* Risk and Tolerability
* General Rules for following the decision diagram
Session 6 — Default Actions 
* Introduction to Default Actions
* Default tasks for hidden failures
* Failure Finding Task
* Failure finding Interval
* Design Out Maintenance — to do or to be
* Walk around checks with right timing
Session 7 — RCM Audits 
* Introduction to Audits
* Fundamental of Technical Audit
* Technical Audit process
* Fundamentals of Management Audit
* General Management Audit process
* What RCM achieves
Session 8 — Setting up a Successful Living Program 
* Using the power of facilitated group
* RCM Training
* Knowledge development and its process
* Failure Modes and Design Maturity
* RCM during scale up or expansion
* Summary and Conclusion

The Sad Story of the HFO pump

This is a HFO (Heavy Fuel Oil) screw pump used in Power Plant for running boilers. There was a catastrophic failure of the pump. Though this pump was regularly monitored by vibration (in velocity mode — mm/sec) it didn’t give any indication of the impending failure.

The screws of the pump rubbed against each other and the case hardened layers of both screws were crushed. The force was so great that the body of the pump also cracked. Evidence of corrosion was also noticed.

What caused it? 

For want of HFO oil, the plant personnel were forced to pump LDO (Light Diesel Oil) through this HFO pump for the past one year.

Hence the I, A, R factors that contributed to this catastrophic failure are the following:

Initiator(s)I — factor(s), which triggers the problem — low viscosity of LDO compared to that of HFO was the significant ‘initiator’ in this case. While viscosity of LDO ranges from 2.5 to 5 cSt, the viscosity of HFO varies between 30 to 50 cSt (depending on the additives used). Use of lower viscosity oil ensured metal to metal contact thereby increasing Hertz stress that led to collapse of the hardened layer of the screws.

Accelerator(s)A — factor(s), which accelerates the process of failure —  a) Indian HFO does not contain friction modifiers such as vanadium and magnesium. Their absence causes higher friction between the screws (approximately 70 times increase in friction), which accelerates the wear process. b) Moreover, presence of vanadium and magnesium additives in HFO and LDO acts as anti-corrosive agents. Notice that the failure happened a year after the management decided to pump LDO rather than HFO through the HFO pump — enough time for corrosion to take effect. So, we may say that there are at least two factors that accelerated the failure process. There are other effects too on system performance, which we shall discuss in a moment (refer “Note”).

Retarder(s)R — factors that slow down the failure process — a) surface finish of the screws b) right clearance of the bearings c) presence of chromium in the screws.

Surface finish plays a very important role in reduction of metal to metal friction and also allows fluid film development. Ideally the surface finish should be between 3 to 6 microns CLA (Centre Line Average) for best effect. This can be introduced as a specification of the MOC (Material of Construction).

Similarly, excessive clearance in bearings would modify the hertz stress zone or profile — both in width and depth, which would cause shear of the hard layer (depth of which depends on the type of hardening and the type of steel used) and the soft layer (core material). Depth and type of hardening might also be specified in the MOC to prevent failures and extend life of the equipment. Presence of chromium in the metal would help formation of Vanadium – Oxygen – Chromium bond which would effectively enhance the life by providing better lubricating property which in turn would ensure a high level of  reliability of the equipment.

Hence, once the I, A and R s are identified appropriate measures can be taken to modify maintenance plan, MOC etc to ensure long life of the equipment without negative safety consequences (heart of reliability improvement).

Example:

  1. Specify addition of Vanadium and Magnesium in the HFO during supply or these may be added at site after receipt of supply. (Material specification during purchase)
  2. Ensure the right viscosity of oil to be pumps through HFO pumps. (Monitor viscosity of the supply oil — not higher than 50 cSt and not lesser than 30 cSt)
  3. Specify surface roughness of the screws — 3 to 6 microns (CLA).
  4. Specify depth of hardness of the screws (below 580 microns so that the interface between the hard layer and the soft core remains unaffected by the Hertz stress) during procurement and supply. Preferable type of hardening of the screws would be nitriding.
  5. Specify chromium percentage in the screws (during purchase).
  6. Monitor bearing clearance on a regular basis and change as needed (by vibration analysis based on velocity and acceleration parameters).
  7. Monitor the body temperature of the pump to notice adverse frictional effects
  8. Monitor growth of incipient failures in the screws by vibration monitoring (acceleration and displacement parameters)

Note

1. (Effect of IAR on system performance — i.e. the boiler – superheater – pipes):

Problems of high temperature corrosion and brittle deposits drastically impair the performance of high-capacity steam boiler of Power Plants, using HFO. Research* shows that heavy fuel oil (HFO) can be suitably burned in high capacity boilers. However, if HFO is chemically treated with an anticorrosive additives like Vanadium and Magnesium, it diminishes high temperature corrosion that affect some operational parameters  such as the pressure in furnace and pressure drop in superheaters and pipe metal temperature, among others like atomization and combustion processes. Therefore, inclusion of right additives like Vanadium and Magnesium have been found to diminish high-temperature corrosion and improved system performance.  It therefore makes sense to monitor these parameters, which can provide direct information on the degree of fouling, as well as of the effectiveness of the treatment during normal boiler operating conditions.

*Source

2. Effect of Vanadium Oxide nano particles on friction and wear reduction

Ref:

  1. Two approaches to improving Plant Reliability:
  2. Rethinking Maintenance Strategy:
  3. Applying IAR Technique:

By Dibyendu De

Two approaches to improve — Plant wide Equipment Reliability

The first approach is to conduct a series of training programs along with hand-holding. During such programs, participants apply the concepts discussed in the programs on the critical machines to modify the existing maintenance plan or methods to improve equipment reliability over a period of time. It is effective if the organization fulfills two vital conditions. First, the organization has in place a reasonably competent condition monitoring team and the use of condition based maintenance strategy is quite widespread in its acceptance and application throughout the plant. Second, the number of failures/component replacement in the plant in a year is not more than say 60. We would call this method — The Interactive Training Method.
The second approach is a more hands-on, direct and intensely collaborative. Each critical equipment is thoroughly examined in its dynamic condition to find out its inherent imperfections that cause failures to happen. Such imperfections, once identified by deep study, are then systematically addressed eliminate the existing and potential failure modes to improve MTBF and Safety. Based on the findings, the maintenance plan is formulated or appropriately modified to sustain the gains of implementing the findings. This activity is to be done during the program. This approach is effective when the failure rate in the plant is random and high (more than 60 failures/component replacement in a year) and/or maintenance load is heavy and repetitive along with high maintenance cost in spite of having a reasonably equipped condition monitoring team in place. We would call this — The Deep Dive Approach.   
 
Outline of the two methods: — The processes involved along with approximate costs. 
 
The Interactive Training Method:  
 
1. Such training sessions are conducted once every two months for a duration of 4 days each over a period of 24 months.
2. The training programs would essentially focus on the following == a) the RCM process focussed on Failure Modes b) Vibration Analysis c) Lubrication analysis and management d) Bearing failures and practical reasons e) Root Cause Failure Analysis method — FRETTLSM method. f) Friction, Wear Flow, Heat, g) Foundations and Structures. h) Condition Monitoring of Electrical failures i) Maintenance Planning based on nature of Failure Modes j) Life Cycle Costing k) Auditing RAMS (Reliability, Availability, Maintainability and Safety).that would help in self auditing the process — in total 12 programs
3. Accordingly, there would be 12 visits to the plant. During each visit one of the above topics would be covered. Once the improvement concepts are delivered, the participants (assigned for focussed plant improvement) would collaboratively engage in designing appropriate measures to improve or modify the existing maintenance plan of each critical machine to improve its MTBF and Safety. This activity that involves a fair amount of handholding would be done during the visit. Number of critical machines to be taken up for each visit would be decided by the management or participants. Number of participants = 10 maximum
4. Subsequent paid audits to refine the process would be optional — after the completion of 24 months intervention period.
The Deep DIve Approach:  
 
Such interactive sessions would be conducted once every two months for a duration of 4 days each over a period of 18 months.
2. Each interactive session of 4 days duration would focus on one critical equipment at a time. In total 9 critical equipment would be covered during the 18 months period with a selected group of people, assigned to the project of improving reliability. During each sessions each of the critical equipment would be examined deeply and in totality to find the inherent imperfections that cause different failures in the system.Once, these imperfections are identified, time is taken to appropriately address the “imperfections” and simultaneously formulate or modify the existing equipment maintenance plan for sustaining the gains on an on-going basis. This collaborative activity would be done during the program. In this process, participants learn by doing.
3. In total there would be 9 visits to the plant. During each visit one critical equipment would be taken up for the deep dive study taken to its full logical conclusion. Number of participants = 10 maximum.
4. Subsequent paid audits of the progress is optional.- after the completion of 18 months intervention period.

Rethinking Maintenance Strategy

As of now, maintenance strategy looks similar to strategy taken by the medical fraternity in themes, concepts and procedures.

If things go suddenly wrong we just fix the problem as quickly as possible. A person is healthy to the point when the person becomes unhealthy.

That might work fine for simple diseases like harmless flu, infections, wounds and fractures. And it is rather necessary to do so during such infrequent periods of crisis.

But that does not work for more serious diseases or chronic ones.

For such serious and chronic ones either we go for preventive measures like general cleanliness, hygiene, food and restoring normal living conditions or predictive measures through regular check ups that detects problems like high or low blood pressures, diabetes and cancer.

Once detected, we treat the symptoms post haste resorting to either prolonged doses of medication or surgery or both, like in the case of cancer. But unfortunately, the chance of survival or prolonging life of a patient is rather low.

However, it is time we rethink our strategy of maintaining health of a human being or any machine or system.

We may do so by orienting our strategy to understand the dynamics of a disease. By doing so, our approach changes radically. For example. let us take Type 2 diabetes, which is becoming a global epidemic. Acute or chronic stress initiates or triggers the disease (Initiator). Poor or inadequate nutrition or wrong choice of food accelerates the process  (Accelerator) whereas taking regular physical exercise retards or slows down the process (Retarder). Worthwhile to mention that the Initiator(s), Accelerator (s) and Retarder (s) get together to produce changes that trigger of unhealthy or undesirable behavior or failure patterns. Such interactions, which I call ‘imperfections‘ between initiator (s), accelerator (s) and retarder (s) change the gene expression which gives rise to a disease, which often has to be treated over the entire lifecycle of a patient or system with a low probability of success.

The present strategy to fight diabetes is to modulate insulin levels through oral medication or injections to keep blood sugar to an acceptable level. It often proves to be a frustrating process for patients to maintain their blood sugar levels in this manner. But more importantly, the present strategy is not geared to reverse Type 2 diabetes or eliminate the disease.

The difference between the two approaches lies in the fact — “respond to the symptom” (high blood sugar) vs “respond to the “imperfection” — the interaction between Initiators, Accelerators and Retarders”. The response to symptom is done through constant monitoring and action based on the condition of the system, without attempting to take care of the inherent imperfections. On the other hand, the response to imperfections involve appropriate and adequate actions around the I, A, R s and monitoring their presence and levels of severity.

So a successful strategy to reverse diabetes would be to eliminate or avoid the initiator (or keep it as low as possible); weaken or eliminate the Accelerator and strengthen or improve the Retarder. A custom made successful strategy might be formulated by careful observation and analysis of the dynamics of the patient.

As a passing note, by following this simple strategy of addressing the “system imperfections“, I could successfully reverse my Type 2 Diabetes, which even doctors considered impossible. Moreover, the consequences of diabetes were also reversed.

Fixing diseases as and when they surface or appear is similar to Breakdown Maintenance strategy, which most industries adopt. Clearly, other than cases where the consequences of a failure is really low, adoption of this strategy is not beneficial in terms of maintenance effort, safety, availability and costs.

As a parallel in engineering, tackling a diseases through preventive measures is like Preventive Maintenance and Total Productive Maintenance — a highly evolved form of Preventive Maintenance. Though such a strategy can prove to be very useful to maintain basic operating conditions, the limitation, as in the case of human beings, is that it does not usually ensure successful ‘mission reliability’  (high chance of survival or prolonging healthy life to the maximum) as demonstrated by Waddington Effect. (You may refer to my posts on Waddington Effect here 1 and here 2)

Similarly, predictive strategy along with its follow up actions in medical science, is similar to Predictive Maintenance, Condition Based Maintenance and Reliability Centered Maintenance in engineering discipline. Though we can successfully avoid or eliminate the consequences of failures; improvement in reliability (extending MTBF — Mean Time Between Failures) or performance is limited to the degree of existing “imperfections” in the system (gene expression of the system), which the above strategies hardly address.

For the purpose of illustration of IAR method, you may like to visit my post on — Application of IAR technique

To summarize, a successful maintenance strategy that aims at zero breakdown and zero safety and performance failures and useful extension of MTBF of any system may be as follows:

  1. Observe the dynamics of the machine or system. This might be done by observing  energy flows or materials movement and its dynamics or vibration patterns or analysis of failure patterns or conducting design audits, etc. Such methods can be employed individually or in combination, which depends on the context.
  2. Understand the failures or abnormal behavior  or performance patterns from equipment history or Review of existing equipment maintenance plan
  3. Identify the Initiators, Accelerators and Retarders (IARs)
  4. Formulate a customized comprehensive strategy  and detailed maintenance and improvement plan around the identified IARs keeping in mind the action principles of elimination, weakening and strengthening the IARs appropriately. This ensures Reliability of Equipment Usage over the lifecycle of an equipment at the lowest possible costs and efforts. The advantage lies in the fact that once done, REU gives ongoing benefits to a manufacturing plant over years.
  5. Keep upgrading the maintenance plan, sensors and analysis algorithms based on new evidences and information. This leads to custom built Artificial Intelligence for any system that proves invaluable in the long run.
  6. Improve the system in small steps that give measureable benefits.By Dibyendu De

 

 

Fretting Corrosion

In a plant it so happened that a machine with its shaft and pulley assembly was kept idle for little over three years.

Then one day the engineers decided to run the machine. After two months of running, the pulley came loose on the shaft and started rattling – making just enough noise for the operator to notice it and promptly stop the machine thus averting a nasty accident.
This is a case of fretting corrosion. This happens when things are kept in assembled condition for long without running or components are assembled loosely. The asperities at the contact surface that help to hold two components together are lost; thus loosing the vital grip forcing the components to come loose. This wear process is accelerated in presence of low frequency vibration that usually travel to such joints por assemblies from other running machines. The confirmation of fretting corrosion lies in observing reddish coloured powder in between the closely fitting joint interfaces and assemblies.

The pictures of fretting corrosion as seen in this case are the following:

Ways to manage this failure mode:

1. Take care to assemble correctly

2. Don’t leave a machine idle for a long time.

3. Prevent, as far as possible, low frequency vibrations to travel to a machine.

4. If an idle machine is to be commissioned then take care to inspect the joints and interfaces and replace assemblies as found necessary.

5. May be monitored by Wear Debris Analysis for lubricated joints and interfaces and by vibration monitoring for dry joints and interfaces or simply by visual monitoring.

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.