Case of Missing Gear Mesh Frequency


“Why don’t we see the Gear Mesh Frequency (GMF) on the output side of a splash lubricated slow speed gear box?”

This is quite puzzling since common sense dictates that such peaks should be present.

My Answer:

The principles involved are the following:

1. Air, water and oil produce turbulence when worked on by machines like pumps, gears, fans, propellers etc.
2. Such turbulence creates damping force.
3. This is proportional to the square of the velocity.
4. But this damping force acts in quite a funny manner.
5. For slow speed machines (say below 750 rpm; slower the better) damping is positive that is it goes against the motion and so neutralizes the entropy as seen by the decrease in the vibration levels. Hence the gear mesh frequencies vanish. Coriolis Effect on the output side of the gear box also helps in attenuating the vibration.
6. But for high speed machines damping is negative. That is it goes in the direction of the motion and therefore enhances the entropy as seen by the increase in the vibration levels.
7. So, for low speed machines it goes against the motion and suppresses the GMF. In some cases it suppresses the fundamental peak as is found in the case of the vertical Cooling Water Pumps of Power Plants. GMF is produced when the fundamental frequency is superimposed onto the vibration generated through gear impacts.
8. It therefore follows that for high speed gear boxes it magnifies both fundamental and GMF peaks.

Missing peaks therefore indicate fluid turbulence, which might also be indicated by other peaks like vane pass frequencies. The condition monitoring of such gear boxes might best be done through Wear Debris Analysis/Ferrography.

So, this is the mystery of the missing GMF in splash lubricated slow speed gear boxes.

Therefore, splash lubrication for a low speed gear box is a good idea. It enhances the life of the gear box since it balances the entropy in the system.

But at the same time, with higher oil level in a splash lubricated high speed gear box the vibration level would increase, specially the fundamental and the GMF. That would spell trouble.

Similarly, it is better to have a turbulent air flow in low speed fans and blowers. It suppresses the vibrations and therefore enhances the life of bearings.

Nature also uses these principles of fluid turbulence and damping? Applications?

1. Bird’s nest are made up of loosely placed twigs and leaves usually not bound to each other. But these don’t break up or fall off in turbulent winds. Damping keeps them in place and provides the necessary security to birds.

2. Swift flowing rivers allow fishes to grow bigger and better.

3. Winds, storms etc neutralize the increase in entropy.

Design Ideas for Reliability & Sustainability?

1. Low speed gear boxes might best be lubricated by splash lubrication.
2. High speed gear boxes might best be lubricated by spray lubrication
3. Hotter and turbulent air might best be handled by low speed fans and blowers.


Schematic to Understand and Resolve Vibration Problems.

Screen Shot 2017-10-23 at 9.44.29 AM

The above is a simple but comprehensive schematic to understand and resolve vibration problems of industries.


  1. Resolving vibration problems
  2. Design
  3. Manufacturing
  4. Design Review
  5. Machine Testing
  6. Modeling



Fractional Gear Mesh Frequencies

Recently I received an email which asked me give my option on a phenomenon the analyst observed.


Observing high vibs on pressing and lifting pinion Drive End (DE) and Non Driven End (NDE) bearing on a ball mill. Motor and main Gear Box drive are OK. Clear predominant gear mesh frequency is appearing in the spectrum along with harmonics and side bands. But 1st GMF (Gear Mesh Frequency) is predominant. side bands with pinion speed is also seen. no Girth Gear speed side band was observed

Some of the vibration data, spectrums and photos shown in the attachment. Phase measurements indicate inconsistency in the readings near pressing pinion bearing. Impacts were also seen in time waveform data along with modulation.pinion speed 122 rpm.  On pressing side bearing 2.03 Hz side bands are seen, On lifting side i can see side bands spaced at 6.09 Hz (That is 3 times of pinion speed). Both Pinion lifting and pressing bearings are behaving differently. the vibs are high on DE as compared to NDE on both pinions. Can we suspect eccentric moment of the pinions with looseness. Why am i seeing 2.03 side bands on pressing and 6.09 side band on lifting side bearings. What is the significance of this. One sample of GG tooth photo shows uneven shining surface on either side (refer photo). In this case I am seeing  (30 T = 1 X 2 X 3 X 5) and (210 = 1 X 2 X 3 X 5 X 7) 2 X 3 X 5 as the common factor. Pinion 30 teeth and GG has 210 teeth. Will this create gear ratio issues uneven locking and releasing of 2 mating teeths. But no 1/2 or 1/3 or 1/5 GMF seen in the data.


My reply was:


But after a quick look this is what I see as the problem: –

1. We are seeing 1/2, 1/3 and 1/5 of GMF — these appear due to common factors 2, 3, 5 as you wrote.

This means that the pinion is badly worn out and as the common factor teeth mesh they generate these fractional frequencies.

It also means that the GMF and the natural frequency are not separated by 2.5 times. [The natural frequency in the horizontal direction = 28.5 Hz; natural frequency = 30.9 Hz; Gear Mesh Frequency = 60.6 Hz]

Looking at the signatures it is clear that the GMF falls within 2.5 times the natural frequencies.

Also note how the GMF (60.6 Hz) falls right between two natural frequencies in both the vertical and horizontal  directions. (31.1 Hz and 83 Hz). This makes the situation worse.

2. From the time waveform, we can see vibration relaxation waves. It means that the wear out or damage is towards the addendum region of the pinion/gear
3. This means that the spray nozzles are wrongly placed or jammed. The nozzles must be placed after the gear mesh not at or before the gear mesh. Also ask the client to check for jamming of the nozzles and the present viscosity of the grease/oil and the quantity that is fed per hour.
4. We can also suspect eccentricity of the pinion and looseness.
5. There is a strong resonance. This appears to have generated from the top cover.
Dibyendu De
Deeper Lessons:

It is important to question as to what else we can do other than detect a problem or detect an incipient fault?

With the above analysis and information we can easily see the relationship between fractional GMF and lubrication and wear. It means we can build an algorithm that would warn us about an imperfect lubrication system that would in fact accelerate wear and put the system out of service.

Further, we can refine the specification of a purchase a gear box. The specification should state  — a) number of pinion teeth should be a prime number to prevent accelerated wear b) if a prime number can’t be achieved then the natural frequency in the three directions must be away from the GMF by at least 2.5 times the GMF.

Similarly, we can specify the gear box top cover natural frequency should be at least 4 times the GMF.

Scheduled running checks may include — a) rate of lubricant flow b) motor current c) placement of lubricant nozzles etc.

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Details of the case: (relevant data)


Steps for vibration measurements

Impact test was carried out at selected locations on the torsion bar to know its natural frequency
Normal vibration signatures were recorded with motor speed being 994 rpm and pinion speed 122 rpm

Vibration data was recorded on selected bearing locations of motor, gearbox and pinion bearings
Data was recorded along horizontal, vertical and axial direction with 90% load on the mill

Phase measurements were recorded to know the behavior of pinion DE with respect to pinion NDE of pressing and lifting side


Vibration signatures recorded on Pinion DE and NDE of both pressing and lifting side bearing shows predominant gear mesh frequency and its harmonics
Side bands were observed along with gear mesh frequency and its harmonics
Gear mesh frequency 60.9 Hz is appearing predominantly in all HVA direction

Time waveform recorded on pinion DE and NDE bearings clearly shows modulation which occurs due to above phenomena
Impacting of the gear teeth was also observed. Refer time plots provided in this report in subsequent pages

Only Side bands of pinion speed (2.03 Hz or 122 rpm) are seen, no side bands of Girth gear was seen in the data
The phase measurements recorded on pressing pinion DE and NDE along axial and horizontal direction shows the phase is not consistent with time suspecting looseness due to uneven movement of pinion

Vertical vibrations recorded on pinion DE bearing lifting side shows the vibrations are low (5 mm/sec) on one end while its high (11 mm/sec) on the other end even though it’s a common top cover of that bearing
For any normal 2 mating gears the selection of no. of teeth on each gear should be such that when factorizing is done no common factor should be found apart from 1

In this case pinion has 30 teeth and Girth gear has 210 teeth o Then as per calculations
Pinion 30=1x2x3x5,GG 210=1x2x3x5x7
So common factors are 2x3x5


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Would Lubrication Cause a Sudden Failure?

This case is about a sudden failure of cooling tower fan motor of a copper mine.

The motor failed almost immediately after Planned maintenance, which was just about lubricating the motor bearings.

What Happened?

Electrical department conducted a scheduled PM task on this piece of equipment on 25.05.17. After 3 hrs of running; motor Non Driven End (NDE) bearing was damaged.

When the motor was opened it was observed:

1. One of the poles was severely damaged.

2. Bearing cage was also found damaged and all roller elements were crushed.


Why did this happen? 
1. Sudden application of load or abrupt change in load. It happened when the machine was started after PM — i.e. starting the machine from rest under loaded condition.
2. This caused hunting of the motor in which a rotor starts seeking equilibrium position. Such an equilibrium is reached when the load torque is equal to the electromagnetic torque. This equilibrium position gets disturbed if a sudden change occurs in the load torque, which has been the case when the motor was started the after the motor was stopped to lubricate its bearings.
3. In this situation, the rotor slips too much, i.e. — the rotor moves around trying to find its steady state equilibrium state and in this process the rotor and stator touched and shorted — damaging one of the poles.
4. Point 1 to Point 3 describes the root cause of the case. A  broad at the base 1N (1 times running speed) peak was observed.  This indicates presence of rubbing and resonance.
5. Resonant frequency excited the resonant frequency of the NDE bearing  which caused complete collapse (crushing) of the motor NDE bearing.
6. Another point which is important to consider is the time taken for a freshly lubricated bearing to stabilise. After lubrication, an anti-friction bearing generally runs hot (temperature greater than 75 degrees C but lesser than 95 degrees C) for a few hours (5 to 6 hours at times) to stabilise to a normal operating condition; with a temperature around 65 degrees C. This phenomenon can abruptly and adversely affect vibration levels of the bearing.

1. The vibration signature did not indicate lubrication starvation of the bearing.

Hence the question is — why stop a machine for re-lubrication when the activity isn’t needed at all?

2. In the future, if the system is stopped, then during start up it has to be ensured that the load is zero or near zero or it has to start at no-load condition.

If that isn’t possible, the system has to be started at low rpm and then the rpm can be gradually increased, all the while maintaining a steady state. It might take up to 6 hours for the system to stabilise after a bearing is lubricated.

Dibyendu De


Corolisis Effect & Negative Damping – a Report

Report on Thaisen Fan (Scrubber)


Brief description of the phenomenon:

After cleaning of the fan blades, vibration of the fan gradually increases during operation and in a span of 10 to 14 days vibration level reaches an unacceptable level, which necessitates the next cleaning cycle. However, for so long, this matched the scheduled production window provided by operation. However, after the recent changing of the rotor and the bearings, the fan now reaches unacceptable level of vibration within a short span of time that does not coincide with the scheduled “production window” of the operation, which causes “unplanned downtime.”

Goal of the investigation: To correct the imperfection in the system so that the fan cleaning cycle coincides with.the scheduled production window.

Result of the investigation:


1. The problem of rising vibration within a short period of time is an inherent problem (a birth defect) of the fan. The main reason is the Coriolis effect on the fan. Coriolis force is a force exerted by a moving fluid on the disc or impeller rotating in the fluid. If the rotation is CCW (counter clockwise) then the fluid moves to the right of the impeller and away from the centre. Similarly, when the impeller moves in the CW (clockwise direction) the fluid moves towards the left of the impeller and away from the centre.

In this case, with the fan moving in the CCW direction the Coriolis force moves toward the right of the impeller in the same direction as the damping force. This effect (the fan moves in the CCW direction) produces negative damping (since the two forces are in the same line of action).

Negative damping is a phenomenon, when damping force, which usually opposes the driving force, acts in the same direction as the driving force. In such a case the vibration of the system is amplified.

Combination of negative damping and Coriolis effect produces this phenomenon of gradually rising vibration of the fan in a short period of time, which goes away upon regular cleaning. In the present context nothing can be done to eliminate the phenomena of Coriolis Effect and Negative damping. However, if a similar system is to be installed in the future, we would be pleased to provide necessary suggestions and recommendations so that such phenomena are eliminated right from the start.

2. Present signatures indicate misalignment and dynamic imbalance

3. Weak foundations

Actions to be taken to increase the cleaning cycle to match scheduled “production window.”


1. Take care to align the rotor properly. Care to be taken while putting shims.

2. Dynamically balance the fan in two planes to eliminate the imbalance

3. Cleaning cycle can be initiated when vibration of the fan on the bearings reaches 7 mm/sec (rms). It is safe to run the fan upto this point.

4. Monitor the condition of the foundation by taking vibration measurements in displacement and acceleration modes. Displacement should be taken in the horizontal direction on the topmost accessible point of the columns and at the base.  Acceleration should be taken in both vertical and horizontal directions. Displacement should not cross 50 microns in the horizontal direction or at the base of the columns. Similarly acceleration both in the vertical and horizontal directions must not cross 1.5 g. This would ensure safety of the equipment. In case it crosses corrective actions are to be taken to rectify the foundation.


After alignment and dynamic balancing in two planes vibrations came down to below 1 mm/sec and maintained its reliability till the next cleaning cycle (10 to 14 days) which matched the scheduled production window of operation — thus avoiding unplanned downtime.
Dibyendu De

Speed Dependent Vibration

Speed dependent vibration is associated with forced mechanical vibration.

Application: rolls where the strips processed through the rolls exhibit roll chatter that leaves permanent imprint on the strip in the form of chatter (equally spaced markings of about 20 to 45 mm width) pattern. It is generally considered to be a defective product and often can’t be sold in the market.

The way to check the cause of such chatter patterns or marks is to take the vibration in displacement mode. When displacement increases by approximately 0.6 microns at the highest rolling speed it significantly points to surface roughness of the strip and so creates the pattern of chatter marking on the product (e.g. aluminium sheets). It indicates a loss of stiffness or the presence of variable stiffness, which may be coming from coupling, defective gears or from loose or defective anti-friction bearings.

Usually we may observe sidebands on either side of the forced vibration peak. The spacing of the sidebands is an exact multiple of the rotational frequency of the work roll. This is commonly seen for inner race defects where the inner race is rotating freely on the roll. The defect rotates through a variable load zone and produces a modulated time waveform. This is seen as a peak with sidebands in the vibration spectrum. Also pronounced on chocking and de-chocking.


  1. Reconditioning of the bearing races or replacement of bearings
  2. Improve the chocking operation.

This eliminates the strip chatter or markings.


Dibyendu De


Course Structure for Vibration Level 3 Analyst

Vibration Principles: (1 hour)

  • Basic Motion
  • Period, Frequency
  • Amplitude (Peak, Peak-to-Peak, RMS)
  • Measurements (Displacement, Velocity, Acceleration)
  • Units, Unit Conversions
  • Time Orbital and Frequency Domains
  • Vectors, Modulation
  • Phase
  • Natural Frequency, Resonance, Critical Speeds
  • Force, Response, Damping, Stiffness
  • Instabilities, Non-linear Systems
  • Mode Shapes
Data Acquisition: (1 hour)

  • Instrumentation (and acquire readings)
  • Dynamic Range
  • Transducers
  • Sensor Mounting, Mounted Natural Frequency
  • Fmax Acquisition Time
  • Proximity Sensor Conventions
  • Triggering
  • Test Planning
  • Test Procedures
  • Recognition of Poor Data
  • Vibration System Calibration
Signal Processing: (5 hours)

  • RMS/Peak Detection
  • Analogue/Digital Conversion
  • Analogue and Digital; Sampling
  • FFT Computation
  • Windows (Uniform, Hanning, Flat-top)
  • Filters (Low pass, High Pass, Band Pass, Tracking)
  • Anti-aliasing
  • Band-width, Resolution
  • Noise Reduction
  • Averaging (Linear, Synchronous Time, Exponential)
  • Dynamic Range
  • Signal to Noise Ratio
  • Spectral Maps
  • Run-out Compensation
Condition Monitoring: (2 hours)

  • Computer Database Set-up and Maintenance
  • Equipment Evaluation and Prioritization
  • CM Program Design
  • Alarm Set-up (Narrowband and Envelope)
  • Baseline Assessments, Trending
  • Route/Task Planning
  • Alternate Technologies (e.g. Oil Analysis, Wear Debris Analysis, Infrared Thermography, Motor Current Analysis, Acoustic Emission)
  • Alarm and Trip Level Determination
  • Procedure Writing (and methods of working)
  • CM Program Implementation and Management
  • Integrated Health Analysis
  • Prognostics
Fault Analysis: (6 hours)

  • Basic Spectrum Analysis
  • Spectral Harmonics and Sidebands
  • Time Waveform Analysis
  • Phase Analysis
  • Transient Analysis
  • Orbital Analysis
  • Shaft Centre-line Analysis
  • Enveloping
  • Mass Unbalance
  • Misalignment
  • Concentricity Errors
  • Mechanical Looseness
  • Rubs
  • Instabilities
  • Shaft Bow
  • Bearing (Rolling Element, Journal) Defects
  • Electric Motor Defects
  • Flow Induced Vibration, Aerodynamics and Liquids
  • Gearbox Defects
  • Resonance and Critical Speeds
Corrective Action Recognition: (4 hours)

  • Shaft Alignment
  • Concentricity
  • Balancing
  • Machine Part Replacement
  • Flow Control
  • Isolation and Damping
  • Resonance Control
  • Basic Maintenance Action
  • Lubrication
Acceptance Testing: (1 hour)

  • Specifications and Relevant Standards
  • Acceptance Test Reporting
Equipment Testing and Diagnostics: (2 hours)

  • Impact Testing
  • Forced Response Testing (e.g. Coherence, Transfer Function)
  • Transient Testing
  • Damping Evaluation
  • Operating Deflection Shapes
  • Modal Analysis
  • Torsional Vibration
  • Axial Vibration and Thrust
  • Process Safety
Reference Standards: (1 hour)

  • Relevant International (ISO, IEC), National and Regional Standards
Reporting and Documentation: (1 hour)

  • Machine History Records
  • Vibration Diagnostic Reports
  • Vibration Prognostic Reports
  • Failure Investigation Report
  • Decision Making and Recommend Action
Fault Severity Determination: (2 hours)

  • Levels (Overall, Narrowband, Component)
  • Spectrum Analysis
  • Time Waveform and Orbit Analysis
  • Severity Charts, Graphs, Formulae
Theoretical Rotor and Bearing Dynamics: (2 hours)

  • Rotor Characteristics
  • Bearing Characteristics
  • Rotor Dynamic Computation (using approved procedures)
  • Rotor Dynamic Fault Modeling
Field Balancing: (2 hours)

  • Single-plane
  • Two-plane
  • Multi-plane

Bent Shaft

General Symptoms:

  1. High overall vibration in the axial direction in displacement and velocity parameters
  2. Generally we would get 1N in the axial direction if the bend in at the centre of the shaft
  3. We may also get 2N in the axial direction if the bend in near to the coupling.
  4. Vertical and Horizontal axis measurements will also often reveal peaks at 1N and 2N but the key to catch a bent shaft is to pay attention to what we get in the axial direction.

Reasons of bending:

  1. Excessive heat. E.g. in motors that are overheated for various reasons, like for example, loose connections of the terminals. Also refer to the problem of Rotor Bow .. here.
  2. Physically bent or run out
  3. Sag of a long shaft — also called catenary. For example — turbine shaft.
  4. Half critical speed — a phenomenon seen in horizontal machines operating close to the earth’s resonant frequency


Phase measurement is an effective test to confirm presence of bent shaft. Phase at 1N measured in the axial direction at opposite ends of the components will be 180 degrees out of phase.

However, if the phase measurements are taken around the shaft we would find that they are all in phase since the shaft will appear to be moving back and forth in the axial direction.


In addition to the prominent presence of 1N and 2N in the axial direction we would also find higher than normal 1N and 2N peaks in the radial directions.

Time waveform:

In this case time waveform would not prove to be a good indicator for bent shaft. However, a sinusoidal waveform is expected in the axial direction if the vibration is predominately 1N. In the case of a predominate presence of 2N there would be a “wobble” depicting the classic “M” or “W” pattern depending on the phase angle, if the bend is closer to the coupling.


Dibyendu De






Typical Symptoms: High 1x in the axial direction and 2x in the radial directions; at time 3 x is also present in severe cases (e.g. when coupled to coupling imbalance).

Reasons for misalignment:

  1. Skill
  2. Thermal growth
  3. Movement of foundation

Types of misalignment:

  1. Parallel misalignment — we would find strong presence of 2x component in radial direction along with 1x in the axial direction.  This is because two opposing forces act together at the coupling — both trying to align the shafts to each other.
  2. Angular misalignment — we would find strong presence of 1x component in the radial direction along with strong 2x in the axial direction. This is because angular misalignment produces a bending moment on both shafts.
  3. However, vibration patterns don’t change in very predictable patterns as described in points 1 and 2 above. This is because there is usually a mix of the two different types of misalignment. In addition foundation problem and stiffness (directional or variable) create further complexity in the situation.
  4. The 1x and 2x components would be strong in the radial directions (V and H) but these components would be in phase.

Usually we would find high 1x peak in the axial direction with small 2x and 3x peaks depending on the “linearity” of the vibration. There may be both 1x and 2x (at times accompanied by 3x) in the radial directions.

Time waveform in the axial direction would be dominated by sinusoidal 1x vibration

Phase: Motor and say Pump would be out of phase axially due to angular misalignment (across the coupling in the same direction).


Dibyendu De

Eccentric Gears

Typical Symptoms: 1x radial (in Vertical and Horizontal directions)

Like eccentric pulleys, Eccentric gears generate strong 1x radial components, especially in the direction parallel to the gear.

They would also generate sidebands of the running speed of the eccentric gear around the GMF (gear mesh frequency). However, harmonics of GMF may also be generated (depends on the severity of the problem). Natural frequency might also be excited.

Time waveform: The waveform will have combination of 1x running speed of input and output shafts plus strong gear mesh vibration modulated by the running speed of the shaft having the eccentric gear.

Phase: Not applicable.