Understanding the Basic Theory of Vibration & Analysis

Understanding The Basic Theory

Behind Vibration Analysis General Introduction (What IS Vibration) Conventions

Characteristics

o Amplitude

o Frequency

o Phase

Acquiring & Displaying Data

Database Setup

Data Plots

o Trend Plots

o FFT Plots

o Time Domain Plots

o Envelope Spectra

Spectrum Interpretation (Troubleshooting Charts)

General Introduction What Is Vibration ?

What Causes It ?

Why Measure It ?

What Does The Transducer Measure ?

What Are "Vibration Characteristics" We Measure ?

o Amplitude

o Frequency

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o Phase

What Is Vibration ?

Vibration is a "back and forth" movement of a structure. It can also be referred to as a "cyclical" movement

What Is Vibration Caused By ?Imperfections in the Machine:

Design Assembly

Manufacture Operation

Installation MaintenanceWhat Are Some Common Machine Problems

That Generate Mechanical Vibration:

Misalignment Unbalance

Worn belts & pulleys Bearing Defects

Hydraulic Forces Aerodynamic Forces

Reaction Forces Reciprocating Forces

Bent Shafts Rubbing

Gear Problems Housing Distortion

Certain Electrical Problems Frictional ForcesWhat Are Some Common Machine Problems

That Amplify Mechanical Vibration (But Don't Cause It):

Resonance Looseness

Why Do We Measure Vibration ?


1. Assess the condition (primarily the bearings) of a machine. By performing this task effectively, we can eliminate catastrophic failures due to component degradation.

2. Diagnose the root cause(s) of any excessive (destructive) vibration. By performing this task effectively, we can extend the life of bearings and other components that are absorbing the stresses and fatiguing forces that are causing the symptom of excessive vibration.

It should be understood that short-term event-based failures (i.e. loss of lubrication, sudden fracture of a component, etc.) are not protected against via any program that only collects data periodically. The time between onset and failure in these cases - which are rare - may take only minutes (in extreme cases), hours, days or weeks. For example, many programs are based on monthly data collection. Any event occurring during that month interval may cause failure prior to the next data collection. This is not a failure of the program or the technology any more than driving a fork truck into a machine and destroying it is. The good news is that the vast majority of potential and actual failures will NOT fall into this category and DO lend themselves to being detected, monitored and corrected through a well-run vibration program.

What Does The Transducer Actually Detect ?

Actual Bearing Movement:

Elliptical

A Transducer Mounted Vertically "Sees" Only

Vertical Movement

A Transducer Mounted Horizontally "Sees" Only

Horizontal Movement

What Vibration "Characteristics" Do We Measure ?

Amplitude Tells Us:

How Much Movement Occurs


Frequency Tells Us:

How Often The Movement Occurs(How many "cycles" in a period of time: a second or a minute)


Phase Tells Us:

In What Direction Is The Movement(Relative To Other Locations On The Machine At A Given Moment In Time)

Conventions What Are "Conventions" ?

Bearing Nnumbering (Position) Conventions

Position Naming Conventions

Directional Conventions

o Belt Drives

o Vertical Units

What Are "Conventions" ?Conventions are standards that you set or adopt that apply to every machine and application in the program. These conventions simplify training of new personnel and make sure everyone involved in the program is on the same page. There are at least three basic conventions that should be set up. They are:

1. Bearing Numbering ("Positions")

2. Position Naming

3. Direction Definitions




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Common Bearing Numbering Conventions Most programs use numbers to identify bearings. Some use letters

instead. By FAR the most common convention is to begin the numbering (or lettering) on the non-drive end of the "driver" component (motor, turbine, etc.). That bearing will be denoted as Position "1", or Position "A".

Following the drive train in a logical manner, the next bearing reached will be Position "2" or "B". That bearing will be found at the drive end of the motor or turbine (the driver component).

Continuing to logically follow the drive train, the next bearing reached will be Position "3" or "C". This bearing will almost certainly be on the "driven" component.

With a typical 4-bearing machine, the last bearing reached would be Position "4" or "D".

The image below shows a typical 4-bearing, belt driven fan with the bearings numbered.

Common Bearing Numbering Conventions

What about components that have more than 2 bearings such as gearboxes. The image at right (which does NOT show the motor containing bearings 1 & 2) shows a typical numbering convention for components with more than 2 bearings. Again, it is based on following the drive train in a logical manner. The important thing is to set up a simple, straight forward convention and adhere to it consistently. You can use other people's ideas and conventions or develop one yourself that makes sense to your people for your machines. The gearbox shown here is a "double reduction" gearbox (it has two separate gearmeshes). This gearbox has three (3) shaft speeds (the input shaft speed, the speed of the shaft supported by bearings 5&6 and the output shaft speed) and two (2) gear mesh frequencies.

Common Position Naming ConventionsAlthough bearing numbering is (and should be) the primary identifier of the position of the reading, bearing names are often used as well. Since there are a variety of common names used for naming the different bearing positions - several for each position, in fact - a list of the common ones is put forth here. There are no right or wrong ones - the only important aspect is complete consistency in your usage.

Common Position 1 Names o Outboard motor bearing

o Opposite drive end motor bearing

o Opposite shaft end motor bearing

Common Position 2 Names

o Inboard motor bearing

o Drive end motor bearing

o Shaft end motor bearing


o Inboard ?? bearing (the "??" will be fan, pump, etc. depending on what the driven component is)

o Drive end ?? bearing

o Shaft end ?? bearing


o Outboard ?? bearing

o Opposite drive end ?? bearing

o Opposite shaft end ?? bearing

You may have applications that do not fall neatly into the 4-bearing machine category. Long drive lines with dozens of bearings, gearboxes like the one shown on the previous page, multi-stage machines, etc. may each require their own unique solution for bearing naming. In the case of a long drive line, the bearing may be named to coincide with the piece of equipment along that drive line that bearing is closest to. Conversely, you may decide to rely strictly on position numbers in that case and not use position names at all. Terms such as "Intermediate Shaft" may be used. There is no single, universal naming convention that will apply to all machine configurations. Remember the objective:

Consistency Is The Key

Common Direction Naming ConventionsDirectional conventions are also of the utmost importance to set up and use. A simple, common sense convention insures that whomever is collecting the data is aware of the correct transducer location and direction. It also means the analyst, if different than the data collection technician, can analyze the data with confidence. This convention goes to the heart of one of the most important aspects of a vibration program - the repeatability of readings from one data collection to the next (what good is a trend without good repeatability ?). Its importance goes hand-in-hand with the importance of making sure the exact transducer locations are clearly marked. The convention begins with ONE hard rule:

Axial Direction is always, Always, ALWAYS parallel to shaft axis

Let's start with horizontal, direct drive machines. These machines are the most simple to define. 1. Axial Direction - Runs along the axis of the machine's shaft (parallel to the shaft & ground).

2. Vertical Direction - The shortest line possible connecting the machine shaft and the machine base. 3. Horizontal Direction - A line drawn out from the machine shaft that runs exactly parallel to the ground.

Common Direction Naming Conventions

Belt drives can be oriented in any direction and thereby require a directional convention. The convention shown here has been adopted for some very simple reasons which help illustrate not only its usefulness but the importance of conventions in general:

Reason #1: The belt (reaction) forces are usually directed in-line (parallel) with the belts.

Reason #2: In order to capture these belt related vibrations and separate closely matched frequencies, higher resolution readings are set up in the database parallel to the belts. Details of this subject - spectrum resolution - are covered in the "Spectrum" section.

Reason #3: To make it easier to both set up the database and to analyze collected data, these higher resolution readings are always taken horizontally.

For these reasons, a convention is used that defines "parallel to the belts" as horizontal is used. By default, that leaves the measurement taken perpendicular to the belts defined as Vertical. By adopting this convention, both collection and analysis are simplified - a stated objective of using conventions.

Common Direction Naming Conventions

Vertical machines present another opportunity to assign a directional convention since parallel to the shaft (axial) is now straight up out of the ground. Since we must adhere to our one hard and fast rule for directional conventions, the axial direction remains parallel to the shaft (perpendicular to the ground; what would be defined as vertical on a typical, horizontal direct-drive machines).

That leaves vertical and horizontal to be defined. For reasons similar to those discussed previously for the belt drive convention, it is recommended that horizontal be defined as parallel to the discharge of the machine. That would leave vertical as being defined as perpendicular to the discharge (and parallel to the ground).

Vibration Characteristics:

Amplitude What Does Amplitude Tell Us ?

What Are Amplitude "Units" ?

Measuring Displacement Units

The Displacement "Sine Wave"

Measuring Velocity Units

Velocity vs. Displacement

The Velocity Sine Wave

Measuring Acceleration Units

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Acceleration vs. Displacement

The Acceleration Sine Wave

What Does Amplitude Tell Us ?

Before we answer that question, let's keep in mind what exactly we are measuring. Everyone taking this class has touched a part of an operating machine (even if it is your car or even your lawn mower) and felt the back and forth movement. Because that movement is back and forth, it is defined as "cyclical", or "sinusoidal", and we call it "vibration". Obviously, we would want to quantify the amount of movement. That measurement is known as "amplitude". However, there are several different ways of quantifying the amount and that is what we will discuss in the following pages.

What Does Amplitude Tell Us ?

The 'amplitude' is a measure of the amount of movement.

The amount of movement is related to the severity of the vibration.


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Simply put, it measures:

How Much ?

What Are Amplitude "Units" ?There are several different ways to measure "how much". These different ways are known as amplitude "units". The transducer is the mechanism we use to measure vibration and, in the case of rolling element bearings (i.e. ball bearings, etc.), we can assume the transducer, being affixed to the bearing housing, is going to move very close to the same amount as the shaft itself since a rolling element bearing has very small internal clearances. The first amplitude unit is the simplest to visualize and understand:

Displacement - measures the total distance the transducer (bearing) travels back and forth during one 'cycle' of movement (a 'cycle' is the process of moving from one extreme to the other and back again to the starting point).

To understand the second amplitude unit, you must first understand that if a bearing is going to move back and forth a certain distance in a certain amount of time (the 'period'), it is going to achieve a certain maximum, or 'peak', speed (velocity) during that cycle. That speed is constantly changing as it goes from 0 (when the bearing is displaced a maximum amount in one direction and has stopped momentarily to reverse direction) to some maximum value it achieves as it passes the center point in the movement. Once it passes that center point, the bearing starts slowing down until the speed again reaches 0 as it reaches the maximum displacement in the opposite direction.

Velocity - measures the maximum speed the transducer achieves during a cycle.

To understand the third amplitude unit, you must understand that to change velocity, a body must be accelerated or decelerated. To speed a car up, you press the "accelrator" pedal. To slow it down, you remove your foot from the accelerator and let frictional forces (wind resistance, road surface, brakes) take over. On machines, this "acceleration force" can be visualized as the reaction of the bearing housing and surrounding structure to being pushed (displaced) in one direction - the housing pushes back because it wants to assume a neutral, or "at-rest", position.

Acceleration - measures the force(s) that are causing the back and

forth movement.

Now let's look at each of these units more in-depth and see how they are inter-related.

Measuring "How Much" in Displacement Units Displacement measures the length of the "trip" back and forth from (in this case) +X to -X (2X would be the total distance travelled - the "peak-to-peak displacement"). One of these "trips" is known as a "cycle" of vibration. The sequence of images about to be presented show the bearing at various important points during a single cycle with the transducer oriented vertically (remember, the transducer only "sees" movement in the direction of its orientation, or axis).

Since this movement must occur over time, when we measure it we plot the amount (amplitude) on the y-axis and the time taken (period) on the x-axis. The resulting shape, in its simplest form, is called a "periodic signal", a "sinusoid" or a "sine wave". That is the S-shape you see below the word "cycle" in the image at right. Mechanical vibration generates a wave shape that is rarely as simple as what we see here but the intricacies of processing more complex data will be covered in later sections.

The "At-Rest" position ("0") is the position the bearing would assume if the machine was not running.

During a single (1) cycle, the bearing passes this position twice - once travelling towards +X and once travelling towards -X.

We'll begin our sequence of images with the bearing just passing the '0' point moving towards '+X'.

The red ball (seen at the very ends of the sine wave) indicates the amplitude level during the cycle.

Measuring "How Much" in Displacement Units

The bearing has just reached the '+X' position and has stopped momentarily to reverse direction.

The bearing is 1/4 of the way through the cycle (1/4 of a shaft revolution).


The bearing is now passing the '0' position again moving towards '-X'.

The red ball has completed 1/2 cycle (1/2 shaft revolution).


The bearing has now reached the '-X' position - its maximum displacement in the '-' direction.

The bearing has again stopped to reverse direction.

The red ball has completed 3/4 of a cycle (3/4 of a shaft revolution).


The bearing is now back where it started, having completed one "cycle" of movement.

We want to know the total length of the "trip" being made by the bearing.

Travelling from the "+X" position to the "-X" means the total distance travelled = 2X). That is known as Peak-to-Peak signal detection and that is how displacement amplitudes should be measured.

Since displacement measures the amount a component is being bent back and forth, it is a measure of the STRESS that the bearing structure is being subjected to. It is, in other words, an amplitude unit that is particularly sensitive to the likelihood of a stress failure occurring.

Stress failures are most likely to occur on slow speed equipment and are not a very common failure mode (hence we do not normally use displacement amplitudes as a primary monitoring tool).

The "Displacement Sine Wave"

English or 'Imperial' Units: Mils (1 mil = 0.001")

Metric Units::Microns (1 um = 0.001 mm)

Conversion::1 Mil = 25.4 um

Measuring "How Much" In Velocity Units What is a "velocity" amplitude ? Technically, velocity measures how

much the displacement is changing over a period of time.

The units of measure are inches per second or millimeters per second.

With sinusoidal motion the velocity constantly changes as the displacement changes.

Since the velocity is constantly changing over time, measuring velocity amplitude over time generates a sine wave just as measuring displacement amplitude does.

Measuring "How Much" In Velocity UnitsThe "Velocity Sinusoid" vs. The "Displacement Sinusoid"

As we began discussing the relationship between velocity and displacement on previous pages, let's now look at a direct comparison between the two and see how they relate to one another at the most significant points in the cycle:

The bearing is shown here at its maximum displacement of '-X'. Velocity must be zero at this moment since the bearing must stop

momentarily to reverse direction.

From this moment until the bearing passes the "at-rest" (0) position, the bearing will be speeding up (the velocity amplitude will be increasing).


The bearing is now passing the "at-rest" position as it moves towards the "+X" position:

The displacement amplitude is '0'. Velocity is at a '+' peak since the bearing has reached its maximum

speed (remember, it has been accelerating since leaving the "-X" position.

From this moment until the bearing reaches the "+X" position, the bearing will be slowing down (velocity amplitude will be decreasing).


The bearing has reached its maximum displacement in the '+' direction: The displacement is "+X". The speed (velocity) is 0 since it has (again) momentarily stopped to

reverse direction.

From this moment until the bearing passes the 'at-rest' position, the bearing will be speeding up (accelerating - the velocity amplitude will be increasing).


The bearing is passing the "at-rest" position again moving moving in the "-" direction:

The displacement amplitude is "0". Velocity is at a "-" peak since the bearing has reached its maximum

speed (the speed is the same as previously reached when travelling in the "+" direction - only the direction has changed).

From this moment until the "-X" position is reached, the bearing will be slowing down ("decelerating" - the velocity amplitude will be decreasing).


With displacement, we were concerned with the total distance travelled (stress-related failures).

With velocity, we are only concerned with the maximum speed (velocity amplitude) reached during that trip. It matters not which direction the bearing is moving in.

Since we are concerned only with the maximum velocity reached, we use Peak signal detection (not Peak-to-Peak).

Velocity measures the how often (frequency) the stress (displacement) is being applied.

Velocity is measure of the likelihood of FATIGUE being the mode of failure.

Fatigue failures are by far and away the most common cause of general machinery failures.

Velocity is the best monitoring tool for general machines.

Speciality machines, components or specific problems may not be best monitored by velocity.

Examples of machines, components and problems not suited to velocity are gears and certain electrical symtoms (i.e. very high frequency vibration: >120,000 cycles per minute) and very slow-speed equipment (< 100 rpm).

It should be noted that even though velocity is suited to monitor problems in the 60kcpm - 150kcpm range, it may be advantageous to use our third amplitude unit - acceleration - in those cases.

The "Velocity Sine Wave"

English or "Imperial": Inches per Second (ips -or- in/sec)

Metric: Millimeters per Second (mm/sec)

Conversion::1 ips = 25.4 mm/sec

Measuring "How Much" In Acceleration UnitsWhat exactly is "acceleration" ? Acceleration measures the rate of change of velocity (how quickly the velocity is changing). There are two methods of applying an acceleration force (deceleration is simply a negative acceleration):

1. A Pushing Action similar to you compressing a spring between your hands. The more you compress a spring, the more force it pushes back with. If you were to push a pillow block bearing away from its "at-rest" position, it would push back. If you went farther, it would push back more. That is a simple way to visualize the acceleration force we are measuring.

The amount of movement at a particular frequency is a combination of the force being generated by the rotation of the rotor (unbalance, for intsance, is simply a centrifugal force due to a heavy spot on a rotor), the stiffness and masses of the materials and structure involved and other variables that are structure related.

2. A Striking Action similar to you hitting a nail with a hammer. This action can be extremely destructive since it can cause structural flaws (cracks, for instance) to develop. Consider a jack hammer. It is the striking action that breaks up the cement. One example In the case of a rolling element bearing, a rolling element may pass a defect on one of the races and an impact results similar to hitting a pothole with your car.

What Is The Difference Between

Pushing Forces And Striking Forces ?1. Both are destructive but one is far more destructive - the striking action. 2. The Pushing Action causes sinusoidal motion. Since the velocity changes steadily (creates a sine wave), the acceleration also changes steadily and plotting it generates a sine wave just as displacement and velocity do. This is the type of acceleration we will be discussing in the following pages. 3. The Striking Action causes instantaneous, transient motion. Consider striking something with a hammer. The velocity undergoes a nearly instantaneous increase when the hammer strikes. Any movement then dampens out until the next impact. This type of acceleration must be measured differently and will be covered in a later section on "enveloping signals".

Measuring "How Much" In Acceleration UnitsThe "Acceleration Sinusoid" vs. The "Displacement Sinusoid"

Let's see how displacement and acceleration relate to one another at the significant points in the cycle:

The bearing is shown here at its maximum displacement of "-X". If you were pushing the bearing housing down to this position, in which

direction would the bearing housing be pushing back ? The housing structure in this position will be pushing back in the "+"

direction since it is trying to return the bearing to the "at-rest" position.

As mentioned before, the "amplitude" we measure is a combination of many variables but what do we actually measure ?

The bearing is achieving a certain peak velocity once per cycle. That velocity is a combination of the amount of movement (displacement) and the time it takes for one complete cycle (from which we calculate frequency). The less time a cycle takes, the higher the frequency of the vibration and the more force it requires to generate a particular peak velocity. In other words, going from 0 velocity to 1 in/sec (25 mm/sec) 1000 times a minute requires a lot less force than doing it 100,000 times per minute. The forces being applied to make that happen may destroy a component before metal fatigue (what velocity is sensitive to) even becomes a factor.

That makes acceleration an amplitude unit that is particularly sensitive to the likelihood of a component failing due to the forces being applied to it due to the machine's operation.

When either displacement peak is reached, an acceleration peak is reached in the opposite direction.

From the moment shown until the '0' position is reached, the acceleration amplitude decreasing.


The bearing is passing the "at-rest" position moving in the "+" direction. At the instant the bearing passes "0", the acceleration force

(amplitude) is 0 since the bearing is located in its at-rest position.

From this moment until the "+X" position is reached the bearing

acceleration amplitude is increasing to a peak value in the "-" direction (remember, as it is being displaced increasingly in the "+" direction, it is increasingly pushing back towards the at-rest position).


The bearing has reached the "+X" position (the "+" displacement peak): The acceleration force (amplitude) is at a maximum (peak) pushing

DOWN towards the "0" position (it has reached its maximum value in the "-" direction).

From this moment until the "0" position is reached the bearing acceleration amplitude is decreasing as the bearing approaches its at-rest position.


The bearing is passing the at-rest position moving in the "-" direction. At the moment the bearing passes the at-rest position, the

acceleration force (amplitude) is 0.

From this moment until the "-X" position is reached the bearing acceleration amplitude is increasing to a peak value in the "+" direction (remember, as it is being displaced increasingly in the "-" direction, it is increasingly pushing back towards the at-rest position).


As with velocity, we were concerned only with the maximum value reached - not the direction.

As with velocity, we use Peak signal detection.

Acceleration measures how rapidly the velocity is changing.

Acceleration is measure of the likelihood of APPLIED FORCE being the mode of failure.

Applied force failures occur at higher frequencies - almost invariably 60,000 cycles per minute and higher. There are a limited number of high frequency generating machinery problems.

Those problems include primarily rolling element bearing defects and gears.

The "Acceleration Sine Wave"

English or Metric - G's (1 g = force of gravity)


Frequency What Does Frequency Tell Us ? How Does Frequency Relate To Amplitude ?

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How Do Displacement, Velocity & Frequency Relate ?

Practical Effect On A Bearing Of Velocity Vs. Displacement

How Amplitude Units Relate to Different Failure Modes

Stress Failures vs. Fatigue Failures

What Failure Mode Are Acceleration Units Sensitive To

Where Are Acceleration Amplitudes Useful

Recommended Frequency Ranges For Different Amplitude Units

When To Use Which Amplitude Unit(s)

Formulas Relating Amplitude & Frequency

Examples Of When To Use Which Unit(s)

General Equipment Amplitude Guidelines

Amplitude Guidelines For "Other" Equipment

What Does Frequency Tell Us ?

By taking the reciprocal of how many seconds a single cycle takes (reciprocal of "seconds per cycle" is "cycles per second"), the number of cycles occurring in a given period of time such as a second or minute can be calculated.

For example, if a cycle takes 1/50th of a second, the frequency is 50 cycles per second (50 "Hertz"), or 3000 cycles per minute (3000 cpm or 3kcpm).



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That number - how many cycles occur in a given time period - is known as the vibration "frequency".

Simply put, it measures:

How Often ?

What Does Frequency Tell Us ? Machines will generate mechanical vibration at multiples (harmonics)

of their running speeds. This type of vibration is called "synchronous" vibration.

For example, unbalance causes a force that moves the bearing (causes vibration) in any direction (plane) at a rate of once per revolution (1x RPM). That movement occurs at exactly once per rev - not 1.1x per rev, not 0.9x per rev - ONCE per revolution.

A pump with 5 vanes on the impeller can generate hydraulic pulses (which can be measured as mechanical vibration) at 5 times per rev (5x rpm) - not 4.9x per rev, not 5.1x per rev - exactly 5 times per revolution.

Different mechanical problems (unbalance, misalignment, etc.) tend to generate their own characteristic vibration 'patterns'. Because the effect each problem has on the vibration signal we measure, they each tend to generate vibration at specific (rpm related) frequencies that the analyst learns to recognize and look for.

Other vibration generators may not be tied specifically to the machine's rotational speed.

Bearing problems and electrical problems, for example, tend to generate vibrations at specific frequencies other than exact multiples (harmonics) of running speed. This type of vibration is referred to as "non-synchronous" or "sub-synchronous" (below 1x rpm) vibration.

By correctly linking the frequency to the various possible sources, the source of the problem can be identified.

Frequency Identifies The Vibration SourceHow is Frequency Calculated ?

Measure the time it takes for 1 cycle: (Seconds / Cycle)

Take the reciprocal of that to get the frequency:

Cycles / Second (Hertz) Hertz x 60 = Cycles / Minute (CPM)

Since cpm is easier to relate to RPM, it is more commonly used and recommended for ease of use.

How Does Frequency Relate to Amplitude ?

The frequency of any periodic signal is mathematically related to each of the amplitude units: displacement, velocity and acceleration - if you know any two of these variables, you can mathematically calculate the other two. For instance, if you know: 1. How far a bearing is moving back and forth (the displacement amplitude), and 2. How much time it takes to complete the trip (the 'cycle', from which the frequency is derived)

Then armed with the proper mathematical formula, you can calculate the peak velocity reached during that trip. For instance:

A bearing vibrates 10 mils (254 microns) in 0.1 seconds. We know two of the variables:

o The pk-pk displacement is 10 mils.

o The period is 0.1 seconds (time required for 1 cycle).

Frequency is represented as the number of cycles during a certain period - a second or a minute. The bearing will make 10 of these trips in one second. Since the total distance travelled in one second is 100 mils, your average speed is 100 mils/sec (0.1 inches per second or 2.5 mm/sec). Of course, that is the average speed. Since you are constantly speeding up or slowing down, your peak speed would be about twice that average speed

(0.2 in/sec or 5 mm/sec).

Let's look more closely at the relationship between these 4 variables.

How Do Displacement, Velocity & Frequency Relate ?As stated, there are some simple mathematical formulas that relate the frequency of the vibration, the amount of movement (displacement), the speed of movement (velocity) and the force generated during the movement (acceleration). The mathematics involved is always handled by the software and hardware but it is illustrative to understand the simple principles involved. Let's first look at the relationship between frequency, displacement amplitude and velocity amplitude. Consider:

A bearing moves back and forth 10 mils (pk-pk displacement). The bearing moves at 10 cycles per minute (the 'frequency).

By setting those two variables, you establish a third - namely the speed at which the bearing must travel to satisfy those two conditions.

Consider: Another bearing is moving at 10 mils pk-pk. This bearing moves at 70 cycles per minute.

What is the speed of this bearing vs. the first bearing to satisfy those conditions ?

This bearing must have a peak speed of 7x the first bearing. The relationship between the 3 is linear (e.g. if the frequency increases 7x and the displacement remains same, the velocity must increase 7x).

So increasing the frequency 7x while leaving the displacement the same results in increasing the velocity at which the bearing must move by 7x.

The point here is simple. There is a direct relationship between the frequency, the displacement and the velocity. Knowing two - any two - allows the third to be mathematically calculated (along with a constant value). Without getting into further examples, the same direct relationship exists between frequency, velocity and acceleration. Therefore, all four of these variables are related - knowing any two allows the other two to be calculated. Let's look at the practical aspect of the relationship in a more graphic way.

Practical Effect On A Bearing Of Velocity Vs. Displacement

These animations graphically illustrate the previous example. The displacement in each is the same but the bearing on the right is completing 7 cycles for each cycle completed by the bearing on the left.

But what we are really interested in, of course, is the effect of the vibration on the bearing's life and the machine's health. Again, knowing nothing about vibration analysis and using only your common sense and knowledge of machines, which bearing will fail in a shorter period of time ? It doesn't take a vibration 'expert' to recognize that it will be the bearing on the right. But since the displacement (a measure of stress) is constant, the determining factor must be something else.

It is actually two failure modes that are increasing in likelihood with the frequency:

The fatiguing effect on the bearing components.

The forces being applied to make the bearing move.

But since the units are all related, why don't we just use a single amplitude unit and simplify things ?

How Amplitude Units Relate to Different Failure ModesThe reason has to do with each amplitude unit's sensitivity to different modes of machinery failures. In other words, each unit has a specific usefulness in monitoring machinery health. There are three types of failure causing effects that we are monitoring with vibration:

Stress (bending a component excessively causes it to fail) Fatigue (something simply wears out over time)

Force (the 'pushing' and/or 'striking' actions being applied to cause

the movement)

The graph below shows the sensitivity of each amplitude unit to the likelihood of a failure over a wide range of frequencies.

Notice that at low frequencies (primarily below 300 cpm or 5 Hz), displacement is the most sensitive unit to the likelihood of a failure. That is due to the fact that a stress failure (something being bent back and forth until it breaks) is the most likely failure mode at those low frequencies - the fatigue and applied forces become, as frequency approaches 0, simply too low to cause a failure.

Once you get above 300 cpm, the most likely failure mode increasingly becomes the 'fatigue' mode (to which velocity is the most sensitive unit).

Fatigue failures basically occur when a component simply wears out - it tires of the repeated back and forth movement (even a relatively small total distance) over an extended period of time and many, many cycles. Between about 300 cpm and 120,000 cpm (5 - 2000 Hz), fatigue is the most likely failure mode and therefore velocity is the most effective and reliable amplitude unit to monitor with.

Once you reach 120,000 cpm (2000 Hz), the most likely failure mode is 'force'-related. What is a force-related failure ? When you reach these very, very high frequencies (remember, you are dealing with moving an entire rotor structure back and forth 2000 times per second or more), you are dealing with massive amounts of force to move that structure back and forth even a tiny distance at such a tremendously high frequency. Therefore, it is that tremendous pushing or striking action that causes the failure.

It must be understood that there are areas of the chart where the units overlap and two conditions (stress and fatigue effects, for instance) exist.

Stress Failures vs. Fatigue FailuresThe chart at right shows the number of failures vs. the number of running hours. Notice that a relatively high number of failures occur during the first hours of runtime. These failures are known as 'infant mortality' because they occur shortly after start-up. In other words, a machine that is new or rebuilt is started up and has severe problems. Within a few hours, days or possibly weeks, a catastrophic failure occurs. If the failure is mechanical in nature (it could also be electrical or lubrication related), stress will often be a primary cause of failure - components being bent back and forth so much that something simply breaks.

However, once a machine runs for a certain number of hours (rotations), it becomes stress relieved and the likelihood of failure changes to fatigue - a component wearing out. Of course, if the movement (vibration) is high but not quite high enough to cause an 'infant mortality' stress failure, the fatigue failure will still occur in a relatively short period of time (which is one reason why the number of failures on the curve doesn't ever quite get to zero).

So if displacement is sensitive to stress, and velocity is sensitive to fatigue, where do the acceleration amplitude units fit in ?

What Failure Mode Are Acceleration Units Sensitive To ?Acceleration amplitude is the trickiest to understand. To begin with, you must understand that due to the nature of sinusoidal motion (the back and forth action), the velocity is constantly changing. It goes from zero to a peak back to 0 back to the peak and so on. To change the velocity of something, acceleration must be applied. To speed your car up, you apply the accelerator. To slow your car down, you apply the brake.

Acceleration measures the rate of change of velocity. Velocity is changed when a PUSHING or STRIKING action is applied.

Pushing or striking something is applying a 'force' and acceleration is, of course, force.

So why is acceleration used in the high frequency range ?

The rate of change in velocity (acceleration) is more affected by frequency - how often something is changing direction - than displacement - how far it is moving.

Components moving at high frequencies will never fail due to stress (displacement) because the displacement amplitude is very small.

Although there are frequencies where velocity and acceleration overlap in their sensitivity to failures, the higher the frequency involved (especially above about 120,000 cpm), the less likely a fatigue failure is and the more likely it is that the forces being applied that are causing the movement will be responsible for any failure that might occur.

Acceleration is sensitive to the likelihood of a FORCE related failure. In other words, a failure due to the pushing and/or striking action the component is being subjected to.

Let's look at one simple example to illustrate where acceleration is of use.

Where Are Acceleration Amplitudes Useful ?Consider a high speed centrifugal compressor. This machine, through its normal operation, generates some incredibly high vibration frequencies - well over 1,000,000 cpm (16.67kHz) in certain cases depending on the specifics of the machine components. These vibrations are generated by the gear teeth meshing together and referred to as gear mesh frequency.

Let's briefly look at the following example: Consider a machine that generates a gear mesh frequency of

1,080,000 cpm (18kHz). Let's assume that there is some vibration (movement) occurring at

the gear meshing frequency due to the interaction of the gear teeth.

Let's further assume that the amount of physical movement - the distance back and forth, so to speak - is 3 millionths of an inch (0.003 mils, or 0.076 um).

Everyone can visualize the tiny, tiny amount of movement generated.

However, to cause the structure (rotor) to move back and forth even such an incredibly tiny amount 18,000 times per second requires a force equal to 50x the force of gravity. That's right, 50 g's.

The failure will occur due to that force being applied repeatedly.

Let's look at some examples relating the different amplitude units to the

likely failure mode.

Recommended Frequency Ranges for Different Amplitude Units

Displacement Units: < 600 cpm (< 10 Hz) There are instances where the use of displacement amplitudes is essential even at very

high frequencies.

Velocity Units: 300 - 120,000 cpm (5 - 2,000 Hz)

Acceleration Units: > 60,000 cpm (> 1,000 Hz)

When To Use Which Amplitude Unit(s)Every machine has certain operational characteristics which must be considered when creating the database. Similar machines have similar characteristics and similar (many times identical) database point set-ups. The critical question that must be asked for every machine for which you are creating a database is simply what problems may develop on this machine and what vibration frequencies will be generated by each of these problems.

You may need multiple measurements on a particular location to get the level of

protection you would like.

In other words, you must create each database point with a specific purpose in mind.

Consider a motor driving some component connected with a coupling. What problems may occur on the motor and what vibration frequencies will each generate ?

Mechanical influences (unbalance, misalignment, etc.) at 1x, 2x, and 3x rpm (also be referred to as orders).

Pumps can generate hydraulically-related vibration at the number of vanes x rpm - vane pass frequency.

Compressors do likewise at lobe pass and vane pass frequencies (to name only 2 types).

Fans can generate at blade pass frequency.

With rolling element bearings, vibration at 30kcpm - 50 x rpm (up to

150kcpm) is typically generated during stages leading up to failure.

When To Use Which Amplitude Unit(s) ?

Compressor ExampleConsider the following example for which we will discuss the frequencies encountered: a direct driven screw compressor with an input speed of 3580 rpm. The motor directly drives a bull gear with 48 teeth which drives a pinion gear with 36 teeth. The rotor being driven by the pinion gear has 4 lobes while the driven rotor has 6 lobes. To determine what frequencies the potential problems may create, we need to specifically lay out the frequencies that will be generated on this machine and consider what problems can develop from the machine components. The machine schematic is shown here:

Let’s calculate exactly what frequencies need to be monitored on the compressor end only:

Frequency Name Calculation Frequency

4-Lobe Rotor Speed

3580 x 48T/36T 4773 rpm

4-Lobe Pass Frequency 4773 x 4 19092 cpm

6-Lobe Rotor Speed

4773 x 4T/6T 3182 rpm

6-Lobe Pass Frequency 3182 x 6 19092 cpm

Bull Gear Mesh Freq:

3580 rpm x 48T

171,840 cpm

Pinion GMF 4773 x 36T 171840 cpm

2x GMF 2 x GMF 343,680 cpm

3x GMF 515,520 cpm

Compressor Schematic Motor Speed = 3580 rpm

So we need to monitor the compressor bearings over a range of frequencies spanning 3182 cpm (1x 6-lobe rotor) to 515,520 cpm (3x gear mesh frequency). Although it can technically be done with a single reading, using only one amplitude unit would be a problem since velocity is no good

at 515,520 cpm and acceleration is no good at 3182 cpm.

But why would using only one amplitude unit be a problem ? The answer goes back to the relationship between the units and their sensitivity to different failure modes.

Let's look at some examples.

Formulas Relating Amplitude & FrequencyAs stated earlier, there are formulas that relating each of the amplitude units to one another through the vibration frequency. The following just lists a few of the possible variations. You should note that the software carries out the formulas - the following pages attempt to illustrate the concept only.

Imperial Units:

Displacement = mils Velocity = in/sec

Acceleration = g's Frequency = cycles/min

Metric Units:

Displacement = um Velocity = mm/sec Acceleration = g's

Frequency = cycles/min

Displacement = (19,231 x V) / F Displacement = (19,231 x V) / F

Velocity = 0.000052 x D x F Velocity = 0.000052 x D x F

Acceleration = 0.00027 x V x F Acceleration = 0.0000107 x V x F

Example #1:

A Bearing Vibrates 100 Mils Pk-Pk @ 30 cpmDisplacement @ 1x rpm = 100 mils Displacement @ 1x rpm = 2540 um

English Units: Velocity = 0.000052 x D x F

V = 0.000052 x 100 mils x 30 cpm

Metric Units: Velocity = 0.000052 x D x F

V = 0.000052 x 2540 um x 30 cpm

V = 0.16 ips V = 4 mm/sec

Acceleration = 0.00027 x V x F A = 0.00027 x 0.16 x 30

Acceleration = 0.0000107 x V x F A = 0.0000107 x 4 x 30

A = 0.0013 g's A = 0.0013 g's

Failure Likelihood: Stress = HIGH Fatigue = Low

Force = None

What unit is best to monitor with at this frequency ? Displacement

Example #2:

A Bearing Vibrates 10 Mils Pk-Pk At 1000 cpmDisplacement @ 1x rpm = 10 mils Displacement @ 1x rpm = 250 um


V = 0.000052 x 10 mils x 1000 cpm


V = 0.000052 x 250 um x 1000 cpm

V = 0.52 ips V = 13 mm/sec

Acceleration = 0.00027 x V x F A = 0.00027 x 0.52 x 1000

Acceleration = 0.0000107 x V x F A = 0.0000107 x 13 x 1000

A = 0.14 g's A = 0.14 g's

Failure Likelihood: Stress = MODERATE

Fatigue = MODERATE Force = None

What unit is best to monitor with at this frequency ? Velocity

Why not displacement ? Because it can also be used to monitor higher frequencies on this machine.

Example #3:

A Bearing Vibrates 3 Mils Pk-Pk At 9,000 cpmDisplacement @ 9,000 cpm = 3 mils Displacement @ 9,000 cpm = 75 um


V = 0.000052 x 3 mils x 9,000 cpm


V = 0.000052 x 75 um x 9,000 cpm

V = 1.404 ips V = 35.1 mm/sec

Acceleration = 0.00027 x V x F A = 0.00027 x 1.404 x 9,000



A = 3.41 g's A = 3.41 g's

Failure Likelihood: Stress = None Fatigue = HIGH

Force =Low

What unit is best to monitor with at this frequency ? Velocity

Example #4:

A Bearing Vibrates 0.2 Mils Pk-Pk At 60,000 cpmDisplacement @ 60,000 cpm =0.2

milsDisplacement @ 60,000 cpm = 5

um


V = 0.000052 x 0.2 mils x 60,000 cpm


V = 0.000052 x 5 um x 60,000 cpm

V = 0.62 ips V = 15.6 mm/sec



A = 10 g's A = 10 g's

Failure Likelihood: Stress =None

Fatigue =Moderate Force = Moderate

What unit is best to monitor with at this frequency ?

Velocity or Acceleration

Choice will be determined by what other problems (frequencies) need to be monitored for developing problems.

Example #5:

A High Speed Compressor Rotor Shaft

Vibrates 0.003 Mils Pk-Pk At 1,080,000 cpmDisplacement @ 1,080,000 cpm =

0.003 mils (3 millionths of an inch)

Displacement @ 1,080,000 cpm = 0.077 um

(7.7 millionths of a centimeter)

English Units: Velocity = 0.000052 x D x F V = 0.000052 x 0.003 mils x

1,080,000 cpm

Metric Units: Velocity = 0.000052 x D x F V = 0.000052 x 0.077 um x

1,080,000 cpm

V = 0.17 ips V = 4.32 mm/sec

Acceleration = 0.00027 x V x F A = 0.00027 x 0.17 x 1,080,000

Acceleration = 0.0000107 x V x F A = 0.0000107 x 4.33 x 1,080,000

A = 50 g's A = 50 g's

Failure Likelihood: Stress = None Fatigue = Low

Force = REALLY HIGH

What unit is best to monitor with at this frequency ?

Acceleration

General Equipment Amplitude Guidelines:Before discussing amplitude guidelines it should be clearly understood that these are only guidelines - a starting point to begin from. The best vibration analysts get to know the normal vibration characteristics of their machines and look for deviation from that norm. The values that follow here are generally regarded in the categories shown but they are and should be considered guidelines.

Displacement Units:

All Frequencies:

Must know frequency to assess severity. At very low frequencies, even displacement amplitudes of 40 or 50 mils pk-pk or even more can be only moderately harmful to the bearing and the structural components affected.

Note: The values listed here as guidelines for velocity and acceleration are 'peak' amplitudes. Equivalent RMS values are 30% lower.

Velocity Units:Within Frequency Range: 300 - 120,000 cpm

Hard Supports Condition Soft Supports

English Metric Very Good English Metric

< 0.10 in/sec < 2.5 mm/sec < 0.15 in/sec < 4 mm/sec

0.10 - 0.30 ips 2.5 - 7.5 mm/s Satisfactory 0.15 - 0.45 ips 4 - 12 mm/s

0.30 - 0.45 ips 7.5 - 11.5 mm/s Fair 0.45 - 0.67 ips 12 - 17 mm/s

0.45 - 0.60 ips 11.5 - 16 mm/s Rough 0.67 - 0.90 ips 17 - 23 mm/s

> 0.60 ips > 16 mm/s Destructive > 0.90 ips > 23 mm/sec

Acceleration Units:Frequencies: <

30,000 kcpm:Below 30kcpm, the problem will be better monitored with velocity as the amplitude unit of choice.

Frequencies: 30k-120kcpm:

Between 30kcpm and 120kcpm, you must know frequency to fully judge the severity. Velocity can confidently be used as a partner unit in this range.

Frequencies: > 120kcpm: < 2.00 g's Good

2.0 - 5.0 g's Fair

5.0 - 10.0 g's Rough

> 10.0 g's Very Rough

Amplitude Guidelines For "Other" Equipment Types:Slow Speed: Typically generates lower amplitudes. For shafts < 300 rpm, Time Domain plots should be used.

Machine Tool or "Precision" equipment: Typically tolerates much lower amplitude levels. Guidelines (vibration alarms) for each machine must be established. Since this equipment usually involves keeping the finish quality within certain tolerances or specifications, establishing a vibration level just below which those machines go "out-of-tolerance" can be a very effective method. Bearings should be monitored regardless of the overall machine condition.

Complex Vibration Generators: Typically generates higher amplitude levels: Refers to machines that have large forces normally or a lot of vibration sources. High pressure, lobe-type blowers (Roots, for instance) often involve motor frequencies, belt frequencies, lobe pass frequencies, 2-rotor speeds, gear frequencies and aerodynamic forces as well as loaded and unloaded conditions. The resulting vibration patterns can be high relative to the General Machine amplitude references and yet normal for your machine. Be careful in over-reacting. At least one manufacturer's vibration guidelines are as follows:

English Units: in/sec Metric Units: mm/sec Classification:

< 0.45 < 11.4 Excellent

0.45 - 0.90 w / no peak > 0.45

11.4 - 22.8 w / no peak > 11.4 Good

0.45 - 0.90 w / 1+ peaks > 0.45

11.4 - 22.8 w / 1+ peaks > 11.4 Fair

> 0.90 w / no peak > 0.90 > 22.8 w / no peak > 22.8 Rough

Peak(s) > 0.90 Peak(s) > 22.8 Very Rough

Program Needs: Programs must be set up based on the needs of the individual pieces of equipment. Unless your program has loads of similar or identical pieces of equipment, a broad brush cannot necessarily be used. The actual frequencies being generated on the machines must be determined or at least estimated reasonably well. That information should then be used to specify the plots and data collected based on that. The successful analyst will also get to "know" the machines and their typical vibration patterns. That knowledge is possibly the analyst's strongest line of defense against unexpected failures.


Phase What Does Phase Tell Us ? What Is Meant By "Direction" ?

Rules For Measuring Phase And Phase Data Convention

What Methods Are Used For Measuring Phase ?

How Is Phase Measured With A Strobe Light ?

What Is Phase Telling Us ?

Radial Phase Analysis On A Single Bearing

o What Do These "Phase Angles" Mean ?

o Facts Established By Phase: Frequency Confirmation

o Facts Established By Phase: Rough Orbit Shape

o What Is The Significance Of "Orbit Shape"

Radial Phase Analysis Across Adjacent Bearings

http://www.vibrationschool.com/mans/Phase/Phase10.htm






http://www.vibrationschool.com/mans/Phase/Phase03a.htm






Axial Phase Analysis On A Single Bearing: Planar vs. Twisting Motion

Complete Axial Phase Analysis

Understanding Transducer "Orientation"

Most Common Use Of Phase: Diagnosing Misalignment

How Amplitude Units Affect Phase

How Is Phase Measured With A Photoeye

What Is Time Synchronous Averaging ?

What Does "Phase" Tell Us ?

Phase enables us to compare the relative direction of movement of various locations on a machine.

Simply put, phase tells us:

What Direction ?Still not clear ?

What Is Meant By What Direction ? Imagine a snapshot of a machine operating. In the snapshot, imagine

being able to see arrows drawn at each bearing indicating what direction that bearing was moving in at that moment in time.

From the snapshot, you can thereby determine if the bearings are moving in the same direction at the same time (in unison or 'in








phase') or not.

Phase helps determine how different locations on the machine (different bearings, usually) are moving relative to one another

Rules For Measuring PhaseRule #1: Phase is a relative measurement.

Readings at different locations on a bearing are analyzed relative to one another.

Readings at the same angle (direction) on adjacent bearings are analyzed relative to one another.

Readings at different times at the same exact location are analyzed relative to one another.

These comparisons give us information on how the components behavior - namely how they are moving relative to one another.

There is only one use for a single phase reading which we will discuss shortly.

Rule #2: Phase is collected at ONE frequency at a time. The analyzer must be told what frequency. This is done by tuning the

analyzer with either a strobe light or a tach pulse from the shaft.

Rule #3: The analyzer must be able to detect a vibration signal at that frequency.

Since the angle is calculated based on the arrival of a sinusoidal peak from the vibrating component, there must be an amplitude peak to get a phase angle.

Simple Phase Analysis

Data Conventions

In order to discuss phase at the most basic level, we need a convention to use. Phase is represented by the 360° of a circle. Since a high degree of accuracy is not required in a simple, general phase analysis (what we will be discussing here), phase is most easily referred to in terms of clock face numbers: 1 o'clock through 12 o'clock. The phase "angle" is based on where the mark appears (the red key in the example shown here) on the clock face. It is shown here at 12 o'clock but could appear at any angular location.

Applications requiring more precise detail (i.e. balancing or phase monitoring on a turbine) will require the use of specific angular references (0 - 359°).

Clock Face Numbers Use For Simple Phase Analysis

What Methods Are Used for Measuring Phase ? A 'Phase-Triggering' Strobe Light. This type of strobe light differs in

two ways from a conventional, hand held strobe light:

o It either feeds frequency information (its flash rate) into the analyzer or has its flash rate set by the analyzer.

o It can be triggered by a vibration signal from the analyzer.

A Photoelectric Eye (or related mechanism that provides a 1x rpm pulse from the shaft).

How Is Phase Measured With A Strobe Light ?This involves several steps - each one designed to satisfy one of the rules

for measuring phase. We must start with a couple of assumptions. We have a machine with a 'problem' - higher than desired amplitude

at a particular frequency.

The frequency we are concerned with in this case (for simplicity sake) is 1x rpm.

Step #1 - Mount Transducer The first step in collecting a phase reading is

to place the transducer on the bearing in the direction desired.

The transducer provides the analyzer with the vibration signal necessary (as per Rule #3).

Step #2 - Locate a Reference Mark Commonly a key or keyway, this mark is what

we will be using as our 'clock face' reference when it shows up under the strobe flash (as per Rule #4).

Step #3 - Tune the strobe to 1x rpm (the pertinent frequency)

Tuning the strobe light properly will freeze the shaft with 1 mark as shown here. Be careful you haven't tuned it to 1/2 rpm since that will also show 1 mark.

By tuning the strobe light, you have told the analyzer at which frequency we will be measuring phase (as per Rule #2).

With a strobe light (as opposed to a photoeye). This allows the analyzer to focus on a specific vibration signal - a relatively clean sinusoid (since all other frequencies are being filtered out) that is occurring at or very close to (+/- 0.75%) the tuned frequency.

You can compare this to what a radio does - it tunes to one frequency and filters all others out.

What Is Phase Telling Us ?So far, nothing. The strobe light is being triggered by an internal trigger on either the analyzer or the light itself - it is acting exactly like a typical,

hand-held strobe light. There is one final step which must be performed: A switch (or keystroke) on either the analyzer or the strobe can be

activated which changes how the strobe is being triggered.

Once this switch activated, the strobe stops to using its internal trigger to flash and starts to use the vibration sinusoid being detected. Therefore:

Every time a peak signal is detected by the analyzer, it sends a signal to the strobe light to flash.

The strobe light therefore flashes at exactly the frequency of the vibration being detected.

If the vibration is being mechanically generated by the shaft (rotor), the strobe will flash at an exact harmonic of running speed (1x rpm in our example but it could be 2x, 3x or any higher harmonic) and the shaft (mark) will freeze under the strobe flash.

If the vibration is being generated by some other source - any other source (bearings, electrical, other machines nearby, etc.), it will not flash at an exact harmonic of running speed and the shaft will (mark) will not freeze under the strobe flash.

Let's look at a graphic example of how this process works and why it is important.

Radial Phase Analysis Around A Single Bearing

Phase Angle #1

What is happening in the animation here ? The transducer is mounted vertically so the movement (vibration)

being measured is vertical only. The red dot represents the "at-rest" position of the shaft.

The black dot represents the center point of the shaft.

There is a "heavy" spot on the rotor that causes a centrifugal force to be generated that results is causing the shaft center point (the black dot) to rotate around the 'at-rest' center point (the red dot).

The "+"peak' occurs when the bearing is displaced the maximum amount towards the transducer. In other words, as the black dot passes the 12:00 position (passes the transducer).

The location of the heavy spot can be determined at any moment in the shaft's rotation by imagining a line drawn from the red dot directly through the black dot. This is, of course, not able to be seen in real life on a real machine.

What we can see is some "mark" (usually a key) that becomes visible under the flash of the strobe light once per revolution (the yellow dot). This is our reference mark. The mark is 45° behind the heavy spot.

In real life, we would not know where the mark is located relative to the heavy spot. However, we do know that unless we do something to change the location or size of the heavy spot, those two positions will not change relative to one another as we move the transducer. They will remain 45° apart.


Phase Angle #1

With the transducer mounted vertically, the peak signal arrives when the black dot is at the 12:00 position (0°).

The strobe light is set up to flash when an amplitude peak arrives so it

will flash at that moment.

When the strobe flashes, the key shows up at 10:30 (315°).

We now have 1 piece of phase data on this bearing at a frequency of 1x rpm:

With the transducer mounted vertically, our phase angle is 10:30 (315°).


Phase Angle #2

What has been changed in this animation ? The transducer is mounted horizontally so the movement being

measured is horizontal only. Another way to say this would be that the transducer has been moved 90°.

So now what is happening ? The peak signal will still be detected when the bearing is displaced the

maximum amount towards the transducer - as the black dot passes the 3:00 position (90°).

The strobe light is set up to flash when an amplitude peak arrives so it will flash at that moment.

The mark remains 45° behind the heavy spot so when the strobe flashes, the mark will show up at about 1:30.

We now have 2 pieces of phase data on this bearing at a frequency of 1x rpm:

With the transducer vertical, our phase angle is 10:30

With the transducer horizontal, our phase angle is 1:30

What Do These Phase Angles Mean ?We have checked the radial vibration at 2 angular locations around a single bearing. This has provided us with two valuable pieces of information. The first is:

When triggering the strobe light from the vibration signal, the shaft appeared frozen. In other words, the mark was not rotating - it remained stationary (even if it wobbled back and forth a bit).

What does this mean ? It means the vibration IS coming from this shaft. This is now

established as FACT - something only a phase reading can do (as we will see later in the 'Plots' section).

What is the second piece of information ? When moving the transducer to a new angular location (moving from

horizontal to vertical is 90°), the location of the mark (the phase angle) shifted the same amount (90°).

What does this mean ? The shaft is vibrating in a more circular orbit that typically indicates

unbalance.

Let's examine each of these facts more closely and see how they were arrived at from the phase measurements we recorded.

Facts Established by Phase:

Frequency ConfirmationFact #1: The vibration IS (or IS NOT) coming from the shaft

First, you must remember that the strobe light is actually being triggered by the vibration signal. Every time the analyzer detects a peak signal from the transducer, it instructs the strobe light to flash. The strobe flash will, therefore, flash at exactly the same rate as the vibration is occurring.

Second, mechanical vibration - i.e. vibration being generated by the rotation of the rotor - occurs only at exact multiples (harmonics) of the rotational speed (rpm). These vibrations are known as synchronous vibrations.

Third, sources of vibration other than the rotor - belts, bearings, electrical vibrations and other non-synchronous vibration sources will not generate vibration at exact multiples of the rotational speed. This is true regardless of how close they are to being synchronous. Even if the adjacent machine is running at 0.1 rpm different speed, it is still a different speed - it is still non-synchronous.

Since the strobe is flashing at exactly the vibration frequency being generated, whether or not the mark (shaft) appears frozen under the strobe light reveals whether the vibration is synchronous or non-synchronous. This test will be referred to as a:

Frequency Confirmation

Frequency confirmation simply means you are confirming the source of the vibration is the rotor that appears frozen under the strobe flash and it is the ONE use for a single phase reading.

Frequency confirmation is a simple test that requires only a few seconds to perform but can be crucially important to the successful diagnosis of a machine's problem.


Rough Orbit ShapeFact #2: Comparing the phase angles at 2 separate transducer locations (vertical and horizontal in our example) allows you to make the rough judgement of the shape of the orbit - one that is more circular or one that is flatter in shape.

Before explaining this, you must understand what is meant by the 'shaft orbit'. Consider the following:

A shaft is generating vibration at only 1x rpm.

The amplitude horizontally is 'X' ips or mm/sec.

The amplitude vertically is exactly the same - 'X' ips or mm/sec.

In fact, no matter what direction the transducer is oriented (pointed), the amplitude at 1x rpm is 'X' ips or mm/sec.

By plotting the recorded amplitude values in the appropriate direction (Figure 1), you can plot the 'orbit', or shape, of the shaft center

Figure 1

point.

In this particular example, the orbit is a circle. In the 'real' world, this would be virtually impossible.

Another shaft is generating vibration at only 1x rpm.


The amplitude vertically is 80% of the horizontal amplitude - 0.8(X) ips or mm/sec.

By plotting the recorded amplitude values in the appropriate direction (Figure 2), you can again plot the 'orbit', or shape, of the shaft center point.

In this example, an elliptical orbit is plotted. These relative amplitudes would not be considered unusual.

Figure 2

A third shaft is generating vibration at only 1x rpm.


The amplitude vertically is 50% of the horizontal amplitude - 0.5(X) ips or mm/sec.

By plotting the recorded amplitude values in the appropriate direction (Figure 3), you can again plot the 'orbit', or shape, of the shaft center point.

In this example, an elliptical orbit is plotted. These relative amplitudes would not be considered unusual.

Figure 3

When the amplitudes are relatively equal, you can see how the 'orbit' approaches a circle. But let's look at the other extreme. What if the horizontal amplitude were 'X' and the vertical amplitude were very, very low - even 0.00 ips or mm/sec. That 'orbit' would be a straight line - linear movement (vibration).



So we have examined the extremes that are possible:

Circular orbits (where the amplitudes are exactly the same regardless of transducer direction)

Linear orbits (where the amplitude is zero in one direction).

These extremes are equally unlikely. Everything in between is an ellipse. We can therefore realistically use the rule of thumb that all orbits are elliptical.

However, it can be helpful in determing the nature of the problem to know whether the orbit is approaching circular or linear (which, it should be noted, can be better "quantified" by plotting amplitude values).

When the transducer was in the vertical position, the peak signal arrived at a specific moment and caused the strobe to flash at that moment. Under this strobe flash, the key showed up ay the 10:30 position (315°).

When shifted to the horizontal position - 90° away - the moment the peak signal arrived changed by 1/4 rotation - the same 90°. Under this strobe flash, the key shows up at 1:30 (45°) - a shift of 90° from the first phase reading.

Vertical Transducer Location

Because the movement shown here is very circular in nature, the phase angle will change based on the angular location of the transducer. Regardless of the angular location you place the tranducer at, the peak signal will arrive as the black dot passes the transducer location. This type of orbit - an ellipse that approaches circular - is characteristic of one of the most common vibration problems: unbalance. When excessive vibration is detected at 1x rpm (the only frequency unbalance generates vibration at), unbalance is one of several possible sources. This type of phase test can help differentiate between unbalance and the other potential sources of the high vibration levels.

Horizontal Transducer Location



We have discussed what it means when the phase shifts an angular amount very close to the angular amount you move the transducer - a rounder elliptical orbit.

Now let's examine what a 'flatter' (more linear) orbit might reveal during a phase analysis:

The animation at right is similar to the previous without the 'strobe flashes'. The red dot still represents the 'at rest' shaft center point and the black dot is still the actual shaft center point during operation.

Note the black dot passes just above and below the red dot. The amplitude difference is on the scale of 10:1 with horizontal being higher.

Linear Vibration

The red arrow actually represents the phase angle. It follows the direction of displacement and is always pointing from the red dot towards the black dot. In the previous animation (where we had a circular orbit), we didn't show an arrow from the red dot to the black

dot - we showed a once per revolution 'flash' that occurred based on where the transducer was but the flash occurred only when the red dot, black dot and transducer were in that order in a straight line.

You can see that the arrow remains relatively steady for relatively long periods of time (as it passes 3:00 and 9:00) during the revolution.

Under this condition, you could place a transducer anywhere between about 1:00 and 5:00 and observe basically the same phase angle - the arrow moves very little as the black dot passes that area.

Likewise, you could place a transducer anywhere between about 7:00 and 11:00 and observe basically the same phase angle but it would be 180° different than if the transducer were between 1:00 and 5:00.

If the transducer were located between 5:00 and 7:00 (150°-210°) or between 11:00 and 1:00 (330°-30°), you would get an unsteady phase reading although it would NOT rotate - only wobble back and forth.

What Is The Significance Of The Orbit Shape ?A more circular ellipse (i.e. when you move the transducer a certain angular amount, the mark shifts an equal amount) usually indicates:

More of an 'unbalance' type vibration force (centrifugal force that is fairly equal all the way around)

A flatter ellipse (i.e. when you move the transducer a certain angular amount, the mark either does not shift or shifts 180°) usually indicates:

Flatter, more 'linear' motion indicates problems that affect a specific direction such as looseness, resonance, and (on belt or chain drives) bent shafts or eccentricity.

These are Rules of Thumb and a number of variables such as structural strength (which can influence amplitude values in one direction versus another) much be considered. Phase analysis, however, can provide some important information related to how the components are moving.

Radial Phase Analysis Across Two Adjacent Bearings

Up to now, we have only analyzed radial phase readings taken on a single bearing at different angular locations. What about comparing adjacent bearings ? Phase is still used as a "relative" reading.

When comparing phase angles between bearings, you compare phase angles with the transducer mounted in the same angular location (vertical to vertical, horizontal to horizontal, etc.).

Analysis will reveal how the bearings are moving relative to one another at the frequency being measured. Bearings "In-Phase"

In the animation here, the yellow balls represent heavy spots on the rotor. Since they are located at similar angular locations, the forces generated will cause the bearings to move together, or "in-phase".

If a transducer were mounted vertically on either of the two bearings, the strobe would flash as the heavy spot passes the 12:00 position since the peak signal arrives at that moment.

Our mark (the red key on shaft) is in the same position (i.e. same phase angle) regardless of which bearing the transducer is mounted on.

The bearings are in-phase.

Radial Phase Analysis Across Two Adjacent Bearings In the animation shown here, the heavy

spots are opposite one another.

The heavy spot on the left hub affects the left bearing more than the right.

The heavy spot on the right hub affects the right bearing more than the left.

If the transducer were mounted vertically on the right bearing, the strobe would flash as the heavy spot on the right passed the 12:00 position. That occurs when the key is just past 12:00.

Bearings "Out-of-Phase"

If the transducer were mounted vertically on the left bearing, the strobe would flash as the heavy spot on the left passed the 12:00 position. That occurs when the key is just past 6:00.

The bearings, therefore, are 180° 'out-of'phase'.

What is the significance of this ? The significance is in balancing the rotor. Unlike the previous

example, a 2-plane balance such as this requires 2 separate corrections (solutions) - one for the left side heavy spot and one for the right side heavy spot - while the 1-plane (the previous example) requires only 1 correction.

Axial Phase Analysis Around A Single BearingPhase analysis can also reveal some important information when performed in the axial direction. Let's examine what is happening in the animation here:

There are 6 transducers mounted axially - the movement being measured is axial only.

We are measuring phase in the same manner as for radial phase - namely triggering the strobe light at a peak amplitude and freezing some reference mark (a key ?).

"Planar" Motion

With the transducers mounted in this manner, the peak signal will arrive when the bearing is displaced its maximum to the right.

Each of the 6 transducers are displaced the maximum amount to the right at the same moment.

Therefore, regardless of which transducer you are analyzing from, the phase angle (location of the mark) will be the same.

Just as our radial phase analysis provides important information on the 'shape' of the movement radially, an axial phase analysis provides important information on the 'shape' of the movement axially. In the above animation, we have found there is no phase shift as we move the transducer around the face of the bearing. But how else could it be moving ?

The Bearing Is Moving Axially In A "Planar" Motion (Not Twisting On The Shaft)

What is the significance of this ?

The Source Of The High Axial Vibration Is Not Caused By Incorrect Installation Of This Bearing

Axial Phase Analysis Around A Single BearingThe bearing could be moving as shown here - a 'twisting' action on the shaft or in the housing. Let's examine this animation:

The transducers are mounted in identical positions to the last animation.

The peak signal will arrive at each individual transducer location when the bearing is displaced its maximum to the right at that location.

That peak arrives at a different moment for each transducer.

Since the transducers are 60° apart, the phase angle measured at each will be 60° different than the adjacent transducers.

How can this information help the analysis ?

"Twisting" Motion

The most likely source of 'planar' axial motion (as in the previous animation) is:

Misalignment

The most likely sources of 'twisting' axial motion (as shown above) are: A bearing cocked on the shaft A bent shaft through the bearing

Housing distortion (i.e. soft foot) causing twisting motion

The phase analysis thereby helps in differentiating between machine problems that cause similar vibration symptoms (aids in diagnosis of root cause).

Axial Phase Analysis Across Adjacent BearingsAn 'axial phase analysis' is a procedure that is conducted one bearing at a

time. On a smooth running machine, all axial phase readings (on any bearing at any angular location) will be similar. On a machine with high axial vibration, the following procedure should be used if possible:

Each bearing should be checked for planar vs. twisting motion. Any twisting motions detected should be corrected.

The bearings should be compared to one another. Any significant (> 60°) phase shift should raise a flag that something is not right.

Most commonly, a phase shift >60° will be detected when comparing the bearings closest to the coupling and will typically indicate misalignment.

When a phase shift is detected between bearings on the same component (i.e. motor), housing distortion such as soft foot should be checked.

However, transducer orientation must be accounted for (see the next page).

Understanding Transducer OrientationThe "orientation", or direction, of the transducer is extremely important. The reason for this is simple.

The '+' and '-' directions are defined by the transducer. Either '+' is towards the transducer or away from it.

The strobe will be triggered by a '+' signal.

If you change the orientation, you change the definition of '+'.

Are These Bearings "In-Phase" ?

The animation here shows both transducers oriented (pointed) in the same direction:

The '+' direction is defined as 'towards' the transducer.

The strobe will trigger on a '+' peak so each transducer will cause the strobe to flash when they reach their maximum displacement to the left (towards the transducer).

The strobe flashes when the reference mark is just past 6:00.

The transducers have the same orientation and generate the same phase angles so they are in-phase.

Understanding Transducer OrientationIt is common to collect phase readings across a coupling. In that case, you will almost always have the transducer orientation shown below - the transducers are oriented in opposite directions.


The transducer mounted on the left bearing will cause the strobe to trigger when the bearing is at maximum displacement to the right (towards that transducer). At that moment, the reference mark is approaching the 12:00 position.

The transducer mounted on the right bearing will cause the strobe to trigger when the bearing is at maximum displacement to the left (towards that transducer). At that moment, the reference mark is approaching the 6:00 position (just out of sight).

Since they have phase angles 180° different, the bearings may appear out of phase - but are they?

The bearings are moving in the identical fashion as the previous page and we established they are 'in-phase'.

The difference is the transducer orientation. It must be accounted for in the final readings.

Since the orientation of the two transducer is 180° different, a 180° adjustment must be made to one of the measured phase angles. Once that adjustment is made, the phase angles become equal - the bearings are moving "in-phase" with one another.

Understanding Transducer Orientation


In the animation at left, the peak signal is arriving at each transducer simultaneously.

Regardless of which transducer orientation is being used, the strobe is being triggered with the mark approaching 12:00. But are they "in-phase" ?

Of course not - not if you make the required 180° adjustment to one of the angles to account for transducer orientation.

The bearings are 180° 'out-of-phase'.

The Most Common Use of Phase:

Diagnosing Misalignment

Are the machine faces "in-phase" or "out-of-phase" with one another ?

Phase is a common and reliable way to diagnose misalignment.

The procedure involves conducting an axial phase analysis around bearing faces as well as from bearing to bearing.

The point at which you find a phase shift of > 30° is typically the source of a problem (possibly not the only problem).

Note in high axial vibration in the animation shown here. These components are 'angularly misaligned'.

Are the faces of the machine "in-phase" or "out-of-phase" with one another ?

How would the transducers be oriented in this case ? Almost certainly 180° opposite (one pointing left and one pointing right). You will have to

make an adjustment for transducer orientation.

How Amplitude Units Affect Phase AnglesOnce you start a phase analysis, you should never change the amplitude units you are using. Although we have been creating examples using displacement units, velocity units are the most versatile and commonly used. Let's review how phase angles are determined:

The strobe flash is triggered by the arrival of the peak amplitude signal from the transducer.

The location of the reference mark is determined by the moment of the strobe flash.

The timing of the arrival of the peak amplitude signal determines the location of the mark.

The key to why amplitude units affect phase angles is that:

The moment the peak signal arrives is determined by which amplitude unit is being used.

Using displacement units, the peak will arrive when the transducer is displaced the maximum amount in the '+' direction. The mark is at 10:30 (315°).

How Amplitude Units Affect Phase Angles Now let's look at velocity

units - the most commonly used. When will the peak arrive ? Remember what we are measuring - the speed of the bearing in one direction.

Using velocity amplitudes, the peak occurs when the bearing is moving towards the transducer at the fastest speed. At that moment, the mark is at 7:30 (225°). That is 90° different than what we measured with displacement units.

By simply changing amplitude units from displacement to velocity, we have caused a 90° phase shift.

How Amplitude Units Affect Phase Angles

Finally, let's look at acceleration units. When will the peak arrive in that case ?

Using acceleration amplitudes, the peak will arrive when the bearing housing/structure is pushing (applying force) the greatest amount in the "+" direction.At that moment, the mark is at 4:30 (135°). That is 90° different from what we measured with velocity units.

By changing from velocity to acceleration, we have induced another 90° phase shift (180° from the phase angle using displacement units).

How Amplitude Units Affect Phase Angles

Displacement Sinusoid Velocity Sinusoid Acceleration Sinusoid

Comparing these images (from the 'Amplitude' Section) will help you understand why the peaks arrive at different moments for different amplitude units.

Velocity is 1/4 cycle (90°) ahead of displacement and 1/4 cycle behind acceleration.

Acceleration is 1/2 cycle (180°) away from displacement.

When is this information important ? When doing any work with phase (general analysis, balancing, etc.),

don't change the amplitude unit with which you are working.

How Is Phase Measured With A Photoeye ?The procedure for collecting phase with a photoeye is somewhat different than with a strobe light. Let's measure phase at 1x rpm as shown here.

Step #1 - Mount Photoeye & Trigger

The first step in measuring phase is to properly set up the photoeye. It must be mounted rigidly next to the shaft so it can detect a trigger mark rotating on the shaft. The mark is often a piece of reflective tape. With some modern detectors (like 'Lasertachs'), pattern recognition is used and reflective tape is often not needed. The trigger gives the analyzer a 1x rpm pulse (gives it the frequency).

Step #2 - Mount Transducer Mount the transducer at the location and

direction desired.

Step #3 - Instruct Analyzer to collect a phase measurement.

A keystroke will tell the box to collect a phase reading.

How does the photoeye calculate the phase angle ? The 1x rpm trigger provides the box with the period of the frequency

being measured - the period of 1 cycle at 1x rpm. The box takes that period (measured in seconds) and divides it by

360.

Once all the math is completed, the box is ready. When instructed to collect a phase angle, it waits for the trigger mark to pass so it can begin a count up to 360.

After beginning it's count, it awaits the arrival of a peak signal from the transducer. The moment it has that, it stops the count. That is the phase angle.

For the sake of accuracy, several angles are checked and an average is what is eventually displayed as the phase angle.

What Is "Time Synchronous Averaging" ?It is a procedure that differentiates between synchronous and non-synchronous frequencies. When applied properly, it is a powerful tool.

The analyzer and photoeye are set up as outlined on the previous page.

The analyzer is instructed to collect a spectrum. The specifics on how to perform this are different for each box and exact instruction will be left to the various manufacturers.

The analyzer will collect a spectrum that contains ONLY synchronous vibration. That is, only vibration frequencies that are exact harmonics of the trigger rate (usually 1x rpm).

Any non-synchronous frequencies - no matter how close they are to being synchronous - are filtered out and disappear from the spectrum. This allows for comparison with a normally collected spectrum and subsequent analysis of whether a particular frequency is coming from the rotor or some other (non-synchronous) source.

For more information on this powerful troubleshooting tool, see the 'Field Tests' manual.

End Of Phase Section:End Of Vibration Characteristics

You have now completed the "Vibration Characteristics" section of our training. If you feel satisfied with your understanding of the subjects, you should now move on to:

How vibration is measured and how a database should be set up, or Plots: The trend plot, the spectrum plot, the "envelope" plot and time

domain plot.

Acquiring and Displaying Data Data Display:

o Trend Plot

o Time Domain Plot

o FFT Spectrum Plot

o Envelope Spectrum Plot

How Are Amplitudes Determined ?

Difference Between RMS, Peak and Peak-Peak Values

Acquiring Data: Transducers

o Acceleration

o Velocity

o Displacement

How Data is Displayed:

The Trend Plot

Y-Axis Data:

Amplitude

X-Axis Data: Time (typically days or months)

A 'Trend' plot is simply a number of amplitude values - snapshots of the total vibration (vibration at all frequencies) - over a period of time.

The interval between readings will be the time elapsed between those readings. That time interval could be anything from months to milliseconds depending on the specifics of the vibration program and

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system(s) involved.

A trend plot offers limited analysis tools (there is no identification of specific frequencies, for instance) but can be an important indicator of developing problems.


Time Domain Plots

Y-Axis Units:

Amplitude

X-Axis Units: Time (seconds or milliseconds)

The first process the data collected is put through is to convert what is an analog signal (the transducer moving with the bearing) to a digital signal - seen here. This is a "time domain" plot. Typically, the length of a time domain plot will be very short - commonly in milliseconds. It is common to want to capture 5-7 revolutions of a shaft. To capture 5 revolutions of a shaft running (for instance) 3000 rpm (50Hz, or revolutions per second), you would need 5/50 = 0.1 seconds = 100msecs. On that plot, you should be able to see 5 sine waves for 5 revolutions of the shaft plus any wave shape distortion (is it a perfect sine wave or an unusual shape) plus any higher frequencies that might be occuring (electrical, bearings, gears).

A 'Time Domain' plot displays amplitude vs. time. However, unlike a trend plot, the amplitude is a continuous

representation of the amplitude value.

For instance, if the amplitude unit for the above plot were displacement, the line would represent the actual bearing location as it moves back and forth.

Also unlike a trend plot, the values can be negative or positive since, for instance, the displacement can be on either side of a neutral, or 'at-rest' position, and velocity or acceleration amplitudes can be in one direction or the other (defined as the '+' and '-' directions depending on the direction the transducer is pointing).

The time domain is more difficult to analyze than the next plot we will discuss - the "Spectrum" - but under certain conditions it can provide insights and information not available on the spectrum plot.


The "FFT" Spectrum Plot

Y-Axis Units:

Amplitude

X-Axis Units: Frequency (cpm or Hz)

A "Spectrum" is plot of amplitude vs. frequency. The above plot is a spectrum that was created from a time domain plot using a mathematical principle called the "Fast Fourier Transform", or "FFT". This plot is often simply referred to as an "FFT".

This principle states that any periodic signal (what we measure with vibration) can be broken down into a series of simple sinusoids that, when combined, will generate the periodic signal we have just analyzed. In practical terms that means this process can generate the spectrum we see here from a time domain signal it has analyzed. By plotting amplitude versus frequency (instead of time), it becomes far easier to analyze. By relying on complex mathematical processes, however, it also becomes susceptible to generating what can be misleading information. The plot displays a certain number of amplitude values (400, 800, 1600, etc.) over a range of frequencies. The plot seen here tells the analyst that there is:

'A' amplitude at a frequency of approximately 3534 cpm (58.9 Hz)

'B' amplitude at approximately 7084 cpm (118.07 Hz)

'C' amplitude at approximately 10,633 cpm (177.22 Hz) and so on.

This plot is the most commonly used analysis tool since, by enabling frequency identification, it allows for preliminary identification of the source of the vibration.


The "Envelope" Spectrum Plot

Y-Axis Units:

Amplitude


An 'Enveloping Spectrum' plot is identical to a conventional spectrum in the way it displays data: amplitude vs. frequency.

However, there is a significant difference in the way the raw data is processed.

Whereas conventional FFT processing extracts simple sinusoids from complex motion, enveloping spectrum signal processing looks for transient (instantaneous) impacts - the "striking" action discussed earlier versus the "pushing" action the FFT works well with.

These impacts do not usually survive the conventional FFT process and therefore are kept hidden from the analyst.

However, knowledge of the frequency of these impacts provides extremely important information towards proper diagnosis of

machinery problems at an earlier stage than would be possible with conventional FFT analysis.

This additional analysis tool is particularly useful in diagnosing bearing faults.

This plot, which is a spectrum in its appearance, is extremely useful in the identification of rolling element bearing defects and a number of other impact generating vibration problems.

How Are 'Trend' Amplitudes Determined ?

Practical Definition: The 'Overall' Amplitude is the sum of all of the vibration energy

occurring between 0 cpm and the data collector's maximum frequency (its "Fmax" - well over 1,000kcpm). In other words, if you were to collect a spectrum over a frequency range of 0 - collector's Fmax and added all of the amplitude peaks together, that would be your 'overall' amplitude. Although not technically correct, that is one way to look at it.

Technical Definition: Consider again collecting a spectrum from 0 - the collector's Fmax.

Take every amplitude value, square it, add them together and take the square root of that sum. Although not exactly perfectly accurate, that is closer to what actually goes into calculating an 'overall' amplitude. That is known as a "Root Mean Square", or RMS, value.

All data is collected as an "RMS" value. That is an ISO convention and applies no matter what collector you may have.

The RMS value was settled on in order to guard against a transient spike in the signal distorting the true value significantly.

But there are several different 'signal detection' units available - RMS, peak and peak to peak. How exactly are they related and calculated ?

The Difference Between RMS, Peak and Peak to Peak Amplitudes

Again, all data is collected as an "RMS" value ("Root Mean Square"). That is an ISO convention and applies no matter what manufacturer's collector you may have.The "RMS" value is calculated by simply multiplying the peak amplitude (shown in the graphic below) by 0.707:

RMS = Peak x 0.707

But is that technically correct ?

o Technically , the RMS value of a pure sinusoid is equal to the area under the half-wave.

o That corresponds to (peak x 0.707) on a pure sinusoid.

o Pure sinusoids are rarely encountered in the world of mechanical vibration.

o Due to that, the trend amplitude value is calculated by simply multiplying the peak amplitude by 0.707.

But some analysts prefer to display the amplitudes as a 'peak' amplitude (usually because the vibration severity charts they are using are in peak amplitude values). So how is that value calculated ?

To calculate the 'Peak' amplitude, we divide the RMS value by 0.707. For those of you paying close attention, you may have noticed that,

from start to finish, the way a peak amplitude is calculated is:

o Measure the peak amplitude.

o Multiply by 0.707 to obtain the RMS value.

o Divide by 0.707 to obtain the Peak value.

In some cases - specifically the use of displacement amplitudes where the analyst wants the total amount of bearing movement back and forth - the 'Peak to Peak' value is desired by the analyst. In that case, the peak value is simply multiplied by 2. Velocity and acceleration units are not typically displayed as peak to peak since the important piece of information is what the maximum (peak) value is.So let's summarize:

The highest (peak) value of collected data is multiplied by 0.707 to obtain the ISO standard of RMS amplitude. The majority of programs world-wide use this value.

For those programs that wish to display the data as a 'peak' value, the RMS value is then divided by 0.707 to obtain the peak amplitude.

For those situations where peak to peak amplitudes are desired, the peak amplitude is simply multiplied by 2.

Summary: It doesn't matter which value you use - RMS or Peak - so long as you are CONSISTENT (another very important convention) !! Amplitude is, after all, simply a number from which we make certain generalizations about the machine condition. There is no exact, precise number above which disaster awaits and below which you are safe. Be aware of the conversion if comparing values between programs that use RMS and Peak values. This applies to spectrum plots as well.Now let's look at the vibration sensors - transducers.

TransducersA vibration transducer is the instrument that measures or senses the vibration and is commonly referred to as a pickup or sensor. The basic understanding and proper selection of an appropriate transducer is important. This text will not deal in extensive detail with all the different types and technical characteristics of transducers but will attempt only to provide a basic understanding of the important aspects. There are basically three types of transducers commonly used. They are:

Accelerometer Velocity Transducer

Displacement Transducer

Transducers:

AccelerometersAccelerometers are by far the most common and versatile types of transducers in use. The seismic, or piezoelectric, accelerometer produces a output charge when held against a vibrating surface due to the characteristics of the piezoelectric disks that are inside the transducer. These transducers contain no moving parts and as such are quite rugged. The charge that is generated through the compression and expansion of the piezoelectric disks is proportional to the amount of vibration acceleration (force).

Generated voltage is very small - most models have built in hi-gain electronic amplifiers.

Output charge is proportional acceleration force accelerometer is exposed to.

Accelerometers are the only transducer capable of reliably measuring high frequency vibration that is related to problems such as bearing defects and gear problems.

Accelerometers have fair to poor accuracy at low frequencies where acceleration amplitudes can become quite small even in the presence of high displacement amplitudes.

Some are somewhat susceptible to radio frequency interference

Some can have problems with thermal growth (putting the transducer on a very hot bearing) which can cause false amplitude values at low frequencies unless they are given time to thermally stabilize.

Transducer should have sensitivity of 100 mv/G or higher. The more mv/G the accel generates, the more accurate it will be in the low frequency (< 120 cpm) roll-off ranges.

One Design of a Piezoelectric Accelerometer

Recent years have seen the development of affordable accelerometers that are reasonably accurate to frequencies even well below 120 cpm. Low frequency will remain, however, a weakness of accelerometers due to the nature of acceleration amplitudes at low frequencies. Accelerometers are also useful because they are much more compact and lightweight than velocity transducers and therefore can be used in more environments and applications. They are also not as susceptible to magnetic fields generated by electric motors or other magnetic sources as velocity transducers.

A final advantage of using an accelerometer is the ability to integrate the results in order to obtain velocity readings and double integrate the results in order to obtain displacement readings. This ability means that a single transducer can be used to register and quantify all three of the primary amplitude units of acceleration, velocity and displacement over a wide range of common frequencies.

A monitoring program tracks the condition of your equipment through the measurement of vibration amplitudes on a regular interval. Deviation from the norm then triggers further investigation to determine the source and correct the actual cause of the excessive vibration.

Database Setup:

Purpose of a Monitoring ProgramWhat is the purpose of a vibration monitoring program ? Well, the operative word is “monitoring”. The purpose is to monitor the vibration levels. This means collecting data that will alert you to any developing problems while not over-burdening you with collecting overly detailed or excessive amounts of data. A monitoring program is not intended nor is able to do is allow for specific diagnose of every problem that arises while sitting behind your computer.

To be sure, a well designed vibration monitoring program will nearly always give you a specific direction in which to search for a problem and it will help you prioritize work by gauging the severity and source of most of the problems you will encounter. However, further analysis, or at the very least confirmation checks, are always a wise course of action to take before proceeding with any corrective actions.

Database Setup:

Selecting Point ParametersAs an example let us look at a simple AC motor. The details surrounding each of the frequencies we have to monitor are found in the "Troubleshooting Charts" (accessed from the main menu). The question we will address is - what are the different potential problems we need to be looking for:

Frequency(s) to monitor Explanation1x, 2x, 3x rpm Running speed harmonics

2x AC Line Frequency Torque Pulse Frequency (variation in motor air gap)

1x, 2x, 3x Rotor Bar Pass Frequency (RBPF)

or Winding Slot Pass Frequency (WSPF)

Electrically related frequencies equal to the number of rotor bars or winding slots x rpm. These can reveal certain electrical problems and/or conditions.

30kcpm - 120kcpm Frequency range in which symptoms of rolling element bearing defects usually show up initially.

So the questions are - what are the Fmax's, how many lines of resolution should be used, what amplitude units should we use, what is the best way to analyze the data and basically, how can we make our database work for us as efficiently as possible ? How can the need for

occasional high resolution readings be squared with the need to monitor relatively high frequencies ? Accuracy vs. speed of data collection.

Database Setup:

Selecting Point ParametersThe solution, of course, is that several different measurements must be taken at each position with each one addressing one or a few specific problem areas (and hence a specific frequency range).

Mechanically Caused Vibrations A complete protection set-up would collect a reading horizontally

and verticallyon each bearing plus one axial reading on position 2 with an Fmax of 120000 cpm in order to monitor potential bearing defects developing and the common problems occurring at 1x, 2x and 3x rpm. That's five readings.

Electrically Caused Vibrations In addition to those two readings, you may wish to take a high

resolution reading on one motor bearing (typically a 12000 cpm Fmax with up to 1600 lines of resolution). This reading would separate the electrical and mechanical vibrations at the low frequency end.

Finally, you may want to collect a reading with an Fmax of 720000 cpm to look for the high frequency electrical problems (loose windings, loose or cracked rotor bars). The reason the word may is used is because electrical problems are relatively uncommon and extra electrical readings can be collected separately if a problem is suspected. A full set of baseline readings should be collected in any event to initially check for any such problems. The only one of these readings that should not be collected with velocity amplitude units is the 720000 cpm Fmax reading which should utilize acceleration units.

That's two more readings.

Bearing Protection: An enveloping spectrum should also be taken on each bearing to

check for any frequencies at which impacts are occurring. That's two more readings. What you are left with is this:

However, let's get back to the word monitoring - as in a monitoring program. You could, depending on the proactivity of the program personnel, eliminate a few of the readings and rely on the others to tip

you off that something is wrong. You could then go into full-blown anaysis mode and collect lots of data. Using that logic, the readings could be divided into "necessary" and "optional" readings as follows:

Necessary

Readings Max Freq # of Lines Units Direction Position

1 120kcpm 400 Velocity horiz Brg 1

2 60kcpm 400 Enveloping horiz Brg 1


4 60kcpm 400 Enveloping horiz Brg 2

5 60kcpm 400 Velocity axial Brg 2

The necessary readings shown here monitor for early stage bearing defects as well as providing general information on machine health. In-depth analysis may be difficult, depending on the specific problem, and a problem developing may require more and better data be collected.

Optional Readings Max Freq # of Lines Units Direction Position

6 720kcpm 1600 Acceleration horiz Brg 1

7 120kcpm 400 Velocity vertical Brg 1


9 120kcpm 400 Velocity vertical Brg 2

The optional readings shown here monitor in additional planes (vertical) and for more specific problems with high frequency (720kcpm, 1600 lines) and high resolution (12kcpm, 1600 lines) spectra.

Database Setup:

Further Example of Selecting Point ParametersLet's look at a component other than the motor - a screw compressor (note that we have already discussed what is needed to adequately monitor the motor). You would need:

To collect a reading with an Fmax of 120000 cpm on each of the four bearings in order to monitor potential bearing defects developing and the common problems occurring at 1x, 2x and 3x rpm and aerodynamic (# lobes x rpm) pressure-pulse related frequencies.

An enveloping spectrum to help in analyzing any impact generating frequencies.

By calculating the gear mesh frequency at 48 teeth x rpm, you would want to collect a reading with an Fmax of 3x gear mesh frequency (3x48=144), or approximately 150x rpm to look for the high frequency, gear-related problems.

Screw Compressor: 48 x RPM = Gear Mesh Frequency

48/36 Gear Ratio = 1.33 Speed Increase 4 x 1.33 = Lobe Pass Freq.

(Aerodynamic)

Necessary

Readings Max Freq #Lines Units Direction Position

1 120kcpm 800 Velocity Horizontal All compressor bearings

2 60kcpm 800 Enveloping Horizontal All compressor bearings

3 150 x RPM 1600 Acceleration Horizontal All compressor

bearings

Note that there are no low Fmax readings being taken (lowest Fmax is 60kcpm). The simple reason for this is that none are necessary. There are no frequencies so close as to be inseparable on a normal spectrum. The expected dominant frequencies on the spectrum will be related to the aerodynamic pulse frequency and the motor rpm. The use of these three readings on each bearing (12 readings on the compressor side alone) will protect against occurrence of a unforeseen problem -assuming, of course, proper interpretation of the data as well as proper

operation and general maintenance of the machine.

Note that implementing a global default change from 400 to 800 lines is a good technical change with practical advantages and, with the speed of processors and amount of memory available, there are minimal downsides.

Database Setup:

How Much Data is Enough ?So you see that a simple AC motor may require as many as nine separate spectra in order to catch all the potential problems that may develop on it. The driven component as many or more. How do you collect all of this data ? More importantly, how do you analyze all the data you've collected in an efficient yet productive way ? That is the main problem. Of course, some problems are much more likely to develop than others and a reduction in the number of readings may be unavoidable in order to decrease data collection and analysis time.

As with many other maintenance or management decisions, trade-offs between time and accuracy of information must be made.

Good news: The more readings you have, the more information you will have, the more protection you will have, etc.

Bad news: The more readings you take, the longer your data collections will take, the longer your analyses will take and the more paperwork you will have.

Once again, let’s return to the basic rules governing the purpose of a monitoring program. Although it is possible, very few types of problems will show up in only the vertical direction without also affecting the horizontal readings. So we could eliminate some of the vertical readings with a slight decrease in the protection level. Note that only one reading is taken axially. Typically, bearing 2 is where the axial reading is taken due to easier access but that is not always the case.

So how much data should your program collect ?

The answer is actually fairly simple: It depends on how proactive your maintenance department is

relative to a PdM program. In other words, the faster and more efficiently you investigate and

solve problems, the less data you can get by collecting.

I've personally seen tremendously successful programs that collect a bare minimum of data periodically - trend (overall) values and

spectrums on overall alarm only. The secret to their success is simple - the moment something goes into a (well set up) statistical alarm, the collector is triggered to collect a spectrum. When the data is uploaded, they analyze the spectrum (no spectrums are collected that are not in alarm) and immediately send someone out to investigate and correct as necessary. Average plant-wide vibration around 0.16 in/sec (3.9 mm/s) - not bad for a plant that runs 25+ routes a week and has two full-time analysts.

Database Setup:

Trading Time Versus AccuracyThere is one good arguument against bothering to collect the two special electrical readings:

Electrical problems are often apparent through means other than a velocity spectrum. Many problems, including high 2x line frequency and broken/cracked rotor bar problems, will almost always cause an audible, pulsing hum in the motor that anyone can notice without vibration equipment.

Can we therefore collect these two readings only when a problem is suspected and not every data collection ?

For a purely monitoring purpose, we would then be down to only five readings, reducing data collection time by more than 50% since we would be eliminating the most time consuming of these readings.

To take this reduction to an even further extreme, we could collect only overall values for each of these points and trend amplitude changes (increases) only, collecting spectra only when the trends indicate it is necessary.

What data should be collected on this motor ? 10 spectra and overalls, or . . . 5 overalls ONLY ?

These are decisions that must be made by the people in charge of executing the program. They should be based on a number of criteria including machine criticality, manpower availability, instrumentation used (speed and capability) and available software. Each reduction in the amount of readings taken increases the potential for an unforeseen failure. Any use of vibration analysis, however, is an improvement over reactive maintenance, which merely reacts to breakdowns or imminent

problems.

How does Vibe-Assist address this dilemma ?

Database Setup:

An Example Of An Effective Database SetupThe exact nature of your database setup and the specifics must be addressed according to the vendor you purchased your software from. Most programs fail because usable, worthwhile data can not be extracted from the database. Why does this happen ? The software usually has certain useful features such as reporting capabilities that can be accessed - if the database is created in such a way as to not only take advantage but to make the best use of those features.

By way of a single example - and their are numerous ways to set up a database - the service company Vibe-Assist looked at two ingredients that went into the collection and analysis of data - what information they wanted vs. what the reporting capability of the software was (Entek's Odyssey™) - and came up with database setup templates that are used for creating an effective database structure that uses software features of Odyssey to provide information we want. By generating a database structure that takes maximum advantage of a powerful software reporting feature, Vibe-Assist reduced their analysis time by an incredible 80% or so. This new database structure did not generate this huge improvement by reducing machinery protection or analysis accuracy. On the contrary, the new setup improved the reliability of the analysis and improved the level of protection possessed by the machines they monitor. In order to illustrate the value of an effective database setup, Vibe-Assist has agreed to share a few of their component setups along with an explanation of the logic behind the database structure. Shown below are examples of a direct drive, 4-bearing machine and a belt-drive, 4-bearing machine. The links below under the "Type" of reading will take you to explanation pages for each of the readings.

Direct Drives Belt Drives

Explanation of Readings

Sample Report

Direct Drive

Bearing 1

http://www.vibrationschool.com/mans/DBSetup/DBSet08.html#Report

http://www.vibrationschool.com/mans/DBSetup/DBSet08.html#Explanation

http://www.vibrationschool.com/mans/DBSetup/DBSet08.html#BDP1

http://www.vibrationschool.com/mans/DBSetup/DBSet08.html#DDP1

Reading Type Max Freq # of Lines Units Direction

1 Trend & Spectrum

30kcpm 800 velocity horiz

2 Trend & Spectrum

120kcpm - or -

60kcpm*800 acceleration horiz

3 Spectrum Only 20x rpm up to 60kcpm

800 envelope horiz

4 Time Domain5-9 revolutions or

relevant period2048 bytes

acceleration

or velocityhoriz

5 Trend & Spectrum

240x rpm 800 acceleration horiz

* - For the acceleration spectrum, use 120kcpm for machine speeds over 1200 rpm and 60kcpm below that.

Direct Drive

Bearing 2


1 Trend & Spectrum


2 Trend & Spectrum

120kcpm - or -



800 envelope horiz



acceleration

or velocityhoriz


Direct Drive

Bearings 3 & 4


1 Trend & Spectrum


















2 Trend & Spectrum

120kcpm - or -



800 envelope horiz

4 Time Domain5-9 revolutions

or relevant period

2048 bytes

acceleration

or velocityhoriz


Top Belt Drives Explanation of Readings Sample Report

Belt Drive

Bearing #1


1 Trend & Spectrum 12kcpm 800 velocity horiz

2 Trend & Spectrum120kcpm

- or - 60kcpm*

800 acceleration horiz


800 envelope horiz



acceleration

or velocityhoriz

5 Trend & Spectrum 240x rpm 800 acceleration horiz


Belt Drive

Bearing #2


1 Trend & Spectrum 12kcpm 1600 velocity horiz










http://www.vibrationschool.com/mans/DBSetup/DBSet08.html#Top





2 Trend & Spectrum120kcpm

- or - 60kcpm*

800 acceleration horiz


800 envelope horiz



acceleration

or velocityhoriz


Belt Drive

Bearings 3 & 4


1 Trend & Spectrum


2 Trend & Spectrum

120kcpm - or -



800 envelope horiz

4 Time Domain5-9 revolutions

or relevant period

2048 bytes

acceleration

or velocityhoriz


Top Direct Drives Belt Drives Sample Report

Explanation of Readings

There are numerous other component setups in the templates - these are for generic, rolling element bearing machines running at normal speed (1000 - 3600 rpm). But this seems like an extreme amount of data - how does this help with analysis ? Well, first, each reading has a














specific job to do: Reading 1: Velocity Trend - Tool that is sensitive to fluctuation

(increase) in low - mid frequency ranges where mechanical problems develop (1x - 5x rpm) and, to a lesser degree, higher frequency problems such as rolling element bearings.

Reading 1: Velocity Spectrum - Analysis tool for low - mid frequency problems. Higher resolution readings collected on belt drives and inboard motor bearings.

o Note: By properly setting some simple statistical alarms on the trend plot, this spectrum may be turned off because the analyst will be alerted by the overall alarm to any situation where a spectrum is required and eliminate many of these most time consuming readings.

Reading 2: Acceleration Trend - Tool that is not affected by influences at 1x - 5x rpm but is increasingly sensitive to problems developing above 30kcpm such as gears, bearings and high frequency electrical. Another good candidate for statistical alarms.

Reading 2: Acceleration Spectrum - Analysis tool for high frequency problem detection and analysis. Used in conjunction with the next reading . . .

Reading 3: Envelope Spectrum - e.g. gSE, ESP, Peakvue, HFB and more. This plot gives information on transient impacts occurring that may be related to a bearing defect or several other sources.

Reading 4: Time Domai n - Can be de-activated if the analyst prefers but is an important tool to use at times. Can be set to whatever time sample the analyst chooses.

Reading 5: Acceleration Spectrum - On motors only, looks for 2x and 3x rotor bar pass frequency and winding slot pass frequency - very high frequencies.

So what are we left with in the best of environments ? By turning off the time consuming velocity spectrum and rely on trends only to monitor the low-frequency end of the spectrum, we are left with:

Velocity overall Acceleration overall

Acceleration spectrum

An enveloping spectrum

That is a total of about 5 seconds of data collection. If the velocity trends into alarm, we turn on the velocity spectrum for analysis. If an acceleration overall trends into alarm, we check the enveloping spectrum for impact frequencies and try to match up harmonics on the acceleration spectrum. This database structure protects against all possible trendable problems (as opposed to "event-based" problems that can lead to short-duration failures).

Top Direct Drives Belt Drives Explanation of Readings

Sample ReportThe key, however, is in the simple reports that can be run. An amplitude threshold is set for the report (perhaps 0.2 in/sec or 5 mm/sec). A line is triggered for the report for every single peak that exceeds the pre-set amplitude threshold. The line on the report, shown below, includes all the location information, the Fmax, peak amplitude and frequency of the peak as well as the rpm and date. This makes initial review of the data simple and brief. This report addresses the low-mid frequency ranges that require velocity units for effective monitoring (> 30kcpm). This is the frequency range in which mechanical problems will show up: 1x - 10x rpm or so. This report does not address bearings, gears, certain electrical vibrations or any other high frequency vibration sources.

To address the high frequencies, an identical report is created to handle the acceleration spectral data. The amplitude trigger for acceleration units will typically be about 1G - a very safe, fairly low amplitude threshold. Any line on the acceleration report is investigated by first looking for any impact frequencies on the associated envelope spectrum and then by making an assessment of the vibration source. Further investigation may be necessary but the report(s) give easily accessed, easily analyzed information that prompts immediate investigation in the problem areas. Much of the data does not get looked at but that is simply because the vibration levels too low to be





concerned with.

Database Setup:

SummaryThe creation of a database, with all the associated decisions that must be made, is a job that requires a very good technical understanding of vibration analysis, machinery operational characteristics and good doses of common sense. Always question what you are doing, especially whether or not the desired goals are being achieved and, if not, what other methods might be used to achieve those goals.

The database setup shown on the previous page that Vibe-Assist is successful with was not presented as an example of the only way a database can be setup. It was included only as an example of a setup that is known to provide high levels of protection while being simple to manage and easy to analyze - three very important aspects. There are certainly other database structures that are successful. No matter the database setup, the individuals involved are of crucial importance; the machines, the maintenance environment and numerous other factors also affect the success. However, the importance of the task of setting up a database cannot be overstated. Although doing it properly does not guarantee success, doing it improperly guarantees failure. There are many variables to consider and options to choose from.

The particular database setup we've just gone through utilizes a strength of the Odyssey™ software - the ability to generate a report with the specific information we wanted. Your software may or may not have that ability. You may need or want to focus on some other strength of your software (since it is the key determining factor in what database setup will work for you). The database is comprehensive yet manageable and scaleable to the user's needs. If you have Odyssey™ software and are struggling with your database setup, feel free to copy the database setup laid out above and customize the report as you saw on the previous page. You can also, for a small fee, obtain the templates (including the different components, a written manual the reports, etc.) directly from Vibe-Assist.

Plots:

Trends What Is A 'Trend' Plot ?

http://www.vibrationschool.com/mans/Plots/Plots01.htm

How Is A Trend Amplitude Determined

RMS, Peak, Peak-Peak Values

Analyzing A Trend

What Is A "Trend" Plot ?

Y-Axis Units:

Amplitude

X-Axis Units: Time (typically days or months)

A 'Trend' plot is simply a number of amplitude values - snapshots of the total vibration (vibration at all frequencies) - over a period of time.

The interval between readings will be the time elapsed between those readings. That time interval could be anything from months to milliseconds depending on the specifics of the vibration program and system(s) involved.

A trend plot offers limited analysis tools (there is no identification of specific frequencies, for instance) but can be an important indicator of developing problems.

How Are 'Trend' Amplitudes Determined ?

http://www.vibrationschool.com/mans/Plots/Plots04.html



Practical Definition: The 'Overall' Amplitude is the sum of all of the vibration energy

occurring between 0 cpm and the data collector's maximum frequency (its "Fmax" - well over 1,000kcpm). In other words, if you were to collect a spectrum over a frequency range of 0 - collector's Fmax and added all of the amplitude peaks together, that would be your 'overall' amplitude. Although not technically correct, that is one way to look at it.

Technical Definition: Consider again collecting a spectrum from 0 - the collector's Fmax.

Take every amplitude value, square it, add them together and take the square root of that sum. Although not exactly perfectly accurate, that is closer to what actually goes into calculating an 'overall' amplitude. That is known as a "Root Mean Square", or RMS, value.

All data is collected as an "RMS" value. That is an ISO convention and applies no matter what collector you may have.

The RMS value was settled on in order to guard against a transient spike in the signal distorting the true value significantly.

But there are several different 'signal detection' units available - RMS, peak and peak to peak. How exactly are they related and calculated ?

The Difference Between RMS, Peak and Peak to Peak Amplitudes

Again, all data is collected as an "RMS" value ("Root Mean Square"). That is an ISO convention and applies no matter what manufacturer's collector you may have.The "RMS" value is calculated by simply multiplying the peak amplitude (shown in the graphic below) by 0.707:

RMS = Peak x 0.707

But is that technically correct ?

o Technically , the RMS value of a pure sinusoid is equal to the area under the half-wave.

o That corresponds to (peak x 0.707) on a pure sinusoid.

o Pure sinusoids are rarely encountered in the world of mechanical vibration.

o Due to that, the trend amplitude value is calculated by simply multiplying the peak amplitude by 0.707.

But some analysts prefer to display the amplitudes as a 'peak' amplitude (usually because the vibration severity charts they are using are in peak amplitude values). So how is that value calculated ?

To calculate the 'Peak' amplitude, we divide the RMS value by 0.707.

For those of you paying close attention, you may have noticed that, from start to finish, the way a peak amplitude is calculated is:

o Measure the peak amplitude.

o Multiply by 0.707 to obtain the RMS value.

o Divide by 0.707 to obtain the Peak value.

In some cases - specifically the use of displacement amplitudes where the analyst wants the total amount of bearing movement back and forth - the 'Peak to Peak' value is desired by the analyst. In that case, the peak value is simply multiplied by 2. Velocity and acceleration units are not typically displayed as peak to peak since the important piece of information is what the maximum (peak) value is.

So let's summarize: The highest (peak) value of collected data is multiplied by 0.707 to

obtain the ISO standard of RMS amplitude. The majority of programs world-wide use this value.

For those programs that wish to display the data as a 'peak' value, the RMS value is then divided by 0.707 to obtain the peak amplitude.

For those situations where peak to peak amplitudes are desired, the peak amplitude is simply multiplied by 2.

Summary: It doesn't matter which value you use - RMS or Peak - so long as you are CONSISTENT (another very important convention) !! Amplitude is, after all, simply a number from which we make certain generalizations about the machine condition. There is no exact, precise number above which disaster awaits and below which you are safe. Be aware of the conversion if comparing values between programs that use RMS and Peak values. This applies to spectrum plots as well.Now let's look at the vibration sensors - transducers.

Analyzing A TrendAnalyzing a trend is not typically a difficult thing to do . . . providing you know what it is you are trending.

Are you trending high frequency vibration ? Not if you only use displacement.

Are you trending the typical, general equipment speed ranges of 1000 - 3600 rpm and associated mechanical problems.

Not with displacement or acceleration - only with velocity.

Are you trending very low frequency vibration - below 100 rpm, for instance ?

Only with displacement and, if the frequency is low enough, only by changing type of transducer.

With vibration, a trend headed in the wrong direction almost certainly means it is increasing. With a properly set up program, properly collected data and proactive personnel, a program can be successful with collecting little more than trend values. For whatever reason, however, that is rarely the case.In any event, trending can be useful but it is not usually enough to make specific judgements. A determination of the exact frequencies involved is usually required and should be attempted in any event to avoid a

possibly embarassing and expensive mistake. A determination of frequencies can be made two separate ways - viewing the data as a raw time domain plot or putting it through an FFT process to generate a spectrum. An overview of the process of analyzing a spectrum will now be presented followed by an in-depth look at how, in a practtical sense, the FFT process works. Understanding that will help you view the spectrum with an appropriate amount of respect and skepticism.

Plots:

The FFT (The Spectrum) What Is An FFT (Spectrum) Plot

FFT "Tools" (How We Analyze)

FFT Terminology (Terms We Use)

How An FFT Is Created

What An FFT Is Actually Made Up Of

How Is An FFT Is Analyzed ?

Important Facts To Remember When Analyzing An FFT

Parameters That Determine "Spectrum Resolution"

The Importance Of Spectrum Resolution

Understanding Spectrum Resolution - Direct Drives

Understanding Spectrum Resolution - Belt Drives

How Do You Know What Spectrum Resolution Is Required ?

Where To Collect High Resolution Data

What Are "Beat" Frequencies ?

Summary

What Is An FFT (Spectrum) Plot

http://www.vibrationschool.com/mans/Plots/SPlots22.html

http://www.vibrationschool.com/mans/Plots/SPlots21.htm














Y-Axis Units:

Amplitude

X-Axis Units: Frequency (number of cycles per minute or per second)

Whereas a Trend is amplitude values versus time, a "Spectrum" Plot is amplitude versus frequency.

A spectrum, a.k.a. an "FFT", allows you to assess severity (with the amplitude) and helps identify the source (with the frequency).

This is the most commonly used analysis tool and is usually sufficient protection for general speed machinery.

FFT ToolsVibration spectra provides important clues to machine problems. There are tools provided in all software packages that help with this analysis. The most important are:

Moveable Cursor - A "base" cursor that can be moved to any frequency and identifies the amplitude at that frequency.

Harmonic Cursors - Activating this tool creates additional cursors (as many as are required) that appear at integer multiples of the base cursor. If the base cursor is located at 1x rpm, harmonics will appear at 2x, 3x, 4x, etc. This is the most important analysis tool

available. All harmonic cursors are at higher frequencies than the base cursor.

Sideband Cursors - Activating this tool creates additional cursors at frequencies to either side of the base cursor. If the 1st (closest) sideband cursors are located 50 cpm to either side of the base cursor, additional sideband cursors (as many as required) will each be located an additional 50 cpm away. For instance, the 2nd sideband cursors will be 100 cpm away from the base cursor, the 3rd will be 150 cpm away, etc.

These three tools are sufficient for the beginner and for 99% of most analyses. There are, of course, other useful tools such as " "labels" and frequency groups but that is more vendor specific and should be learned in a software class and through experience.

Remember, ALL spectral analysis is limited in its use and accuracy by the spectrum resolution.

FFT TerminologyCommonly used terms include:

Fundamental Frequency - 1x rpm. Remember that a belt drive, for instance, has three fundamental frequencies.

Dominant Frequency - Frequency at which the highest amplitude occurs.

Synchronous Vibration - Vibration harmonically related to a fundamental frequency.

Non-synchronous Vibration - Vibration not harmonically related to a fundamental frequency.

Sub-synchronous Vibration - Vibration occurring at a frequency below the fundamental frequency.

How An "FFT" Plot Is Created ?First, the vibration is "sampled" (collected) over a pre-determined period of time. The period of time used for the sample will be based on parameters programmed into either the database (for interval-based, route data collection) or the analyzer (for in-depth, or "spot", analysis).

Although sometimes a relatively simple sine wave, it will far more often be a complex signal with a number of different frequency components.

The "complex" signal shown below (still simplistic compared to data collected on most real machines) is made up of a 1x rpm component (e.g unbalance) and a 5x rpm component (e.g. number of vanes on the impeller - "vane pass" frequency) being generated by the machine.

There can be (and usually are) far more influences - background (frictional) noise, misalignment, bearing problems, soft foot, looseness, frequency modulation, amplitude modulation, etc., etc., etc.

What the transducer actually 'senses' is an analog signal - one that mirrors the actual movement of the bearing at the location of the transducer. The signal processing that follows the analog signal collection consists of a couple of mathematical processes:

A/D converter - Converts the analog signal to a digital one. Fourier Transform - This process is based on the principle that any

periodic signal (e.g. vibration) can be broken down into a series of simple sinewaves that, when combined, result in the shape of the original signal.

Using the above "complex" signal as an example, in practical terms the principle means that the FFT process can deduce the two frequencies (1x and 5x) that were present to create the signal we see. The signal is fairly simple, though. Despite the presence of two signals, even we could make that judgement.

That principle, however, can be extended to any periodic signal. For each signal the FFT analyzes, there is one and only one mathematical solution to the problem - a specific series of simple sinewaves of precise amplitude values and phase relationships (which do NOT show up on the resulting plot but ARE considered by the FFT as we will see later) that, when combined, create the precise shape of the signal the FFT is analyzing.The FFT process is an extremely complex mathematical process that is being applied to mechanical vibrations. Although a fairly reliable and useful tool, it MUST be understood that a spectrum is always suspect because these mathematical processes (A/D and FFT) often cause either or both of the following to happen:

Vibration peaks get added (like sidebands and harmonics) that don't actually exist. That is not to say either are to be ignored - they can still provide valuable clues to the analyst.

Occurrences (events) that may be obvious when viewing the raw time domain signal are completely lost.

It is the signal shape that is being analyzed and deviations due to any mechanical problem from purely sinusoidal motion can cause the above phenomenon (harmonics, sidebands) to occur. For these reasons, it is strongly recommended that at the very least the time domain be used where it is most useful and the spectrum is the weakest:

Slow Speed Equipment Gear Applications

Sleeve (Plain) Bearings

The reasons for this lie in what the FFT process actually does and what factors influence its output (the spectrum).

What An "FFT" Is Actually Made Up Of ?One of the "parameters" that must be programmed into the database or the analyzer is known as the "Number of Lines" (of resolution). This parameter determines how many individual amplitude values will make up the final FFT plot. That is what a spectrum is made up of - a certain number of amplitude values (e.g. 800) that each measure the vibration found in a relatively small frequency range. This parameter - number of lines - works in conjunction with your Maximum Frequency, or "Fmax", to establish your "Spectrum Resolution" - a critically important subject. The Fmax divided by the # of lines equals the spectrum resolution. The units are: "CPM per Line of Resolution"

Spectrum Resolution

=

Fmax Number of Lines

The spectrum shown here shows 15 of the amplitude ranges that make up this spectrum.

Each frequency range in this spectrum is 30 cpm wide. Each red circle is labeled as an exact multiple of 30 except the peaks.

The frequency values shown

Close-up Look At FFT Plot Shows Individual, Frequency-Based Amplitudes

With Straight Lines Connecting The Dots

at the tops of the peaks are able to be calculated more accurately.

The y-axis value of each red circle is the amplitude for that frequency range. For instance, the y-axis value for the red circle with the number 2130 above it is the amplitude of vibration detected by the FFT process between frequencies of 2101 - 2130 cpm.

The number of lines of resolution can be 100, 200, 800, 1600, 3200 (and others) but typically is 400, 800 or 1600.

The maximum frequency shown on the plot is called the Fmax. If you select an Fmax of 60,000 cpm (60kcpm, 1000 Hz, 1kHz - all mean the same thing), your spectrum will cover a frequency range of 0-60kcpm. With 400 lines, for instance, each line of resolution will be 150 cpm wide (60k/400=150).

The width of each frequency range is called the Spectrum Resolution.

It is of CRUCIAL importance to understand spectrum resolution.

How Is An FFT AnalyzedAnalysis is performed by asking one seemingly simple question:

"Are any of the amplitude values higher than desired ?"

o If the answer is "No", move on. Remember, this includes all areas of the spectrum from 1x rpm thrugh harmonics out to high frequency, bearing related frequencies while keeping in mind the amplitudes in these ranges should be judged by different standards. For instance, you should become alarmed at much lower amplitudes when analyzing bearing-related vibrations than when analyzing 1x rpm amplitudes.

Sample Spectrum: Q1 - Are Any Amplitude Values Higher Than Desired ?

o If, however, the answer is "Yes", you must move on to a second question:

"Where are they coming from ?" More technically, what is the source of the "excessive" amplitudes that you are concerned with ?

o The source of the vibration is judged by the frequency(s) of the amplitude peak(s) being examined. Spectrum resolution must be kept in mind during this process. The better the resolution, the better your judgment.

Since the frequencies displayed actually cover frequency ranges, the best judgment of frequency you can ever make from a spectrum is an estimate.Spectrum resolution goes to the heart of a very important question - how accurate is the data (frequencies) you are using for your analysis ? Without fully understanding the implications spectrum resolution has for the data you are analyzing, you will never be a good analyst.

How Is An FFT Analyzed

Sample Spectrum: Q2 - Where Are (Any) High Vibration Amplitudes Coming From ?

This sample spectrum is taken from a machine as described above. How do we analyze ?

There is no indication of bearing problems (in the "Bearing Defect Frequency Harmonics" area) so we would have no indication of a problem developing in that range.

Does the peak at 1800 concern us ?



There are no amplitude values shown here. The answers to the questions are part of a judgment must be made by the analyst based on their understanding of general vibration and that specific machine's normal operating (vibration) characteristics.So if the answer is YES, further judgment must be made of the source (unbalance, misalignment, soft foot, etc.) and the problem must be corrected. Part of the judgement will be an assessment of the severity of the problem based on the vibration levels seen, type of problem, criticality of the machine, etc.

Important Facts To Remember When Analyzing An FFT

1) Frequencies on a spectrum are always estimates. Therefore, judgements you make are always based on assumptions.

2) Turning an estimate into a fact can only be done with field testing (phase readings, etc.).

3) A spectrum is not necessarily an accurate reflection of what the machine is doing - it should always be looked at with a certain level of skepticism and supplemented with time domain analysis.

Spectrum Resolution

Spectrum Resolution =

Max Frequency (Fmax) # of Lines of Resolution

Spectrum Resolution Units: "CPM per Line of Resolution"

Common Choices for: Fmax:

3,000 90,000 720,000

6,000 120,000 900,000

Common Choices for: Lines of Resolution:

200

400

12,000 180,000 1,200,000

24,000 240,000 1,500,000

30,000 300,000 1,800,000

60,000 600,000 2,400,000

800

1,600

3,200

6,400

The Importance Of Spectrum Resolution

Question: What Does Spectrum Resolution Actually Do ?

Answer: It determines the accuracy of the frequency data you are analyzing.

Question: Why is that important ?

Answer: Frequency is how we identify the source of the vibration.

Lets look at a couple of examples where understanding spectrum resolution can be the difference between a correct diagnosis and an incorrect diagnosis.

Understanding Spectrum Resolution:

Direct-Drive / Example 1

The FFT shown here displays data from 0 - 120kcpm. You have made the judgement that one of the peaks shown in the low-mid frequency range (1800-7200 cpm in this case) is excessive. How reliably can you answer the following questions:

What is the source of the vibration at 1,800 cpm ? Obvious choice - 1x rpm: Since it is a direct drive machine and we

will make the assumption that there is no other vibration feeding into this machine from another, you have a very good probability of being right (note that it is not a 100% probability) if you say that peak is the vibration 1x rpm.

What is the source of the vibration at 3,600 cpm ? Obvious choice - 2x rpm: Since the machine is running around

1800, chances are again fairly good you will be right if you say this peak is related to 2x rpm.

What is the source of the vibration at 7,200 cpm ? Obvious choice - 4x rpm: This could be the 4x running speed

harmonic and many people would think that is the obvious choice - but that would be very risky because there is another vibration source very close to this range. 2x AC line frequency in the U.S. is 7200 cpm (6000 cpm in countries with 50 Hz power supply) and could very well be any proportion of that amplitude.

For example, if the machine is running 1780 rpm (1480 rpm in 50Hz countries), 4x that is 7120 cpm (5920 cpm in 50Hz countries). That is 80 cpm away from 2x line frequency (7200 cpm or 6000 cpm) - much less than the 300 cpm/line spectrum resolution. That means the energy from both of the vibrations will be quantified in the same line of resolution (i.e. combine into one, single peak).

Are you monitoring bearing defect frequency harmonics sufficiently ? Yes. With a machine running 1800, collecting an FFT to 120kcpm is

sufficient to monitor the full range of frequencies in which bearing-related peaks will appear.

Summary: This is a good general purpose spectrum for fully monitoring the frequency ranges in which likely problems will show up but with a spectrum resolution of only 300 cpm/line, that could be a problem for any detailed analysis. Let's continue by reducing the Fmax.




What is the source of the vibration at 1,800 cpm ? Obvious choice - Still 1x rpm: Since it is a direct drive machine and

we will make the assumption that there is no other vibration feeding into this machine from another, you have a very good probability of being right (note that it is not a 100% probability) if you say that peak is the vibration 1x rpm.

What is the source of the vibration at 3,600 cpm ? Obvious choice - Still 2x rpm: Since the machine is running around

1800, chances are again fairly good you will be right if you say this peak is related to 2x rpm.

What is the source of the vibration at 7,200 cpm ? Obvious choice - ?: This could be the 4x running speed harmonic

but could also be 2x AC line frequency and could also very well be a combination of the two vibrations since the vibration energy from each falls within the same line of resolution.

Are you monitoring bearing defect frequency harmonics sufficiently ? No. With a machine running 1800, collecting an FFT to 60kcpm is

probably NOT sufficient to monitor the full range of frequencies in which bearing-related peaks will appear.

Summary: Not the best choice for fully monitoring the frequency ranges in which likely problems will show up since not only do you have mediocre spectrum resolution (150 cpm/line) but you also are not monitoring the full range of vibration frequencies in which bearing problems will show up. Let's again reduce the Fmax.




What is the source of the vibration at 1,800 cpm ? Obvious Choice - Still 1x rpm: Notice that the frequencies listed

have changed. Now that each line of resolution is only 30 cpm wide (12000/400), the accuracy of the frequencies displayed has improved as well. As the resolution improves, the likelihood that the peak is 1x rpm continues to improve but will never reach a 100% certainty.

What is the source of the vibration at 3,600 cpm ? Obvious choice - Still 2x rpm: See the explanation for 1x rpm.

What is the source of the vibration at 7,200 cpm ? Obvious choice - ?: At this point, you may notice the harmonics not

lining up perfectly with the4x rpm peak. Note that it is also labelling a bit higher (7190 cpm) than 4x rpm would be. This may well be 2x AC line frequency and could still be a combination of both vibrations since the vibration energy from each falls in adjacent lines of resolution.

Are you monitoring bearing defect frequency harmonics sufficiently ? No. Not even close. This is a spectrum useful only for monitoring

low-mid frequency sources.

Summary: A reasonable choice for monitoring the lower, mechanical frequency ranges in which likely problems will show at running speed harmonics. There is no monitoring of vibration frequencies in which

bearing problems will show up. Let's now increase the number of lines instead of reducing the Fmax.



The FFT shown here displays data from 0 - 12kcpm but with 1600 lines of resolution instead of the 400 lines each of the previous FFTs contained. How reliably can you answer the following questions:

What is the source of the vibration at 1,800 cpm ? Obvious Choice - Still 1x rpm: Notice that the frequencies listed

have changed. Now that each line of resolution is only 7.5 cpm wide (12000/1600), the accuracy of the frequencies displayed has improved as well. As the resolution improves, the likelihood that the peak is 1x rpm continues to improve but will never reach a 100% certainty.

What is the source of the vibration at 3,600 cpm ? Obvious choice - Still 2x rpm: See the explanation for 1x rpm.

What is the source of the vibration at 7,200 cpm ? You can finally differentiate between 4x rpm and 2x line frequency:

2x line frequency (7200 cpm) is the higher amplitude vibration. Note that there is also vibration at 4x rpm (7160 cpm) but it is of lower amplitude. The choice for corrective action if the vibration was 4x rpm vs. 2x line frequency is completely different. Failure to recognize the limitations of the previous FFTs and make this further anaysis could lead to embarassing and expensive mistakes.

Are you monitoring bearing defect frequency harmonics sufficiently ? No. Not even close. This is a spectrum useful only for monitoring

low-mid frequency sources.

Summary: A very good choice for monitoring the lower, mechanical frequency ranges and separating the mechanical frequencies from the electrical frequencies in that range.There is, of course, no monitoring of vibration frequencies in which bearing problems will show up. Let's repeat the process on a belt-driven piece of equipment.

Zoom-In On Smaller Frequency Range (6k - 9kcpm)

Note that with a >400 line spectrum, you can "zoom-in" on narrow frequency ranges and appear to have "normal" spectrum resolution. This is because the software stores however many amplitude values (800, 1600, 3200, etc.) even though it can only display 400 or so due to limitations of the CPU monitor.


Belt-Drive / Example 1

The FFT shown here displays data from 0 - 120kcpm. You have made the judgement that one of the peaks shown in the low-mid frequency range (< 12kcpm) is excessive. How reliably can you answer the following questions:

What is the source of any of the vibrations apparent in the <12kcpm range ?

Entirely Unclear: As a belt-driven piece of equipment, there are 3 rotating components (motor, fan, belts) plus the same 2x line frequency we touched on in the direct-drive example. If you venture a guess as to the source of any particular peak, you have about a 1 in 3 or 4 chance of being correct - not the best of odds.

Are you monitoring bearing defect frequency harmonics sufficiently ? Yes. With a machine running 1800, collecting an FFT to

120kcpm is sufficient to monitor the full range of frequencies in which bearing-related peaks will appear.

Summary: A spectrum really suited to bearing monitoring and low-mid frequency trending only - no specific frequencies are identifiable in the lower frequency ranges.Let's proceed with the same sequence of FFTs as shown in the previous example.



The FFT shown here displays data from 0 - 60kcpm. You have made the judgement that one of the peaks shown in the low-mid frequency range (< 12kcpm) is excessive. How reliably can you answer the following questions:


Still Very Unclear: As a belt-driven piece of equipment, there are 3 rotating components (motor, fan, belts) plus the same 2x line frequency we touched on in the direct-drive example. You may have improved your chances of guessing right but you are still guessing..

Are you monitoring bearing defect frequency harmonics sufficiently ?

Not really. With a machine running 1800, collecting an FFT to 60kcpm is probably not sufficient to monitor the full range of frequencies in which bearing-related peaks will appear.

Summary: A spectrum not really fully suited for either purpose - bearing monitoring or low-mid frequency trending. Let's drop the Fmax further still.



The FFT shown here displays data from 0 - 12kcpm. You have made the judgement that one of the peaks specifically in the low-mid frequency range we are looking at is excessive. How reliably can you answer the following questions:


Much Clearer: Knowing that mechanical vibrations occur only at exact multiples (harmonics) of running speed (including 1x), we can assume the following:

o 900 cpm - 1x Fan (high likelihood)

o 1170 cpm - 2x Belts (high likelihood)

o 1770 cpm - 1x Motor (reasonable possibility - could also be 2x Fan or 3x Belts, couldn't it ?). Most likely - ???

o 2340 cpm - 4x Belts (high likelihood)


o 3540 cpm - 2x Motor (probable - 4x Fan and 6x Belts could also be affecting this peak although the probability is pretty low for either of those). Most likely - 2x Motor.

o 7200 cpm - 2x Line Frequency (with a resolution of 30 cpm/line and the motor running at 1785, 4x motor will be 7140 - 2 full lines of resolution away from 2x line freq.), or 8x fan rpm (8 could be the number of blades on fan). The most likely is 2x line frequency but that doesn't make it so.

Are you monitoring bearing defect frequency harmonics sufficiently ? No. This spectrum does not serve that purpose.

Summary: A fairly good spectrum for resolution at the low-frequency end - but is it enough ? Let's increase the number of lines to 1600.



The FFT shown here displays data from 0 - 3.6kcpm. You have made the judgement that one of the peaks specifically in this "mechanical" range (dealing with rpm's) we are looking at is excessive. Because you have sufficient resolution, you can now incorporate the "process of elimination" into your thought processes (when a source becomes the only logical possibility). How reliably can you answer the following questions:

What is the source of any of the vibrations apparent in the <3.6kcpm range ?

Much Clearer Than Before: Knowing that mechanical vibrations occur only at exact multiples (harmonics) of running speed (including 1x), we now have a much more reliable assumption than with the e following:


o 1177 cpm - 2x Belts (high likelihood simply via process of elimination)

o 1770 cpm - Three separate mechanical vibrations had previously combined to form this peak. Because of the new spectrum resolution of 7.5 cpm/line, they are now separated on the FFT once you zoom-in on that portion of the plot. Now they can be judged for cause and severity and what might have mistakenly been called motor unbalance (1x motor) can correctly be called belt problems (3x belt typical frequency generated by belt problems - could be wear, resonance, etc.) along with possibly some mechanical looseness on the fan (2x fan typical frequency generated by looseness around the fan bearings and/or the surrounding structure).The three are:

3x Belts is the highest amplitude of the three.

2x Fan is the second highest amplitude of the three.

1x Motor is by far the lowest of the three.

o 2340 cpm - 4x Belts (high likelihood by process of elimination)

o 2700 cpm - 3x Fan (high likelihood by process of elimination)

o 3540 cpm - 2x Motor (probable - 4x Fan and 6x Belts could also be affecting this peak although the probability is pretty low for either of those). Most likely - 2x Motor.

What About The 7.2kcpm peak ? 7200 cpm - Can't see from this spectrum but we can also zoom-

in on that frequency range when done analyzing this frequency range.

Are you monitoring bearing defect frequency harmonics sufficiently ? No. This spectrum does not serve that purpose.

Summary: A very good spectrum for resolution at the low-frequency end - but is it enough ?

But is it possible that the three frequencies in the 1762 - 1807 cpm range could have lined up even more closely ?

Of course. It is not uncommon to find belt-generated frequencies aligning themselves very closely with driven or driver component frequencies. Let's discuss a not-to-remote possibility:

The belts run at 600 rpm and the fan runs at 1192 rpm. 2x belts - a normal frequency belts will generate when experiencing wear or other problems - would then be 1200 cpm - a mere 8 cpm apart from one another. Furthermore, you don't know the belt speed. After all, it is probably more common to not know the belt speed than it is to know it. How easy would it be to try to go balance that fan (the most likely source of 1x rpm vibration; especially on a fan: unbalance). And how embarassing and expensive could that be for you and for the credibility of the vibration program.

You should always, Always, ALWAYS confirm your vibration source before before attempting any significant corrective actions such as balancing (tightening loose bolts, for instance, can be done as they are found).

How Do You Know What Spectrum Resolution Is Required ?

Rule of Thumb:

Spectrum Resolution should be 33% of difference between the frequencies.

In previous example, frequencies of interest were:

o 1,762 cpm

o 1,785 cpm

o 1,807 cpm

Smallest difference is 22 cpm (1,807 - 1,785 = 22).

Spectrum resolution should be 22/3 = 7.33 cpm/line

Why 1/3 ? It means that there will be at least TWO lines of resolution

between the frequencies in question.

This assures proper separation of the peaks.

Where To Collect "High Resolution" Data

Spectrum Resolution = Max Frequency (Fmax) # of Lines of Resolution

Direct Drive Machines:

[12,000 Fmax / 1,600 Lines] Collected for all >10 HP Motors. Will allow separation of mechanical / electrcial

frequencies.

This is particularly important on 2-pole ac induction motors since it will be easy to confuse 2x rpm for 2x line frequency.

Belt Drive Machines:

[12,000 Fmax / 1,600 Lines] Collected for >10 HP Motors. In addition to

performing the above tasks; Will greatly improve chances of being able to

separate motor, driven and belt frequencies from one another. Note that it does not say guarantee the separation of those frequencies.

[6,000 Fmax / 400 Lines] Collected on inboard (pulley end) of driven

component bearing for same (mechanical) reasons as listed above.

This can be adjusted to meet specific needs if the actual speeds are determined.

Beat Frequencies:

Any time there is a cycling or "beat" frequency is encountered there are two frequencies very close to one another. Understanding spectrum resolution will enable you to calculate what is needed and use it appropriately.

What Are "Beat" Frequencies ?What is meant by the term: "beat frequencies" ? If you work in a place with lots of machines, you have probably felt or heard one. Have you ever walked by a machine and felt or heard the vibration increasing . . . and then going away . . . and then increasing . . . and then going away . . . etc., etc. That is a "Beat" vibration.

Beat vibrations are caused by vibrations that have very close to the same period and similar amplitudes.

The animation shown here shows two separate sine waves - the red 1x rpm component of a 2-pole motor and the line frequency being supplied to that motor. Either can cause mechanical vibration.

Note that the amplitudes are the same. The amplitudes must be at least similar to produce a beat. Otherwise, the dominant amplitude will be only slightly affected by the much lower amplitude and the effect will not be felt.

What does this interaction of these signals produce ?

You can see here that when the peaks coincide (they are 'in-phase'), they add together and create more vibration than either single signal produces by itself.

When they oppose one another (they are out-of-phase), they cancel each other out and the vibration disappears - for a moment, anyway.

The "Beat" frequency is simply how often these separate signals go in-phase with one another. It might be 10 times a

minute or 20 times a minute.

The difference between the two frequencies IS the beat frequency. By measuring the frequency of the beat (when you can feel or hear it), you can actually determine what spectrum resolution you need to separate the 2 peaks on a spectrum by simply counting the number of beats that occur in one minute or so (or portion of a minute) and dividing by 3.

For example, a 2-pole US motor is running at, say, 3580 rpm. Line frequency is 3600 cpm. The difference is 20 cpm. That means if the 1x rpm component and the line frequency component have similar amplitudes, there will be a beat frequency occurring at 20 cpm. If you have ever walked past a motor and heard it "humming", it is a beat vibration being generated by the interaction of mechanical and electrical frequencies.

SummaryThe FFT is without a doubt the most widely used vibration analysis plot. But it would be a mistake to consider the FFT to be the infallible or the only analysis tool. Spectrum resolution is perhaps the single most important plot characteristic to fully and completely understand. It is also very important to understand how a spectrum is generated - the concepts behind the FFT process without getting into the technicalities. An understanding of the FFT process will further boost your ability to effectively analyze an FFT.

Plots:

The Time Domain What Is A "Time Domain" Plot

How Do You Analyze A Time Domain Plot

The Relationship Between The Time Domain and The FFT

o Frequency Modulation (Harmonics)

o Amplitude Modulation (Sidebands)

Where Time Domain Plots Can Be Invaluable

http://www.vibrationschool.com/mans/Plots/TPlots09.htm

http://www.vibrationschool.com/mans/Plots/TPlots08a.htm





o Beat frequencies

o Bearing defects

o Gear tooth defects

o Rubs (Truncated Wave Shapes)

How To Become Comfortable With Time Domain

Setting Up Time Domain Plot Parameters

Summary

What Is A "Time Domain" Plot ?

Y-Axis Units: Amplitude


The "Time Domain" plot is a powerful tool to use for analysis since it is as close to the raw (analog) data as you are likely to get. It also can be quite intimidating to learn to use (with good reason) and many analysts do not use it at all. Even more than the FFT, it creates a number of questions for the analyst:

How is it interpreted ?








How is one set up ?

Should I use it everywhere ?

Why do I need it at all when I have the FFT to use ?

This section of the manual will provide you with information on how to use and interpret the time domain plot. More importantly (since it is from this signal that an FFT plot is produced) this section will attempt to give you a general understanding of how the FFT process views the signals we feed into it and how these signals impact what we see when we look at an FFT.The time domain, of course, is where the reading begins - an analog measurement of how the surface is moving. This analog signal is fed from the transducer to the analyzer where it is converted to a digital signal - it goes through an A/D converter. The result of this process can be seen above in the plot above. It is important to realize that it is experience (i.e. practice) that creates a 'comfort' level for the analyst in interpreting the time domain plot. Experience in setting it up properly and experience in being able to recognize what you are seeing - the pattern of what you are seeing. Let's zoom in on this plot.

How Do You Analyze A Time Domain Plot ?

Y-Axis Units:

Amplitude


The time domain plot shown here is a small portion (time-wise) of the previous plot - a zoom-in. At first glance, what do we see ?

A series of spikes - perhaps 50 or so. Each of these 'spikes' is a cycle of vibration just as the nice smooth animated sine waves we previously examined were. The difference, however, is obvious - these are not nice, smooth sine waves. This is a 'real-world' time domain plot.

The amplitude of the 'spikes' varies a great deal.

There appears, at times, to be changes in frequency of the spikes (in some areas, there are 2x or 3x as many spikes than in other areas).


Y-Axis Units:

Amplitude


But let's look a little more in-depth. What are we actually seeing here ? It would only be fair to tell you the reading was collected on a gearbox. Let's break our analysis into the frequencies and amplitudes.

Frequency

o The 50 or so cycles occur in a very short period of time - they are measuring 'high frequency' vibration (the shorter the period of the cycle, the higher the frequency). As you probably guessed, it is actually the gear mesh frequency.

o What is the source of the 'extra' cycles we noticed in the areas of low amplitude ? They appear to be occurring about twice per (gearmesh) cycle when they do occur. One possible explanation would be a momentary 'chattering' of the teeth (the teeth bouncing back and forth) due to excessive backlash.

o Also, some of the spikes appear fatter than others. What this means is that particular cycle (or part of that cycle) is taking slightly longer (in milli or even micro seconds) than other cycles. In vibration terms, this is known as frequency

modulation. When a signal is put through the FFT process, frequency modulation causes harmonics.We will see why in a few more pages but the first question should be - what could cause this ?

o Have you ever tried turning a shaft - even in a childrens toy - that is easy to turn for part of a rotation and hard to turn for the other part of the rotation ? That binding action can occur in industrial machinery for any number of reasons. But why is it occurring here ?

So we can find a number of seemingly small details by analyzing the time scale and how the cycles are occurring. Let's now examine the amplitude data.


Y-Axis Units:

Amplitude


What can we see from the amplitudes being displayed ?

The gear mesh peaks are changing size - "modulating". That means the amplitudes are not always the same. But how are

they modulating - are the amplitudes changing a predictable amount within a predictable period of time ? Or does it seem more random in nature ?

If you had the tools necessary to analyze the plot, you would find the amplitudes get high once per shaft revolution and low once per shaft revolution. In vibration terms, the gear mesh amplitudes are modulating at 1x rpm.

There is no obvious 1x rpm sinusoid - the dominant amplitude is at gear mesh frequency.

So putting all of this analysis information together, what can be seen ?


Y-Axis Units:

Amplitude


Let's review what we have. A dominant gear mesh frequency that is experiencing both

amplitude and frequency modulation. 'Extra' cycles that appear to occur twice as often as the

dominant gear mesh cycle.

A low amplitude 1x rpm signal. Possible Explanation

A possible explanation (only testing and inspection can prove anything) for these patterns would be improper gear mesh setting (pitch diameters not in-line at all times). For part of the gear's rotation, the teeth are too tightly set. That increases the resistance to rotation and drives up the gear mesh amplitude. For the balance of the rotation, the teeth have excessive backlash. That decreases any resistance to rotation and reduces the gear mesh amplitude but also allows the teeth to bounce back and forth (chatter).

Action RecommendedUnfortunately, we have only reached the level of an educated guess at this point. The data points in a direction but there could be any number of other problems influencing the patterns we are seeing and analyzing. Our "explanation" is based on probabilities and, if we have it, previous experience. We must now go into our LEARN MODE. What is the learn mode ? It is the mode where we are actively involved in any investigation and corrective action(s) taken so we can learn from what we find. If you do not use the LEARN MODE (and sometimes it requires you making it happen), you will not learn from your successes or (and more importantly) your mistakes.

Importance Of Understanding The Relationship Between

The Time Domain Plot And The FFTThis may all seem a bit overwhelming (ok, it is overwhelming - at least for beginners) but there is an important point to be made here and it has nothing to do with analyzing the time domain plot - it has to do with analyzing the FFT plot.Even if you don't plan on using time domain plots, it is important to understand how the FFT is generated from them and how different wave shapes affect the FFT process and the spectrum we see.

The Relationship Between The Time Domain And The FFT

The following pages contain plots that will allow us to look at the FFT process backwards. These "complex" time domain signals are the result of programming in a series of amplitudes and frequencies from an FFT and then seeing what the resulting time domain looks like. Although mechanical vibration will always be more complex than what we analyze here, it is illustrative to see the process working in reverse.In order to understand the complexities of the FFT process, let's look at how it works in its most basic form - analyzing a simple sinusoid. That is what you see in Figure 1. Performing an FFT on Figure 1 would generate the plot you see in Figure 2 - a single peak at 1x rpm.

Pure Sinusoidal Motion

Result Of Running Fig. 1 Signal Through FFT Process

The FFT process sees a simple sinusoid and calculates the period (time required) for a single cycle. In Figure 1, the period is 40 msec (the x-axis units are milliseconds = 0.040 seconds). Then, do the following:

Period =40 msecs per cycle [0.04 secs / cycle]. We have

seconds per cycle - we want cycles per second since we are interested in frequency.

Frequency (Hz) = 1 / 0.040 = 25 cycles per second [25Hz]. If we want cycles per second:

Frequency (cpm) = 25 Hz x 60 seconds / minute = 1500 cycles per minute [CPM].

The FFT is created with a peak at 1500 cpm (25Hz). The amplitude shown will be based on the Window type shown and whether you have a signal detection of RMS, peak, peak to peak or true-peak.Unfortunately, in the mechanical world there are only two problems that cause such a pure sinusoid to occur (and it will only be pure if they are the only problems present):

Unbalance

Resonance


What about less than pure sinusoidal motion. Any thoughts on what could possibly cause the signal shown below ? More importantly, what does the FFT process "see" as the combination of signals that would create what we see in this signal ?

Figure 1: A Signal That Is Not Sinusoidal

The FFT looks like thsi when applied to the signal shown above. Why ?

The FFT Generated By Figure 1

Because the FFT process "sees" the combination of two distinct signals: one at 1x rpm and one at 2x rpm. The two signals are in-phase with each other (the "+" peaks line up). When the "+" peaks line up, the very high peaks occur (0, 40, 80 msecs). When the "-" peak on the 1x wave lines up with the "+" peak on the 2x wave (20, 60, 100 msecs), you get the small "bump" at the bottom of the wave.

The Actual Signals Used To Generate Figure 1


Let's look at another signal with a completely different shape. Can you see in your mind a bearing moving in this manner ? What types of mechanical problems do you think could cause the shape of the signal shown here in Figure 1 ? What does the FFT process see ?

Figure 1 - The Raw Signal

It may surprise you to find that putting this signal through an FFT will generate an identical spectrum to the one we saw on the previous page.

Figure 2 - The Resulting FFT

Why ? It is clearly a very different signal. Or is it ? As a matter of fact, exactly the same combination of signals went into creating this one with one difference - the 2x component has shifted 1/4 of a cycle on the time line relative to the 1x component - the 2x signal is a 90° out-of-hase with the 1x signal.

Figure 3 - What The FFT "Sees"

The Relationship Between The Time Domain And The FFT:

Frequency ModulationSo is it safe to assume that each of the previous signals were generated by a machine that is generating vibration at 1x rpm and 2x rpm (i.e. a reciprocating compressor) ? Or could there be another explanation for the signal shape seen on those pages (which is really what is being analyzed - the signal shape) ? Let's return to our discussion of the actual, real-life vibration signal we looked at a few pages back.

We discussed how there can be some variation in the free rotation of the shaft - a momentary "binding" action that occurs as the shaft rotates through a particular portion of it's rotation.

That phenomenon could occur for a number of reasons. In that situation, we considered the possibility of the gears being improperly set. That would create more resistance to rotation when the teeth were bottomed out than opposite that point. It would momentarily slow down the rotation.

Let's examine the 'frequency modulated' signal shown here:

Figure 1: A "Frequency Modulated" Signal

Figure 2: A Bearing Undergoing

Frequency Modulation During Each

Rotation

Let's first examine the positive-going portion of the signal. The bottom of the cycle (the '-' peak) first occurs at about 19 msec. The '+' peak occurs at about 32 msec so it takes a total of about 13 msec to move from the "-" peak to the "+" peak. The reciprocal of the period will give us the frequency during that portion of the signal:

o 1/(0.013 x 2) x 60 = 2308 cpm (the 13 msecs is multiplied by 2 to calculate a full cycle).

Now let's examine the negative going peak. From the "+" peak at 32 msec, the signal descends to a "-" peak by about 53 msec - a total of 21 msec. For that portion of the signal, the shaft rotates:

o 1/(0.021 x 2) x 60 = 1429 cpm.

Yet if we simply calculate the total time for one cycle (peak to peak), we measure from 19 msec to 53 msec - about 34 msec.

o 1/(0.034) x 60 = 1765 cpm.

This is called frequency modulation. What is happening here may or may not be evident if we were to analyze the time domain signal - it will depend on the resolution (yes, time domain is just as dependent on resolution as the FFT is), the time sample, number of bytes, etc. But remember, the question we are discussing here is how will the FFT treat this phenomenon ?

The FFT only deals in pure sinusoids. So how will it account for the frequency modulation we see here ? We will unquestionably have a peak around 1765 cpm but the signal is not a pure sinusoid - it is

distorted by the frequency modulation we see. How does the FFT mathematically explain this phenomenon ?

In other words, what combination of simple sinusoids, when combined, will generate the signal we see above ?


Frequency ModulationSo the FFT has fed into it the following signal:

Figure 1 - Signal Being Analyzed

So what does the FFT "see" ? This plot was generated from the signal in Figure 1:

Figure 2 - Spectrum Generated by FFT Process

So we have peaks at 1x, 2x and 3x rpm. But how can the spectrum we see in Figure 2 be the result of performing an FFT on the signal we see in Figure 1 ?

If the signal shape in Figure 1 is a result of a "binding" action, then there are no 2x or 3x components present - only 1x rpm. Why does the FFT add these peaks ?


Frequency ModulationThe answer is actually very simple - it is precisely that combination of simple sinusoids - 1x, 2x and 3x - in exact amplitude and phase relationships that generates the signal shape we see. Any change in the amplitude values of any of these simple sinusoids or their phase relationship to one another and the resulting signal shape will be altered. Here are the 3 signals that combined to generate the previous signal:

Figure 1 - The Three Simple Sinusoids

What, exactly, are these signals ? 1x rpm w/ amplitude of 1.8 (pk-pk) and no phase shift ('+' peak

on y-axis) 2x rpm w/ amplitude of 0.45 (pk-pk) and 90° phase shift

3x rpm w/ amplitude of 0.05 (pk-pk) and 180° phase shift ('-' peak on y-axis)

Note that the phase relationships are not displayed on the FFT - it only displays amplitudes and frequencies although the FFT process does use phase in its analysis.

So this "distorted" signal shape:

is explained (by the FFT) as the result of this combination of simple sinusoids:

and the FFT process generates this plot:

So what does all of this mean ? The frequency modulation we see in the original signal generates the presence of harmonics.

Frequency Modulation creates harmonics.

Are all harmonics the result of frequency modulation ? No. There are mechanical viration sources that generate vibration at multiples of running speed (i.e. reciprocating units @ 2x rpm). But some harmonics - more often than not those associated with problems such as misalignment - are the result of frequency modulation. They are mathematically created.


The previous example may or may not have impressed upon you a rather stunning fact:

Many (even most, at times) peaks on the spectrum are not actually being generated by the machine - they are generated by the FFT process due to the shape of the signal being processed.

That's a rather depressing statement - many of the peaks are not being generated by the machine (they don't actually exist). It shouldn't be a suprise though. This is a process that relies on a complex mathematical principle to analyze data that comes from dynamic machines with many, many different variables being applied to them (do you have unbalance, misalignment, is the base solid, the pipes lined up, etc., etc., etc.).

On the bright side, it also illustrates why it is useless to try to identify every peak on a spectrum (a trap many analysts, unfortunately, fall into). Let's look at the situation another way.

If you knew that when a machine had a misalignment problem that your computer would blow out a puff of blue smoke - the more misalignment the more smoke - would you care about the precise details of why your computer would do that or would you simply be happy knowing you could count on that notification ?

The point is that when machines have particular problems - misalignment, for instance - those machines will vibrate in certain ways characteristic to the problem they have and those problems will affect the shape of the signal they generate. This applies, for instance, to the binding action seen on the previous page attributed to gears bottoming out. The shape of the signal being generated due to that particular problem will be affected in a reasonably consistently way. Under those conditions, the FFT process will

generate a reasonably consistent result (the plot we see). Subtle changes to the shape will change the spectrum but on the whole, certain patterns you learn to recognize on the FFT plot will lead you to investigate certain problems based on the likelihood of finding that problem - the more likely (and easier to check) problems go first and on down the list. Three or four different problems may each generate similar spectrums - it is up to you to differentiate between those similar symptoms and solve the problem.

YOU CAN'T DO THAT SITTING AT A COMPUTER !!

Why is all this important ? Because: Understanding the inherent limitations and shortcomings of an

FFT should impress upon you the tremendous importance of field testing and troubleshooting.

It must be recognized that the spectrum provides clues and insights - not facts. It is only one tool you have in your battle to protect your machines.

Although the FFT always "works" (we will get a plot), sometimes we do not understand what it is telling us. To attempt corrective actions without a thorough investigation can be . . risky.

The time domain plot can provide valuable clues and insights and in some situations will provide information that is impossible to determine from the FFT.


Amplitude ModulationWe have discussed frequency modulation and its impact on the spectrum plot - namely, it creates harmonics. But we have also touched on amplitude modulation - now let's cover it more in-depth. Amplitude modulation is a increase and decrease in the amplitude of a particular frequency at a different frequency. So for instance your gear mesh amplitude gets high once per shaft revolution and gets low once per shaft revolution - the gear mesh amplitude is modulating at 1x rpm. That's simple enough but what effect does that have on the FFT (i.e. how doe the FFT explain it) ? Let's look at some examples:

What do you make of the time domain plot shown in Figure 1 ?

Figure 1

You can see a low frequency cycle (occurring 15 times over the time sample) and a high frequency (occurring many times for each of the low frequency cycles). One way to describe this is as "a high frequency riding a low frequency". For analysis, let's zoom in:

Figure 2 - One Cycle Of Low Frequency

Figure 2 shows only just over one of the low frequency cycles (one peak to just past the next peak). The high frequency could be a gear meshing frequency. The low frequency is at 1x rpm. How many teeth are on the gear ? This is another advantage of using time domain on gearboxes - you can actually obtain detailed internal information that you can only guess at on the spectrum. Count the small peaks from the top of one low frequency peak to the next. There are 23 teeth. What does the spectrum look like ?

Figure 3 - The Resulting FFT

Both the amplitudes and the frequencies are constant - there is no modulation in either. You will only get the peaks that are actually being generated. Now let's consider some variations on this "perfect" gearbox.


Amplitude Modulation (Sidebands)Remember this plot from the first page in this section ? Well, Figure 2 shows a computer generated plot that is somewhat similar:

Figure 1 - Actual Time Domain Signal

Figure 2 - Computer Generated Time Domain Signal

You can see the low frequency (usually 1x rpm) cycle still occurring but this shape looks somewhat like an Angel Fish. This shape is typical of an amplitude modulation. Let's zoom in on the computer generated signal to get a clearer picture of what is happening.

Figure 3

Figure 3 shows only a bit more than a single one of the low frequency cycles. It is clear that the high frequency signal (the gear mesh amplitude) is increasing and decreasing in amplitude at a rate of once per shaft revolution. Figure 4 shows the two signals involved separated:

Figure 4

This represents what we were discussing before - a modulation of gear mesh amplitude once per shaft revolution due to a gear problem. The amplitude varies significantly at a rate of once per revolution. How does the FFT handle amplitude modulation ? Figure 5 shows you:

Figure 5

Figure 5 shows a peak at 1x rpm and a peak at gear mesh frequency (GMF) with smaller peaks surrounding it. It you could measure the frequencies involved, you would see that the smaller peaks are equally spaced around the large peak - the separation is equal to the frequency of 1x rpm. There may be a series of these peaks called sidebands around the gear mesh frequency. This series of peaks are what would mathematically cause the amplitude to go up and down (modulate) as the peaks go in and out of phase with one another. The difference between sidebands and other noise around a peak is the equal spacing (1x rpm in this case). Peaks that are not equally spaced are most likely not sidebands.

Peaks on the higher frequency side of the large peak will be located at GMF + 1x rpm, GMF + 2x rpm, GMF + 3x rpm, etc. On the low

frequency side of GMF, the peaks will be located at GMF - 1x rpm, GMF - 2x rpm, etc. The spacing of the peaks is the key indicator in where the problem lies. The spacing at 1x rpm indicates the gear running at that frequency (speed) is the source of the problem.

Although not nearly as common as harmonics, sidebands are critically important to learn to recognize for a couple of reasons:

Sidebands always indicate a problem (amplitude modulation is never "normal").

Sidebands are only generated by three types of problems:

o Gear-related problems

o Bearing-related problems

o Electrically-related problems

Sidebands can be significant at very low amplitudes (their mere presence can be significant).

Sidebands should be analyzed on a logarithmic scale (as opposed to a linear amplitude scale) so the low-amplitude peaks can be detected.

The Addition Of Sidebands Is The FFT's Explanation Of The Presence Of Amplitude Modulation

The Relation Between The Time Domain And The FFT:

Frequency And Amplitude Modulation Now let's have some real fun !! What do you see in the time domain plot shown in Figure 1 ?

Figure 1 - The "Complex" Signal

The most noticeable characteristic is the 'Angel Fish' pattern we saw on the previous page. Let's start to zoom in and see what else we have.

Figure 2 - A Close Up Of The "Complex" Signal (Perhaps 60msecs)

Figure 2 above looks very similar to the signal analyzed on the previous page except that the gear mesh amplitude actually drops to about 0 once per shaft revolution - there is more gear mesh amplitude modulation than we previously had - so we would expect to see a similar FFT except that the sidebands would be higher and possibly greater in number. Let's look at the individual signals that went to create Figures 1 and 2:

Figure 3 - The "Complex" Signal Components Separated

It is now clear that the 1x rpm signal is nowhere near a pure (clean) sinusoid ? Note how wide the trough of the wave shape is compared to the peak. Something is causing the 'binding' action we have discussed (frequency modulation) - at once per revolution (1x rpm). So we can expect to see 1x, 2x and 3x rpm peaks on the spectrum plus a peak at gear mesh frequency with sidebands surrounding it at 1x rpm. That's it, right ? To be on the safe side, let's look even closer:

Figure 4 - A Close Up Of The Gear Mesh Signal (~5 msecs)

We've been hasty again. It is now clear that the gears are also binding momentarily as they go in and out of mesh - perhaps they are incorrectly aligned (note that the seemingly straight green line shown in Figure 4 is actually a small portion of the 1x rpm signal). The gold signal shows about 3-1/2 cycles of the gear mesh signal. Clearly, the slope of the gear mesh signal is steeper in the positive going direction than in the negative going direction - more frequency modulation but this frequency modulation is for the gear mesh signal. Now let's look at the resultant FFT:

Figure 5 - The FFT Generated From Figure 1

We have: 1x, 2x, 3x rpm peaks 1x, 2x, 3x gear mesh frequency peaks

Sidebands around gear mesh frequency harmonics spaced at 1x rpm

How many mechanical vibration generators are present ? Two: 1x rpm

1x gear mesh

Of 12 identifiable peaks on this spectrum, 2 are actual mechanical vibrations. The FFT has 'created' the other peaks due to the specific shapes of the signal being processed. The FFT sees things that we cannot see except in its detailed and precise mathematical analysis of the data. It also makes judgements that may be faulty (creating peaks) due to lack of resolution and data accuracy.

But in spite of that, what kind of action(s) might be performed if the amplitudes of the peaks shown were considered unacceptable ?

Balance (high 1x rpm peak) Alignment (harmonics of 1x rpm)

Mechanical looseness (harmonics of 1x rpm)

Gear eccentricity and settings (due to sidebands around gear mesh harmonics)

Gear wear and alignment (due to gear mesh harmonics)

These are only some of the most likely problems but you will most probably find the problem during the course of this investigation. Also, consider that we are assuming with our list here that it is not just one or two of the amplitudes to be excessive but all of them. That is quite unlikely.

You are far more likely to be mislead by spectrums if you are ignorant

of the FFT process than if you have a proper understanding of it.

Where Time Domain Plots Can Be InvaluableObviously, time domain is a powerful tool. But what kinds of problems and situations are better analyzed with the time domain plot ?

Slow Beat Frequencies

Impacts

Transients

Rubs

Chipped / Broken Gear Teeth

Amplitude Modulation

Frequency Modulation

Slow Speed Bearing Defects

Additionally, you can gather information related to the machine condition such as:

Misalignment Eccentricity

Looseness

# of Teeth on a Gear

Waveform Shape

Instabilities

Let's see how the time domain can be of help with some of these.

Using Time Domain Plots To Find:

Beat FrequenciesA beat frequency occurs when two closely matched frequencies occur with similar amplitudes. Figure 1 shows an uneventful spectrum with a resolution of about 25 cpm per line.

Figure 1

But as we discussed in the 'Frequency' section, that spectrum resolution (25 cpm/line) will be insufficient to separate peaks less than about 50 - 60 cpm apart - the FFT will combine those frequencies into a single peak. Figure 2 shows the signal from which Figure 1 was generated.

Figure 2

We can see from Figure 2 that the beat is occurring over about 4000 msecs (4 seconds) which means it is occurring 15 times per minute. With a beat frequency such as this, chances are you would be able to hear and/or feel the beat occurring. By timing it, you can find the 'beat' rate (15 beats per minute). From the 'Frequency' section, we know that we need a spectrum resolution of about 1/3 of that beat - 5 - 6 cpm/line of resolution - to be able to separate the peaks on the FFT.


Impacts Created by Bearing DefectsAn impact can occur due to a number of different problems - bearing defects being #1 on the list (most common and most important). But because of exactly how the FFT works, the impact frequency gets filtered out of the displacement, velocity or acceleration spectra. Figure 1 shows a outer race defect occurring on a bearing rotating about 1200 rpm.

Figure 1 - A Signal Showing An Impact Occurring

But why does the impact frequency get filtered out ? It is simply because there is no sinusoid at the impact frequency (no sinusoid associated with the rate at which the impacts are occurring). The only sinusoids present are:

The 1x rpm sinusoid (we see 3+ cycles of that);

The sinusoid associated with the ringdown occurring just after the impact occurs (similar to a bell ringing down after being struck).

So how does the FFT process the signal shown ? The 1x rpm sinusoid

is no problem but how does it account for the periodic impacts occurring ?


Impacts Created by Bearing Defects

Figure 1 - A Time Domain Signal Showing Bearing-Related Impacts Approximately 3 Impacts Occur For Each Shaft Revolution

Even though there is no sinusoid associated with the impact frequency (about 3 impacts per revolution of the shaft), note that there is a short-duration sinusoid occurring immediately following the impact. In fact, it is generated by the impact itself.

When you strike (impact) a bell, what happens ? It rings (down) until it dampens out and stops ringing (or until it is struck again). This is also known as "free" vibration. The same effect occurs when the bearing component is struck. Notice in Figure 1 that for each impact, there are several high frequency (closely spaced) peaks. That is the "ringdown" of the bearing components and assembly after the impact has occurred. Just as the bell rings at its resonant (natural) frequency, the bearing will ring down at its resonant frequency. THAT will typically be found by the FFT process because it is sinusoidal.

However, that ringdown sinusoid is not a continuously occurring frequency - it is transient (it comes and goes). How does the FFT explain the spike suddenly appearing, quickly ringing down and then disappearing until the next spike (impact) occurs ?

What will show up on the spectrum is the 1x rpm peak and the harmonics of the bearing defect frequency that occur closest to the

ringdown frequency of the bearing components. Those peaks will be at relatively high frequencies since they are associated with the ringdown frequency of the bearing components (and that is a high frequency). Figure 2 shows the FFT generated from the signal shown in Figure 1.

Figure 2 - The Resulting FFT From The Signal In Figure 1

Notice the lack of any peak near the impact (defect) frequency (about 3.1 x rpm).

The use of time domain for bearing defects is particularly useful for slow speed equipment. A spectrum will often provide no warning or very late warning of a defect developing.

Please note that this subject is covered far more in-depth in the 'Enveloping Spectra Plots' section.


Impacts Created by Gear TeethWhat is the result of a single broken, cracked or chipped gear tooth ? It is an impact once per shaft revolution (1200 rpm). What does the FFT look like ? Figure 1 shows the time domain:

Figure 1 - Shows Once Per Revolution Impact

Figure 2 shows the FFT generated from the signal seen in Figure 1.

Figure 2 - The Resulting FFT Plot

The spectrum shown goes out to about 22,000 and the number of teeth is 25. The amplitude at 30,000 cpm (GMF - which is not shown on the plot) is increased on slightly under this circumstance. So what is the FFT symptom you can expect with this problem ? The time plot shows a peak amplitude for for the 1x rpm signal of perhaps 0.8 ips (20 mm/s). The FFT amplitude is under 0.5 ips (12 mm/s). There may be a slight increase in GMF.

Just as impacts in a bearing excite the natural frequencies of the bearing structure, there will almost certainly be some excitation of the gear train's natural frequency due to the impacting. That is an important clue and typical of excessive wear or impacting between gears but unfortunately you won't, in all likelihood, know what that natural frequency is. Therefore . . .

The only effective way to detect this problem from its early stages is

with time domain analysis.


RubsWhat does a rub cause on the spectrum ? Well, it is quite unpredictable but can, because of the wave shape, cause extensive harmonics, half-harmonics (0.5, 1.5, 2.5, etc. x rpm) or even sub-harmonics. But what does the time domain look like ?

Figure 1

Once the rotor contacts the side (begins the rub), it is prevented from moving any further in that direction. It will rub until the forces present pull it away from the contacted surface in the other direction. This is another example of a problem where the diagnostic capabilities of the time plot far exceed those of the spectrum. For instance, the length of the flat portion (the rub) relative to the length of the entire cycle will tell you how much of the rotation is rubbing. You should note that this condition would not be apparent if the was mounted horizontally because the rub is strictly in the vertical direction.

This is also known as a TRUNCATED wave shape and a rub is one of the

problems that would generate such a wave shape.


Truncated Wave ShapesSince we've touched upon the truncated wave shape let's consider the wave shape shown in Figure 1. What is happening ? A great deal of movement in the positive going direction (amplitude reaches about 1.0) and not much in the negative going direction (amplitude

reaches about -0.2). Can you think of any conditions that could lead to a signal shape like this ?

Figure 1 - A "Truncated" Signal Shape

In case you aren't quite sure yet, let's sum up what we can see from the wave shape:

The '+' peak amplitude = 1 The '-' peak amplitude = - 0.2

The wave is 'cut off' (truncated) on the bottom.

There is a little bounce or bump at the bottom.

Let's take a look at the FFT generated by the signal in Fig. 1 in case you would like that to help with your analysis:

Figure 2 - The FFT Generated From The Signal Shown In Figure 1

The FFT shows a peak at 1x rpm (about 1800 cpm) and 2x rpm (about 3600 cpm). There is nothing at higher frequencies.

Perhaps the animation on the next page will help.


Truncated Wave ShapesHindsight being 20/20, you can see that the time wave shape was telling you how the bearing is moving. The fact that the bearing is moving a great deal in one direction and not the other is a valuable piece of information on how the bearing is moving if you put it to use in your mind. Figure 1 shows a bearing moving in this manner.

Figure 1 - One Possible Cause Of The Previous Page's Signal Shape

Ok, ok, the animation is a bit exaggerated. An unbalance force (the yellow ball on the rotor you see flashing by) is present. If properly fastened in place, this (centrifugal) force would be sufficient to move the bearing housing a certain amount (far less than what you see). Since, however, the bearing is not properly fastened in place, the force is able to move the bearing a great deal further. The impact of the rotor dropping back onto its base causes a bit of a bounce.

But the wave being shown in Figure 1 is actually very close in shape to that in Figure 1 on the previous page - the sharper edges on the previous signal shape are simply due to a loss of resolution (longer time sample, same number of data bytes). Figure 2 (below) shows the signal from the previous page in much greater detail - only a couple of cycles are being visible (better resolution). The signal shape is virtually identical to the signal shape in the animation.

Figure 2 - Small Segment Of Signal Seen On Previous Page; Approx. 70msecs Versus 1200msecs On Previous Page

One of the key methods used in time domain analysis is to use the wave shape to see (in your mind) how the bearing or structure is

actually moving and using that to think about what might be happening.

What You Need To Do To Be Able

To Analyze Time Domain PlotsIt is extremely important to understand the limitations of the FFT and the unpredictability of the FFT process when several problems are present simultaneously. The time domain plot should be used whenever applicable or in the presence of a stubborn or unusual problem. But there are three things you must do to get comfortable with and good at analyzing time domain plots.

Practice

PRACTICE

PRACTICEWell, that's not entirely true - you also need to understand how to set them up. We can't help you with the practice part but we can help you with the setup.

Setting Up The Parameters For A

Time Domain PlotTo set up a time domain reading can be a bit cumbersome. This is mainly due to the fact that the setup is often done using FFT parameters such as Fmax and lines of resolution. This section will first explain how a time domain is set up and then provide some

easy to use examples. The time domain equivalent to Fmax and lines of resolution are:

Fmax = Period (length of time sample being collected) Lines of Resolution = Bytes (how many pieces of data are

collected to create the sample)

o 512 Bits is equivalent to 200 lines of resolution

o 1024 bits is equivalent to 400 lines of resolution



As you may already know, a time domain plot is just as susceptible to resolution limitations as an FFT is. Figures 1, 2 and 3 are each from the same time domain plot - the latter two are zoomed in on.

Figure 1 Figure 2 Figure 3

The plot shown in Figure 1 - an actual, real-life time domain plot - was collected with 2048 amplitude values (the time domain equivalent of "lines of resolution"). The length of the time sample is 0.114 secs.

Figure 2 shows a portion of the same time domain plot with the sample reduced to 0.04 seconds (by zooming in). This is done in the same manner as one would zoom in a an FFT. It still looks pretty good but just as with a spectrum, zooming in has done nothing to improve the accuracy of the data. Once collected, you can never improve or in any way change the accuracy of any plot - time domain or spectrum. The resolution is dictated by the parameters set up and cannot be altered after the fact.

Figure 3 shows the same plot with the sample reduced to only 0.01 seconds. It is now quite clear that the time domain plot is generated

by compiling a series of amplitude values and connecting them with lines - the same way an FFT is generated. This is JUST AS IMPORTANT and must be stressed just as much as with the spectrum. Zooming in to this level does nothing to improve the resolution and is about as helpful in viewing the big picture as looking at a forest with your face 2 inches from a particular tree would be - in other words, not helpful at all.

So how do we set up a time domain reading using FFT parameters from this information ?


Time Domain PlotThe first thing we need to do is figure out how long (in seconds) our time sample needs to be. How do we do that ? Well, it depends on what we are trying to analyze. Let's take a machine rotating at 3600 rpm (60 Hz). How many shaft rotations do you want to see in your time sample ? If you said 5 - 7 for a normal analysis, go to the head of the class. So we'll shoot for 6 shaft rotations:

6 rotations / 60 rotations per second = 0.10 seconds

We now have our desired time sample - 0.1 seconds (100 msecs). We also have a formula for future reference (for the sake of consistency, we'll call the rotation an "event"):

# of events desired / # of events per second = time sample desired (seconds)

By using events, we can more easily apply the formula to anything from gear mesh to bearing defects - not just shaft revolutions. Shaft revolutions will, however, be the most common 'event'.

At this point, there are two possibilities which will determine how you proceed:

Your analyzer or software requires a time sample length and the number of data bits desired. If this is your option, you're about done. Simply choose 0.10 seconds (or 100 msecs) for the sample length or period and the corresponding data bits for the number of amplitude values on the plot you want (512 for 200 lines, 1024 for 400 lines, 2048 for 800 lines, 4096 for 1600 lines). It is recommended you collect either 2048 or 4096 bits of data.

Your analyzer or software forces you to set up the reading in

FFT parameters. In this case, you have a bit more math to do.

For option 2, choosing the number of lines of resolution we want is straight forward - simply select the number you want. It is recommended that you use 800 lines as the minimum and we will use that in our example. Once you've decided on the desired resolution and you know the time sample you want, use the following formula to find the Fmax you must select:

Fmax = # Lines / Time Sample Fmax [Hertz] = 800 / 0.1 seconds = 8000 Hz

Fmax [CPM] = 8,000 Hz x 60 = 480,000 cpm

If you want 1600 lines with the same length time sample, you would use:

Fmax = 1600 / 0.1 seconds = 16,000 Hz x 60 = 960,000 cpm

If you want 400 lines with the same length time sample, you would use:

Fmax = 400 / 0.1 = 4,000 Hz x 60 = 240,000 cpm

Note that you can generate the Fmax in cpm directly by using the # lines x 60 and dividing it by the desired time sample:

800 lines x 60 / 0.1 seconds = 48,000 / 0.1 = 480,000 cpm

Also note that the shorter the time sample desired or greater the resolution, the higher the Fmax selected.


Time Domain PlotLet's run another example where we want to capture 10 bearing defect impacts on a shaft running 1200 rpm. Well, first let's convert to Hz: 1200 cpm = 20 Hz. Next, we need to know the defect frequency. For the example, we will use the very common outer race defect frequency found just over 3x rpm. That means we will need approximately 3 shaft revolutions to capture 10 impacts. 20 shaft revolutions per second and we want 3 - that's 150 msecs (0.15 secs). We'll stick with our 800 lines and go straight to the cpm answer:

Fmax = 48,000 / 0.15 = 320,000 cpm

How about if we wanted to see 6 revolutions of a shaft turning at 60 rpm (1 Hz). Well, the fact that you want to see 6 revolutions on a

shaft going 60 rpm should tell you that you want 1/10th of a minute - 6 seconds. Again, we'll stick with 800 lines.

Fmax = 48,000 / 6 = 8,000 cpm

The table shown below shows some time domain setup parameters. The table values assume 800 lines of resolution (2048 data bits).

By using 800 lines and the Fmax shown, you will obtain a time sample that contains 5 - 10 revolutions of the shaft providing the machine is in the RPM range shown. In other words, if you have a machine running 1500 rpm and you want about 7 revolutions of the shaft on your time domain plot, find the 'RPM Range' below that contains 1500 (1314 - 1838) and use the Fmax shown (180,000 cpm or 3kHz) and 800 lines.

Fmax RPM Range

1,500 1 - 20

3,000 20 - 39

6,000 40 - 79

12,000 80 - 131

18,000 132 - 184

24,000 185 - 236

30,000 237 - 289

36,000 290 - 368

48,000 369 - 473

60,000 474 - 656

90,000 657 - 919

120,000 920 - 1313

180,000 1314 - 1838

240,000 1839 - 2363

300,000 2363 - 2888

360,000 2888 - 3413

420,000 3413 - 3938

480,000 3938 - 4725

600,000 4725 - 5775

720,000 5775 - 7875

1,080,000 5776 - 11288

1,500,000 11288 - 16000

Note that the Fmax's shown in the table above are based on 800 lines.

If you want to use 1600 lines (4096 bits), double the Fmaxs used for each speed range.

If you want to use 400 lines (1024 bits), cut in half the Fmaxs used for each speed range.

If you are looking for an event occurring more than once per revolution (e.g. bearing defects), use the next highest frequency range listed.

If you are looking for a "beat" frequency, use the Fmax listed next to the beat frequency rate (a very low Fmax) - not the shaft rpm.

Time Domain Plots:

SummaryTime domain analysis is a powerful but intimidating tool. Hopefully, this section of the manual has helped you understand some of the secrets of the time domain as well as some of the secrets of the FFT process. Again, there are specific areas where we recommend using time domain analysis without exception:

Slow Speed Equipment (< 300 rpm)

Sleeve Bearings (particularly if readings reflect true shaft movement)

Gear Applications

However, there are many people who would argue that time domain is a valuable tool on all applications and we cannot argue with them - the wave shape can provide information that you will not get from an FFT. If you are comfortable with it and have the time to collect it, by all means - it is another way to look at how your machines are behaving.

We also cannot argue with the people who claim: Time Domain is complicated Time Domain is difficult to interpret

Often you can't make head nor tail of a time domain plot

Each of these is also true. So . . . . the sooner you start using it and getting comfortable with it, the sooner you'll become proficient at using this powerful tool. Remember the three things you need:

PRACTICE PRACTICE

PRACTICE

Plots:

The Enveloping Spectra What Is An "Enveloping" Spectra Plot ?

How Are They Processed Differently ?

Bearing Defect Multipliers

How Does "Impact Energy" Generated ?

How Does Impact Energy Affect The FFT ?

What Information Does The Enveloping Spectra Provide ?

What Are Some "Impact Sources" Besides Bearing Defects ?

Words Of Warning

What Is An "Enveloping Spectra" Plot ?

http://www.vibrationschool.com/mans/Plots/EnvPlots07.htm





http://www.vibrationschool.com/mans/Plots/envplots02a.htm



Y-Axis Units:

Amplitude


The term "enveloping" spectra plot is not always a technically correct description of the signal processing involved but will be the term we use for simplicity sake.

An enveloping spectra is the same in appearance (amplitude vs. frequency) as a conventional spectrum - it simply displays different information.

An enveloping spectra is not sensitive to sinusoidal motion - unlike the FFT plot that determines what simple sinusoids combined to generate a complex signal in displacement, velocity or acclereration units.

An enveloping spectra is sensitive to impact related events.

The ability to quantify both the frequency of impacts and their intensity is very helpful and important to the vibration analyst. Although there are machines that generate impact energy normally (i.e. reciprocating equipment), most machines don't. Impacts are destructive forces and normally indicate some type of problem is developing. Most typically, this plot is used to detect bearing defects.

How Are Enveloping Spectra Plots Processed ?

What is the enveloping signal and how is it processed ? The unit of amplitude measurement is acceleration but the

signal is processed differently than a conventional acceleration signal is.

The names for the amplitude unit are manufacturer specific - they each have their own name and/or acronym for the unit. A few of the manufacturers are:

o CSI (Emerson) uses Peakvue

o Entek (Rockwell Automation) uses gSE (spike energy - the original IRD acronym)

o SKF uses HFD (high frequency domain) and ESP (envelope signal processing - originally a DI unit)

Filters are used to help process the signal and focus on any impacts that may be occurring.

The filters come in two classes:

o Envelope filter - this type of filter sets a frequency 'envelope' that includes a high frequency (Fmax) and a low frequency (Fmin). Any vibration occurring outside that range is filtered out.

o Hi-Pass filter - this type of filter eliminates the Fmax but still sets an Fmin filter below which all vibration influences are filtered out.

o Each manufacturer sets up its own signal processing and filters. Therefore, although they each provide similar information, they are not directly comparable in the amplitude realm.

The signal processing focuses on the transient, impact type events (spikes on the time domain signal) that the FFT process "misses" (it would be more accurate to say "makes more difficult to find") due to the way it processes the time signal.

If there is a consistent period between impacts (i.e. the impacts are occurring at a regular interval), that period will be converted into the desired frequency units (Hz or cpm).

The intensity of the impacts will also be assessed. This is related to the size of the impact spike on the signal versus any

background noise occurring.

The results are displayed on a spectrum with amplitude peaks at the frequency(s) they are occurring at.

The enveloping spectrum provides us with valuable information unavailable on displacement, velocity and acceleration spectra. It provides another useful weapon for the analyst.

Enveloping Spectra Plots:

Bearing Defect MultipliersTo understand the envelope plot's importance in diagnosing bearing defects, you need to understand how bearing defect frequencies work. To understand bearing frequencies, we begin with bearing "multipliers". A bearing defect multipliers is based on the geometry of the bearing. The important geometric characteristics include the pitch diameter, the number of rolling elements, the rolling element diameter and, for ball bearings, the contact angle. There is a multiplier for each of the four bearing components you see here. The purpose of each multipler is to tell you how many impacts (spikes on the time domain plot) will occur for each shaft rotation for a defect on any of the four different bearing components. These components are:

Cage or Train (black) Balls or Rollers (dark gray)

Outer Race (light gray outside)

Inner Race (light gray inside)

Figure 1 - A Typical Ball Bearing

For example, consider the defect shown the outer race of a bearing in Figure 2. For each revolution of the shaft (inner race), a certain number of balls or rollers will pass that spot (the defect) on the outer race and strike (impact) the defect. The number of impacts per shaft revolution is the "outer race defect multiplier" for that bearing. It is important to note that a bearing defect multiplier is never a exact multiple of running speed (it is never synchronous). Rolling element bearings always generate non-synchronous vibration frequency.

Figure 2 - Outer Race Defect Being Impacted As Each Ball Passes


Bearing Defect MultipliersSince these multipliers are based on the geometry of each individual bearing, you can obtain specific numbers for any bearing from numerous sources (vendors, manufacturers, etc.). To turn a multiplier into a frequency requires applying the multiplier to the speed of the machine in question. If your multiplier is 3.05 and the machine runs at 1000 rpm, the defect frequency is 3050 cpm. That means there are 3050 impacts occurring each minute due to the presence of that defect.

What are the ranges of these bearing defect multipliers ?

FTF [Fund. Train Freq.] 0.30 - 0.45 x RPM

BSF [Ball Spin Freq.] 1.5 - 4.5 x RPM

2xBSF [2x Ball Spin Freq] 3 - 9 x RPM

BPFO [Ball Pass Frequency Outer] 2.5 - 9 x RPM

BPFI [Ball Pass Frequency Inner] 4 - 13 x RPM

These are typical ranges you will find on common bearings. Some bearings may have considerably higher defect frequencies - the determining factor is primarily the number of rolling elements (which is related to the load rating of the bearing). The higher the load rating

of the bearing, the more rolling elements there are and the higher these multipliers can be. The inner race multiplier, for instance, can be well over 20 but that is unusual.

There are some important facts about these defect multipliers that the analyst should always keep in mind:

They are based on proper installation (i.e. proper fit) and proper lubrication. Certain conditions can alter these multipliers and in some cases actually increase them.

They can be very close to exact harmonics of running speed - 3.05 x RPM, for instance. That means if the machine runs at 1780 rpm, the defect frequency is 5429 while 3x rpm is 5360 cpm - only 69 cpm difference. These could be easily confused and misdiagnosed.

It is extremely important to understand that no matter how close they are to exact running speed harmonics, bearing defect frequencies CAN NEVER BE exact running speed harmonics. They are always non-synchronous vibration sources - a fact vital to their correct diagnosis.


How Does "Impact Energy" Occur ?Let's examine how impact energy due to a typical bearing defect occurs:

Figure 1 Figure 2

In Figure 1, as each rolling element passes the defect, an impact occurs. As we began discussing in the Time Domain section, if you strike a bell, the bell will vibrate at its natural frequency. That is true of any structure. The time it vibrates will be determined by the force of the impact, the mass, the damping characteristics of the object and other variables. This is called "free" vibration (as opposed to the "forced" vibration caused by energizing a machine and keeping it

rotating and, consequently, vibrating). The bearing impact causes the bearing assembly to "ring" briefly until the free vibration due to the impact dampens out. There are two frequencies occurring here that are specifically related to the bearing defect:1) The bearing assembly natural, or "resonant", frequency (based on the period of the bearing assembly resonance).

Since the impact causes the bearing structure to ring, there is a sinusoid generated briefly related to the bearing assembly's resonant frequency.

Because there is a sinusoid generated, this frequency is detected by the FFT process and amplitude peaks will be generated initially on the acceleration spectra (since it is more sensitive to high frequency vibration) and eventually the velocity spectra (displacement units are useless at those frequencies).

The difficulty lies in the fact that the FFT will have to mathematically account for the fact that the spike suddenly appears, briefly rings down and then is gone until the next impact occurs. It is not a constant sinusoid, it is transient.

2) The "impact" frequency (based on the period between impacts). The impact frequency itself has no sinusoidal motion associated

with it. In other words, there is no sine wave that connects the start of one impact to the start of the next impact - they are individual 'events' that occur.

These impacts (spikes) are specifically what the enveloping signal processing looks for and measures.

It will calculate the intensity of the impact (the size of the spike) and the frequency (based on the period between impacts) while filtering out any sinusoidal motion it finds.


How Does Impact Energy Affect The FFT ?Let's review how the FFT process works by examining the following computer generated signal:

Figure 1 - Shows Approximately 9 Shaft Rotations (470 msecs)

The conventional FFT process focuses on sinusoids - namely, mathematically calculating what series of simple sinusoids (signals) were combined to generate the signal we see here. What can we see from the above plot ?

A low frequency sinusoid that shows about 9 cycles across Fig. 1. That is the 1x rpm signal.

Some frequency modulation of that signal (compare the positive going side of the wave to the negative going side of the wave).

A large number of spikes, or impacts, that occur across the plot and appear to vary somewhat in intensity (the size of the spike).

Figure 1 is a typical example of a plot that an analyst might collect - 9 rotations of a shaft. But although the 1x sinusoid is fairly clear, the impacts are not. Let's zoom in a bit.

Figure 2 - Shows Approximately 2 Shaft Rotations (115 msecs)

Cutting the displayed sample to just over 115 msecs (about 2 shaft rotations), we can now clearly see:

The frequency modulation of the 1x rpm signal.

The ringdown frequency of the impacts.

If we simply count the number of impacts in one cycle (from 30 - 80 msecs, for instance), we would find about 4-5 per shaft revolution (or "x RPM").

It should be clear to us as analysts that this is an impact occurring and investigation of the period involved (time between impacts) should lead us to a diagnosis. But more often than not, the analyst will not be using the time domain - they will be using FFT analysis. What does an FFT performed on this signal generate ?

Figure 3 - FFT Generated From Signal In Figure 1

1x, 2x and 3x rpm peaks. These are probably due to the frequency modulation present.

A series of peaks at high frequencies that are spaced about 5400 cpm apart.

The absence of a peak at or near 5x rpm - the impact frequency. This is because there is no sinusoidal motion associated with the frequency of the impacts - only the ringdown frequency that results from the impacts.

But where do the peaks between 31,000 and 65,000 cpm come from ? How does the FFT process come to "see" them ?


How Does Impact Energy Affect The FFT ?The answer lies in the mathematics involved in the FFT process. Let's look again at a time domain plot that is representative of what a bearing defect will look like:

Figure 1 - A Time Domain Plot With Bearing Related Impacts Occurring

The time domain in Figure 1 is clearly symptomatic of a bearing defect - impacts at a frequency not related to rpm (the larger sine wave). The time sample is 333 msecs.But let's look at the FFT. What does the preceeding signal generate when subjected to the FFT process ?

Figure 2 - The FFT Resulting From The Signal Shown In Figure 1

The FFT in Figure 2 shows series of peaks out in the 50k - 90k range. These peaks are the "symptom" of a bearing defect developing. But why ? Why does the FFT generate vibration at those frequencies ? The answer is in the math. There is only one series of simple sinusoids that would result in the shape of the signal shown above. Want more proof ?Figure 3 (below) is a 30 msec slice of Figure 1 - a close-up, so to speak:

Figure 3

Figure 4 shows the entire series of simple sinusoids that were programmed in to create the exact signal shape you see in Figures 1 and 3.

Figure 4

When the signal shown in Figure 1 is put through the FFT process, that process is asked "what simple sinusoids create that exact periodic signal".

The process "sees" the series of sine waves shown in Figure 4 as the mathematical solution to the question.

Note the varying amplitude values of the sinusoids in Figure 4.

Note the three instants (65-66 msecs, 76-77 msecs and 87-88 msecs) all of the high frequency signals are in phase (adding together).

Note the high number of out-of-phase sinusoids at 71 msecs and 82 msecs.

There is only 1 combination of simple sinusoids that will combine to

mathematically create any periodic signal. Alter the signal in any way and the series of sinewaves creating that signal will change.This analysis does not, of course, include the larger '1x rpm' and '2x rpm' sine waves you can see. Those are 'seen' by the FFT due to the frequency modulation on the 1x rpm signal (Fig 1).Since this is such a complex subject, let's go through the details in a different way.


How Does Impact Energy Affect The FFT ?The answer has to do with the transient nature of the impacts and the principles involved in the FFT process. Looking at the question from the FFT's perspective, we can re-phrase it as:

What would cause a sinusoid to appear and then disappear at regular intervals ?

Since the FFT is based on the principle that any periodic signal can be broken down into a series of simple sinusoids, there must be some combination of sinusoids that would produce a sudden spike followed by a subsequent "ringdown" (high) frequency followd by nothing until the next spike occurs.

The answer is actually fairly simple. When a series of sinusoids separated by a common frequency (5400 in this case) are combined to generate a periodic signal, the signal will appear as a transient sinusoid (a spike, or impact, followed by a ringdown followed by nothing until another spike suddenly appears).

The following list of simple sinusoids were fed into a signal generating software program. Note that although the amplitudes are different, the frequencies are all separated by 5,400 cpm. Although there were other variables inputted to create a more realistic looking signal, this list is, in fact, the exact series of sinusoids that were combined to create the transient (impact) sinusoid you saw on the previous page.

0.05 @ 31,800 cpm 0.16 @ 37,200 cpm

0.28 @ 42,600 cpm

0.30 @ 48,000 cpm

0.18 @ 53,400 cpm

0.10 @ 58,800 cpm

0.06 @ 64,200 cpm

What would the signal look like if we only used the above 7 signals (plus some background noise and amplitude modulations) ? See for yourself:

Figure 1

The result is only impacts and background noise. What is happening is that this combination of signals will all

come into phase with one another at about the same time, rings down to the noise level in about 4 msecs as the signals go out-of-phase with one another and remains at background noise level for another 6-7 msecs.

The result is a large, brief amplitude increase (a spike, or impact) every 11 msecs or so. That equals an impact frequency of 5,400 cpm (the difference between the frequencies).

Of course, the FFT does not have the benefit of knowing which sinusoids went into generating this signal. In fact, that is exactly it's job - to calculate those simple sinusoids from the complex signal (including other influences like 1x rpm, other mechanical vibrations, amp and freq modulation, etc.). So the process is:

The above signal is fed into the FFT process. That process then calculates what simple sinusoids combined to generate the signal.

The FFT can deduce that there is a combination of sines and cosines (signals) that will result in the above complex signal - the combination listed.

Adding or removing any signals that are a multiple of 5,400 will alter the appearance by making the impact either sharper (more signals) or less well defined (less signals).

In fact, there is only one solution to each signal - only one set of simple sinusoids.

So when the FFT process is presented with the above signal, what does the spectrum look like ?

0.05 @ 31,800 cpm

0.16 @ 37,200 cpm

0.28 @ 42,600 cpm

0.30 @ 48,000 cpm

0.18 @ 53,400 cpm

0.10 @ 58,800 cpm

0.06 @ 64,200

cpm

Figure 2 - FFT Generated From Signal Shown In Figure 1

Above: The

Signals Used To Generate The FFT Shown Here

Note that there is no indication whatsoever of the impact frequency (about 5400 cpm) on the spectrum.

Why is there no peak at the impact frequency ? Because there is no sinusoid associated with it !

There are several problems complicating the analysis of a velocity or acceleration FFT such as the one shown in Figure 2.

You must notice the existence of the peaks (separated by the defect frequency). This may seem silly but keep in mind that:

o You may be analyzing dozens or hundreds of machines - thousands of bearings.

o The high frequency peaks you see in Figure 2 will initially be low amplitude - particularly if you are using a velocity spectrum (which most people use).

The analyst relies on these peaks being harmonics of the bearing defect frequency. You must be able establish that pattern.

Before you even try to determine the defect frequency (which often requires time and effort), you must somehow notice or sense that there is a harmonic or sideband pattern that should be investigated.

Eventually, You must know the defect frequency (the impact frequency). The peaks you see in the 33k-63k range are harmonics of the defect frequency (6x - 12x defect frequency). That is how you will diagnose the problem - by identifying the source of those peaks through the use of harmonics. Without knowledge of the defect frequency, it can be far more difficult.

So now, let's return to the subject at hand. What will the enveloping spectrum look like and how will it help with the analysis ?

Enveloping Spectra Plots

What Information Do They Provide ?Figure 1 shows an actual enveloping spectrum collected on a bearing with a defect:

Figure 1 - Enveloping Spectrum

The bearing defect frequency identified is just over 3x RPM. Notice that there are no significant peaks at 1x, 2x or 3x rpm on Figure 1 (there were on the velocity spectrum). There are, however, extremely significant peaks at 1x, 2x and 3x the impact frequency - in this case a bearing defect frequency (there are other impact sources). The enveloping signal provides the following:

The impact frequency:

This piece of information can be used on the velocity or acceleration spectrum to help determine the condition of the bearing (how bad is it ?).

After identifying the defect frequency from Figure 1, inspect your velocity or acceleration plot and place your cursor on that same impact frequency and turn on your harmonics.

If you are able to relate, through the harmonics, the high frequency peaks to this impact frequency, you have confirmed the presence of a bearing defect.

You can then make an assessment of condition based on the amplitudes present, noise level, etc.

The intensity of the impacts:

This piece of information can be used to help determine how quickly a bearing can be expected to deteriorate since the impacts are so destructive.

You can compare this to hitting a small pothole in your car or hitting a huge, sharp edged pothole - the first is annoying, the second can destroy your wheel.

The assessment can be made by displaying the amplitudes on a 'dB' scale (see Figure 2) and comparing the peak amplitude to the surrounding 'carpet' level (which is affected by lubrication and load, among other things).

Figure 2 - Enveloping Spectrum From Figure 1 on dB Scale

In Fig. 2 (which is the same plot as Figure 1 except the amplitudes were on a linear scale in Fig. 1 and are on a dB scale in Fig. 2), the amplitude on the peak is about 125 dB.

The surrounding carpet level, which is an estimate of the surrounding amplitudes, is in the 100 - 102 dB range. The following guidelines can be used:

o Difference of 12-18 dB is a significant level of impacting and should be watched closely.

o Difference of > 18 dB is a severe level - intense impact

energy, very destructive.


Impact SourcesWhat are the common impact sources that the enveloping signal and spectrum are helpful in detecting and what are the frequencies associated with each. Each of the subjects listed below is discussed more in-depth in the 'Troubleshooting Charts' section.

Bearing Defects - Frequency of peaks will be the specific bearing defect (impact) frequency.

Looseness - Typically occurring between the shaft and bearing; the housing and bearing; and/or the internal bearing clearances. The observed frequency on the enveloping spectrum will be harmonics of running speed (1x, 2x, 3x, etc. x RPM).

Electrical Looseness (ac motors) - Looseness in windings, end turns, loose iron, loose connections, etc. Frequency will be 2x AC line frequency and harmonics. This also applies to Variable Frequency Drives (VFDs) but the ac frequency must be determined for each case.

Lubrication - Lack of lubrication will drive up metal to metal contact (high frequency noise). No specific frequencies are triggered but a general lifting of floor, or 'carpet' level, will occur.

Reciprocating Equipment - Analyst must determine the specifics of the machine to determine what frequencies to expect. Running speed harmonics are common with even numbered harmonics of even higher amplitude (there are a lot of events at 2x rpm in typical recips), number of pistons x rpm in some hydraulic pumps. Impacts are normal in equipment such as this and the analyst should be looking for change from the norm.

Gears - Backlash, other impact sources. Frequencies typically will be related to the number of teeth.

Note that each of these 'problems' generates its own, specific frequency(s). Each of these subjects is covered more extensively in the 'Troubleshooting Charts' section but there is one common thread to using the enveloping spectrum (a word of warning, so to speak):


Words of Warning The enveloping spectrum is extremely sensitive. It will pick up

impact energy that is not necessarily a problem or is a very early stage problem.

For instance, it can detect bearing defects before they have migrated to the surface of the bearing. Pulling the bearing at that point will not reveal a defect and may cost you something more valuable than money - credibility.

Enveloping spectra should be used in conjunction with other analysis tools (velocity and acceleration spectra, thermography, time domain, your experience, etc.) before performing any corrective actions. It is a powerful tool but must be used with care.

Like other aspects of vibration analysis, experience will help greatly as it is acquired.

Spectrum InterpretationThe following pages are designed to provide typical examples of the vibration spectrums that will result from different problems a machine might experience. They are probability based and field testing should always be performed regardless of how "sure" you are of the diagnosis. Remember:

EVERY diagnosis made from an FFT interpretation (i.e. sitting, staring at a computer screen of data) can be characterized as:

An ASSUMPTION based on an ESTIMATE

Click on the plot below that best approximates what you are seeing. You can also browse

through one page at a time by clicking on the <Next> button at the top or bottom of each page.

Unbalance Misalignment Cocked Bearings and Shafts Bent @ Bearing

Structural Looseness Bearing Looseness Housing Distortion: Soft Foot, Piping

Stress, etc.

Structural Resonance Critical Speeds

Belt Problems: Wear, Resonance, etc.

Belt Problems: Pulley Alignment

Belt Problems: Eccentric Pulley / Bent

Shaft

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Sleeve Bearings (Looseness/Rubs)

Oil Whirl

Rolling Element Bearings

Hydraulic / Aerodynamic

Pump Cavitation / Flow Turbulence

AC Motor Problems: Broken / Cracked Rotor

Bars

AC Motor Problems: Uneven Air Gap

AC Motor Problems: Loose Rotor Bars /

Windings

DC Motor Problems: Drive Problems

DC Motor Problems: Speed Fluctuations
































Gear Problems: Misalignment

Gear Problems: Wear, Eccentricity,

Backlash

UnbalanceUnbalance - Usually the simplest problem to diagnose (and one of the most common). Unbalance is a centrifugal force. Consider the following about a 3 foot (0.91 meter) diameter fan rotating at 2000 rpm:

Circumference = 3 x 3.14 = 9.42 feet (2.87m). 2000 rpm = 120,000 rev/hour (rph)

120,000 rph x 9.42 ft/rev = 1,130,400 ft/hour (344,546 m/hour)

1,130,400 ft/hr / 5280 ft/mile = 214.1 mph OR 344.6 km/hr

An unbalance mass (whatever that mass is) at the rim of the fan is travelling close to the top speed of an Indy race car. In addition to that, remember that:

Force = Mass x Velocity squared

Single Plane Unbalance

Figure 1 - Typical Radial FFT Generated By Unbalance Figure 2 - Single Plane Unbalance








In the absence of other problems, unbalance causes a pure sinusoid (one of the only problems that does not distort the signal shape in some manner) and therefore generates a peak at 1x rpm.Single-Plane Unbalance Symptoms:

Radial vibration @ 1x rpm. Phase around bearing shifts with transducer shift - 90°

transducer shift causes 90° phase shift.

Little or no phase shift across or "between" bearings [bearings vibrating "in-phase"]

Two-Plane Unbalance

Figure 1 - Typical Radial FFT Generated By Unbalance Figure 2 - Two-Plane Unbalance

Two-Plane Unbalance Symptoms: Radial vibration @ 1x rpm. Phase around bearing shifts with transducer shift - 90°

transducer shift causes 90° phase shift.

Significant phase shift (> 60°) across or "between" bearings [bearings vibrating "out-of-phase"]

Overhung Rotor Unbalance

Figure 1 - Typical Axial FFT Generated By Unbalance Figure 2 - Overhung Rotor Unbalance

Figure 1 - Typical Radial FFT Generated By Unbalance

Overhung Rotor Unbalance Symptoms: Radial vibration @ 1x rpm. Axial vibration @ 1x rpm.

Phase around bearing shifts with transducer shift - 90° transducer shift causes 90° phase shift.

Axial phase readings usually in-phase.

Radial phase readings may be out-of-phase.

Balancing may require use of axial phase readings.

Direct Drive Misalignment

Figure 1 - Perfect Alignment

Figure 2 - Pure Angular Misalignment

Figure 3 - Pure Offset Misalignment

Misalignment - The most common vibration problem. Unlike unbalance, does not have a single vibration symptom. As a result, it should always be considered as a possibility.

Definition of Perfect alignment - Shaft centerlines are parallel and intersect.

Types of misalignment: Angular - Shaft centerlines intersect but are not parallel Offset - Shaft centerlines are parallel but do not intersect.

It is extremely unlikely that you will encounter a case of either pure angular or pure offset misalignment - it will always be a combination. That results in the wide variety of vibration symptoms.

Angular Misalignment

Figure 1 - Typical FFT Generated By Angular Misalignment

Definition: Shaft Centerlines Intersect But Are Not Parallel

Figure 2 - Shaft Centerlines Intersect @ The Coupling. Note The

Absence Of Coupling Movement And The High Radial & Axial Bearing

Movement.

Angular Misalignment Symptoms: High axial vibration @ 1x rpm, possible

harmonics at 2x & 3x. 2x rpm axial component may be as

high or even higher than 1x component.

Radial vibration, probably lower amplitude than the axial, at 1x, 2x and 3x.

Radial vibration will depend on where the shaft centerlines intersect the assembly centerline.

Axial phase across coupling shifts significantly (> 60°).

Figure 3 - Shaft Centerlines Intersect @ The Bearings.

Note The High Radial Coupling Movement, The Low Radial & The High

Axial Bearing Movement.

Offset Misalignment

Figure 1 - Typical FFT Generated By Offset Misalignment

Definition: Shaft Centerlines Are Parallel But Do Not Intersect

Figure 2 - Shaft Centerlines Do Not Intersect. Note The High Radial & Axial Bearing

Movement.

Offset Misalignment Symptoms: High radiual vibration @ 1x rpm,

harmonics at 2x & 3x. 2x rpm axial component may be as

high or even higher than 1x component.

Axial vibration, probably lower amplitude than the axial, at 1x, 2x and 3x.

Radial phase across coupling shifts significantly (> 60°).

Axial phase across coupling shifts significantly (> 60°).

Figure 3 - Shaft Centerlines Do Not Intersect. Note The Even Higher Radial & Axial

Bearing Movement.

Cocked Bearing / Shaft Bent Through BearingCocked Bearing / Shaft Bent Through Bearing - Creates similar or even identical vibration symptoms (with the exception of phase) to misalignment - primarily angular misalignment (axial vibration). Must be diagnosed with axial phase analysis or inspected for.

Cocked Bearing

Figure 1 - Typical FFT Generated By Cocked Bearing

Figure 2 - Cocked Bearing

Cocked Bearing Symptoms: Vibration symptoms very similar to direct

drive angular misalignment. High axial vibration @ 1x rpm, harmonics

at 2x & 3x.

2x rpm radial component often as high or higher than 1x component.

Axial phase shift around the face of the bearing equal to change in transducer location.

8:00 Transducer

11:00 Transducer

Note The Phase Shift Occurring When

The Transducer Is Shifted. This Is Due

To The Twisting Action Of The Bearing

Bent Shaft @ Bearing

Figure 1 - Typical FFT Generated By Shaft Bent Through The Bearing

Figure 2 - Note The Axial,

Twisting Action Of The Bearing

Shaft Bent Through Bearing Symptoms: Vibration symptoms very similar to direct drive

angular misalignment. High axial vibration @ 1x & 2x rpm.

2x rpm radial component often as high or higher than 1x component.

Axial phase shift around the face of the bearing equal to change in transducer location (twisting action).

Radial phase shifts significantly on either side of bearing (> 60°). This can best be seen in Figure 2 below. When the shaft just to the right of the bearing is moving up, the shaft just to the left of the bearing is moving down and vice versa. This measurement, of course, requires a direct shaft reading with an attachment such as a shaft stick.

Figure 3 - Note The Axial,

Twisting Action Of The Bearing

LoosenessLooseness - Not a vibration source but an amplifier. That means that when a component is loose, whatever forces are present will be able to move the affected components much more easily. If there are little or no forces present, however, vibration may only increase a very small amount. To understand this, imagine a perfect machine - no mechnical imperfections to cause any vibration. Now loosen the bolts holding down the feet and . . . nothing happens because there are no forces attempting to lift it off of its base.Looseness can occur at a number of locations that affect the

vibration measurements. They are: Bearing / Shaft (Bearing Looseness) Bearing / Housing (Bearing Looseness)

Internal bearing clearances (Bearing Looseness)

Adjacent, fastened surfaces (Structural)

Areas of the base (Structural)

Each, however, gives different likely symptoms.

Structural Looseness

Figure 1 - Typical Radial FFT Generated By Mechanical (Structural) Looseness

Figure 2 - Looseness Allows Movement In

The Direction Of The Looseness

Structural Looseness Symptoms: High radial vibration @ 1x, 2x rpm

(often higher at 2x) and possibly 3x (lower).

Amplitude may be extremely high in direction of looseness only (vertical or horizontal) - far higher than in the perpendicular radial direction.

Found easily with background vibration checks of adjacent surfaces.

Slow Motion Study can be a very useful tool in diagnosing this condition.

Animation simulates a loose motor foot moving vertically under a slow motion study.

Note how vertical amplitudes in this case are far higher than horizontal amplitudes would be.

Foot lifts and drops once per shaft revolution.

2x rpm component may appear due to the bounce (shape of the time domain plot - see time domain section for more

information on that).

Additional harmonics can be created due to the shape of the time domain signal. As it changes from a sinusoid towards a square wave, more harmonics appear.

Bearing Looseness

Figure 1 - Typical Radial FFT Generated By Bearing Looseness

Figure 2 - Bearing

Looseness Generates More Of A "Square" Wave Than A

Sinusoid. That Shape

Creates Harmonics

Structural Looseness Symptoms: High radial vibration harmonics of 1x.

Harmonics can stretch all the way across the spectrum in cases of severe looseness and can even generate half-harmonics in extreme cases (1.5, 2.5, 3.5, etc.).

Housing Distortion (Soft Foot, Pipe Stress, etc.)

Figure 1 - Typical Axial FFT Generated By Housing Distortion

Figure 3 - Soft Foot Or Other Housing Distortion Such As

Pipe Stress Can Cause Bearings Within A Component To Misalign And Can Throw Off

Normal Clearances.

Figure 2 - Typical Radial FFT Generated By Housing Distortion

Housing Distortion Symptoms: High axial vibration @ 1x & possibly 2x rpm. Axial phase analysis may show phase shift across bearings within

component.

Axial phase analysis may show twisting bearing (like cocked bearing).

2x Line frequency on motors due to air gap variation, especially radially.

Pumps / fans may develop clearance problems (vane or blade pass).

High axial vibration on non-direct drive components (belt drives, integral fans, etc.).

Pipe stress can develop similar symptoms on pumps, compressors & fans/blowers.

ResonanceResonance is simply the natural frequency of a component or combination of components (assembly). All structures have a resonant frequency. If you impact the structure with enough force to make it move, it will vibrate briefly at its natural frequency. A structure will have a resonant frequency in each of its 3 directional planes (x, y and z, or as we call them, horizontal, vertical and axial). Resonance serves to amplify the vibration due to whatever vibration force is present at (or near) that resonant frequency. It is important to note that resonance does not cause vibration - it amplifies it. Resonance problems occur in two primary forms. They are:Critical speeds - occurs when a component rotates at its own natural frequency.

A "critical speed" is simply when the rotational speed (rpm) coincides with the natural frequency of the rotor (cpm).

The tiniest amount of residual unbalance (something that is always present) is enough to cause huge amounts of vibration when rotating at a critical.

Rotors that are sped up or slowed down slowly are susceptible to this (i.e. turbines). In these cases, the critical speed is usually well known.

The most common problem related to unknown critical speeds is probably belts. Belts rotating at their resonant frequency (or having a nearby source of excitation of that resonant frequency) can vibrate excessively and cause other problems. For example, if the natural frequency of the belts coincides with the rpm of the fan, the belts will vibrate at their natural frequency.

2nd and 3rd criticals also may occur if the rotor speed gets high enough.

Structural resonances - This is far more common than a critical speed problem. It becomes a problem when some forcing frequency comes close (+/- 10%) to the resonant (natural) frequency of a structure.

The structure can be the machine housing itself or some nearby structure such as a hand rail or I-beam.

A common example of this is a vertical pump. Due to the lack of a support at the top of the unit, these typically have very low

resonant frequencies (~ 300 cpm). While running, this is not a problem but during start-up or coast-down, the unit experiences a "shudder" as it passes through the structural resonance (this is not a critical speed - it is a structural resonant frequency).

The structure itself will vibrate excessively - do not confuse with a critical speed.

The "shape" of the structure's vibration is an important clue and is known as a "mode shape".

Testing for the structure's natural frequency is crucial (required) to confirming a resonance problem.

Resonance, once diagnosed, can be simple to correct. It can also be extremely complex and difficult to correct. The trick is in the diagnosis. But how do you diagnose it ? One method for determining a critical speed is a "Coast Down/Start Up Plot". This plot consists of the 1x vibration amplitude being collected simultaneously with a 1x rpm phase reading as the machine coasts to a stop or goes from stopped to full running speed. This test requires a 1x rpm reference (from a photoeye or some other speed tracking signal) in order to track the amplitude and phase at that frequency. Two things are observed as the rotor passes through a critical:

The 1x rpm amplitude will increase until the rotor reaches it's critical and then decrease to the normal level as the speed continues to change.

Phase will shift 180° as the rotor passes through the critical. This is due to the rotor changing from a rigid rotor (while operating below it's critical) to a flexible rotor (while operating above it's critical). It practical terms, on a rigid rotor, the heavy spot pulls the rotor around as it rotates. On a flexible rotor, the heavy spot pushes the rotor around as it rotates.

Structural resonances can be first suspected by several characteristics:

Disproportionately high amplitude at a single frequency (the resonant frequency) in the direction in which the resonant frequency is being excited.

A "mode shape" analysis shows the structure vibrating in a way that models resonance. Those models are covered on the next

page. Neither of those characteristics confirms resonance as a problem. A test must be performed that actually determines the natural frequency of the structure in question - a "bump test". Although there are high-tech methods available for this test (and some work very well), this test can be as simple as bumping the structure (causing it to vibrate) while it is not running and measuring the response (i.e. the frequency it vibrates at). A simple method for doing this involves collecting a 2 second sample (time domain plot) while bumping the structure, measuring the period of one cycle and converting it to a frequency. The time sample may have to be adjusted depending on the resonant frequency being measured (longer sample for very low resonant frequencies, shorter sample for high frequencies).If the measured response of the structure (i.e. it's resonant frequency) is within about 10% of the forcing frequency (i.e. the rpm of the machine although it can be at any frequency), resonance should be considered a problem. The closer the two frequencies are, the more of a problem it is.To correct a resonance problem, there are 4 methods:

Stiffen the structure - This method raises the resonant frequency of the structure.

Add mass to the structure - This method lowers the resonant frequency.

Change exciting frequency - Change the speed of the machine.

Add a dynamic absorber to the structure - This method attaches the equivalent of a tuning fork to the structure. This attachment is tuned to have the same resonant frequency as the structure and sets up an out-of-phase signal that has the effect of cancelling out (reducing) the signal being generated by the structure. The dynamic absorber must be properly sized to handle the forces being generated.

Structural Resonance

Figure 1 - Relatively High Amplitudes Will Be Generated.

The Closer The Exciting Frequency Is To The Structure's Resonant Frequency, The Higher The Amplitude Will Be.

Structural Resonance Symptoms:

High (at times, extremely high) vibration in one direction. This is an important symptom - the vibration in one direction will be disproportionately high compared to the other directions.

The structure shape, mass and rigidity will determine what is proportionate and what is disproportionate. It could be as low as 2 or 3:1 or as high as 10 or 20:1.

The structure itself will also determine whether or not the vibration is high in more than one direction (i.e. vertical pumps tend to have very similar resonant frequencies in all radial directions all raidal directions have the same mass and structural stiffness).

Figure 2 - Shape Of A "Supported Beam"

Vibrating in Resonance

Figure 3 - Shape Of A "Cantilevered Beam"

Vibrating in Resonance

Figure 4 - Example Of A "Bump" Test

Similar (identical) machines exhibiting similar vibration symptoms (as described above).

Shape analysis can be initially used to see if the shape fits one of the models shown above. This test simply involves plotting amplitude values taken along the structure to determine the "shape" in which it is moving, or vibrating. This does not confirm

resonance.

Some test (i.e. bump test) must used to determine the actual structural resonant frequency(s). The existence of the above symptoms does not prove resonance, it only makes it one of the strong possibilities (looseness, for instance, can cause disproportionately high vibration in the direction of the looseness).

Shape analysis should be performed before attempting to stiffen, or brace, the structure to correct the problem.

In the case of a nearby structure (i.e. an I-beam), a clue will be that the structure will often be vibrating more than the machine itself at the resonant frequency.

Critical Speeds

Figure 1 - Relatively High Amplitudes Will Be Generated.

The Closer The Exciting Frequency Is To The Structure's Resonant Frequency, The Higher The Amplitude Will Be.

Structural Resonance Symptoms:

Radial vibration @ 1x rpm. Phase will shift 180° once range has

been completely passed through.

Vibration usually satisfactory when rotating sufficiently above or below critical - only when rotating near the critical is there a problem.

Figure 2 - Shape Of A Supported Rotor Running At

Its 1st Critical

Figure 3 - Shape Of A Supported Rotor Running At

Its 2nd Critical

Figure 4 - Shape Of A Overhung Rotor

Running At Its 1st Critical

One test used for determining the critical speed of a rotor is the test shown below. By measuring the amplitude @ 1x rpm simultaneously with the phase at 1x rpm as speed is increased ("Start-Up" plot) or decreased ("Coast Down" plot), the critical speed can be determined. The amplitude spike accompanied by the phase shift indicates a critical speed. Click here to see an example of this test.

Figure 5 - Shape Of A Overhung Rotor

Running At Its 2nd Critical

Belt-Drive ProblemsBelt-drive problems, which include shaft misalignment, pulley misalignment, belt wear, belt resonance, belts too tight, belts too loose, pulley eccentricity and bent shafts, can be relatively straight forward to detect but can be far more difficult to specifically diagnose and correct. That is mainly due to the wide variety of problems that can occur in the installation and assembling of the belt drive, the difficulty of doing field testing on belts and the possibility of other influences (i.e. the base) having some effect.

It is important to realize that some of the belt-drive vibration problems listed above do NOT cause vibration at belt related frequencies. Problems due to the shafts or pulleys (misalignment, eccentricity, etc.) cause vibration at 1x rpm of the component with the problem (i.e. eccentric pulley on the fan causes vibration at 1x rpm of the fan). Worn belts, on the other hand, will cause vibration at harmonics of belt running speed.

The good news, especially in the case of component (belt and pulley) wear, is that belts and pulleys are typically relatively easy to inspect and inexpensive to replace. The bad news is that outside of that, they're often difficult to correct. One positive development in recent years has been the availability of laser alignment units for belt drives for a moderate price. Unfortunately, in more cases than not the old string & straight edge is still the alignment method used for belt drives. The first step to identifying a belt problem is to determine the belt speed.

Determining the Belt Speed:

Obtaining belt speed can be a bit difficult but there are a few tricks.

http://www.vibrationschool.com/mans/SpecInter/SpecInter15ba.html

Some methods are listed here:

Calculate it. It can be calculated mathematically if you know some of the

variables: belt length, pitch diameters, center distances, etc.; but usually that is not the case. The formulas are listed below.

Measure it. Detecting it with a strobe light is very difficult since it is usually

a slow flash rate and the mark used may be unreliable (lettering on the belt, etc.).

A photoeye will be very accurate but will require proper setup and a mark applied to the belts.

A "lasertach" would be the best option for an accurate belt rpm since it does not require a traditional "mark" - a good one will operate on pattern recognition.

Estimate it. With a bit a practice and understanding of a simple technique, an analyst can actually extract the probable belt rpm from the spectrum. One important requirement for this technique to be successful - there must be at least some vibration at belt-related frequencies. The following steps should be used:

First, identify any driver and driven related peaks (1x rpm and harmonics). Label them or make a mental note of which peaks they are.

Second, imagine cutting the belt in half and wrapping it around one of the pulleys. How many times will it wrap around - twice ? three times ? This will give you a very rough estimate in your mind of the belt speed (if it wraps 3 times, the speed would be 1/3 of that pulley's speed).

Finally, do the following:

o Display your velocity spectrum on a logarithmic scale.

o Move your spectrum cursor to your estimated belt rpm and turn on the harmonics.

o Move your cursor left and right in the smallest increments possible (some software allows movement of 1/10th of a line of resolution - this helps with identifying harmonics) and try to get the harmonics to line up on top of any significant but previously unidentified amplitude peaks.

o If there are significant belt related peaks on the spectrum, you should be able to get them lined up at some point.

o If you cannot find any pattern of previously unidentified peaks of significant amplitude, that means one of two things:

Either you do not have the spectrum resolution necessary, or;

There is no significant belt vibration (in which case, why do we need to know the belt rpm ?).

Formulas for Calculating Belt Frequencies: If you know:

The Belt Length

- and -

Either of the Pulley RPMs and Its Diameter:

Driver Pulley Diameter and Speed

or

Driven Pulley Diameter and Speed

You can calculate belt RPM with the following:

3.14 x PS1 x PD1/BL = Belt RPM

- or -

3.14 x PS2 x PD2/BL = Belt RPM

Variable Definitions: PS = Pulley rpm (PS1 = Driver Pulley Speed, PS2 = Driven Pulley Speed) PD = Pulley diameter (PD1 = Driver Pulley Dia., PD2 = Driven Pulley Dia) SD = Distance between shaft centers

BL = Belt Length

- OR -If you only know the pulley sizes and diameters, you can roughly calculate belt length and plug it into the formula above by using the following:

Belt Length = 1.57 x (PD1 + PD2) + 2(SD)

In other words, 2x the center to center distance plus 1/2 the circumference of each pulley will provide the belt length.

Belt-Drive Problems

Pulley Misalignment

Figure 1 - FFT Typical Of Pulley Misalignment (Which Can Also Be Caused By

Shaft Misalignment As Shown In Figures 3 & 4). This Condition Often Results

In High Axial Vibration At Both Components 1x RPM. This Is Due To

The Axial "Pulling" Force Generated As The Belts Ride Up The Side Of The

Pulleys In An Effort To Properly Align Themselves.

Pulley Misalignment Symptoms:

High axial vibration @ 1x rpm on component A at component B frequency.

Uneven wear axially on pulleys and belts.

Figure 2:

Offset

Figure 3:

Angular 1

Figure 4: Angular

2

Belt-Drive Problems

Belt/Pulley Wear, Improper Tension & Belt Resonance

Figure 1 - Typical FFT Showing Belt/Pulley Wear

Figure 2 - Belt Problems Tend To Generate

A Large Amount Of Belt "Flap"

Problems; Resonance Can Also Be A Problem If The Belt

Resonance Coincides With One Of The Forcing Frequencies (Driver, Driven, Belt

RPMs)

Belt / Pulley Wear, Belt Resonance Symptoms: High radial vibration @ 2x, 3x, 4x & 5x belt rpm. Excessive belt "flap" can often be seen.

Belts and/or pulleys will show excessive wear patterns, cracking, etc. if wear is the problem.

Belt tension may be a problem - belts shouldn't be too loose or too tight.

Belt resonant frequency can be checked by placing transducer on bearing (radially) and "twanging" the belt like a guitar string while collecting a time domain or spectrum.

Belt-Drive Problems

Pulley Eccentricity / Bent Shaft (Near Pulley)

Figure 1 - Typical FFT Showing Pulley Eccentricity / Bent Shaft Near Pulley

Figure 2 - Eccentricity Causes High Vibration

At 1x RPM Of The Problem Component.

Bent Shaft Near Pulley Causes Same Symptom.

Eccentric Pulley / Bent Shaft Near Pulley Symptoms: High radial vibration @ 1x on both components - can easily be

misdiagnosed as unbalance. Belts act as rubber bands being stretched and relaxed -

"reaction" forces - cannot be corrected through balancing of the component.

Directional vibration far higher parallel to belts than perpendicular to belts.

Phase will show 0° or 180° phase shift around bearing.

Sleeve Bearing ProblemsSleeve Bearing Problems - Sleeve bearings are in some ways much more forgiving and easier to analyze than rolling element bearings since there are no fundamental defect frequencies and the like to analyze. However, sleeve bearings also demand different techniques and insights that do not apply to rolling element bearings. For instance:

Measuring vibration on the housing of a sleeve bearing is unreliable since the housing moves only a small fraction (perhaps 10% or even less) of what the shaft is moving.

Vibration is due to mechanical forces being generated by the machine's rotation. In the absence of such forces (slow rotational speeds combined with excellent alignment and balance, for example), extensive wear can take place with absolutely no indication on a vibration spectrum - especially if the readings are taken on the housing.

Unlike greased bearings, sleeve bearings usually have an oil system. If the oil flow stops or the oil becomes severely contaminated, failure can occur very quickly.

What should be done with sleeve bearings to alleviate these concerns ?

Oil analysis - This will monitor bearing condition far more accurately than vibration analysis will.

Direct Shaft Vibration Readings - Although sometimes impractical or impossible, taking readings with a proximity probe, a shaft stick or shaft rider will give far more useful vibration data than readings taken on the housing since these techniques measure what the shaft is doing - not the housing.

Time Domain - Looking at the raw time signals will give information on exactly how the shaft is moving and give visual notice of problems such as rubs that spectra will not give.

Sleeve Bearing Problems:

Bearing Wear (Looseness)

Figure 1 - FFT Showing Sleeve Bearing Looseness

Figure 2 - Looseness

Allows Signal Shape To Become More Of A Square Wave. This

Causes Harmonics On

The FFT.

Sleeve Bearing Looseness Symptoms The precise symptoms detected and amplitudes recorded on a

spectrum will depend on the amount of force being generated by the shaft's rotation, where we are taking the readings and other variables.

Even if direct shaft readings are taken, if there is not enough force being generated to cause the shaft to throw itself around as in Figure 2, the shaft will simply spin as the bearing continues to wear and the clearances continue to increase. In this case, vibration symptoms of the problem will be minimal or even non-existent.

If the readings are taken on the housing instead of the shaft, you may be measuring only 10% or so of shaft movement and the chances are even greater that vibration symptoms of bearing wear will not be generated. Other factors now involved include the relative masses of the rotor and bearing housing / structure (how much can the relatively lightweight shaft move the massive housing ?).

It is important to understand that vibration is not monitoring bearing condition as it is with rolling element bearings. It is monitoring a result of the bearing wear - looseness - that does not cause vibration. Looseness merely allows the forces present to have more of an effect than they would if everything was properly fastened in place. If there are insufficient forces to throw the rotor around, vibration symptoms are not generated.

Oil analysis - which monitors oil properties, contaminants and wear metals, is the best predictive tool to use for sleeve bearing systems.

Most Common

Symptoms:

1. High radial vibration @ 1x and numerous harmonics of rpm - like bearing looseness. In severe cases, peaks may appear at 1/2 harmonics (0.5 x rpm, 1.5 x rpm, etc.).


Oil Whirl

Figure 1 - FFT Resulting From Oil Whirl (0.42-0.48xRPM Peak Indicates Oil Whirl)

Figure 2 - Note Shaft Is

Spinning At Different Rate

Than It Is Rotating

Around Bearing Sleeve.

Oil Whirl Symptoms High Radial Vibration at 0.42 - 0.48 x RPM.

Oil Whirl, although unusual, can occur when clearances become excessive. An oil wedge is formed that is held in place by the rotation of the shaft. The friction of the shaft against the wedge then pushes the shaft around the housing. Fortunately (for the analyst), it occurs in a very precise sub-synchronous frequency range. Note that in the animation above the shaft is rotating at a different frequency than it is moving around the bearing sleeve.


Oil Whip

Figure 1 - Oil Whirl Is Present, Rotor Passes Through Its 1st Critical

Figure 2 - Oil Whirl. Note

Shaft Is Spinning At

Different Rate Than It Is

Rotating Around Bearing Sleeve.

Figure 2 - Rotor Speed Continues To Increase Until Its Critical Speed Coincides

With The Oil Whirl Frequency (i.e. Its 1st Critical Equals About 0.45x Current RPM)

Oil Whip Symptoms

Oil whirl is present (bearing clearances are excessive).

Problem develops when rotor is running at 2.1-2.4x critical speed (at this speed, the frequency of the rotor's 1st critical is

between 0.42-0.48xRPM - the oil whirl range).

Figure 3 - Rotor Speed Continues To Increase But Destructively High

Vibration Remains At Frequency Of Rotor's 1st Critical Speed

High vibration develops at frequency of rotor's critical speed. This occurs when the vibration due to the oil whirl condition acts to excite the resonant frequency of the rotor. High vibration remains at frequency of 1st critical even as rotor speed continues to increase.

Belt-Drive Problems











Sleeve Bearing ProblemsSleeve Bearing Problems - Sleeve bearings are in some ways much more forgiving and easier to analyze than rolling element bearings since there are no fundamental defect frequencies and the like to analyze. However, sleeve bearings also demand different techniques and insights that do not apply to rolling element bearings. For instance:



Unlike greased bearings, sleeve bearings usually have an oil

system. If the oil flow stops or the oil becomes severely contaminated, failure can occur very quickly.









Allows Signal Shape To Become More Of A Square Wave. This

Causes Harmonics On

The FFT.



Even if direct shaft readings are taken, if there is not enough force being generated to cause the shaft to throw itself around

as in Figure 2, the shaft will simply spin as the bearing continues to wear and the clearances continue to increase. In this case, vibration symptoms of the problem will be minimal or even non-existent.




Most Common

Symptoms:



Oil Whirl

Figure 2 - Note Shaft Is

Spinning At

Figure 1 - FFT Resulting From Oil Whirl (0.42-0.48xRPM Peak Indicates Oil Whirl)

Different Rate Than It Is Rotating

Around Bearing Sleeve.

Oil Whirl Symptoms High Radial Vibration at 0.42 - 0.48 x RPM.

Oil Whirl, although unusual, can occur when clearances become excessive. An oil wedge is formed that is held in place by the rotation of the shaft. The friction of the shaft against the wedge then pushes the shaft around the housing. Fortunately (for the analyst), it occurs in a very precise sub-synchronous frequency range. Note that in the animation above the shaft is rotating at a different frequency than it is moving around the bearing sleeve.


Oil Whip

Figure 1 - Oil Whirl Is Present, Rotor Passes Through Its 1st Critical

Figure 2 - Oil Whirl. Note

Shaft Is Spinning At

Different Rate Than It Is

Rotating Around Bearing Sleeve.

Figure 2 - Rotor Speed Continues To Increase Until Its Critical

Oil Whip Symptoms

Oil whirl is present (bearing clearances are excessiv

Speed Coincides With The Oil Whirl Frequency (i.e. Its 1st Critical Equals About

0.45x Current RPM)

e).

Problem develops when rotor is running at 2.1-2.4x critical speed (at this speed, the frequency of the rotor's 1st critical is between 0.42-0.48xRPM - the oil whirl range).

Figure 3 - Rotor Speed Continues To Increase But Destructively High

Vibration Remains At Frequency Of Rotor's 1st Critical Speed

High vibration develops at frequency of rotor's critical speed. This occurs when the vibration due to the oil whirl condition acts to excite the resonant frequency of the rotor. High vibration

remains at frequency of 1st critical even as rotor speed continues to increase.

Belt-Drive Problems











Sleeve Bearing ProblemsSleeve Bearing Problems - Sleeve bearings are in some ways much more forgiving and easier to analyze than rolling element bearings since there are no fundamental defect frequencies and the like to analyze. However, sleeve bearings also demand different techniques

and insights that do not apply to rolling element bearings. For instance:



Unlike greased bearings, sleeve bearings usually have an oil system. If the oil flow stops or the oil becomes severely contaminated, failure can occur very quickly.








Allows


Signal Shape To Become More Of A Square Wave. This

Causes Harmonics On

The FFT.



Even if direct shaft readings are taken, if there is not enough force being generated to cause the shaft to throw itself around as in Figure 2, the shaft will simply spin as the bearing continues to wear and the clearances continue to increase. In this case, vibration symptoms of the problem will be minimal or even non-existent.




Most Common

Symptoms:


Understanding the Basic Theory of Vibration & Analysis

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