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Vibration Basics

All machines, All Applications have one thing in common…

There are many applications and many types of industry that we may come

across. However, no matter how different or complex that they may appear

to be, we can take comfort in knowing that they all obey Newton’s Laws of

motion. Even non-self excited applications such as structures and

machines that involve linear motion rather than rotary motion obey the

same laws.

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Module 1: Basic physics

All machines, no matter what they are, obey the laws of physics.

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The law that’s of most interest to us is Newton’s second law of physics,

which says that force equals mass times acceleration.

As a simple experiment here to illustrate this point, we have a machine, in

the form of a benchtop grinder, sitting on top of a set of bathroom scales.

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The grinder weighs about 5 Kg so we get a reading because the force of

gravity is pulling the grinder down onto the bathroom scales, giving us a

reading of its static mass.

No matter how well the machine is constructed there will inevitably be

some residual unbalance in the rotor. Even a gyroscope which is very finely

balanced will have some degree of residual unbalance.

The position of this rotor’s “heavy spot” is indicated by the red arrow. When

the rotor is at rest this unbalance has no effect.

When we switch on the motor the unbalance generates a centrifugal force,

which changes in direction as indicated here by the rotating arrow (or

vector).

Our bathroom scales are measuring force in just one place; the vertical

plane, and will respond to the effect of this centrifugal force.

When the centrifugal force acts in an upward direction the reading on the

scales will decrease, and when the centrifugal force acts in a downward

direction the force reading on the scales will increase.

If we were to plot the forces going into the foundation of our machine (as

indicated here by the bathroom scales) then as the vector rotates through

360 degrees we would generate a “sine wave”.

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In the real world, of course, it’s impractical to install scales, or some kind of

force sensors under the feet of a machine in order to measure the effects of

these forces. This would be expensive and invasive.

A more practical way to study this forces and resulting motion is to use an

accelerometer, which we can position on top of the machine

This is a device which measures (as it’s name implies) acceleration. It

contains a piezo-electric crystal which creates a voltage as it moves up and

down. We can capture this signal by connecting the accelerometer to an

instrument.

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So if we look on our instrument at what happens as the vector rotates we

see a sinusoidal waveform representing the effect of the forces acting upon

the machine.

It is the FORCES acting upon a machine that are the cause of vibration.

Vibration is not a CAUSE of a problem, it is a SYMPTOM.

If there are any mechanical tolerances in the build of a machine that allow

movement then resulting movement will correspond to the amount and

direction of the force that is being applied.

If, for example, the machine is not bolted tightly to its foundation then as

the machine rotates the resulting motion can be measured using an

accelerometer. There is a direct relationship between the force that’s being

applied and the corresponding vibration that it generates.

To reduce the vibration on a machine the best approach is to reduce the

forces that generate it.

So if the machine is out of balance, then improving the balance condition

will reduce the forces, and reduce the vibration pro-rata.

The value of the vibration will be proportional to the amount of work that’s

being done by a machine. Logically a small, low-powered machine will

develop lower forces than a bigger, high-powered machine. In

consequence the generated vibration will be less. A bigger machine has

typically more power, and hence we would expect to see higher levels of

vibration.

Another thing that needs to be taken into account is load. The harder the

machine is working the more current it’s going to draw; there’s more work

being done so the levels can be expected to go up.

An analogy; driving a car on a flat road; when you start to go up hill you can

hear then engine working harder, and very often you can feel the vibration

levels in the vehicle increase.

The reason why we do all of this is to detect machine faults. We have

already mentioned unbalance. If your machine is faulty then we can use

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vibration to detect that fault. If you are in the business of manufacturing

machines then you can use vibration as a reflection of the quality of the

machine before shipping it to your customer.

Then, after machine is installed at the customer’s site you can observe how

the vibration deteriorates with time, and that’s called “machinery condition

monitoring” or “predictive maintenance”.

Module 2: Terminology We need now to look at the units of vibration measurement and other associated terminology.

Describing Amplitude

So mechanical structures, when excited, will tend to vibrate with sinusoidal

motion. So to understand vibration we need to understand the quantifying

parameters of sine waves. In the previous module our “machine structure”

was a bench grinder sitting on top of a set of bathroom scales. Like all

machines that structure had mass (m) and stiffness (k), which can be

represented by means of the mass-spring system shown here.

The motion of the mass from one extreme of displacement to the other

extreme, and then back to the start point is referred to as one cycle of

motion.

The time T taken to achieve that cycle is referred to as the period of the

motion. In machinery terms this is typically a very small value, and difficult

to relate to other aspects of the machine’s operation.

Instead we consider the number of cycles that are achieved in a given time,

which we refer to as the frequency of the vibration.

Vibration instruments commonly display the frequency of vibration in terms

of cycles per second, also known as Hertz (HZ).

Thus far we have considered data in the “time domain”.

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The amplitude and frequency of a vibration can also be expressed in a

graphical form as we see here.

The amplitude (in this example the vibration displacement) is plotted on the

Y axis against the frequency on the axis.

This display is called a vibration spectrum. This way of looking at data can

also be referred to as the “frequency domain”. We will return to this topic in

more detail in the “diagnostics” module.

The displacement is constantly changing as the mass vibrates. In

machinery terms it is usually measured in “microns” (1 micron =0.001mm)

or in “mils” (1 mili-inch = 0.001 inch).

Often when people talk of the amount of vibration they use the term

“amplitude”, by which they usually mean the total distance through which

the mass moves (i.e. the displacement from one extreme of motion to the

other). This is more correctly termed the “peak to peak” displacement.

This is one measure of vibration “amplitude” (or amount) but, as we shall

now see, there are others. The terms “amplitude” and “displacement” are

NOT synonymous.

The mass must move with some velocity. In machinery terms velocity is

usually measured in mm/sec or in/sec.

The velocity must also be constantly changing as the mass vibrates. At the

extremes of motion the velocity must momentarily be zero, as the mass

changes direction. The velocity will achieve it’s maximum or peak value as

the mass passes through the “neutral” position, i.e. when the displacement

is zero.

Velocity is another measure of vibration amplitude.

The acceleration of the mass must also be constantly changing as the

mass vibrates. At the point where displacement is zero the acceleration

must also be zero, since the mass has accelerated to it’s peak value and

then starts to decelerate again. The acceleration will be at it’s maximum

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value at the extremes of motion, as the mass accelerates away from zero

velocity.

So we could express the value (or amount of vibration) in terms of

• Displacement (The distance through which the mass moves)

• Velocity (The speed at which the mass moves)

• Acceleration (The rate at which the velocity changes)

Note then: that the word “amplitude” is not a parameter in its own right. It is

possible to have an;

amplitude of displacement,

amplitude of velocity,

amplitude of acceleration.

Therefore “Amplitude” should not be used as a substitute for the word

“displacement”. Any one of these three parameters can be used as a

measurement of vibration amplitude.

Conversions: Acceleration to Velocity & Displacement

For a sinusoidal motion there is a mathematical relationship between the

three amplitude parameters. Given one, and knowing the frequency of

oscillation, then it’s easy to calculate the others.

If we use an accelerometer sensor then we directly measure the

acceleration level. Dividing that figure by 2piF gives us the velocity of the

vibration. If we take the acceleration level and divide by 4 pi squared F

squared the we get the displacement value.

However, you need not be concerned about the mathematics involved.

Most analysers and vibration meters will do the maths for you! You simply

tell the instrument what type of sensor you are using, what parameter you

want to see on the Y axis, and the instrument will do the arithmetic. All you

need to do is hit the required switch.

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In practical terms this also means that using one transducer, such as an

accelerometer, can be used to measure all three parameters. However,

even though this is a very basic introduction to vibration, one thing that you

need to be aware of is the effect that doing this arithmetic has on the

signal.

Seismic vibration

In previous displays we saw how the signal varied against time. When we

look at the signal in that way we speak of the “time domain”.

The display shows the vibration velocity level on the vertical axis, plotted

against the vibration frequency on the horizontal axis. This is commonly

referred to as a vibration “spectrum”. Some people also refer to this as a

vibration “signature”. When we view the signal in this way we speak of the

“frequency domain”. We will return to this way of looking at vibration data

in more detail when we reach the “diagnostics” module.

For now, we see a vibration velocity reading, taken from a stationary

machine. Note that, even though the machine is not running, the instrument

is suggesting that a vibration level of 2.16mm/sec is present.

We see that all of the indicated vibration occurs at the bottom of the

frequency range. This is likely “ground-borne” vibration.

In the real world it’s common that vibration from other sources, for example

adjacent machinery, or even traffic moving along a nearby road, or trains

moving along a nearby track, is transmitted through the ground and is

detected on by the sensor on the stationary machine. This “seismic”

vibration (as it is sometimes known) tends to be always present, and is

typically low frequency in nature.

Ski slope

If a high amplitude of vibration velocity low frequency is observed, then the

most common reason is an amplification of the data caused by the process

of integration from acceleration to velocity.

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The spectrum shown here depicts the vibration acceleration as measured

directly by the accelerometer sensor.

To convert the spectrum from g versus frequency to mm/s versus

frequency, we divide each value of g in the spectrum by 2 x PI x F. (As

explained earlier).

On the left of the spectrum “f” is a low number.

Divide a low number into a bigger number and you get an even larger

number! So when we look at the same signal in terms of the calculated

velocity level it appears that the low frequency peak is much larger.

This effect is exacerbated if we divide the acceleration values by 4 x PI x F

squared to view the vibration in terms of its displacement.

The effect is commonly referred to as the “ski slope”.

Causes of low frequency signals in the vibration spectrum are;

a) It is a real signal i.e. low frequency vibration is actually present.

b) It is a false signal, caused by instrumentation faults e.g.. poor

screening, poor contacts, incorrect selection of an appropriate transducer.

c) Electrical noise generated by the sensors in-built electronics. This is

sometimes referred to as “ICP noise” (ICP = Integrated circuit piezoelectric

sensor”.

Item C is the most common. Some accelerometers will emit a signal at 1

Hz or below which is due to the ICP circuitry. When converting from

acceleration to velocity this signal gets amplified and values of 360mm/s (or

even higher) may be observed on the y axis. To combat this you can install

a low frequency filter (the DI-2200 doesn’t have one though – the PL302

does).

Filter 10Hz to 1kHz

The ISO committees responsible for compiling machinery vibration

standards are obviously aware of this issue, and most specify that readings

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below 10 Hz should be disregarded. (Be aware, though, that some

standards specify 2Hz.) The electronics of most modern vibration

instruments therefore typically offer appropriate switchable filters.

Low frequency sensors

To study real low frequency vibration it is necessary to use a special

accelerometer which is designed for the purpose and which does not emit

ICP noise at low frequency. (For example SKF sensors shown here)

Module 3: Parameters and detectors

Describing Amplitude

In the previous module we learned that there are three measures of

vibration amplitude

• Displacement (The distance through which the mass moves)

• Velocity (The speed at which the mass moves)

• Acceleration (The rate at which the velocity changes)

We also saw that each of these parameters varies sinusoidally during each

cycle of vibration. So how can we express the “value” of a signal that is

constantly changing?

Signal Level Descriptors – Peak to Peak

1. The total signal value, from one extreme to the other extreme is called

“peak to peak” (Pk-Pk). If the peak to peak amplitude is not constant (i.e

changing with time) we usually record the value when it was at its biggest

/ maximum.

Signal Level Descriptors – Peak

2. The signal value from point of rest / reference position to one side only is

the peak value (Pk.)

Signal Level Descriptors – RMS

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3. Most ISO and European standards will require you to measure the

signal’s “root mean squared” value (r.m.s.). The RMS value is the most

commonly used way of expressing the value. It’s a way of “averaging”

the signal, so let’s take a little time to understand it in more detail.

The r.m.s. process

The r.m.s. value is calculated by taking a series of amplitude

measurements over a period of time. (For example 1024 measurements

over 400 milliseconds.) The simple average, or mean value of these

measurements would be zero, because for half of the cycle the values are

positive, and for the other half of the cycle they are negative.

Square each value and then take the average (or mean). When the

negative values are squared they become positive values.

Take the square root of the mean value and that gives the r.m.s.

The signal is measured over a period of time, and so the r.m.s. value is

proportional to the amount work being done by the machine or to the

amount of fault energy.

Note that “Average” measurements are often preferred by the gas turbine

industry, and this is simply 0.9 of the r.m.s.

Signal Level Descriptors – Peak

So there are four ways of measuring the amplitude values:

1. Peak to peak

2. Peak

3. RMS

4. Average (Mean)

This becomes important when we wish to compare vibration data with

some published standard, or if we wish to compare vibration data taken

with different instruments. In such circumstances it is obviously important to

compare like with like.

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In fact if we assume that the motion is sinusoidal then there is a simple

arithmetic relationship between all four quantifiers. For example, the peak

value is root 2 times the r.m.s.

Overall vibration level

So far we have considered vibration as a simple, sinusoidal motion

occuring at only one frequency. Vibration from real machinery is usually

more complex, involving motion resulting from a combination of forces,

associated with different machinery faults.

Consider the machine train shown here. If the accelerometer is placed at

(say) the gearbox input bearing then what is being sensed? The vibration at

that point will represent the total effect of all of the forces present in the

machine, as transmitted to that point.

There will undoubtedly be some vibration present due to unbalance in the

drive motor. It may not represent a problem but it will be present. This

vibration results from the centrifugal force induced by the unbalance. The

frequency of that vibration will therefore equate to the rotating speed of the

motor. (i.e. if the motor is rotating at 1500 rpm then the vibration frequency

will be 1500 cpm or 25Hz).

There will probably be some vibration resulting from misalignment in the

coupling. Again, this may not represent a problem but it will still be present.

Vibration resulting from misalignment will logically occur at a frequency

relating to the rpm of the offending shaft. Depending upon the nature and

severity of the condition it may occur at various multiples (harmonics) of the

shaft speed. For the purpose of this exercise let us imagine that the

vibration occurs at two times shaft speed frequency.

There is likely to be some vibration present at a result of the meshing

action of the gears. The gear mesh frequency is the number of teeth on the

gear multiplied by it’s RPM so this will be higher frequency than the other

vibration components considered so far.

There may well be other vibration components present but for the purpose

of this exercise these will be ignored.

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The total vibration sensed at the gearbox input bearing will be the total of

the various components present..

Adding together vibrations of differing amplitudes at different frequencies

does not result in a new, simple, sinusoidal waveform.

The combination of these different vibration sources results in a more

complex time waveform, the characteristics of which will be dictated by the

individual vibrations present. This total vibration is referred to as “Overall”

vibration, sometimes called “Broadband” vibration.

This overall vibration can still be expressed in terms of its

• Peak value

• Peak to peak value

• RMS value

• Average (mean) value

Benefit of overall severity measurement = simplicity

A lot of “condition monitoring” activity relies on periodic (or continuous)

measurements of the overall vibration level. Indeed, ISO standard 10816-3

defines areas of vibration severity according to overall levels of vibration

velocity.

This approach to condition monitoring has the advantage that it can be

applied with relatively simple, inexpensive instruments and systems, and it

works on the basis that, if the total vibration does not change, then it’s a

reasonable assumption that the individual vibration components have

stayed the same. So when the total vibration increases then these basic

measurements give warning of an impending problem, but typically lack the

ability to identify the particular component of vibration that has deteriorated.

This requires instrumentation that provides information regarding the

individual vibration frequency components that are present. We shall

discuss this in more detail later in this course.

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What to measure?

We learned earlier that we can express the value (or amount of vibration) in

terms of

• Displacement (The distance through which the mass moves)

• Velocity (The speed at which the mass moves)

• Acceleration (The rate at which the velocity changes)

So which of these parameters should we use when attempting to monitor

change in machinery condition?

ISO standards are available to guide you in this but if you don’t have

guidance from a standard then you’ll need to choose your own, so consider

the following.

We also learned that there is a mathematical relationship between the

three parameters.

Velocity varies with the frequency, whilst acceleration varies with the

square of the frequency.

A-V-D relationship

Here we see the relationship between the three parameters expressed

graphically.

For a constant displacement we can see the resulting velocity and

acceleration levels at various frequencies.

High frequencies – Destructive forces

It’s evident that, at high frequencies, relatively low levels of displacement

can result in high levels of acceleration, because acceleration is a function

of displacement and the square of the frequency.

Newton’s law tells us that Force = Mass x acceleration. This means that, at

high frequencies, even moderate excursions can result in the generation of

very destructive forces.

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Therefore, if we are measuring high speed machinery or machines which

can generate high frequency vibrations (>10kHz) then acceleration is a

meaningful parameter to measure.

Low frequencies – Stress failures

Conversely, at low frequency even relatively high levels of displacement

will result in low levels of acceleration. Here the problem is not one of force,

but rather one of stress. Components may suffer degradation as a result of

stresses induced by deflecting them through too great a distance. So where

low frequency vibrations (below 10Hz) are of concern displacement is a

meaningful parameter to measure.

Mechanical fatigue

Fatigue failures occur when components are subjected to repetitive, cyclic

stresses. The time taken to reach failure is typically a function of the

deflection that occurs (i.e. displacement) and the rate at which the

deflections occur (the frequency). As we saw a few moments ago, velocity

is a function of displacement and frequency, so for general machinery use,

where fatigue failures are of concern, velocity is a meaningful parameter to

measure.

Module 4: Impulsive signals

Demo - Peak, RMS & dealing with impulsive signals

Impulsive signals result from impacts.

As an example, consider what happens if we use a screwdriver handle to

tap this bench grinder as we collect vibration data using an accelerometer

mounted on one of the bearings, as shown.

Demo - Peak, RMS & dealing with impulsive signals

Here we see the resulting time waveform.

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During the time taken to collect this data the machine was struck twice with

the screwdriver handle. We can see the two spikes in the signal that

resulted.

The effect of these two spikes on the RMS level of the signal will be very

small, as a result of the “averaging” that occurs in calculating the RMS

value.

Dealing with impulsive signals

Now think about bearings.

Bearings are precision components, designed to have a long service life.

When bearings become damaged, usually as a result of some underlying

problem such as lubrication faults, misalignment, excessive loads etc. they

do generate impulsive signals.

These result from impacts which occur as (for example) raceway defects

are over-rolled by the bearing elements.

Dealing with impulsive signals

Impulsive signals are also generated by the rolling action that occurs

between damaged or broken gear teeth.

Selection of amplitude descriptor

Consider this signal’s time waveform. It exhibits some tall peaks due to

short duration impacts – could these be the result of bearing defects?

If we use an RMS amplitude descriptor to arrive at an “overall value” for this

signal then the effect is to average the individual values and reduce the

measured level to a much lower calculated value. Individual peaks would

have to grow massively before they had an impact on the RMS value.

Selecting a Peak or Peak-to-Peak detector would still not capture the data

correctly, as instruments calculate these two descriptors from the RMS

value (See module 3: Pk =1.414* RMS) (Pk-Pk = 2 *Peak)

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Note that some instruments, such as the SKF Microlog, offer a true peak

detector which would be the correct selection for studying this type of data.

Enveloping technique (Demodulation)

To detect bearing damage in its early stages a technique is needed that

can detect the small impulsive signals that are generated when impacts

occur between microscopic flaws in bearing elements. This vibration is

typically very small in comparison with general machinery vibration

resulting from misalignment or unbalance.

So it becomes evident that simply monitoring the RMS vibration level is

inadequate for this task. Whilst this is effective for detection of common

machinery faults such as unbalance, misalignment and looseness it cannot

be relied on to give early warning of impending bearing problems.

Development of SKF’s implementation of Enveloping (demodulation) was

carried out in a practical research environment. No other condition

monitoring company has real bearing test facilities such as those of SKF in

the Netherlands, India & China. SKF uses the technology of enveloping in

their own factories. It was first used in the 1960’s as a quality tool.

Band-pass filtering

Let’s take a look at how enveloping works. The illustration here shows a

time domain signal (acceleration) , resulting from low frequency shaft

related vibration.

In the illustration at lower left we now see the effect of the impulsive signals

resulting from a bearing defect.

The first stage of the process involves band-pass filtering of the time

domain signal using a band pass filter that centers on the region of high

frequency energy. The figure on the right above shows the filtered output

in the time domain. The filtering process results in a series of spiky bursts

of energy, which are the impacts from the rolling elements hitting the defect

as the bearing rotates.

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Key to SKF’s implementation of enveloping (gE) was standardizing on 4

band pass filter values across all SKF instruments:

ENV1: 5 Hz - 100 Hz

ENV2: 50 Hz - 1 kHz

ENV3: 500 Hz - 10 kHz

ENV4: 5 kHz - 40 kHz

Standardized Band-pass filters

The next stage of the process is to pass this filtered time signal through an

enveloper in order to extract the repetition rate of the spiky bursts of

energy. Historically, the enveloper is an electronic circuit that demodulates

or rectifies the signal. In today’s vibration data analysis equipment, this

process is done using digital signal processing (DSP) enveloping

algorithms.

The result of passing the signal through the enveloper is shown here in the

time domain. Units of measurement applied to the enveloped signal are gE

(i.e. gs of envelope). It provides a “figure of merit” that can be used to

reliably monitor change in the condition of bearings and gears. Enveloping

can also be applied as an diagnostic tool, and we shall return to this in the

“diagnostics” module.

Alarm limit calculation

SKF software is available to aid correct filter selection, and to suggest

appropriate tolerances.

Module 5: Taking Data

Where to measure

The keys to a successful vibration-based condition monitoring program is

consistency in measurement location and in trandsucer mounting method.

Let’s begin by selecting our measurement locations. Vibration readings are

usually taken at the bearing housings. This is logical because vibration is

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generated by forces that result from the rotating parts of the machine, and

these make contact with the machine structure at the bearings.

On this machine there are four bearings; two on the drive motor and two

supporting the fan impeller. Enveloped acceleration readings are to assess

change in bearing condition, so again it is logical to take measurements at

the bearing housings. Where machines include a gearbox, then enveloped

acceleration signals generated by gear meshing will also be detectable at

the housings of the supporting shaft bearings.

Measurement planes

General machinery problems such as unbalance, misalignment and

looseness will generate vibration in a radial direction.

Tab 1:

Due to gravity, most machine structures are stiffer in the vertical plane, and

so the horizontal plane of measurements is often (but not always) the most

responsive to changes.

Ideally, enveloped acceleration readings should be taken in the bearing’s

load zone. However, in most cases this is not possible, and the

compromise is to take the readings in the horizontal plane.

Tab 2:

However, when looseness develops, especially in the machine’s mounting,

this often causes a vibration increase in the vertical plane.

It’s common practice, therefore, to take measurements in both horizontal

and vertical directions.

Tab 3:

Misalignment conditions, on the other hand, also generate thrusting forces,

and so tend to cause a vibration increase in an axial direction. When you

take axial measurements be sure that the instrument’s tip is held firmly

against a suitable surface, such as the bearing housing or some other

machine face.

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Where a machine employs thrust bearings these are taking load in the axial

direction, and therefore measurements of enveloped acceleration should

also be taken in the axial plane.

Mounting the sensor

Many portable instrument systems provide an accelerometer that has a

magnetic head with which to temporarily attach it to the machine. Properly

used this does provide better consistency of data than is obtained by hand-

holding the sensor against the target surface.

Remember though that one of the faults that can be detected by vibration

monitoring is looseness. If the sensor is loosely mounted on the machine

then we shouldn’t be surprised if that fault is detected! Make sure that the

magnetic head sits firmly on the target surface. If that surface is curved

then rotate the magnet so that it does not rock.

Where it is necessary to hand-hold the sensor then hold it with a firm even

pressure against the machine surface. Don’t press so hard as to dampen

out the vibration that you are trying to measure, especially on light , flexibly

mounted machinery.

Recording the data

Many modern data collection instruments store readings as they are

collected, and then transfer the data to a host software system for storage,

analysis and reporting.

In the absence of such a package it is important to have a disciplined

approach to record keeping. Condition monitoring is essentially about

detecting change in condition, so good record keeping is vital.

Evaluating collected data

It is important to have an action plan in place to investigate suspect

conditions as they arise, and to instigate timely investigation and corrective

activity.

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There are three principal ways of evaluation collected data. The first is the

use of published standards.

ISO 10816-3 is probably the most widely used standard for general

machinery monitoring. It classifies machines according to size and

foundation type, and suggests tolerances in terms of vibration velocity.

Machinery manufacturers are also often able to provide information

regarding the vibratory behaviour of their machinery.

Evaluating collected data

The use of graphical trend charts makes it easier to observe significant

changes, irrespective of indicated alarms. Trend charts also allow the rate

of deterioration to be assesses and to guide in the prioritization of further

action. Software supplied with modern data collection systems usually

makes it very easy to produce these graphical reports, and to even

generate alarms based on the rate of change and other statistical analyses

of the collected data.

In this simple example we can see that the vibration velocity reading is well

in excess of the higher alarm threshold suggested by ISO10816-3.

Furthermore we can see that when the machine was checked a month

earlier, the reading had, in fact, exceeded the first level of alarm, and that it

has been generally deteriorating over a period of two or three months. This

illustrates the importance of having an action plan in place, to ensure that

out of limit conditions are recognized and investigated in a timely manner,

otherwise the effort expended in monitoring the machine will have been

wasted.

Evaluating collected data

The trend for the Enveloped Acceleration data from the same

measurement location shows that, despite the significant increase in

vibration velocity, there is no indication at this time that the bearing

condition has been adversely affected by the as yet undiagnosed

mechanical problem which has caused the increase in vibration velocity.

Timely investigative and corrective action now might afford the opportunity

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to protect the bearing from damage, and thereby avoid need for bearing

replacement.

Evaluating collected data

The third method is to compare data with readings collected from similar

machines operating under similar conditions. Such comparisons can help

reinforce opinions based on the use of tolerances and trend data.

Module 6: Diagnostics

Vibration frequency

Each and every rotating component will produce forces and vibration that

relates to the frequency at which it operates i.e. its rotating speed.

Time domain analysis – often tells us very little

When we view the overall vibration in the time domain it is usually very

difficult to identify the individual components.

Vibration frequency analysis – clarifies the picture

However, when we view the signal in the frequency domain the picture

becomes much clearer.

We briefly saw this view of the data earlier, in the “terminology” module.

The process by which modern digital instruments generate this view of the

signal is called “fast fourier transform” (FFT). For this reason people often

refer to the spectrum plot, or time domain plot as an “FFT”.

Baseline technique

If we observe an amplitude increase at a frequency then we know that the

forces have increased and we can diagnose which component inside the

machine is at fault.

A common way of using this data is to use the “baseline” technique.

The “baseline” is the spectrum from a machine in acceptable condition.

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When the monitoring process indicates that significant change has

occurred, a new spectrum is prepared, and compared with the baseline.

It’s the differences that tell the story. In this example we can clearly see

that it is the high frequency vibration from the gearmesh that has increased.

Frequency Analysis – an Alterative View

The gearbox output drives into the “driven” machine, which could be fan or

pump, so there will be forces due to the residual unbalance of the driven

rotor. Plus, if it is a fan or pump the number then add forces at the number

of blades times the rotor speed.

The rotors of the motor, gearbox and driven machine will all be supported

by at rolling element bearings all generating forces at which the rolling

elements spin.

In short, every single moving component will generate forces at the speed

of their motion to result in multiple excitation frequencies. The time domain

trace for a complex waveform is difficult to interpret……

The “FFT” as a fundamental tool

However with the aid of a spectrum analyser, we can break the complex

waveform back into its constituent sine waves. As was explained earlier,

the process by which modern digital instruments perform this analysis is

called “fast fourier transform” (FFT). For this reason people often refer to

the resulting display as an “FFT”.

There is no “black art” to interpreting a spectrum. Armed with the

knowledge of the rotating components that make up the machine and

knowing their rotational speed tells us where to look in the spectrum for an

increase in vibration due to a developing fault.

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Enveloping as a diagnostic tool

The impulsive signals generated by bearing faults are repetitive and

predictable.

For example, the frequency with which a rolling element passes over a

defect in the outer raceway is simply a function of bearing geometry and

shaft speed.

Each bearing component has a unique defect frequency, which enables a

specialist to pinpoint damage.

The following defect frequencies can be calculated:

• BPFO, ball/roller pass frequency outer ring raceway(s) [Hz]

• BPFI, ball/roller pass frequency inner ring raceway(s) [Hz]

• BSF, ball/roller spin frequency [Hz]

• FTF, cage frequency (fundamental train frequency)[Hz]

A program to calculate bearing defect frequencies and thereby pinpoint

damage is available online at www.skf.com/bearings.

Enveloped signals in the frequency domain

We can also view enveloped signals in the frequency domain.

Earlier we looked at an enveloped signal in the time domain. This clearly

shows the regular repetition of the impulses with respect to time. We can

see that there is an impulse every X seconds.

If we view that signal now in the frequency domain we can now see the

repetition rate of the impulses, i.e. the number of impulses per sec, or

impulses per minute.

This makes it easier to relate the signals to the expected fault frequencies,

and their various harmonics.

In the case of bearings, of course, we are not often concerned with whether

the fault is (for example) on the inner raceway or outer raceway. However,

the ability to be so specific aids confidence in decision making, especially if

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the decision to take a machine out of service has significant operational

implications.

This is also useful when the readings come from a gearbox. It becomes

possible to discriminate between a bearing fault and a gear problem.

Gearbox r.m.s velocity spectrum versus enveloped

acceleration spectrum

To illustrate the power of enveloping to detect gear mesh signals:

The upper trace shows the 10kHz velocity spectrum from a crane gearbox.

It is almost impossible to see the gear mesh frequency.

The lower trace shows the 1kHz enveloped acceleration spectrum from the

same gearbox. The gear mesh frequency is prominent along with

harmonics.