Process Engineering Equipment Handbook Episode 1 Part 10 potx

Introduction to rotor dynamics: vibration theoryThe two main categories of vibration systems are: Forced systems Free systems A free system operates under forces that are inherent in t

FIG C-321 Vibration spectrum (rpm = 20,000, P d= 1200 psig) 13

FIG C-322 Vibration spectrum (rpm = 20,000, P = 1250 psig) 13

FIG C-324 Vibration spectrum (rpm = 20,000, P d= 1320 psig) 13

C-293

1200 psig discharge pressure Note a synchronous peak of 0.5 mil at 20,000 rpm(possibly due to unbalance).

In Fig C-324 machine rpm and suction pressure stay unaltered Dischargepressure has been raised to 1250 psig Now a 0.2 mil subsynchronous componentshows up at 9000 rpm Frequently such components may be intermittent and hard

to capture without the use of the peak hold mode on the analyzer

In Fig C-323 with all other conditions remaining unchanged, it is noted that just

a 20 psig increase in discharge pressure raised the 9000 rpm component from 0.2 mil to 1.5 mil

It took an increase in suction pressure by 50 psig while maintaining the samedischarge pressure to allow the unit to regain stability

This shows the importance of keeping track of process conditions in addition tomechanical items that change within the machine system

Other frequency orders. When originated within the machine, these are generallyrelated to meeting contact surfaces

Blades. For instance, blade tip rub would show up a signal of “number of teeth

in the ‘contacting’ stage ¥ rpm.”

Figure C-325 shows an accelerometer’s signature from an axial flow compressorwith strong frequency component of the first, second, and third harmonic of thefifth-stage stator blade row An inspection of this stator row indicated cracks caused

by high-cycle fatigue

Gears. A frequency of “number of gear teeth ¥ rpm” may indicate resonance withthe natural frequency of the concrete foundation, a fabricated base, or supportingbeams

FIG C-325 Axial-flow compressor spectrum showing blade-passing frequency 13

Figures C-326 and C-327 are typical of the kind of information that can beprovided by accelerometers These data would not be possible in the low-frequencyspectra provided by proximity probes Figure C-326 shows two gears in goodcondition (accelerometer is at the low-frequency end of the gearbox).

FIG C-326 Gearbox signature (low-frequency end) 13

FIG C-327 Gearbox signature (high-frequency end) Potential for damaged tooth 13

Figure C-327 shows a problem with gear A that may be a chipped or crackedtooth.

A frequency of 1¥ rpm may be observed when a 1¥ rpm signal elsewhere in themachine (e.g., an unbalanced orbit) is transmitted to a gear and gets it to runeccentrically This eccentric running in turn produces a 1¥ rpm signal with a highamplitude in the direction of the imaginary line joining the centers of the twomating gears At 90° to this position, the 1¥ rpm signal would be lower, producing

an orbit that is a flat ellipse

This orbit in turn magnifies any resonance to gear mesh frequency if present.When troubleshooting resonance, remove sources for lower order frequencies first,

to help analyze the higher frequency vibration

If gear misalignment occurs, a vibration at 2¥ rpm would probably show up Toprove misalignment, use Prussian blue to coat the gear surfaces and run for a fewminutes A clear indication of contact surfaces and wear pattern shows when thegears are examined

Loose assembly. Looseness of a part generally causes vibration at 2¥ thefrequency of the rotating part To visualize this, consider the case of a loose machinebase and compare it to a bench that has two uneven supports First one supporttouches in a cycle, then the other So the frequency is 2¥ rpm

Drive belts. If drive belts are loose, a vibration is caused This can be observedwith a strobe shone on a reference mark on the belt This is often confused with anunbalanced belt and belts are thrown away unnecessarily

Sources of a vibration-causing force from outside the machine include:

1 Piping stresses—static, cantilevered

2 Foundation problems

 Foundation settling

 Frost melting/permafrost problems

 Moving soil (muskeg or other shifting soil insufficiently removed)

 Foundation inclusions (grout problems, soft feet, and so forth)

3 Extreme climatic change

Contingency measures in a mature model (old or approaching scheduled overhaul) and retrofit. In the case of a mature operating model, the problems prevalent with anew train or prototype model can give way to those posed by:

1 Changing field composition

2 Changing environmental regulations: new burner designs, water and steaminjection to reduce NOx, and so forth

These changes may or may not have anything to do with the aerodynamic andmechanical behavior of the machine in question At any rate, they will have to beanalyzed as they come up and an attempt should be made to approximate somebudget figures for retrofit items that are anticipated due to tightening legislation.Vibration signatures may also be a good indicator of when a machine isapproaching the point of requiring overhaul See Figs C-328 and C-329 Figure C-

328 compares baseline signature with one taken after two years of operation Theincrease in high-frequency levels was found attributable to blade flutter caused bycracked blades

Figure C-329 is similar It shows an increase in the component due to one statorstage’s resonant frequency, indicating high blade flutter, that was found to be caused

by cracks in that stator

Precautions on new turbomachinery. To help avoid problems on new turbomachinery:

1 Ask that vibration specifications be included with preliminary information—prior to formal quote request stage

2 Make sure vibration specifications include data on allowable vibration levels,types of probes to be used, and whether the probes are seismic or proximity

3 Arrange to be present for in-factory balance tests as well as final (full or partialload) tests Final assembly should also be witnessed if at all possible,particularly in the case of a prototype Baseline signatures should be taken

4 Be aware of machinery shipping plans

5 During commissioning, run the drive unit alone and take vibration readings

6 Run the drive unit with the machine coupled, but not in complete process loop

7 Record readings during machine rundown Audit surrounding systems, piping,and so forth

8 Before the machine arrives on site, check piping, grouting, and so forth

9 Do hot and cold alignments on the train

10 With electric motors, ensure half key is allowed for during balance

FIG C-328 Machinery analyses showing comparison of baseline signature to signature before overhaul 13

Troubleshooting philosophy

In any problem situation, the indicators may include vibration readings as well

as gas path parameters There may also be other indicators, such as bleed valvebehavior, bearing cavity temperature, and so forth These other measuredquantities may not be conveniently available (although they may be monitored atsome intervals) in a nonexpert comprehensive system However, most problems—over 95 percent for nonprototype applications—that occur with turbomachinery can

be solved with good VA and PA data

A basic philosophy for troubleshooting is as follows:

1 Spend money on diagnostic equipment only if you can use and interpret thedata If you are new to troubleshooting, VA, and so forth, get help, but with a view

to learning how to do all this yourself A good troubleshooter has the right

 Physical equipment

 Mental knowledge

 Relevant training

2 One of the things that is really useful to have is a portable spectrum analyzer

If you have a vibration system already installed, but you need to see if it wouldbenefit you to

 Retrofit more probes on your installation

 Work out how many you need for similar future installationsthen a portable system with:

 A portable probe or probes (velocity or acceleration transducer)

 A spectrum analyzer, including storage capacity to store successive plots and achart recorder to make a hard copy of the spectrum

FIG C-329 Machinery analyses showing comparison of baseline signature to signature before overhaul 13

is very useful You can now build up your own store of information on every item

of machinery you are responsible for

3 You should study the instrumentation—OEM-supplied or otherwise—on yourinstallation and learn about its accuracy, usefulness, and ability to have its signalfed into a retrofitted PLC (programmable logic controller) or a computer Considerwhat additional instrumentation, if any, might be useful

4 Concentrate on gas path monitoring parameters as these are the most useful.Generally, most systems, however basic, supplied by an OEM will have enough datafor you to fit a PA system This is useful for

 Determining the health of the gas path

 Helping diagnose failed blades, combustion liners, crossover tubes, and so forth

 Determining when a module (compressor or turbine) needs to be washed

 Determining if premature shutdown/maintenance is required

For further discussion of PA systems, see Life-Cycle Assessment (LCA).

5 Consider what the return on investment (ROI) might be if you were to get acomprehensive online (perhaps real-time) condition-monitoring system Consideralso if it would ever make life trouble-free for the operator

Problem diagnosis. Let us assume that a problem has occurred Ask these questionswith reference to the occurrence:

 Will this affect anything else?

 What is the cost of doing nothing?

 How much production will we lose meanwhile?

 Can we correct anything else while we correct this problem?

 What can we learn for future installations?

Summary rules

1 There is no one consistently right answer for any symptom in conditionmonitoring

2 Separate the elements of plant, process, and personnel

3 Do not spend money to get more data than you can thoroughly understand or betaught to understand

4 Fully automated intelligent systems might not be worth the money

5 When you think you know all the answers, see rule 1

Tables C-21 through C-27 give commonly accepted guideline limits for vibrationreadings These limits apply to turboexpanders and all associated machinery in theprocess train.

Figures C-330 through C-333 are a few of the diagnostic charts available inindustry They are not new but then neither is much of the machinery beingmonitored in older plants There is no hard-and-fast rule about which is best.Knowledge of a particular machine and process determines which are appropriate

Guide. Note that the limits expressed in Fig C-332 are based on experience inrefineries This guide reflects the typical proximity probe installation close to andsupported by the bearing housing and assumes the main vibration component

to be of 1¥ rpm frequency The seemingly high allowable vibration levels above20,000 rpm reflect the experience of high-speed air compressors (up to 50,000 rpm)and jet engine–type gas turbines with their light rotors and light bearing loads.Readings must be taken on machined surfaces with runout less than 0.5 mil up

to 20,000 rpm and less than 0.25 mil above 12,000 rpm

Warning. Judgment must be used especially when experiencing frequencies inmultiples of operating rpm on machines with standard bearing loads Suchmachines cannot operate at the indicated limits for frequencies higher than 1¥ rpm

In such cases, enter the graph with the predominant frequency of vibration instead

of the operating speed

TABLE C-21 “Normal” Vibration Levels on BRG Housings in IPS (Peak) Highest Noted on Smooth Machine 20

Introduction to rotor dynamics: vibration theory

The two main categories of vibration systems are:

 Forced systems

 Free systems

A free system operates under forces that are inherent in the system, so it operates

at one or more of the natural frequencies of the system

A forced vibration system operates under the influence of an external forceimpressed on the system Vibration occurs at the frequency of the exciting force,which has nothing to do with the natural frequencies of the system When theexciting force frequency and the natural frequency coincide, we have what is termedresonance Large and dangerous amplitudes occur Fortunately, practical systemshave damping, which includes frictional forces

A degree of freedom is the term given to an independent coordinate that describesthe motion of the system Figure C-334 depicts a one degree of freedom system: theclassical spring mass system

If a system has two or more degrees of freedom, then frequency and amplitudehave no definite relationship Among many types of disorderly motion, there will

be a few where each point in the vibration system follows a definite pattern and

TABLE C-22 Maximum Allowable Vibration Limits on BRG Housing in IPS (Peak) for Operation Up to Earliest Possible Corrective Shutdown 20

the frequency is common; these are called principal modes of vibration Such asystem might be a shaft between two supports, as drawn in Fig C-335.

Most vibration occurs in periodic motion, which means it has cycles that repeatthemselves The simplest form of periodic motion is harmonic motion, which can berepresented by a sine or cosine function Periodic motion, however, is not alwaysharmonic, although it may have harmonic components See Fig C-336

The harmonic motion can be represented as:

Displacement = x = A sin wt (C-1)Velocity and acceleration are obtained by differentiating displacement

TABLE C-23 Machinery Lateral Vibrations, Less Than 0.5 ¥ rpm 20

Appears suddenly at a frequency Bearing oil whirl  Bearing clearance

Same symptoms as bearing oil Seal ring oil whirl  Oil ring seal acting

or reduce vibration severity.

Same symptoms as bearing oil Resonant whirl  Same as oil whirl

piping, etc.

Appears suddenly at or above Friction-induced rotor  Encountered in builtup rotor critical speed when critical is whirl rotor or rotors with

appeared.

Vibration appears/disappears Loose component  Rotor sleeves/impellers

 Bearing liners, housings,

or self-aligning spherical casts have loose fits

 Loose casing or supports Vibration peaks at specific speeds and Subharmonic resonance  Usually occurs as a high axial vibration is often present result of loose components

or as a result of aerodynamic or hydrodynamic excitations, areas to

be investigated for correction are seals, thrust clearance, couplings, and rotor stator clearance

TABLE C-24 Machinery Lateral Vibrations, 1 ¥ Operating Frequency 20

Increasing vibration amplitude with Unbalance  Loose rotor component

speed, behavior repeats for  Foreign object lodged in rotor

 Poor balance [initial startup

of rotor or components added to rotor (coupling, etc.)]

 Off-center journal Vibration peaks at specific speeds, Rotor critical

peaks can usually be shifted with speeds

change in oil temperature

Vibration peaks at specific speeds, Structural  Any machine part or

oil temperature changes will generally resonance supporting structure could have not change the speed at which the its natural frequency in the

Increasing vibration with speed Casing distortion  Uneven casing warmup

 External forces Increasing vibration with speed, Bowed or bent rotor  Temporary heat bow

may or may not repeat for successive  Permanent (no change with runs (prime 1 ¥, also up to 5¥ present) time)

Vibration amplitude varies with time Beat frequency  Occurs when two or more

foundations operate at nearly the same speed

 Occasionally a beat can develop

in one machine if its operating speed is close to a structural component resonance Increasing vibration with speed, other Thrust-bearing  Usually result of off-design frequencies and axial vibration usually damage operation (surge, liquid

problem (design, plugged, or worn labyrinths)

Increasing vibration with speed Shaft Sleeve bearing  Increased clearance

bearing housing amplitude about equal damage  Wiped bearing

Increasing vibration with speed (prime Seal rub  Rub usually relieves itself frequency is 1 ¥ rpm plus many other and therefore appears as

High axial vibration, vibration erratic V or other drive  Mismatched V belts

(prime frequency is 1¥, also 2¥ present) belts, component  Drive and driven pulley not

unbalance but disappears when power off armature

Appears on gears like rotor critical speed Torsional resonance  Usually occurs only during Vibration peaks at specific speeds startup or drastic load-speed

change

TABLE C-25 Machinery Lateral Vibrations, 2 ¥ Operating Frequency 20

Increasing vibration with speed (prime Misalignment of coupling  Thermal casing growth

2 ¥, also 1¥ and/or 5¥ present often or bearing  Piping forces

alignment Increasing vibration with speed Loose rotor components  Loose coupling hub

 Loose impellers or sleeves Increasing vibration with speed Coupling machining  Replace coupling

Appears on adjacent rotors inaccuracies Increasing vibration with speed Coupling damage  Pitting of coupling teeth Vibration appears/disappears suddenly  Loose coupling spacer

Increasing vibration with speed Unbalanced  Crankshaft- or

piston-reciprocating part type machinery

 Loose piston or rod Vibration peaks at specific speed Harmonic resonance  Same as critical or

resonance

TABLE C-26 Machinery Lateral Vibrations, Frequencies >2¥ rpm 20

Erratic high-frequency vibration Rotor rub  Labyrinth rubs generally

failure often self-correct temporarily through wear, steel- on-steel shrill noise during wear.

 Rotor deflection is critical speed rpm ¥ no of vanes/blades Vane/blade aerodynamic  No concern for normal

(always present) rpm ¥ no of or hydraulic forces operations Record signal for

permit identification of possible future problem Also record harmonics.

rpm ¥ no of gear teeth Gear mesh frequency  Record signal for reference.

increase in GMF and harmonics.

 1 / 2 GMF—even no of teeth with machining error.

rpm ¥ no of lobes Lobe pass frequency  Record for future reference (always present).

rpm ¥ no of pads Journal tilt pad bearing  Increased vibration with

High-frequency, destructive Steam turbine valve  Rare occurrence; change valve vibrations Unaffected by vibration plug, seat shape, or increase

Multiples of running frequency Harmonic resonance  Multiples of component

natural frequencies (rotor casing, foundation, bearing housing, diaphragms, etc.).

(C-3)

Note the phase angle difference between displacement, velocity, and acceleration.(See Fig C-337.) Velocity leads displacement by 90° and acceleration leadsdisplacement by 180°

In an undamped free system, shown in Fig C-338, if the mass is pulled downward

and then released, the force of the spring, equal to its stiffness coefficient ¥ distancedisplaced, tends to restore equilibrium

This motion is described by

(C-4)where -kx = restoring force or

or casing and support Loose rotor shrink fits Friction-induced whirl Thrust-bearing damage

Loose assembly of bearing liner, bearing case,

or casing and support Oil whirl

Resonant whirl Clearance-induced vibration

Rotor bow Lost rotor parts Casing distortion Foundation distortion Misalignment Piping forces Journal and bearing eccentricity Bearing damage

Rotor-bearing system critical Coupling critical

Structural resonances Thrust-bearing damage

Pressure pulsations Vibration transmission Gear inaccuracy Valve vibration

Blade passage

* Occurs in most cases predominantly at this frequency; harmonics may or may not exist.

If we assume a harmonic solution to the equation, then we can have the followingsolution

FIG C-330 Vibration measured on bearing housing 15

Maximum Allowable (But Possibly Conservative) Vibration Limits for Operation until Earliest Possible Corrective Shutdown (All Measurements in Inches per Second, Peak)

Speed Harmonics

Screw

Note that filtered components add up to unfiltered total amplitude of vibration.

(1) The significance of vane, blade, and lobe pass frequencies is not yet fully understood More field data must be evaluated to arrive at universally meaningful maximum levels.

(2) Vane, blade, lobe pass, and gear mesh frequency amplitudes vary with load and/or speed change The actual sensitivity should be part

of the database.

which gives us the value of the system’s single natural frequency for any x:

(C-7)

Damped system. Types of damping include viscous damping, friction (coulomb)damping, and solid damping (or structural damping within the material itself ).Figure C-339 depicts free vibration with viscous damping

 Misalignment or bent shaft—if high axial vibration

 Bad belts if rpm of belt

 Resonance

 Reciprocating forces

 Electrical problems

 Resonance

 Bad belts if 2¥ rpm of belt

clearances (looseness)

 Subharmonic resonance

 Beat vibration

frequency

frequency) Mechanical looseness May occur at 2, 3, 4, and sometimes higher harmonics if

severe looseness Reciprocating forces

high-frequency vibration

 Improper lubrication of journal bearings (friction-excited vibration)

 Rubbing

Viscous damping force is proportional to the velocity, so if c is the coefficient of

viscous damping,

or

(C-8)or

If we use the trial solution

which, if we substituted into the previous equation, we get

2 4

k m

1 2

2 2

The solution observed in the latter equation will depend on whether the roots arereal, imaginary, or zero If the critical damping coefficient required to make the root

k m

2 2

FIG C-334 System with single degree of freedom 13

FIG C-335 System with infinite number of degrees of freedom 13

FIG C-336 Periodic motion with harmonic components 13

FIG C-337 Harmonic motion of displacement, velocity, and acceleration 13

FIG C-338 Single degree of freedom system (spring mass system) 13

FIG C-339 Free vibration with viscous damping 13

We now define the damping factor

k m

cr 2 2

c m

k m

2 2

4 >

t = c

c c

FIG C-340 Overdamped decay 13

FIG C-341 Critical damping decay 13

i.e., the roots are equal

Underdamped systems have imaginary root solutions With an underdampedsystem,

so the imaginary roots are given by

(C-15)

Then the response becomes

which can be written

(C-16)

where x is the response amplitude.

Forced vibration. In forced vibration there is an external excitation force See Figs.C-343 and C-344

Now the equation of motion is

(C-17)or

Let us say that the steady-state oscillation of this system is given by

c m

1 2

2 2

4

c m

k m

2 2

where D is displacement of the steady-state oscillation Motion lags force by q Sofor velocity and acceleration, we have

to velocity Inertia force is in phase with displacement and acts in the oppositedirection to acceleration This agrees with the physical interpretation of harmonicmotion See Fig C-345 for vectorial representation of the system

FIG C-343 Forced vibration system 13

FIG C-344 Free body diagram of mass (M) 13

 d lags F by q

 kD acts opposite D

 Damping force lags D by 90°

 Damping force acts opposite velocity

From the vector diagram we get the phase angle and the amplitude

ÊË

ˆ

¯+

ÊË

ˆ

¯

2 2

2

w

ww

tanq w

w

=-

FIG C-345 Vector diagram of forced vibration with viscous damping 13