ods & modal case histories 022009

8/3/2019 ODS & Modal Case Histories 022009

1/47

ODS & Modal Case Histories

Barry T. Cease

Cease Industrial Consulting

February 20th, 2009

1


2/47

ODS & MODAL CASE HISTORIES

BARRY T. CEASE, CEASE INDUSTRIAL CONSULTING

FEBRUARY 20TH, 2009

INTRODUCTION

What is ODS analysis and why do we need it?What is Modal analysis and why do we need it?

When should either technique be used?

Example of how to collect ODS & Modal data (test unit)

CASE HISTORY#1 ACCEPTANCE TESTING OF AHU FAN

Equipment & problem description

Route data, coastdown data & determination of offending frequencies

Modal analysis of fan, motor & base

Conclusions & recommendations

CASE HISTORY#2 ACCEPTANCE TESTING OF WATER PUMP

Equipment & problem description

Route data results versus standards & determination of offending frequencies

ODS analysis of pump, step 1 (baseline)

ODS analysis of pump, step 2

ODS analysis of pump, step 3

Conclusions & recommendations

QUESTIONS & CREDITS

Modal Testing, Robert J. Sayer, PE, Vibration Institute 31st Annual Meeting, June 19th, 2007

Applied Modal & ODS Analysis, James E. Berry, PE, 2004

Machinery Vibration Analysis 3, Volume 2, Vibration I nstitute, 1995

Mechanical Vibrations, 2nd Edition, Singiresu S. Rao, 1990

2


3/47

What Is ODS?

ODS stands for operating deflection shape.

ODS analysis generates a computer model of your machinery that depicts its motion

while running at operating speed & load. You literally see how your machine is

moving as it operates. This modeling can be extremely useful to illuminate an

otherwise elusive solution to machinery vibration problems.

First, a CAD model of the machine or mechanical system is created (structure file).

Second, detailed & meticulous vibration measurements are made on the machinetypically during normal operation. These measurements consist of both the amplitude

& phase of vibration at one or multiple frequencies of interest all referenced to a

common point.

Finally, these field measurements are imposed on the model to generate visible

animations of the model/machine at the distinct vibration frequencies of interest

(typically the offending frequencies).

3


4/47

What Is Modal Analysis?

Modal analysis identifies the frequencies & shapes your machine likes to vibrate at

(natural frequencies) and compares these to the normal forces present on the machine

to see if a match exists that produces an undesirable resonant condition.

If a resonant condition is identified, common solutions involve the following: force

reduction (ie: reducing the vibration forces present in the machine), tuning of the

mechanical system (ie: adding or reducing mass or stiffness to the system at the right

spots), or force movement (ie: changing the machine speed as possible to avoid the

condition). The actual process of modal analysis is similar to that of ODS analysis except

measurements are made while the machine is not running typically using a force

hammer and one or more sensors. The hammer provides the input (force) and the

sensor(s) measure the response (motion) at multiple points on the machine.

These modal measurements are then processed thru a technique known as curve-

fitting and then like ODS measurements, imposed on the model to produce animations

that are analyzed.

4


5/47

PLOT 1: Vibration data measured during normal operation. Dominant vibration at 1,789 cpm or 1x RPM of

machine (offending frequency).

PLOT 2: Modal data measured while machine down. Note the strong response at 1,837 cpm which is near 1x RPM.

Vibration Spectra .vs. Modal Data

5


6/47

When Should ODS or Modal Analysis Be Used? When standard vibration analysis techniques have failed to determine the exact

problem.

When resonance is suspected.

An ODS or Modal job begins best with a determination of the offending frequencies of

vibration usually made using standard, route vibration spectra.

6


7/47

Example: Collecting ODS Data From

CMS Test Rotor Kit

Machine operating.

Determine reference point (typically use route data point with strong vibration at all

offending frequencies).

First roving point collected at reference point (ie: 1Y:1Y).

Continue collecting other points all along machine at predetermined points.

Both the total number of points collected as well as the point locations are key to howaccurate the model animation will represent reality (ie: spatial aliasing).

7


8/47

Example: Collecting Modal Data From

CMS Test Rotor Kit

Machine not operating.

Determine reference (driving) point. Like ODS analysis above, we want to use a point

with strong vibration at all offending frequencies, but for modal analysis, we must be

even more picky by applying the impact & measuring the response at many points

until good representation of all offending frequencies is found (driving point).

First roving point collected at driving point (ie: 1Y:1Y).

Usually, we rove around with the sensor(s) and apply impact at the driving point, but

this isnt necessary. We could also rove around with the hammer with similar results

although getting a good impact at all points is typically difficult.

Continue collecting other points all along machine at predetermined points.

Like ODS analysis, both the total number of points collected as well as the point

locations are key to how accurate the model animation will represent reality (ie: spatial

aliasing).

8


9/47

Case History#1: Acceptance Testing Of AHU Fan

Equipment & Problem Description

Newly installed AHU Fan operating atmedical facility.

Vibration acceptance testing requiredfor all rotating equipment at facility.

Fan OEM contacted for vibration

specifications - maximum acceptablevibration at 0.35 ips-pk.

Isolated, center-hung, centrifugal fandriven thru v-belts by a 4-poleinduction motor operating on avariable speed drive.

Entire machine supported by 4-ea

spring isolators mounted on floorarranged per diagram at right.

Two spring isolators are also mountedbetween the fan frame and wall tocounter fan thrust.

Motor

Fan

4-ea Floor

Isolators2-ea Wall

Isolators

9


10/47

INITIAL DATA & FINDINGS, PART 1

Initial vibration data was collected on bothfan & motor at 100% speed and overall levels

were compared to OEM specifications.

Because this machine operated on a variable

speed drive with normal operation anywhere

between 50 and 100% full speed, coastdown

data was collected between this speed

range.

Unfortunately, this machine failed to stay

within OEM specs both at 100% speed and at

many points between 50 & 100% speed.

Maximum vibration levels occurred not at

100% speed, but at lower speeds suggesting

possible resonance problems.

Offending speeds/frequencies were

identified from coastdown data atapproximately 1,500, 1,800 & 1,900 cpm.

Field observations noted the entire machine

visibly jumped when the machine speed

was set to 90-95% and motion at the motor

outboard isolator seemed worst.

Measurement Point

Vibration @

100% Speed

Maximum

Vibration

Level

Fan Speed @

Max Vibration

OEM

Vibration

Spec

Motor, Outboard,

Horizontal 1.289 n/a n/a 0.35

Motor, Outboard -

Vertical 1.475 n/a n/a 0.35

Motor, Inboard -

Horizontal 0.955 n/a n/a 0.35

Motor, Inboard -

Vertical 1.027 n/a n/a 0.35

Motor, Inboard - Axial 1.205 n/a n/a 0.35

Fan, Inboard -

Horizontal 1.929 3.11 1,903 0.35

Fan, Inboard - Vertical 0.605 0.45 1,495 0.35

Fan, Inboard - Axial 0.257 n/a n/a 0.35

Fan, Outboard -

Horizontal 0.797 2.60 1,492 0.35

Fan, Outboard - Vertical 0.672 0.65 1,805 0.35

Fan, Outboard - Axial 0.258 n/a n/a 0.35

10


11/47

INITIAL DATA & FINDINGS, PART 2

AHU SF1.3 MOTOR & FAN, OVERALL VIBRATION AT FULL SPEED

0

0.5

1

1.5

2

2.5

MOH MOV MIH MIV MIA FIH FIV FIA FOH FOV FOA

MEASUREMENT POINT

OVERALLVIBRATION(IPS-PK

Plot of overall vibration levels at all measurement points at full speed.

11


12/47

SPECTRAL DATA AT FULL SPEED

SF-1.3

CPM

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 22,000 24,000 26,00026,000 28,000 30,000

in/s0-

pk

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1.821 in/s1987.5 CPMCursor A:

O/All 1.938 in/s 0-pk

1.4

0

1.4

0

1.4

0

Fan, Outboard

Horizontal

Vel Spec 60000 CPM

12/27/2007 4:45:23 PM


Fan, Inboard

Horizontal

Vel Spec 60000 CPM

12/27/2007 4:42:59 PM


Motor, Outboard

Vertical

Vel Spec 60000 CPM

12/27/2007 4:34:40 PM


Motor, Outboard

Horizontal

Vel Spec 60000 CPM

12/27/2007 4:33:35 PM


Spectral data from points of high vibration at full speed (MOH, MOV, FIH & FOH). Dominant

vibration in all spectra occurs at top fan speed of 1,987 cpm or 33.1 Hz.

12


13/47

FAN COASTDOWN DATA, BODE PLOTS

Bode Plot - 1X - SF-1.3 - Fan, Inboard - HorizontalVel Freq 30000 CPM [Tach]

CPM

800 1,000 1,200 1,400 1,600 1,800 2,000

d

e

g

-60

-40

-20

0

20

40

60

80

3.108in/s 0-pk,55.506deg @1903.091CPM(1903RPM)

CPM800 1,000 1,200 1,400 1,600 1,800 2,000

in

/s

0

-p

k

0

0.5

1

1.5

2

2.5

3

Vel Freq 30000CPM [Tach]

Bode Plot - 1X - SF-1.3 - Fan, Outboard - HorizontalVel Freq 30000 CPM [Tach]

CPM

800 1,000 1,200 1,400 1,600 1,800 2,000

d

e

g

-60

-40

-20

0

20

40

60

80

100 2.6in/s 0-pk,31.233deg @1496.278CPM(1492RPM)

CPM800 1,000 1,200 1,400 1,600 1,800 2,000

in

/s

0

-p

k

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

Vel Freq 30000CPM [Tach]

PLOT 14: Coastdown data at fan, inboard, horizontal

(FIH) position in Bode format shows suspected natural

frequency at approximately 1,900 cpm (31.667 Hz). The

highest vibration level on the fan was measured at this

point at 1,903 rpm at 3.11 ips-pk!!

PLOT 15: Coastdown data at fan, outboard, horizontal

(FOH) position in Bode format shows suspected natural

frequency at approximately 1,500 cpm (25 Hz). The

highest vibration level measured at this point occurred at

1,495 rpm at 2.60 ips-pk!!

13


14/47

INTERFERENCE DATA (MOTOR & FAN SPEEDS)

% Full Speed Fan RPM 1x Fan 2x Fan 1x Motor 2x Motor fn1 fn2 fn3

25 500 500 999 446 892 1,500 1,800 1,900

30 599 599 1,199 535 1,070 1,500 1,800 1,900

35 699 699 1,399 624 1,249 1,500 1,800 1,900

40 799 799 1,598 714 1,427 1,500 1,800 1,900

45 899 899 1,798 803 1,606 1,500 1,800 1,900

50 999 999 1,998 892 1,784 1,500 1,800 1,900

55 1,099 1,099 2,198 981 1,962 1,500 1,800 1,900

60 1,199 1,199 2,398 1,070 2,141 1,500 1,800 1,900

65 1,299 1,299 2,597 1,160 2,319 1,500 1,800 1,900

70 1,399 1,399 2,797 1,249 2,498 1,500 1,800 1,900

75 1,499 1,499 2,997 1,338 2,676 1,500 1,800 1,900

80 1,598 1,598 3,197 1,427 2,854 1,500 1,800 1,900

85 1,698 1,698 3,397 1,516 3,033 1,500 1,800 1,900

90 1,798 1,798 3,596 1,606 3,211 1,500 1,800 1,900

95 1,898 1,898 3,796 1,695 3,390 1,500 1,800 1,900

100 1,998 1,998 3,996 1,784 3,568 1,500 1,800 1,900

Interference data table. Forcing frequencies .vs. suspected natural frequencies.

14


15/47

INTERFERENCE DIAGRAM

INTERFERENCE DIAGRAM, AHU FAN

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

4,500

500 600 700 800 900 1,000 1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 1,900 2,000

FAN SPEED (RPM)

FORCINGF

REQUENCY

(CPM)

1x Fan

2x Fan

1x Motor

2x Motor

fn1

fn2

fn3

Interference diagram of fan & motor speeds .vs. suspected natural frequencies at 1,500, 1,800 & 1,900 cpm.

Potential interference occurs at approximately 750, 850, 900, 950, 1000, 1075, 1,500, 1675, 1,800, 1,900 & 2,000 rpm. 15


16/47

MODAL ANALYSIS OF AHU FAN

A Simple CAD model of the fan,motor & base was created andmodal data collected.

This modal data was imposed onthe model appropriately toidentify the natural frequencies ofthe mechanical system.

The known offending frequencieswere compared with naturalfrequencies found to identify amatch that would result inresonance condition.

Two natural frequencies (modes)were identified which most likely

are being excited by the fanspeeds as: 26.1 & 31.1 Hz or 1,566& 1,866 cpm.

Both these modes involvedistortion of the machine basenear the motor.

Simple CAD Model of AHU fan.

16


17/47

MODAL ANALYSIS 26.1 Hz Mode

Modal animation at 26.1 Hz of AHU fan & motor

inboard. Note distortion of machine frame near

motor.


outboard. Note distortion of machine frame near

motor.

17


18/47

MODAL ANALYSIS 31.1 Hz Mode


inboard. Note distortion of machine frame near motor.


outboard. Note distortion of machine frame near motor.

18


19/47

CONCLUSIONS & RECOMMENDATIONS, AHU FAN

1) This fan failed OEM vibration specifications due primarily to resonances identified in

the machine frame at 26.1 & 31.1 Hz.

2) Unbalance may exist in the fan, but its contribution is minor by comparison to the

resonances identified. If balancing is done to reduce forces, perform at 1,200 rpm fan

speed or lower to avoid resonances and associated balance difficulties.

3) The isolator near the motor outboard may be loose with the floor. Please inspect &

repair as needed.4) Resolving the resonance issues will likely involve either adding an additional pair of

isolators between the fan & motor or stiffening the machine frame near the motor or

both.

5) Stiffening the machine frame might be accomplished by welding either X bracing

inside the base near the motor or welding plate onto the machine frame for the motor

base to rest on.

6) A slightly larger AHU fan of similar design with six isolators instead of four was also

tested as part of this job this six isolator fan passed acceptance testing at all speeds.

7) These conclusions were presented to the customer along with documentation. Months

later I checked with plant personnel who informed me my customer had opted to

balance the fan with disappointing results.

19


20/47

CASE HISTORY#2 - ACCEPTANCE TESTING OF HIGH

PRESSURE WATER PUMP

Equipment & Problem Description

Newly installed critical high pressure

water pump at plant.

Plant vibration specs called for maximum

vibration levels of 0.10 ips-pk.

At first glance, many problems wereseen with the design & layout of the

pump & piping.

What follows are vibration spectral &

ods data at progressive stages of our

attempt to bring this pump into plant

specs.

Initial state of newly installed water pump. What

is wrong with this design & layout?

20


21/47

BASELINE OVERALL LEVELS 9/16/08

Plant vibration specs called for overall levels no greater than 0.10 ips-pk.

Both the motor & pump failed specs during baseline measurements taken on 9/16.

Highest levels were seen at pump with much higher than expected thrust levels.

Movement could be felt at the floor while collecting data.

21


22/47

BASELINE SPECTRA 9/16/08

Pump spectra from 9/16/08 shows dominant vibration at the vane-pass frequency (4x rpm) of the pump.

A higher than normal vibration level at this frequency generally indicates flow problems of some sort with

the pump. From the photo earlier, what did you see that could be causing flow problems at this pump?

Horizontal measurement shows high 1x & 2x rpm vibration as well as vane-pass.

Thus, our offending vibration frequencies are primarily 1x, 2x & 4x rpm for this machine on 9/16/08

(baseline).

22


23/47

BASELINE ODS 9/18/08 MOTION @ 1xRPM (3,590 cpm)

Pump maximum vibration at this

frequency occurred at the pump,

inboard, horizontal measurement

(PIH) at 0.05 ips-pk.

Note 180 degree radial motion

across the coupling at this key

frequency. Shaft alignment & softfoot are suspect.

Note movement of both machine

pedestal & surrounding floor

suggesting significant problems

with this machine foundation.

23


24/47






Note vertical movement of entire

pedestal & surrounding floor at

this frequency (120 Hz) again

suggesting significant problems

exist with this machine

foundation.

24


25/47




inboard, vertical measurement

(PIV) at 0.24 ips-pk.

Note thrusting of both pump

suction area and entire pump

rotor. I suspect this is due in part

to turbulence at the pump

suction from elbow entry.

Note continued pedestal &

foundation movement.

Note little movement at motor.

25


26/47




inboard, axial measurement (PIA)

at 0.04 ips-pk.

Note continued thrusting of

pump & pump suction at this

frequency. Note relatively little motion of the

motor or pedestal at this

frequency.

26


27/47

CONCLUSIONS & RECOMMENDATIONS, 9/18/08

CONFIGURATION

1) The suction piping entering the pump requires modification to allow for a minimum of

5 pipe diameters of straight length before entering the pump (10 diameters length

preferred). The presence of the elbow at the pump suction is no doubt causing

excessive turbulence in the fluid flow as it enters the pump which in turn is exciting the

pump vanepass frequency.

2) The shaft alignment is questionable due to the 180 degree radial motion across the

coupling. Please recheck shaft alignment & soft foot and correct as necessary to plant

specs.

3) The machine pedestal & surrounding floor appear loose from the ground. Movement

of the pedestal & floor were clearly seen in ODS at both 1x & 4x rpm.

4) Both motor & pump were hot to touch and low air flow was noted at the motor.Uncertainty exists as to the existing & proper lube for pump. Install larger fan at motor

endbell & change oil to OEM specs.

27


28/47

PUMP & PIPING CONFIGURATION 10/2/08

1) The suction piping was modified per

9/18/08 suggestions.

2) The alignment was checked &

reportedly corrected to plant specs.

Soft feet were reportedly identified

and corrected.

3) A new pump rotor was installed with

an impeller reportedly balanced to

plant specs.

4) A recirculation line was added.

5) A larger motor fan was added.

6) The pump oil was changed to an ISO 68weight per OEM specs.

28


29/47

OVERALL LEVELS, 10/2/08

Unfortunately, both motor & pump vibration levels actually increased with the 10/2/08

modifications.

Motor vertical measurements were the only ones that decreased.

Both motor & pump remained out of plant vibration specs.

29


30/47

SPECTRAL DATA 10/2/08

High vibration at 1x, 2x & 4x rpm (vane-pass) remained in all pump spectra.

New appearance of vibration at 3x rpm with 10/2/08 modifications not seen in baseline data.

Highest vibration levels remain at 4x rpm (vane-pass).

30


31/47

ODS 10/2/08 MOTION @ 1xRPM (3,590 cpm)




at 0.12 ips-pk.

Note the excessive horizontal

movement of the newly modified

pump suction piping at this key

frequency. Notice how much more the piping

is moving when compared to

motion at either the pump or

motor.

Could the solution to the bad

actor at your plant be found at the

piping or ducting?

31


32/47





at 0.08 ips-pk.

As in the earlier ODS at 1x rpm,

note how piping motion is much

greater than that seen at either

the pump or motor. Note the near perfect 2nd mode

motion (sinusoidal) of the

horizontal run of discharge

piping.

Note the excessive vibration of

both the vertical run of discharge

piping as well as the newly

installed recirculation line (1st

mode).

Note how total motion of the

discharge piping seems to pull

the pump in the axial or thrust

direction.

32


33/47


Pump maximum vibration at thisfrequency occurred at the pump,



Again, notice how the piping motion

dwarfs that seen at either pump or

motor.

Note how excessive motion of therecirculation line (1st Mode) is

pulling the pump.

Note how excessive motion of the

suction line is also pulling the

pump.

Note the excessive motion in the

short section of discharge piping

between the recirculation line &

pump discharge.

33


34/47






Again, notice how much more the

piping is moving (vibrating) compared

to either the pump or motor.

Note how motion of the recirculationline at this key frequency is by far the

most and resembles a possible 2nd

mode.

Note how motion at the suction piping

remains high as well.

34


35/47




inboard, axial measurement (PIA) at

0.05 ips-pk.

Again, notice how motion of the

piping dwarfs that seen at either

motor or pump.

Note the excessive motion of the

discharge piping here.

Note how motion at the recirculation

line is relatively small when

compared to earlier frequencies.

35


36/47

INSPECTION RESULTS 10/2/08

A close inspection of the piping found

a broken discharge pipe hanger just

above the horizontal pipe run in the

ceiling.

It was unknown how long this hanger

had been broken, but its absence no

doubt added flexibility to thedischarge piping run.

36


37/47


CONFIGURATION

1) Remove the recirculation line if possible. The addition of the new recirculation line has had a

negative effect on machine vibration levels due to multiple suspected resonances occurring there.

2) Like the recirculation line above, motion of the discharge piping at multiple frequencies is having a

negative effect on machine vibration. Add additional support to the discharge piping at the points

where high motion is observed in the ODS animations. If possible, try adding support from at leasttwo additional points.

3) Repair or replace the broken discharge hanger found at the ceiling.

4) Provide additional support (if possible) under the suction piping as excessive motion continues

here.

5) No soft foot records were identified from the alignment job performed since 9/16/08 on this

machine. Please perform another soft foot and alignment check on this machine, make corrections

as necessary and document results.

37


38/47

PUMP & PIPING CONFIGURATION 10/16/08

1) A new, larger standpipe was added under

the suction piping for better support.

2) A new support was added to the discharge

piping at the nearby wall.

3) A new stiffening connection was added

between the discharge & suction piping

above the recirculation line.4) The recirculation line was not removed.

5) The broken discharge hanger was not

repaired or replaced.

6) Pump soft foot corrections were made and

documented. Machine alignment is

documented to plant specs.

38


39/47

OVERALL LEVELS, 10/16/08

Both motor & pump overall vibration levels dropped significantly with the 10/16/08

modifications.

Motor overall vibration levels are now below plant spec at every measurement point.

Pump overall vibration levels are much better, but remain out of plant specs with highest

levels being seen at the pump horizontal measurement.

39


40/47

SPECTRAL DATA 10/16/08

Significantly reduced vibration levels at all offending frequencies is seen in all pump spectra.

Remaining vibration still occurring at 1x, 2x, 3x & 4x rpm (offending frequencies).

Vibration at 4x rpm (vane-pass), although reduced, remains the dominant vibration

frequency in most measurements.

Vibration at 3x rpm, although reduced, is the highest single source of vibration in all three

pump measurements.

40


41/47





0.12 ips-pk.

Notice how motion of the piping is

much greater than that observed at

either the pump or motor.

Note how now both the discharge &

suction piping are flexing in the axial(thrust) plane and are pulling the

pump with them.

Notice how the motor is virtually

still at this key frequency any

alignment or coupling problems are

now unlikely here.

Both the addition of the new

stiffening connection between

suction & discharge as well as the

continued existence of the

recirculation line appear to have

negative effects on machine vibration

(transmission path).

41


42/47






The newly installed discharge

piping support at the wall was

found both loose from the wall and

the piping. This looseness is at least partly to

blame for the excessive motion of

the discharge piping seen at or near

the location of this new support.

Both the newly installed stiffening

connection between discharge &

suction piping as well as the

recirculation line must be

eliminated to reduce machine

vibration levels.

42


43/47





Note the excessive horizontal motion

of the discharge piping at this

frequency with maximum deflection

occurring somewhere between the

recirculation line & discharge valve.

The recirculation line should be

removed.

Horizontal bracing of the discharge

line somewhere between the

recirculation line & discharge valve

may be necessary to eliminate this

vibration. Only consider thismodification after the glaring

problems mentioned earlier are

corrected and high vibration levels

persist.

43


44/47






Both the recirculation line as well

as the newly installed stiffening

connection continue their

negative effects on machinevibration levels.

Again, notice how little both the

motor & pump are moving when

compared to the piping.

44


45/47




0.02 ips-pk.

From the earlier spectral plots,

vibration at this frequency is small

when compared to the others.

Machine vibration levels at thisfrequency could be reduced by

removing the stiffening

connection between discharge &

suction lines.

The suction pipe stand is vibrating

excessively at this frequency in the

horizontal direction.

45


46/47


CONFIGURATION

1) Remove the recirculation line & stiffening connection. Excessive motion (vibration) was seen at

both the recirculation line & newly installed stiffening connection at many frequencies. Remove

these two piping components to reduce machine vibration levels.

2) Tighten up the newly installed support between the discharge piping and wall.

3) Repair the broken discharge hanger located in the ceiling.

46


47/47

QUESTIONS & CREDITS

1) Modal Testing, Robert J. Sayer, PE, Vibration Institute 31st Annual Meeting, June 19th,

2007

2) Applied Modal & ODS Analysis, James E. Berry, PE, 2004

3) Machinery Vibration Analysis 3, Volume 2, Vibration Institute, 1995

4) Mechanical Vibrations, 2nd Edition, Singiresu S. Rao, 1990

47

ods & modal case histories 022009

Documents