Admin
مدير المنتدى
عدد المساهمات : 18745
التقييم : 34763
تاريخ التسجيل : 01/07/2009
الدولة : مصر
العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
 |  موضوع: كتاب ASM Metals Handbook of Case Histories In Failure Analysis Volumes 1 & 2 الخميس 29 ديسمبر 2022, 7:29 pm | |
| 
أخواني في الله
أحضرت لكم كتاب
ASM Metals Handbook Of Case Histories In Failure Analysis Volumes 1 & 2
و المحتوى كما يلي :
Part I—Special Cases
Case #1: Vibration in Hydroelectric Dam
The entire structure of a hydroelectric dam would begin to vibrate whenever a hydroelectric turbine operated in a certain
load range. The vibration problem was identified as Rheingan's Influence. Rheingan's Influence is caused by spiral vortex
filaments that rotate at a speed lower than the rotational speed of the turbine. In this case, the load range at which the
Rheingan's Influence occurred varied with the upstream and downstream water level. The vibration supervisory system
did not register any excessive levels during the vibration transient, so the operators, who were located at a remote
location, did not know what load ranges to avoid.
Vibration spectra were taken from shaft proximity probes while the problem was occurring. The plots, taken with a
spectrum analyzer that was DC coupled, showed that there was no difficulty in detecting the vibration. The vibration
supervisory system had not detected the 15 cpm vibration caused by the Rheingan effect because the AC coupling
capacitor filtered out the vibration. Modifications to the supervisory system to allow DC coupling are being considered.
This will allow the operators to avoid the unstable load ranges, because nothing can be done to prevent the Rheingan
Influence.
Case #2: Vibration of Steel Strip Caused by an Induction Furnace in a Steel Mill
An induction furnace in a steel mill was used to heat and diffuse galvanize (zinc) into the steel strips. A loud, high pitch
frequency would radiate from the steel plate during the induction heating process. When the sound began, vertical stripes
would also appear on the plating. The stripes on the galvanized strips caused the steel to be rejected.
An FFT analyzer was set up to determine the frequency of the sound, the vibration frequency of the induction furnace,
and the frequency of the current being supplied to the induction coils. In all three cases the frequency was 7250 cycles/s.
Since the plate vibration frequency corresponded to the operating frequency of the induction furnace, the furnace
frequency was increased to 9000 Hz to see whether a change in frequency would eliminate the problem. When the
furnace was operated at the higher frequency the stripes did not disappear, but merely moved closer together.
It was determined that the induction furnace was exciting the natural frequencies of the plate, creating standing waves that
resulted in the stripes being formed as the molten zinc flowed to the wave nodes. The thin plate had several natural
frequencies within the normal operating range of the furnace, so changing from one frequency to another did not
eliminate the striping problem. Increasing the frequency made the stripes closer together, and decreasing the frequency
resulted in the stripes being further apart. A solution to the striping problem was found by analogy with rotor stabilization
in the turbine industry.
When turbine generators are brought to operating speed there are several speeds that match the natural frequencies of the
various blades. The natural frequency of a blade will depend on blade length as well as other material/geometric
parameters. It is necessary, due to thermal stress and other considerations, to operate in the range of blade speeds where
vibration problems can occur while the rotors get thermally stabilized. The speed on the turbine is continually varied
during the thermal soak period, and this continual variation prevents damage to the turbine blades. This continual
variation approach was applied to the striping problem. Rather than operating the induction furnace at one frequency, thefurnace control circuit was designed to continuously vary the frequency. This modification in operating conditions
completely eliminated the striping problem.
Case #3: Vibration of Microscope in Hospital Microsurgery Room
A microscope used by surgeons during operations that involve replanting limbs was mounted from the ceiling of a
surgery room. The chief surgeon complained that the image was jittery and that it was very tiring to operate under these
microscopic conditions, particularly when the scope was set for maximum magnification.
Vibration was clearly noticeable under test conditions when the scope was set to its greatest magnification, and printed
material placed on the operating table was examined. Vibration spectra taken on both the table and the microscope
showed that the level of vibration on the table was very low across the spectrum, and that the levels of vibration on the
microscope were significant. Examination of the vibration spectra revealed peaks at 225 cpm and 435 cpm.
To trace the source of the problem, vibration levels were measured on the top of the microscope's isolator and on the
structural steel supporting the isolator. It was discovered that the levels on the isolator were 7× higher than the levels on
the steel support. This meant that instead of isolating the microscope from the structural vibration, the isolators were
actually amplifying the vibrations from the I-beam. To find the cause of the amplification, an impact test was performed
on the microscope to determine its natural frequencies. The natural frequency of the scope on its isolation system was
found to match the vibration on the I-beam.
Isolators function by creating a system with a natural frequency tuned much lower than the expected disturbing
frequency. This, in turn, creates a mechanical low pass filter which will not pass the higher frequencies. However, a
problem may occur if a frequency near the low tuned natural frequency of the isolated system is present. In this case,
instead of isolating the frequency, the isolators actually amplified the vibration levels.
The solution to the microscope vibration problem was to ground the isolators. With the isolators grounded, the vibration
levels on the microscope dropped to acceptable levels. The frequencies that were removed by grounding had previously
existed because isolators on the roof fans were tuned to the same frequencies as the microscope. Flow excitation in the
fans excited the fans' isolated natural frequencies that were transmitted through the structural steel and amplified by the
microscope's isolators. Grounding of isolators should only be tried if nothing else works. When the isolators are
grounded, higher frequencies, if any are present, will obviously pass through the ground. However, in this particular case,
grounding out the isolators did not introduce any significant higher frequency vibrations and did reduce the microscope
vibrations to an acceptable level.
Case #4: Torsional Vibration on a Reciprocating Pump
A 66 rpm reciprocating water pump driven by a gear box and belt reduction experienced excessive torsional vibration that
was being picked up at the gear case when the pump was operated.
Torsional testing generally is performed using either one of two methods. The first is the use of a strain gage to measure
the alternating torsional strain. The second method involves measuring the change in the passing frequency of equally
spaced gear teeth or equally spaced reference marks. The change in passing frequency of equally spaced marks on a shaft
is an indication of corresponding changes of angular velocity. This data can be integrated to evaluate the angular
displacement and torsional strain.
For this test, both the strain gage and equally spaced reference mark techniques were used so that a comparison between
the two methods could be made. A strain gage was mounted at a 45° angle on the drive shaft and between the gearcase
and the belt used to drive the reciprocating pump. An FM transmitter and a battery were also mounted on the drive shaft
to transmit the strain information to an antenna and subsequently to an FM receiver-demodulator. The experimental setup
was calibrated by putting one end of the drive shaft in a vice and applying 100 lbf torque to the other end. While the 100
lbf torque was applied, the output of the demodulator was measured with a voltmeter. The calibration constant from this
test was then input into an FFT analyzer, resulting in readings directly in lbf at each frequency present. Equally spaced
photoreflective tapes were placed at 20 locations around the output hub of the gearcase for the second measurement. A
photocell device was then mounted to pick up the pulse train of the reflective tapes. The output from the photocell
provided the input to a torsional-demodulator-integrator that produced an output of 200 mv/° peak to peak. With the
above combination it was possible to measure the torque being fed to the gear case from the pump and the resulting
amount of angular displacement. When the pump was operating against no appreciable back pressure, there was 1.5° of
angular displacement present at the gearcase hub at 66 cycles/min. The torque from the strain gage at this condition was
27 lbf. As the back pressure on the pump was increased, both the displacement and torque also increased. When the
output pressure from the pump was 180 psi, the torsional vibration had increased to 8.79° and the alternating torque to
123 lbf. The pump speed was 66 cycles/min during these measurements. These data showed that the alternating torque
peaks from the pump were too high. To correct this problem, a flywheel was added to level the torque peaks by absorbing
energy during one half of the cycle and return in energy to the system during the other half cycle. The alternating torque
values were reduced by a factor of three with the addition of the flywheel.This case history shows how two different measurement techniques or test methods led to the same conclusion. The test
method used will depend on the needs of the investigator, the test equipment available, and the accessibility of the
machinery to be tested. Another interesting note concerning the test results is that when coherence was measured between
the two signals with a dual channel analyzer the level of correlation was 0.98. This shows a direct correlation between the
alternating torque on the drive shaft and the displacement on the gearcase hub.
Case #5: Ghosts
The residents of a small Midwestern town complained that they felt movement of their houses, particularly at night. One
of the residents stated that her sister would no longer come visit her because she thought the house was haunted by ghosts.
She felt this way because lampshades would move, pictures would rattle, and rocking chairs would rock without anyone
being in them.
Vibration measurements were made at several of the houses in the community, along the sidewalks, and at a factory
located near the houses. The testing was performed with an SD-380 analyzer that used a 1000 mv/g low frequency
seismic accelerometer to convert the mechanical motion into an electronic signal.
The vibration signature taken at one of the houses where complaints had been registered showed vibration-induced
displacements at a level of 1.22 mils at 300 cpm. It was also observed that the amplitude of the vibration would oscillate,
indicating the possibility of a beat frequency and suggesting the presence of more than one driver frequency. (Beat
frequencies are generally produced by two or more closely spaced frequencies adding and subtracting as they go in and
out of phase.) The zoom feature of the SD-380 analyzer was used to determine if there was more than one frequency
present. A 16:1 zoom plot of the vibration at one of the residences clearly showed the presence of several frequencies, all
close to 300 cpm.
The next step in the investigation was to make a survey of the vibration present at the nearby factory. The factory was a
foundry containing several vibratory conveyors that moved parts from one area to another. Zoom plots were taken at each
conveyor to determine their vibration frequencies. Exact matches were found between the frequencies present at the
houses and several of the vibratory conveyors in the factory. Additional testing confirmed the correlation between the
operation of the conveyors and the vibration at the houses.
These studies demonstrated that, rather than having ghosts, the residents of the small town were experiencing low
frequency vibrations from the operation of the vibratory conveyors in a nearby factory. The 5 Hz (300 cpm) frequency is
easily perceived by the human body, particularly at night when other motion and noise are at a minimum. It also can
excite low stiffness tructures such as lampshades and rocking chairs. The factory installed balancing devices to reduce the
amount of force entering the ground from the conveyor systems that induced the highest offsite vibrations, consequently
removing the “ghosts” from the community.
Case #6: Vibration of Nuclear Magnetic Resonance Machine
A Nuclear Magnetic Resonance (NMR) instrument used to test chemical samples was moved from a second floor location
to a third floor room. After the move, the NMR instrument performed poorly even though testing demonstrated that
everything was operating properly within the unit. The technician conducting the tests thought that vibration might be the
cause of the problem, so a vibration analysis was performed.
A signature taken at the probe of the NMR unit showed vibratory accelerations of 8190 micro g's at a frequency of 26 Hz.
At the same frequency, the floor beside the NMR unit showed accelerations of 1550 micro g's. The readings meant that
the vibration on the NMR unit was 5.2× higher than the level measured on the floor at the 26 Hz frequency. A resonance
check was performed to determine the cause of the amplification. The floor was impacted and the response was measured
on the detector of the NMR unit. The transfer function clearly showed a peak at 26 Hz, indicating that the unit was
resonant at the frequency that was present on the floor.
It was concluded that fans in an HVAC room near the third floor location were providing the 26 Hz forcing function. The
resonant condition was significantly amplifying the vibration. It was recommended that the NMR unit be installed on
isolators that were 95% efficient in attenuating the 26 Hz vibration. The 95% reduction in the forcing function resulted in
vibration levels that were lower than the unit had experienced in its original location and allowed for satisfactory
operation of the NMR.
Case #7: Vibration Induced by Sound
The installation and operation of a rotary casting conveyor apparently caused high levels of vibration of the walls and
windows in the control room of a foundry.
The windows in the control room displayed the highest levels of vibration. A plot of the vibration measured on the
foundry windows showed a level of 39.2 mils of displacement near the center of one of the windows. A frequency of 885
cpm was predominant in the spectrum. The 885 cpm vibration on the windows was also found to be present on the wallsof all the offices in the foundry. This frequency matched the vibration frequency of the rotary casting conveyor. Vibration
measurements next to the conveyor, however, were low. The conveyor was mounted on springs and also fitted with
dynamic absorbers—which were apparently working as designed, considering the low levels of vibration observed on the
floor next to the conveyor.
The next test involved taking measurements with a microphone. The output from the microphone was analyzed on an FFT
analyzer, and it was found that the sound level at 885 cpm (14.75 Hz) was over 100 dB. It seemed that this sound level
would not have a negative effect because the frequency is below normal hearing range for humans; it could be felt,
however, and caused a sheet of paper held in front of the conveyor to move noticeably.
The final test involved performing a resonance check on the window. A plot of the response of one of the control room
windows showed that the natural frequency of the window was very close to the frequency of the pressure waves being
emitted by the rotary casting conveyor.
The rotary conveyor clearly caused the vibration problem, but the transmission path was through the air rather than
through the structure. The windows being resonant near the operating frequency of the conveyor were further amplifying
the problem. It was recommended that the windows be fitted with cross braces to move their natural frequencies away
from the operating frequency of the conveyor and that a sound absorbing enclosure also be built around the conveyor.
Case #8: Machine Tool Vibration
A machine that cut chamfer on wrist pin holes on piston rods for automotive engines produced a loud, high-pitch sound
during the backside chamfer operation. Examination of the rods showed that the surface that was machined was very
rough and completely unacceptable to the customer. The machine manufacturer suggested that the problem might be due
to bearings or gearing within the chamfer head. Test data proved that this was not the case.
During the 900 rpm cutting operation, a vibration spectrum was taken on the machine being used to cut the chamfer. The
data was taken on the chamfer head in the vertical direction. The frequency of the vibration was at approximately 115,000
cycles per min (1916 Hz). Data were captured in the digital buffer of a spectrum analyzer during the transient. It could be
determined from the captured data that the vibration would build up and then abruptly quit when the cut was completed.
The peak level of vibration measured on the part being machined reached a level of 0.82 in./s. Another test performed
with the machine operating at 1200 rpm showed that the vibration frequency produced on the machine and the part was
the same as the frequency produced when the machine operated at 900 rpm. The observation that the frequency did not
change when the tool rpm was varied was evidence that a natural frequency was being excited. An impact test on the
cutting tool, the most likely source of the problem, showed a resonance peak at 114,750 cpm. Profiling the imaginary
components of the transfer functions taken along the surface of the tool produced a mode shape of the first natural
frequency of the tool. The 114,750 cpm mode was found to be the first cantilever mode of the cutting tool. To complicate
matters, it was discovered that the part in its holder had a natural frequency near that of the tool.
It was recommended that the tool be modified to separate its natural frequency from that of the part. It was also
recommended that the basic process be reviewed, because the problem only occurred when the backside chamfer cut was
made. This observation suggests that the problem may have originated when the tooling bar was under tension rather than
in compression.
Case #9: Extremely High Levels of Vibration on the End Cap of a Large Pipe
A large pipe (37 in. diameter) at a refinery had levels of vibration over 4.0 in./s on an end cap that was located after an
expansion joint. Additionally, there had been failure of several of the expansion joint retaining rods.
A vibration spectrum taken on the end cap showed a 4500 cycles/min vibration with a level of 4.47 in./s. The area
surrounding the pipe was checked for rotating equipment operating at that frequency. No machinery operating anywhere
close to that speed was found.
A visual exam of the pipe showed that there was a large butterfly valve upstream of the end cap. The end cap was on a
dead end section of a tee. Conversations with plant personnel determined when the vibration had started and what, if
anything, had been done to the piping prior to the onset of the high vibrations and the retaining rod failures. The first
response was that work had been performed on the expansion joint, however, “nothing had been changed.” Further
discussions and examination of the piping drawings showed that one thing had indeed changed: a baffle had been
removed just upstream of the expansion joint. The baffle was a thick flat plate with two small holes in it. The plant
personnel were not aware that it served any purpose; however, an overall review of the system showed that it was very
important. The butterfly valve was causing flow disturbances and was found to be operating only 30% open. This resulted
in pressure pulsations in the pipe. The baffle was acting as a low pass filter which allowed the static pressure to equalize
but would not let the dynamic pressure pulsations pass. The pressure pulsations were probably small, but there were two
design features that caused the vibration levels to be high. The first was the amount of area on the end cap. A 37 in.
diameter end cap has 1075 in.2 of surface area. Therefore, even a small pressure pulsation can generate a large force whenacting on such a large area. The second reason for the vibration-induced damage was the low stiffness of the 20 ft long
retaining rods.
The vibration problem was shown to result from pressure pulsations within the pipe acting on a large area with low
stiffness. The removal of the baffle was a key element in the problem. The plant was advised to install short bolts across
the expansion joint until the unit was brought down for its next outage. The purpose of this action was to stiffen up the
system and provide a backup to the long bolts that had been failing. This action was possible because the piping was
already at its maximum temperature, so the joint did not need to accommodate any further expansion. During the next
outage the baffle was reinstalled in the pipe and the short bolts across the expansion joint were removed. The vibration
problem was entirely eliminated.
Case #10: Vibration Noise Affecting Dolphins
The Indianapolis Zoo had recently erected a new whale and dolphin building. It was a state of the art facility that allowed
observation of the dolphins from a large area above the water and also from a restaurant below the facility. The dolphins
arrived with much fanfare and their training began. A problem arose, however, when the dolphins seemed a bit confused
and had some trouble concentrating during their training sessions.
The trainers noticed a sound in the auditorium area and requested that tests be performed to trace down its source. A
spectrum of the sound identified the noise as a pure tonal at 1200 Hz. The level was 52 dB. The sound was traced to the
motor on one of the large vent fans built into each end of the building. The metal shell of the motor was functioning as a
speaker radiating the 1200 Hz frequency. The problem was easily resolved. The vent fans were on variable speed drives
and the speed at which this frequency occurred was programmed out of the drive. With the 1200 Hz frequency eliminated,
there were no further sound related difficulties and the dolphin training resumed.
Case #11: High Vibration on Plate Glass Window
An office building had an open atrium that extended from ground level to the roof. In the center of the atrium was a large
flowing fountain surrounded by meeting rooms. Each meeting room had a large plate glass window, approximately 8 ft
tall by 12 ft wide, that allowed individuals in the meeting room to view the fountain. These large plate glass windows
were vibrating at a frequency of 240 cycles/min.
The floors and walls were all tested and no significant level of the 240 cpm vibration was observed in any location. The
doors were also tested, and the doors that were not held tight against their latches also exhibited the 240 cpm vibration. It
was concluded that the vibration was airborne and affected those items that had large surface areas and low stiffness
values (plate glass windows and loose doors).
The search began for the source of the 240 cpm stimulus. The most obvious location to look for airborne transmission of
pressure pulses was in the air handler area in the penthouse located at the top of the building. The search was difficult
because the frequency was so low that it did not match any fan speed and certainly not any blade pass frequency. A
breakthrough occurred when, walking by an air handler, it was noticed that the pipe to the cooling coils in the discharge
duct of the fan was vibrating. The spectrum on the pipe matched the 240 cpm vibration on the window. When that
particular air handler was shut down the vibration on the windows several stories below immediately stopped.
Examination of the fan system revealed that the screws in the braces that connected the heating coil to the ductwork were
missing. Impact tests of the coils showed that the natural frequency was 240 cpm. Without the supports the coil was
cantilevered off of the heating pipes, resulting in a low natural frequency. When the fan was in operation, broad band flow
energy excited this natural frequency causing the coil to vibrate in the duct at 240 cycles/min. Because the coil was
approximately 6 ft × 6 ft, the vibrations generated significant energy pulses. The pulses were fed directly into the atrium
area where they excited the large windows. The windows responded with high levels of vibration due to their very large
cross sectional area and very low stiffness. Proper attachment of the pipe and cooling coils within the ductwork
eliminated the problem.
Case #12: Vibration on Piping Connected to an Engine Driven Reciprocating Compressor
A large gas piping company called about a problem with one of their reciprocating natural gas compressors. The site
operator thought there was a vibration problem on the suction bottle of the compressor. Reciprocating compressors have
suction and discharge bottles to absorb the pressure pulsations from the pistons. This is similar to adding a capacitor to an
electrical circuit to absorb the voltage ripple.
Because the compressor unit was variable speed, the spectrum analyzer was set in the peak hold mode to capture the
highest level at any particular frequency. The engine speed was then varied from 600–800 rpm. The peak hold plot
showed that the primary frequency of interest was 2× the engine speed. This is not surprising considering that a
reciprocating engine was driving a reciprocating compressor. The highest peak in the peak hold data was 46.5 mils at
1410 cycles/min. Therefore, when the compressor speed was at 705 rpm, the vibration was a maximum and 2× thecompressor speed. Due to a high level of frequency dependent response a resonance test was performed by impacting the
suction bottle in the direction of the highest motion. The test confirmed that a natural frequency of the suction bottle was
being excited by the 2× component of the compressor. The solution was to add stiffeners to the suction bottle.
Case #13: Paper Machine Roll Vibration
A large tissue machine capable of manufacturing a 20 ft wide section of paper at 5000 ft/min was experiencing vibration
problems on one of its tension rolls. The vibration would get as high as 1.0 in./s in some instances. The manufacturer was
in the process of building an identical unit in Europe, and there was a great deal of concern that if this was a design
problem it might also occur in that unit.
During the first series of tests it was apparent that the problem was a resonance in the roll support. The manufacturer
disagreed and said that the roll was merely out of balance. Because the machine was under warranty, the manufacturer
removed the roll, had it balanced, and reinstalled it. This reduced the vibration. However, when a couple small flat lead
weights used to balance a tire were installed to test the sensitivity the amplitude went back up to a high level. This showed
that even a slight change in balance of the large roll would result in very high levels of vibration, again suggesting a
resonance problem.
Three measurement techniques were used to evaluate the resonance theory. The first was to obtain a peak hold plot at
various manufacturing speeds, the second was a map plot produced during the speed change, and the third test was an
impact test using a dual channel spectrum analyzer. All three techniques confirmed that the roll support resonance was the
problem. The most revealing plot was the map plot. It showed that as the speed was increased two of the other rolls would
also excite the resonance as their speeds matched its natural frequency. This evidence demonstrated the futility of the
manufacturer in trying to solve the problem by balancing the large roll and showed that the design needed modification.
The ultimate solution was a complete redesign of the tension roll support.
Case #14: Drag Line
Large drag lines are used to remove the soil above a strip of coal. Sometimes the soil layer is over 100 ft thick. The drag
lines may weigh 5000–7000 tons, and their buckets can remove 100 or more cubic yards at a time. Typically there are
several motor-generator sets that generate DC current for the drag and hoist motors. One drag line of interest had five
very large motor-generator sets. A motor generator set for this drag line consisted of a large synchronous motor and two
generators on one side of the motor and three generators on the other side. All the motors and generators were solidly
coupled and there was only one bearing per generator (the motor had two bearings). The motors were synchronous, which
means that all the units operated at exactly the same speed—in this case, 1200 rpm. To make the situation worse, all the
motor generator sets were located on the same metal deck. There was a total of 30 rotating elements (five synchronous
motors and 25 generators) operating on one metal deck, all rotating at the exact same speed.
The vibration problem occurred at 1200 cycles/min. The whole structure, even the boom, was shaking at 1200 cpm.
With minimal investigation it was found that the vibration was higher on one of the motor generator sets. Efforts were
made to balance that unit, where the highest displacement reading was 11 mils in the vertical direction on the outboard
generator. The first balance shot was installed in that rotor. The balancing reduced the vibration levels in the horizontal
direction and increased the levels in the vertical direction. Therefore, the influence coefficients indicated that it would not
be possible to balance the unit in that rotor.
In an attempt to simplify the problem, two of the generators were uncoupled from the motor. Even uncoupled the
generator vibration on the outboard generator was still 7.9 mils.
Because the largest component in the motor generator train was the synchronous motor, a balance shot was placed in that
rotor. When a trial shot was added, all the response vectors indicated that a solution could be obtained by adding the
proper amount of weight at the proper angular location on the rotor of the synchronous motor. Fifty ounces of weight had
to be added along a 30 in. radius on the motor. When this was done, the vibration level on the whole unit returned to
normal. This solution was found by using the adage, “When in doubt, add the trial weight to the rotor with the largest
polar moment of inertia.”
Case #15: Sound and Vibration from Pulse Furnaces
A building recently constructed at a university had objectionable levels of both sound and vibration. Both problems were
related to the three pulse furnaces used to heat the building. The furnaces were located in the basement, and the flues ran
under the floors, up a chase, and out through short stacks in the roof.
Vibration and sound spectra were taken in the office areas where there were problems. The primary frequency in both the
sound and vibration spectra was approximately 31 Hz, which was the pulse firing frequency of the furnaces. At the end of
the building next to the offices with the highest levels was a hollow square tower that only contained stairs. The tower
went up past the rooftop much like a church steeple. In the area of tower that stood above the roof, directly across fromthe furnace exhaust stacks, there was a three ft diameter circular window. It was discovered that this window was
vibrating at extremely high levels at the furnace pulsing frequency. When a resonance test was performed, it was
discovered that the natural frequency of the window was very close to the pulse firing frequency of the furnaces. The
window near the top of the tower was effectively functioning as a speaker, three ft in diameter, pumping energy into the
tower. Complicating the matter was the height of the open tower, approximately 30 ft, which matched the wavelength of
the 37 Hz frequency.
To resolve the problems, mufflers were installed on the flue lines and the height of the flues was raised to well above that
of the window in the tower. Raising the flue height prevented the excitation of the window, and these combined actions
solved both the noise and vibration issues.
Part II—Turbines, Pumps, and Compressors
Case #1: High Vibration on a High Pressure Core Injection Pump at a Nuclear Plant
Operators of nuclear power plants are required to comply with section XI of the ASME code regarding In Service
Inspection. When vibrations on a steam turbine driven pressure core pump on a boiling water nuclear reactor were
measured prior to the time of this case history, the code stated that base line readings were to be taken in mils
displacement, and action had to be taken if the base line readings doubled. The code was then changed to recognize
velocity as the acceptance criteria.
The machine train for the pressure core pump consisted of a turbine driver, a high-pressure pump, a gear case, and a low
pressure booster pump. Vibration spectra were obtained for all the bearing locations on the pump train. The readings were
at normal levels everywhere except in the horizontal direction on the high pressure (HP) pump. A level of 1.4 in./s was
present at what appeared to be twice the running speed of the unit. A cascade plot of vibration on the HP pump in the
horizontal direction from the inboard end to the outboard end showed that the vibration was high at each end of the pump
but was nearly zero in the center. Due to the large difference between the vertical and horizontal readings and the
presence of an apparent rigid body-pivoting mode, a horizontal resonance was suspected.
An impact test was performed on the pump, and a natural frequency at nearly twice running speed was found. This mode
matched the response found while the pump was running (i.e., high on the ends and low in the middle). Because the
vibration was predominately at what appeared to be twice running speed, it was suspected that misalignment might be the
source exciting the horizontal structural resonance.
The alignment was found to be out of specifications. The alignment was corrected and a test was run on the unit. There
was no improvement in the level of vibration; in fact, the vibrations were slightly higher on the test run than on previous
runs. This change in the level of vibration followed a pattern that showed that the vibration in the 2× cell would vary from
0.9 to 1.6 in./s from one test run to another.
In an attempt to determine the phasing of the vibration, a once per revolution pulse was used as a reference trigger for the
FFT analyzer, and a signature was taken in the synchronous time average mode. As the number of averages increased, the
vibration at what appeared to be twice running speed disappeared. This was one of the breakthroughs in the analysis of
the problem: it meant that the vibration was not phase locked to the high-pressure pump shaft.
Following the results of the synchronous time average test, the pump train drawings were reexamined. It was found that
the gearcase had a 1.987:1 reduction. In addition, it was discovered that the low pressure pump had a four vane impeller.
The pieces were beginning to come together.
The pump manufacturer was contacted with this information. He recalled that there had once been a case of an acoustical
resonance with a similar pump. To determine if this could be contributing to the problem, the piping between the low
pressure and high pressure pump was measured. It was found that the length of pipe connecting the pumps was equal to
one half wave length of the low pressure pump blade pass frequency. Since the low pressure pump had 4 vanes and the
gear reducer had a 1.987:1 reduction, the vane pass frequency appeared to be twice the running speed of the high pressure
pump.
As a final test to confirm this theory, a tach pulse was put on the low pressure shaft. The vibration pickup was placed on
the high pressure pump. The vibration on the HP pump was found to indeed be phase locked to the low pressure pump.
The problem on the high pressure pump was not at twice the HP pump running speed as it had originally appeared, but
was actually at the vane pass frequency of the low pressure pump. It appeared to be at twice the HP pump running speed
because of the 4 vane impeller in the LP pump and the almost exact 2:1 speed reduction between the two pumps. The
problem was amplified by the acoustical resonance of the pipe connecting the discharge of the LP pump to the suction of
the HP pump. The vibration was further amplified by the horizontal structural resonance of the HP pump casing. The
major clue to the solution of the problem was that the vibration on the HP pump was not phase locked to the shaft on that
pump and was, therefore, originating from another source. The final clue was the past acoustical resonance problem
encountered by the pump manufacturer. The recommended solution was to remove the 4-vane impeller and replace it with
a 5-vane design. The impeller change solved the problem.Case #2: Boiler Feed Pump Alignment Change Causing Pump Failure and Turbine Pedestal Cracking
A boiler feed pump on a 500 mW turbine generator at a new generating station failed after being in operation only a few
months. The inboard seals and the stage next to the coupling were destroyed. Due to the type of failure, the plant initiated
an alignment study.
Dynalign bars were mounted between the pump and the turbine driver to determine the amount of movement from the hot
to cold condition while the unit was in operation. When the unit was brought off line there were no significant changes
recorded. However, a few minutes later, the Dynalign/Dodd bar system was found to be entirely out of range. When the
operators were questioned as to what had happened during that period, they replied that the only thing they had done was
to break vacuum on the main turbine.
To determine if the vacuum had anything to do with the apparent alignment change, the bars were reset and long-range
probes were installed to increase the measurement range of the Dodd bars. The vacuum was then reapplied to the system.
Everything appeared normal until the vacuum reached 11 in. of Hg. At that point the gap voltages of the Dodd bar probes
started to change. By the time full vacuum was achieved, the relative motion between the turbine and the pump was over
0.100 in. When the vacuum was released the readings moved 0.100 in. in the opposite direction. The test was repeated
with identical results. An examination of the system was then performed.
A 20 ft pipe descended downward from the turbine and intersected with a horizontal pipe that was capped on one end and
connected to the condenser on the other end. The horizontal pipe had three expansion joints. The purpose of the expansion
joints was to isolate the boiler feed pump turbine from stresses induced by thermal growth of the horizontal condenser
pipe. Thrust canceling rods were installed between the end cap and the main condenser. The thrust canceling struts
transmitted the atmospheric pressure load (14.7 psi) on the end cap to the condenser. The source of the problem was that
threaded studs in the thrust canceling struts were sliding into the struts. This was the result of failed welds on large nuts
located on the backside of the strut end plates. The net result of the failure was that atmospheric pressure, which was
being applied to the six ft diameter end cap, was pushing on the 20 ft vertical run of pipe attached to the bottom of the
feed pump turbine. This large force, applied to the 20 ft lever provided by the vertical pipe run, had the capability of
generating nearly 1 million lbf torque against the turbine. Examination of the concrete turbine base showed that the
turbine foundation had several cracks that were attributed to the bending torque.
The thrust canceling struts were repaired and the alignment changes were rechecked as vacuum was reapplied. Following
the repair, there were no significant changes in alignment as a result in variations in vacuum.
Case #3: Cavitation Destroying Impellers on Large Circulating Water Pumps
The impellers on large, low rpm, 156,000 gpm circulating water pumps on a cooling lake at a large power plant were
failing. The failure mode appeared to be cavitation. The impellers looked as though they had been attacked by metal
eating termites.
A vibration spectrum showed a large amount of broad band energy with no distinct peaks. The key to the analysis, as is
the case with a good percentage of pump problems, was to examine the flow head curve. The flow head curve indicated
that at the design flow of 156,000 gpm the back pressure would be equivalent to 30 ft of water. However, when the back
pressure was measured, it was only 10 ft. It was found that during cold weather, when the lake water was cool, operations
was using only one pump to reduce power consumption. The system was designed to operate against the back pressure
produced by two pumps in parallel. With only one pump in use the system back pressure dropped, and that pump went
into cavitation.
Case #4: Low Pump Flow Destroying Antifriction Bearings in a Pump
Three identical double suction, single stage pumps sat in a row at a power plant. The bearings were failing on one of the
pumps every few months. The other two pumps had no failures. Alignment was checked and different bearings were tried,
but the problem was not relieved.
It was noticed that while the pump was in operation the shaft vibrated in the axial direction. This type of vibration is
called axial shuttling and can occur when a pump is operating against too much back pressure. The suction and discharge
pressure were consequently measured and compared to the flow head curve. It was discovered that most of the time the
pump was operating at its shutoff head. The system was examined based on this observation.
The pump in question pumped water from a tank located in the basement to another tank that was seven stories above
ground level. The tank on the upper floor had a level switch that shut a control valve when the tank was full. When this
occurred, water from the pump flowed through a bypass line back to the tank in the basement. The flow through this
recirculation line was controlled with an orifice plate. Stamping on the orifice plate said that it had a two in. diameter
hole; however, specifications indicated that the hole should have been three in. The actual hole in the plate was
discovered to be only one in. in diameter. This small hole caused the pump to effectively operate at its shut off point when
the control valve to the upper tank was shut, causing the axial shuttling that destroyed the pump bearings.Case #5: Cracks in Large Vertical Pump Shafts
Large vertical pump shafts were cracking every few weeks. Due to the severity of the problem, underwater proximity
probes, casing probes, and torsional instrumentation were installed on one of the pumps. High levels of subsynchronous
vibration were observed when the pump was put into operation. Natural frequency and mode shape measurements
determined that the subsynchronous vibration was centered about the shaft's 1st lateral natural frequency.
The cause of the problem was traced to a maintenance superintendent purchasing impellers from a non-OEM source. The
design of the impellers varied significantly from the original design. This caused high levels of turbulence that excited the
natural frequency of the shaft. Nonsynchronous vibration produced stress reversals that, in turn, caused the shafts to fail
by fatigue.
Case #6: Problems with Boiler Feed Pumps
Two similar boiler feed pumps would operate successfully for several months, then the running speed levels would start
trending upward. The feed pumps had a history of vibration problems and were overhauled. Following the overhauls the
pumps would operate smoothly, but after a few months the vibration levels would start to increase.
Testing showed that the pumps were operating near a critical speed when fully loaded. This was determined when
changes in speed resulted in large amplitude changes and shifts in the phase angles. A newly overhauled pump did not
show these same traits. Further testing determined that the pump seals were wearing and that this wear reduced the
Lomakin stiffening of the shaft, allowing the natural frequency of the more compliant shaft to drop into the operating
range.
Case #7: Containment Spray Pump-Mass Addition
The containment spray pumps at a two-unit nuclear power plant had a history of high vibration at the vane pass frequency
of the pumps. The pumps were vertical units that turned at 1785 rpm. The pump impellers had 4 vanes. This resulted in a
vane pass frequency of 119 Hz. The highest levels of vane pass vibration occurred at the bottom of the motor in line with
the discharge line. Because the levels were much higher in line with the discharge line as compared to 90° out, a
resonance was suspected. An impact test was performed and there was a resonance identified at 111 Hz.
Based on the natural frequency, the forcing frequency, and the damping, an amplification factor of 5.4 was computed by
using the following equation:
Forcing frequency = 119 Hz
Natural frequency = 111 Hz
Damping = .05 (calculated by phase slope and power method)
ω = Forcing frequency
ω
η = Natural frequency
ξ = Damping
X = Response
X 0 = Unamplified response
In an attempt to understand why the level was the highest at the bottom of the motor, impacts were made at several points
along the motor and the pump. The imaginary parts of the transfer functions were then used to plot the mode shape of the
111 Hz resonance. The mode shape agreed with the data in that the maximum response of the mode was at the base of the
motor.
Based on this information, mass was added at the base of the motor to lower the natural frequency, thereby reducing the
amplification factor. Calculations showed that the addition of 950 lb of mass at the base of the motor would drop the
natural frequency to 101 Hz. According to the calculations, assuming the same damping, the amplification factor wouldbe reduced to 2.5. This amount of weight was added by installing channel iron around the base of the motor and clamping
lead weights between the two pieces of channel. The pump was tested after the addition of the mass. The vane pass levels
dropped to 0.26 in./s. After this same modification was made to all four pumps at this facility, all the pumps easily passed
ISI surveys.
Case #8: Coupling Lock Up of Nuclear Steam Generator Feed Pump Turbine
A steam turbine driven feed pump experienced high levels of twice running speed vibration. The orbits indicated that the
problem was misalignment. According to the plant personnel the unit had been aligned per the specifications. When the
unit was brought down for an outage the coupling was examined. Its teeth were severely worn, the lubricant had failed,
and it had evidently locked up.
Based on this evidence, a study of the operating alignment was made. It was determined that the original specification
was wrong. Originally the pump had been set high relative to the turbine. The final setting required that the pump be set
0.020 in. lower than the turbine. The specification change was due to considerations of the vacuum draw down of the
turbine and an incorrect assumption as to the amount of pump growth.
Case #9: Resonance Destroys Generator
A 500 mW, two pole generator at a fossil plant was destroyed when the phase lead insulation failed due to a 120 Hz
resonance. A massive failure resulting from a phase to phase short led to testing of the natural frequencies of phase leads
on generators of a particular manufacturer.
The testing showed that the phase leads on this style of generator can have resonances just above 120 Hz. This is very
dangerous because 60 Hz current is used in the U.S., and, thus, the two magnetic poles pass by a stationary structure at
120 Hz. This passage provides strong excitation at that frequency. It was discovered that the phase lead natural
frequencies tend to drop as the phase leads loosen with operating time. It was then determined that yearly testing was
required to find and correct approaching resonance problems prior to future failures. These tests were performed until a
major design change was made and the resonance frequency was changed. During several years of operation before the
design was changed, many approaching problems were identified and corrected without any further failures.
Case #10: Oil Whip in a 500 Megawatt Turbine
A large, 500 mW steam turbine had very peculiar behavior characteristics. It would operate with no problems for months
at a time, but if it had to come off line for a few hours it could not be restarted. A high vibration from oil whip in the first
LP rotor bearing apparently prevented the restart. However, if the restart was delayed for a day or so, restart could be
accomplished without any problem. The turbine would also restart immediately after being brought off line. Such a
situation has all the signs of a thermally related alignment problem.
Because normal alignment equipment cannot be used on an operating turbine, a special system was developed to measure
the elevation changes of the bearings. This system showed that when the vacuum was drawn on the unit the low pressure
rotor bearings dropped significantly. When the vacuum draw down effect was combined with differential thermal
shrinkage as the unit cooled (the LP hood cooled quicker than the HP section), it resulted in the first LP bearing being
unloaded enough to cause oil whirl. As the unit came up to speed, the oil whirl locked onto the rotor's first natural
frequency and developed into oil whip. The installation of a tilt pad bearing in the first LP position eliminated the hot
startup problem.
Case #11: Oil Whirl in a Chiller Unit
The inboard bearing of the steam turbine driving a chiller at a university campus heating facility experienced repeated
failures. Examination of the bearing showed that the top half had been fatigued to the point that babbit was separating
from the base metal. Vibration spectra contained high levels of subsynchronous vibration. Because the bearing was
located next to the coupling and oil whirl was present, misalignment was suspected.
A series of alignment measurements were made across the coupling, and it was found that there was significant relative
motion during the first hour of operation. A laser was set up with a receiver mounted on an I-beam to establish which
machine was moving, and it was found to be the chiller. The root cause was determined to be the suction line on the
chiller shrinking as the unit cooled. This shrinking caused the chiller to rock back, subsequently lifting the shaft unloading
the turbine bearing and causing it to become unstable.
Case #12: Centrifugal Air Compressor with 4× Bull Gear Vibration on 1st Stage Compressor WheelA compressed air facility had experienced severe difficulties in bringing its main compressor unit into service. The first
stage shaft of the compressor had a natural frequency near its operating speed of 16,200 rpm. The problem was so severe
that the compressor had to be redesigned to accommodate a new shaft.
Following the redesign, the compressor was brought into service. It was noticed that the vibration level on the 1st stage
was still higher than was desired. When a signature was taken, it was discovered that there was another frequency present
besides the running speed. The frequency turned out to be 4× the bull gear speed. Readings taken on the casing also
showed the presence of the 4× bull gear frequency. A survey of the casing discovered that an oil pump cantilevered to the
case was vibrating at 3.0 in./s at the 4× frequency. This was found to be the lobe mesh frequency of the pump. When an
impact test was performed, the cantilevered natural frequency of the pump matched the 4× frequency.
The level of vibration dropped significantly when a brace was installed on the pump. In addition, the 4× bull gear
vibration that was present in the signature of the 1st stage proximity probes nearly disappeared. When the brace was
removed, it reappeared. It was determined that the oil pump had been shaking the compressor case. The natural frequency
of the newly modified 1st stage was close enough to the 4× bull gear frequency that it amplified the response relative to
the casing and was picked up on the proximity probes. The installation of a permanent brace on the oil pump eliminated
the problem.
Case #13: Coupling Unbalance in High Speed Compressors
A 6000 rpm turbine driving a chiller compressor was in alarm following an overhaul. The vibration level was only high
on the proximity probes on the inboard bearing next to the coupling. Because the vibration on the other end was low and
the critical speed vibration was also low, weights were added to the coupling. It took only 3.8 grams/mil to balance and
eliminate the problem. The vibration level on the probes dropped to below 0.5 mil.
A few months later the unit was down for another inspection and the coupling was disassembled. It was discovered at that
time that the coupling had not been assembled with the match marks aligned during the previous overhaul. The match
marks were put in line and the unit was restarted. The vibration was again high, but when the balance weights were
removed the vibrations level was again under 0.5 mil.
This is a case that illustrates the importance of carefully match marking couplings on high speed units. Couplings
represent overhung weight, and because the proximity probes are often located near the coupling, high speed machines
are very sensitive to any changes in coupling unbalance.
In another case involving a 10,000 rpm ammonia compressor, the owner had spent over $100,000 trying to reduce the
vibration to below the alarm setting. The unit had been disassembled three times and finally was sent back to the factory
for a stack balance. When it came back, the problem had not changed.
The data showed that when the rotor went through its critical at 6000 rpm there was very low response. However, from
about 8000–10,000 rpm the vibration on the coupling end probes increased to well above the alarm level. A point of
interest is that there was no phase shift during the 8000–10,000 rpm range. It took one 11 gram washer on one of the
coupling bolts to solve the problem. Several years later the customer called with a similar problem on the same unit. The
compressor was balanced in the coupling during the phone call using the same sensitivity and lag angle that had been
calculated for the previous coupling shot.
Part III—Fans and Motors
Case #1: Balancing a Large Fan
A 5000 HP 720 rpm fan at a power plant showed above normal levels of unbalance. Several attempts were made to
balance the unit, all of which were unsuccessful. After attempting several balance shots in an I.D. fan, the casing vibration
levels were reduced to around 2–3 mils but would not go any lower.
Because there was difficulty in balancing the fan, shaft stick measurements were taken to determine the absolute motion
of the shaft. The shaft movement was discovered to be over 17 mils. Because the bearing clearance was only eight mils,
there was a strong indication that the bearing was moving in the housing. A large plunger bolt at the top of the bearing
was tightened to reduce the bearing movement. After tightening, the casing vibration increased to 21.5 mils. The fan was
then easily balanced to below the one mil level desired by the plant personnel. The bearing movement in the housing had
caused a nonlinear response that made balancing nearly impossible.
Case #2: Incorrect Selection of Isolators
A number of air handler units in a large city all had the same symptoms. The fans operated with acceptable levels of
vibration; however, the motor drivers all had high levels of vibration in the vertical direction. When the spectra were
examined it was discovered that the primary component of the motor vibration was at the fan's operating speed.An investigation found that the isolators under the motor were sized improperly and were too stiff. This resulted in the
natural frequency of the isolated system matching the operating speed of the fans. The isolators were therefore acting as
amplifiers of the fan vibration rather than isolators of the motor vibration. Apparently the same size isolators were used
for the motor as were used for the heavier fans in similar service.
Case #3: High Axial Vibration on a Fan Due to a Disk Wobble Natural Frequency
The axial vibration of a belt driven exhaust fan operating at 1200 rpm was always high. The fan would be balanced, but
within a few weeks the axial vibration would again increase to unacceptable levels. Due to the sensitivity of the fan to
unbalance, a resonance was suspected and natural frequency tests were performed. There was no natural frequency match
when the fan was struck in a lateral direction. However, when the fan was impacted axially there was a match with
running speed.
The mode shape was measured to gather more information. It was found that the shaft was the node point and that the
opposite sides of the fan were out of phase. This is commonly called a disk wobble natural frequency. Fans that have this
problem exhibit sensitivity to unbalance, particularly in the axial direction. The solution in this case was to simply change
the speed of the fan. If this had not been an option, stiffening of the back plate of the fan wheel would have been
necessary.
Case #4: High Cross Effect from Fan to Motor
A motor/fan combination had high levels of vibration. The motor vibration levels were higher than on the fan, so a
representative from the motor shop tried to balance the motor—with no success.
Past experience on other large fans indicated that the fan may have been unbalanced rather than the motor. When the
phase angles were measured, the fan angles were leading the motor angles. Based on this data, the fan was balanced even
though it had lower levels than the motor. Balancing the fan brought the motor levels down to very acceptable amplitudes.
It is important to remember that the fan rotor will generally have a much higher level of polar rotating inertia than a
motor. It is quite common for a large fan to shake a motor, but much less common for a motor to shake a fan.
Case #5: Unequal Air Gap
An electric motor at a foundry was exhibiting high levels of vibration. In addition to having above normal levels of
unbalance, it had almost 0.4 in./s of 120 Hz vibration.
When the motor was examined, it was discovered that there was a 0.035 in. variation in the air gap from the top to the
bottom of the motor. Air gaps are measured by using long feeler gages to measure the clearance between the rotor and the
stator. This was a static air gap deviation, meaning that when the rotor was turned the narrow gap remained in the same
location. The problem was resolved by making adjustments on the end bells to insure that the rotor was centered in the
stator.
Case #6: Large 3600 rpm Motor in Venezuela with a Thermal Vector
An engineer at a refinery in Venezuela described an unusual sounding problem during a telephone conversation. Their
large motor was not running well after it had been balanced. Further information helped clarify the situation. When the
plant was brought down for an outage, the motor was run unloaded. During the unloaded operation it was noted that the
vibration on the proximity probes was over three mils. Based on this amplitude the plant personnel had elected to balance
the motor. After balancing the amplitude was approximately 1.5 mils. Everything seemed to be going well until the plant
was restarted and load was applied to the motor. As the motor was loaded the amplitude went up to nearly 4 mils. The
plant engineer tape recorded the proximity probe signals along with a tach pulse signal and sent the data to the U.S. for
vibration analysis.
The analysis showed that the motor had a large thermal vector and that the motor had been compromised balanced in the
past. The compromise shot had been designed to let the motor have high levels of vibration in the low load condition
where it seldom operated. This decision was made so that when the thermal vector, which was 180° out phase from the
low load vibration, took effect the motor would operate with low vibration levels at full load, where it spent most of its
time. When plant personnel had balanced the motor at low load they had undone the compromise balance shot.
The story became more involved from that point. Due to the presence of the large thermal vector, plant management
elected to purchase another motor. No specifications were given regarding thermal vectors in the new motor, and only a
vibration limit of two mils was mentioned in the purchase specifications. When the new motor was tested, it also revealed
a thermal vector. In fact, the manufacturer stated that they routinely had to put in compromise balance shots on that
design of their motors. They had performed approximately 128 such balancing operations.This example serves as a reminder when dealing with two pole motors above 1000 HP that the 1× running speed vibration
may vary significantly from low to high load. It is imperative that phase angles be recorded along with the amplitude to
identify this type of situation. For instance, a motor might have two mils at 90° unloaded and two mils at 270° in the
loaded condition. If only amplitude is recorded there would appear to be no problem. However, if phase is taken into
account it becomes apparent in the previous case that there has been a four mil change from low load to high load.
Consequently, that is a situation where balancing out the two mils at low load would increase the vibration at full load.
Case #7: Feed Pump Motor with Thermal Vector
A large 4000 Hp 3600 rpm feed pump motor was sent out for routine inspection and cleaning. Upon return from the
motor shop it was put into operation, and after 45 min high vibration destroyed its bearings. It was returned to the motor
shop where it was repaired and rebalanced. When the motor was returned to the plant it again destroyed the bearings. It
was then sent back to the manufacturer where it was put in a high speed balance pit and balanced at speed. When it was
reinstalled back at the plant it destroyed the bearings for a third time.
Due to the nature of the problem, proximity probes were installed on the motor. When it was first started the vibration
was normal. However, as the motor was loaded the vibration level increased to the point that the motion was nearly equal
to the bearing clearance. It was determined that the motor had a thermal vector. The solution was to balance the motor in
the loaded condition.
It was discovered that the motor shop had dropped the rotor during its first visit. The laminations were damaged, causing
a hot spot to develop. This hot spot on one side caused the rotor to bow as it heated up, resulting in the sensitivity to load.
This motor operated successfully for several years with a thermal compromise shot installed.
كلمة سر فك الضغط : books-world.net
The Unzip Password : books-world.net
أتمنى أن تستفيدوا من محتوى الموضوع وأن ينال إعجابكم
رابط من موقع عالم الكتب لتنزيل كتاب ASM Metals Handbook of Case Histories In Failure Analysis Volumes 1 & 2
رابط مباشر لتنزيل كتاب ASM Metals Handbook of Case Histories In Failure Analysis Volumes 1 & 2 
|
|
