FACTORS AFFECTING VIBRATION OF AXIAL-FLOW COMPRESSOR BLADES SS MANSON, AJ ...

15 Pages·2005·2.09 MB·English

FACTORS AFFECTING VIBRATION OF AXIAL-FLOW
COMPRESSOR BLADES
S. S. MANSON, A. J. MEYER, JR., H. F. CALVERT, and M. P. HANSON,
National Advisory Committee for Aeronautics, Cleveland, Ohio.
SUMMARY , COMPRESSOR / COMBUSTOR
Measurements by means of wire-resistance
strain gages of blade vibrations in an experi-
mental 10-stage axial-flow compressor during
engine operation are used to present informa-
tion relating to:
1, The effect of centrifugal force on natural
frequency of blades.
TURBINE /
2. The common modes of vibration present
and orders of excitation producing them. Fig. 1. Schematic sketch showing
3, The effect of disturbances in the air flow location of compressor in typical
originating in the inlet passage on vibration in jet propulsion engine.
each of the 10 stages.
4. The use of loosely mounted blades as a Inorder to provide a better understanding of
means of vibration suppression (a supplemen- vibration of axial-flow compressor blades, the
tary laboratory investigation on a rotating Lewis Flight Propulsion Laboratory of the
wheel was conducted in conjunction with the National Advisory Committee for Aeronautics
engine tests). has been conducting a program of measurement
5. The importance of aerodynamic damping of vibration stresses and of the factors affecting
in limiting vibration. them. This re-port presents some of the re-
Test methods and techniques for testing full- sults and is divided into four sections. In the
scale compressors under engine operation are first section, the test facilities and techniques
described in detail. are described; in the second and third sections
the factors affecting the vibration excitation
INTRODUCTION and suppression are respectively discussed;
and in the fourth section the important conclu-
The compressor is an important component sions learned from the investigations are sum-
of severaltypes of engines now under rapid de- marized.
velopment for aircraft propulsion. In the jet
propulsion engine, for example, a schematic APPARATUS AND PROCEDURES
sketch of which is shown in Fig. 1, the function
of the compressor is to supply large quantities For the full-scale compressor investigations
of air at relatively high density for combustion an experimental 10 stage axial flow unit, a
and ultimate expansion in the gas turbine and cross-sectionof which is shown in Fig. 2, was
in the exhaust nozzle. While the axial-flow drilled as shown in the figure to permit lead
compressor is more efficient and requires less wires to be taken from strain-gages mounted
frontal area than its competitor, the centrifu- on the blades to a set of slip rings mounted on
gal-type compressor, its adoption for aircraft the nose of the engine. Threads were tapped
use was at first retarded by numerous vibra- in the radial passages to provide a footing for
tion problems encountered in early experimen- a polymerizing thermal setting plastic used as
tal units. Be-cause of the advantageous features a filler to hold the lead wires in place, and the
of axial-flow compressors, the present trend, machining operations were followed by liquid
however, is towards their use while tle vibra- honing process which removed sharp edges
tion problems a rq be;ng ir.2ivirluz!!y ivvesti- that =igh"ltherwise haw damaged the Eeaci-
gated and gradually minimized. wire insulation,
1
2 EXPERIMENTAL STRESS ANALYSIS
Strain gages were then cemented to several
biades of each stage, some gages bemg oriented
to be particularly sensitive to torsion (450 to
axis of blade), others to bending (gages on op-
posite sides of blade). A typical instal1a.+i on is
shown in Fig. 3 for the first stage. The gages
were made of Advance wire of 120 ohms re-
sistance, covered an area of 1/8-inch square,
and were cemented to the blades by Bakelite
COMPRESSOR ROTOR cement. A layer of very sheer pure silk was
cementedover the strain gages and lead wires
Fig. 2. Full-scale experimental principally to provide additional strength to
compressor rotor drilled for strain oppose the high centrifugal forces of rotation.
gage lead wires. The 19 ring slip-ring assembly used in the
Fig. 3. Strain gages mounted on blades of first stage
of experimental compressor.
FACTGRS AFFECTING VIBRATION OF AXIAL-FLOW COMPRXSSOR BLADES 3
Fig. 4, Slip-ring assembly.
tests is shown in Fig. 4. The rings were made To obtain information on problems associ-
of :none1 1-3/8 inch diameter and 3f 6 inch ated with root fastenings, a series of tests were
wide, while the l/8 inch diameter brushes were conducted on a flat disk machined at the rim to
made of 60 percent silver and 40 percent graph- accept simulated blades of various designs.
ite. The electrical connections between engine The setup is shown in Fig, 7. The wheel was
and slip rings were made by a multi-prong powered by a motor through a speed increaser.
plug, thus permitting easy removal of ring as- yiibrationof the blades was induced by a single
sembly when not in satisfactory operation, Ab- stationary air nozzle, and measured by strain
solute cleanliness of the rings was found es- gages mounted at the base of the blades. Slip
sential for good results. The arrangement of rings similar to those of Fig. 4 were used to
the rings in the circuit is shown in Fig. 5. transmit strain signals to stationary recording
There were three groups of six rings, each equipment.
associated with its own battery supply. Each
grcup provided strain indications from four FACTORS AFFECTING VIBRATION
bridges at any one time. By simple re-wiring EXCITATIGN
on the engine when stationary (e. g. changing all
connections fromlto 2 or 3 in Fig. 5) the same Critical speed diagram. - In making any vi-
group of rings could be made to service eight bration analysis of compressor blades, it is
other bridges. One grounded slip ring was very useful to plot a critical speed diagram; a
common to all three groups of six active rings. typical one is shown in Fig. 8. Along the hori-
Thus, the 19 rings serviced 12 bridges at any zontal axis is plotted the rotor speed in rpm,
one time, but a total of 36 bridges could be re- and along the vertical axis the vibrational fre-
cordedby successive tests. A 12-channel am- quency of the blade in cycles per second. Also
plifier and oscillograph was used to record the drawnare a series of radial lines called order
strain signals. lines. These lines define points along which
In the first series of tests, the compressor the vibrational frequency is an integral multi-
was powered by a 2500 horsepower electric- ple of the rotor speed; for example, along the
drive motor, the principal value of these tests order line 2, the vibrational frequency is every-
being the opportunity to increase the pressure where twice the rotor speed (although numeri-
ratio at a given speed by throttling the exhaust. cally the two differ by a factor of 60 because
A schematic diagram of the test setup is shown frequency is customarily stated in cycles per
ifi Fig. 6. In the second sdri~sG; ~esist,h e second, while speed is in revolutions per min-
ComPressor was rebladed and mounted ina full- ute).
scale jet engine. The question arises as to which order lines
4 EXPERIMENTAL STRESS ANALYSIS
nary parts
Fig. 5. Schematic diagram of bridge circuit installed on
ten-stage experimental compressor. Three complete circuits
were used in tests.
DRIVE-MOTOR SETUP
DRIVE MOTOR
SPEED INCREASERS
Fig. 6. Experimental compressor test set-up.
FACTORS AFFECTING VIBRATION CF AXIAL-FLGW CGMPRESSOR ELADES 5
Fig. 7. Test set-up for investigation of effect of mount
looseness for single and double-ball root blades.
should be drawn, and which omitted. In some another section about allowable stresses). It
cases the reasonfor including a given line may is probable that the source of the various orders
be obvious. For example, if there are four front of excitation is the harmonic content of strong
bearing supports, the blade encounters four in- first order excitation, although the first order
terruptions of the airs tream in each revolution; line itself is unimportant because it does not
hence the fourth order and its harmonics, 3, 12, intersect any of the natural frequency lines
etc., should be included. It has been found, ex- within the operating speed range of the engine.
perimentally, however, that orders for which For the sake of completeness, therefore, it is
there exists no rational explanation also induce desirable to include all order lines that may
vibrations. In the compressor tested, for ex- reasonably be expected to intersect a natural
ample, every order from 3 to 17 was found to frequency line within the operating speed range.
induce vibrations in blades of one stage or The series of nearly-horizontal lines in the
another, although the vibrational stresses in diagram are the natural frequency lines, and
most cases were small (more will be said in they deiirle the variation with rotational speed
6 EXPERIMENTAL STRESS ANALYSIS
of thenaturalfrequency of each of the possible
modes of vibration. Only for the fundamental
bending mode is the frequency seriously affect-
ed by centrifugal force of rotational speed. The
effect is given by the formula
ORDER OF ROTOR SPEED
where
f = natural frequency at rotative speed N,
cycles per second
fo = static natural f requency, cycles per second
p = constant depending on physical dimensions
of blade
N = rotor speed, revolutions per second
The results of the present investigation indi-
cate that the constant p can be determined ana-
lytically by the method outlined by Timoshen-
ko.(l)* Fig. 9 shows a typical comparison be-
tween the calculated and the experimentally
ROTOR SPEED, RPM
determined effect of centrifugal force. Num-
erous checks of this type at the National Ad-
visory Committee for Aeronautic s on both lab-
oratory rotating rigs and on fuii-scale com-
860r
FREQUENCY pressor blades operating in engines have veri-
o MEASURED fied the general validity of equation 1.
The static natural frequency, f,, can best be
determined experimentally, if a blade is avail-
able, by fixing the blade in a rigid mount and
exciting it in the lowest resonant mode. Any
looseness in the mount will tend to invalidate
the results, however. If no blade is available,
the method of ~ort(l)c an be used to obtain a
good fir st approximation of the fundamental
mode static natural frequency. Cnce fo, and p
have been determined, the natural frequency
line in Fig. 8 for first mode bending can be
drawn. The natural frequency lines for each
of the other modes is effectively horizontal.
While a blade may have numerous natural
frequencies, there is a great difference in the
ROTOR SPEED, RPM
ease with which the various modes can be ex-
Fig. 9. Typical comparison between
cited. In the particular compressor tested in
calculated and experimental effect of
this investigation, only the first and second
centrifugal force on fundamental bending
. bending modes were at all excited, and only in
mode of frequency
*Superiors in parentheses refer to bibliogra-
phy
FACTORS AFFECTING VIBRATION OF AXIAL-FLOW COMPRESSOR BLADES 7
ORDER OF ROTOR SPEED
the first mode was the magnitude appreciable
during normal operation of the engine. (Appre-
ciable second mode vibration was artificially
induced by partial blocking of the inlet passage.)
For a practical critical speed analysis in this
case, it is, therefore, adequate to coniider
only k ef irst bending mode of each of the stages
of the compressor. Fig. 10 shows a critical
speed diagram for the first bending modes of
STAGE
the ten stages of the compressor tested. 0 I
Each time an order line intersects a natural + 2
0 3
frequency line, there exists a potential critical x 4
0 5
speed. Whether or not vibration is excited de- 6
v 7
pends upon the amount of exciting force present 0 8
of the particular order involved. In Fig. 10, the 9
0 10
experimentally observed resonances are indi-
cated by the various symbols, and it will be
ROTOR SPEED, RPM
noted that most resonant speeds were in fact,
actual resonances. When it is considered that Fig. 10. Critical speed diagram for
in a given stage a wide spread of natural fre- fundamental bending mode of typical
quencies exists among the various blades, it blades of each stage of experimental
is evident that at almost any speed some of the compressor.
blades of the compressor are vibrating. As
much as 20 percent variation in static natural
frequencies. has been observed among the in-
dividual blades of a stage. Undoubtedly, some
of the variation is due to different degrees of
tightness of the blade in the mount, and the
spread of natural frequency may narrow at the
high speeds of operation due t~ tightening by
BLADE
centrifugal force. But at least some of the I
spread is due to manufacturing tolerances, and 2
persists throughout the speed range. Fig. 11
shows a plot of the variation of natural frequency
wit!? rotative speed of two blades on the fourth
stage of the compressor, the static natural
frequencies of which were about 4 percentapart.
If the difference in natural frequency were due Fig. 11. Variation of natural frequency
to mount looseness, the frequencies would tend with speed for two blades from fourth
to converge under the high centrifu,o al forces stage.
of high rotative speed. Actually, in the plot of
the square of the natural frequency against passage of air, and subject the blades to fluctu-
the square of rotative speed, both blades give ating air forces. In the present compressor,
essentially parallel lines, which indicates that there were four such struts, thus providing a
the basic natural frequencies of the two blades source of impulses at 4 per revolution and its
. are different. The possibility of vibration, al- harmonics 8, 12, 16, etc., per revolution.
though not necessarily critical vibration, at all The inlet guide vanes which direct the flow of
en-g -i ne speeds, is therefore substantiat-e d. air at the proper angle to the first stage of
Obstructions as an exciting force: One of rotor blades constitute another effective source
the major sources of excitation in compressors
of air pulsation. In the present compressor,
is obstructions in the air passages leading to there were 56 inlet-guide vanes, and, in general
the compressor. Struts for supporting the front thereare a large number of such vanes, hence
bearing, for example, break up the sniooth
the order of excitation due to this source is
8 EXPERIMENTAL STRESS ANALYSIS
0 BLOCKS
NONE
loTHO RDER
d
STAGE
Fig. 12. Effect of inlet disturbances
ROTOR SPEED, RPM
on stresses throughout compressor,
Fig. 13, Effect of speed and order of
high. The corresponding order lines intersect excitation on vibratory stress of sixth
the lower natural frequency modes at speeds stage.
below the operating range of the engine. But
they may intersect the higher modes near the inlet, In each case, the order of excitation and
rated speed where the likelihood of excitation is the number of blocks reflecting the most pro-
good and the amount of excitation energy avail- nounced effect of the blocking is shown, For
able is high due to high air speeds. In the pres- example, in the third stage little or no stress
ent compressor no higher mdes were excited; wasobserved due to third order at normal op-
but there is no reason to exclude the possibility eration, Three blocks produced tne most pro-
of such excitation in other compressors. nounced effect at third order by increasing the
While it is easy to see how excitations origi- stress to + 37,000 psi. In the seventh stage,
nating in the inlet passage can readily excite the most pronounced effect was produced by
vibrations in the first stage, there would be a the four blocks at fourth order excitation. Un-
question as to how far into the compressor such der normal operation, the stress was + 9,000
excitations can persist. In order to obtain in- psi while four blocks increased the stress
formation on this problem, a series of tests -+ 22,000 psi.
were conducted on the compressor in the jet It should be noted that the results of a test
engine in which sheet metal clips were fitted of this type depend, to a great extent, on the
over adjacent pairs of inlet guide vanes, there- exact placement of the blocks relative to other
by blocking off the air flow through one or more disturbing influences such as the bearing sup-
of the inlet passages. These tests were also ports. Fig. 12 should, therefore, be construed
intended to provide infor mation on the possible to indicate that disturbances in the inlet section
effects of severe icing conditions or the effect can affect the vibration in all the stages of the
of the lodging of any foreign matter in the in- compressor rather than to indicate the quanti-
let section of the compressor. When more than tative effect of any particular number of blocks.
-
one passage was blocked, these passages were Dynamic pressure factor: As the blade ro-
as equally spaced as posqible (exactly equal tates, it is subjected to forces which are pro-
spacing for 3 blocked passages was not possible portional to the dynamic pressure factor p ~ 3 ,
because of the indivisibility of 56 by 3). where P is the air density and V the relative
Some of the results are shown in Fig. 12. The velocity between air and blade. Disturbing in-
single amplitude stresses in several stages for fluences in the air stream alter this dynamic
normal operation are compared with the cor- pressure factor percentage-wise; hence, the
respondingstresses induced by blocking of the amount of vibration excitation is roughly pro-
FACTORS AFFECTING VIBRATION OF AXIAL-FLOW COMPRESSOR BLADES 9
STAG E
PRESSURE RATIO, 1.17
nd
0-
or
SS
-
'P
. - -
'U
;he PRESSURE RATIO, 1.54
$7
Fig. 14. Strain gage signals from first four stages of
by
Jn- 10-stage axial-flow compressor at low and increased
300 total pressure ratios.
2s S
p,v2.
portional to Thus the same source of ex- as well as in most cases, no rational origin
citation will tend to produce greater vibration for the exceptional orders could be found.
-
at the higher speeds of operation than at the Unusual operating conditions: As an example
lower speeds. Since the lower order lines in- of the effect of unusual operating conditions on
tersect the natural frequency lines at the high- vibration of compressor blades, the following
er speeds, resonances of the lower orders will, observation can be reported without drawing
ingeneral, produce the highest stresses. Fig. any particular conclusions: During one of the
13 shows the variation of stress with speed and tests in which the compressor was powered by
order for a blade in the sixth stage in first an electric motor, the speed was set at about
mode bending, which follows the general trend one-half of top speed and in resonance with a
of increasing stress with decreasing order of blade from stage 2. With the valve in the ex-
excitation. The stress at the fifth order which haust line wide open, the pressure ratio of the
does not fall in the general trend curve is char- whole compressor was only 1.17. As shown in
acteristic of exceptions that occurred in every the upper half of Fig. 14 only the blade from
stage. Excitations having particularly weak or stage 2 was vibrating, the other three traces
strong origins can overcome the effect of the representing the noise level of the non-vibra-
Speeds at which they occur, snci proJuce eitLier ting first, riiird, and iourLl stages. By throttling
unusually low or high stresses. In this case, the exhaust valve, the pressure ratio was raised
10 EXPLRIMENTAL STRESS ANALYSIS
to 1.54, at which time the blades from all four engineering materials Hatfield: Stanfield, 2nd
stages vibrated as shown in the lower half of ~otherharn(2p)o int out the importance of chem-
Fig. 14. The vibration was rather irregular. ical composition and heat treatment on damping
Further throttling of the exhaust produced capacity of stainless irons with chromium con-
surging, at which time all vibrations ceased. tent in the neighborhood of 13 percent. Table I
When the surge condition was removed, the vi- taken from Schabtach and ~ehr(3)g ives the
brations resumed. damping capacity of 13 percent chrome iron as
obtained from tuning fork specimens at different
FACTORS AFFECTING VIBRATIGN stress levels.
SUPPRESSIGN Incompressor blades which are subjected to
a steady centrifugal stress and combined alter-
Counteracting the exciting forces are damping nating stress the exact damping value cannot
forces that, under most conditions, prevent the be readily determined. Values in the neighbor-
vibration from building up to dangerous levels. hood of 2 percent or 6 = .02 are not unreason-
These forces are the inherent damping of the able, however, for appreciable amplitudes of
material, the damping at the root, and aerody- vibration in proximity of failure. This value
namic damping. In discussing damping, refer- is rather high and indicates the reason for the
ence isusually made to the logarithmic decre- common use of this material for steam turbine
-
ment. Basically, this term refers to the rate blading and for its use in the experimental com
of decay of the blade amplitude in free vibra- pressor of the present investigation. The value
tion. It is defined as the logarithm of the ratio b = 0.02 agrees favorably with experimental
of the amplitude of one cycle to the amplitude values obtained from die-away curves and fre-
of the next cycle of a blade in free vibration. quency response curves on typical blades from
Hence, the usual method of measuring loga- the compressor vibrating at relatively high
rithmic decrement is from a die-away curve of stress levels.
the blade amplitude in free vibration. An alter- Blade root damping. - It has been the practice
nate method of measurement of this quantity in many designs to provide a very tight fit be-
makes use of the frequency response curve of tween the Made and rotor. m1., nis tight fit, to-
the blade. If the blade is excited by a force of gether with the tightening effect of centrifugal
constant amplitude, and the vibration amplitude force, minimized the possibility of friction in
is observed, the logarithmic decrement can be the mount that might be beneficial in reducing
determined by the formula the amplitude of vibration at resonance. In
order to determine the potential benefit that
might be derived from loose insertion of the
blades, two investigations were conducted. In
the first, a loose mount was provided in one of
where the blades of the tenth stage of the jet engine
compressor, and the vibration of this blade was
b = logarithmic decrement of damping noted during operation of the engine. It was
found that the amplitudes of vibration of this
~f = difference in frequencies at which vibra- blade were approximately the same as those of
tion amplitude response is 50 percent of re- a tight blade in the same stage. However, these
sponse at resonance amplitudes were, in general, small, as there
seemed to be no tendency to excite severe vi-
fo = frequency at resonance brations. It was, therefore, not possible to
determine the effect of mounting looseness in
-
Material damping. The damping due to in- the case of interest- -the region of high ampli-
ternal friction in the material depends to a tude approaching blade failure. The laboratory
great extent on the material and the stress level. investigation on the disk described under "Ap-
The materialused in the blades of the compres- paratus and Procedures" was, therefore, un-
sor investigated was 13 percent chrome iron dertaken. An additional objective of this inves-
common in steam turbine blading use. In a tigation was the comparison of the single and
comprehensive report on damping capacity of double-ball roots from the vibration damping