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