Coupled Vibration of Unshrouded Compressor Part I

International Journal of Rotating Machinery2000, Vol. 6, No. 2, pp. 101-113Reprints available directly from the publisherPhotocopying permitted by license only

(C) 2000 OPA (Overseas Publishers Association) N.V.Published by license under

the Gordon and Breach SciencePublishers imprint.

Printed in Malaysia.

Coupled Vibration of Unshrouded Centrifugal CompressorImpellers. Part I: Experimental Investigation*HEINRICH HASEMANN, DIRK HAGELSTEIN and MANFRED RAUTENBERG

Institute of Turbomachinery, University of Hannover, Appelstr. 9, D-30167 Hannover, Germany

(Received 12 May 1998; In finalform 21 July 1998)

The increased use of small gas turbines and turbochargers in different technical fields has ledto the development ofhighly-loaded centrifugal compressors with extremely thin blades. Dueto the high rotational speed and the corresponding centrifugal load, the shape of the impellerhub must also be optimized. This has led to a reduction of the thickness of the impeller disc inthe outlet region. The thin parts of the impeller are very sensitive and may be damaged by theexcitation of dangerous blade vibrations.

Experimental investigations by means of holographic interferometry and telemetry werecarried out for two different impeller types; one with radial-ending blades and the other withbackswept blades. The results presented in Part I of the paper are able to explain thedominance of coupling effects between the blades and the disc in the middle and higherfrequency range of the two tested impellers. Especially excitations caused by downstreamsources such as vaned diffusers can endanger the blades and the impeller.The finite element (FE) code computations presented in Part II of the paper to investigate

the coupled vibration behavior of the whole impeller were found to be in close agreement withthe experimental results.

Keywords: Centrifugal compressor, Holographic interferometry, Blade vibrations,Coupled vibrations

1 INTRODUCTION

Compressors find wide application in manybranches oftechnology. They serve for compressingand transporting diverse gases and gas mixtures andconvert mechanical energy into pressure energy.

In the further development of centrifugal com-pressor impellers to achieve ever-increasing power

concentrations, considerable effort has beendirected towards the construction of small compactunits with high pressure stage ratios and large massflow rates. As this objective may only be realizedwith increased peripheral speed, it is not onlynecessary to employ improved and also moreexpensive impeller materials but also to reduce theblade thicknesses as well as the wall thicknesses of

This paper was originally presented at ISROMAC-7.Corresponding author. Tel.: (0511)762-2737. Fax: (0511)762-2768.

101

102 H. HASEMANN et al.

the impeller disc in order to ensure that the loadsdue to centrifugal forces remain within permissiblelimits. At the same time, however, there is an

increasing risk of dangerous excitation vibrationsof these very thin and flexible blades. As confirmedby operational practice, the failure ofhighly-loadedimpellers is in many cases due to blade breakageresulting from dynamic overloading of the bladematerial. This leads to plant shutdown and costlyoutage times. The blade vibrations of these impel-lers during operation are thus gaining increasingimportance with regard to design strength criteria.

Generally speaking, the lower mode shapes andespecially the fundamental mode of vibration areconsidered to be the most dangerous. A resonantexcitation in this range should also be avoided at allcosts! The excitation of higher frequency modes,however, also poses a considerable risk potential.Experimental investigations by Haupt and Rauten-berg (1982a) have shown, for example, that vaneddiffusers downstream of the impeller give rise to

upstream excited vibrations of the whole impellerin the higher frequency range, representing a vibra-tion state which is far more dangerous than mostother causes of excitation. Excitation of the rela-tively flexible outer region of the impeller disc there-by results in excitation of the blades at one of theirhigher natural frequencies, leading to vibrationswith significant amplitudes. This results in materialstress peaks in the impeller inlet region approachingthe limits of the maximum permissible load.

Experimental investigations by Haupt andcoworkers (1982b,c; 1985) have shown that in thecase ofhighly-loaded centrifugal compressor impel-lers with small blade thicknesses and thin flexibleimpeller discs in the outlet region, coupled vibrationbehavior occurs which cannot be fully described

interferometry. Further details of the finite elementcomputations are given in Part II of the paper.

2 INVESTIGATED IMPELLERS

Two centrifugal compressor impellers were investi-gated, namely, a 90-impeller with radial-endingblades and a 60-impeller with backswept blades.At the meridional section, both impellers have thesame profile. This means that the hub profile as wellas the casing profile are identical for both impellers.The external diameter of the impellers is 400 mmwith an outlet width of 26.1 mm. The inlet diameteris 280mm while the hub diameter is 90mm. Theimpeller axis extends over a distance of 130 mm.

The 90-Impeller

The investigated impeller with radial-ending bladesis shown in Fig. 1. The impeller outlet angle is 90,and of the 28 blades, every second blade is cut backto reduce blockage at the inlet. The skeleton area ofthe blades is generated by radial rays oriented at

right angles to the axis of rotation. The variation ofthe blade thickness from root to tip was specifiedby considering the static loading due to centrifugalforces as well as low aerodynamic blockage.

in terms of its complexity and danger risk from amere consideration of individual blades.The aim of the present investigations was there-

fore to model the complex coupled vibrationbehavior of the investigated impellers using thefinite element method and to verify the com-

putational results on the basis of experimental FIGURE The 90-centrifugal compressor impeller with 28measurements obtained by means of holographic blades.

COUPLED VIBRATION. PART 103

The 90-impeller was manufactured from amodel by the profile milling method. Great carewas necessary in milling the leading edge of theblade in order to avoid errors due to bending of thevery thin blades as a result of milling cutting forces.

The 60-Impeller

The 60-impeller shown in Fig. 2 has backsweptblades, i.e. the outlet angle is inclined at 60 relativeto the negative circumferential direction. The aero-dynamic advantages of impellers with backsweptblades are reflected in improved efficiency and anexpansion of the performance map comparedwith radial-ending blades. As arched blades are no

longer able to lie on radial rays at the outlet, as inthe case of a 90-impeller, bending stresses may beexpected in this case due to centrifugal forces, thusimposing a limit on operating speeds.

This impeller has 20 blades, of which everysecond blade is also cut back at the inlet in orderto ensure low blockage. The high static loadingexperienced by backswept blades due to thebending stresses induced by centrifugal forcesnecessitates an adaptation of the blade thicknessvariation from root to tip, especially in the outlet

FIGURE 2 The 60-centrifugal compressor impeller with 20blades.

region. Compared with the thickness variation ofthe 90-blade, this blade is only slightly thicker.

In contrast to the impeller with radial-endingblades, the 60-impeller was manufactured on a

5-axis controlled CNC milling machine by the flankmilling method. The use of this method was madepossible by the mathematical configuration of theblade surfaces as ruled surfaces. In this type ofdesign the pressure and suction sides of the bladesare generated from ruled lines, the end points ofwhich are traced along the spatial curves of thehub profile and outer profile in compliance withaerodynamic specifications. The ruled surfacesthus generated by the migration of the ruled lines

may be milled with the aid of 5-axis CNC tech-nology. Although the geometry of the milling headgives rise to unavoidable errors due to the hyper-bolic undercut, these may be minimized by applyinga correction to the milling cutter guide (Hasemannet al., 1995).

3 THE TELEMETRY SYSTEM

In order to detect the blade vibration signals duringoperation, it was essential to deploy vibrationsensors in the proximity of the rotating impellerand to transmit the signals in a suitable manner.

According to Haupt (1984), conventional mea-

suring techniques cannot be applied under therestrictive framework conditions of this type ofinvestigation. It was therefore decided to employ a

telemetry system with 8 transmission channels. Fulldetails of the installation are reported by Hauptet al. (1984). The system operates over a frequencyrange up tof= 10,000 Hz and permits the contact-less transmission of 8 instationary vibration signalsfrom the rotating impeller, as illustrated by theinvestigations of Haupt and coworkers (1978;1982).The latter experimental investigations also

demonstrate that a satisfactory determination ofthe complex vibration behavior of these impellersis only possible by employing a multi-channelsystem with simultaneous measurements of several


vibration signals at different points on the struc-ture. Semiconductor strain gages, which arecapable of detecting local strains with high accu-

racy, were therefore applied to different bladesand at different positions on these blades. As eachmode shape is marked by characteristic and locallyrestricted regions with large strains, whereas otherregions are Virtually strain-free, and also due tocoupled vibration effects resulting from mutualinteractions between the blades, the points ofapplication of the strain gages were carefullyselected to achieve the largest possible detectioncoverage.

Figure 3 shows a longitudinal section of theimpeller shaft, indicating the installations forrecording and transmitting the blade vibrationsignals. The strains are recorded by the strain gagesapplied to the blades and are transmitted via thetelemetry transmitter with its co-rotating antennato the stationary receiver. Power is suppliedinductively via a stationary primary coil and a

rotating secondary coil. The secondary coil alsoserves as a transmitting antenna whereas the

primary coil serves as a receiving antenna for therecording unit, which operates as a frequencymultiplex system.

4 HOLOGRAPHIC INTERFEROMETRY

In order to determine its natural vibration behaviorthe impeller was investigated at rest with the aidof holographic interferometry. By means of holo-graphic interferometry it is possible to determinethe mode shapes of a vibrating body. In contrast tothe strain gage technique, this method providesinformation over the entire surface of the bodyunder investigation, from which the amplitudedistribution may be determined. This is especiallyadvantageous in the case of the complex geome-trical structures under investigation, as it is possibleto identify a mode shape relatively quickly.Among others, the time-average technique was

adopted in the holographic investigations. Figure 4shows the experimental set-up for the optical studyof the impeller. The coherent monochromatic light

A: hub noseB: 8-channel telemetrytransmitterC: cable carrierD: tension screw

E: adapter with plug connectionF: secondary coilG: primary coilH: inductive power supply switch

KL

EFGHI J

I: trigger unitJ: coil holderK: receiver antennaL: inductive power supply

FIGURE 3 Impeller shaft with integrated telemetry transmitter for transmitting the blade vibration signals.


from the argon laser illuminates the vibratingcompressor impeller excited by a shaker via themirrors Sp and Sp2 as well as the beam splitter ST,the divergence optics AO2 and the mirror Sp3.In the beam splitter ST, part of the coherent laserlight is reflected out as a so-called reference beam.The reference beam R arrives at the free-standinghologram plate H as a plane wave without phaseshift via the divergence optics AO and the mirrorSp4. The object beam is also reflected back to thehologram plate H from the compressor impeller.Interference occurs in the fine-grained photo-graphic layer of the hologram plate between theplane, non-deformed wave front A of the referencewave and the diffuse, reflected, deformed wavefront D from the vibrating impeller. This inter-ference in the fine-grained layer of the hologramplate leads to zones of maximum illumination andmutual extinction.The time-average method is very suitable for the

investigations carried out in the present study asthe extreme positions of the vibrating structure are

stored in the hologram whereas the intermediatepositions are not registered due to the short dwelltimes intrinsic to the sinusoidal vibration. When themaximum vibration amplitudes lie in the range of0.2-15 lam, interference occurs once again betweenthe two wave fronts of the extreme positions withsimultaneous reconstruction. These interferencelines represent lines of equal amplitude on thecompressor impeller, i.e. deformation contours.The white areas represent nodal zones with zero

amplitude.

A qualitative evaluation may therefore be easilycarried out as the interference lines provide an exact

picture of the vibration behavior. As the amplitudesalso depend on the excitation intensity, which isneither accounted for in the FE method (see Part II)nor in the time-average method, it is only possibleto compare computations and measurements in

qualitative terms.In order to experimentally investigate coupled

vibration behavior, the impeller with its shaft was

assembled on a small test stand and excited by a

sinusoidal generator via a shaker. Figure 5 showsthe test set-up. The shaker consists of an electro-dynamic excitation unit which introduces sinu-

soidal forces into the outer part of the impellerdisc via a reciprocating rod directly between twoblades. With the aid of a sinusoidal generator whichcontrols the shaker via an amplifier, it was possibleto vary the frequency from 0 to 7000 Hz. As onlytwo channels were available, one strain gage wasmounted on a normal blade and the other on theinside of the impeller disc in the outlet regionbetween two blades. The splitter blade was not

included in the tests. The signals from the straingages were analyzed with the aid of a frequencyanalyzer, thereby enabling the coupled naturalfrequencies to be determined.

V shutters m,ST beam splitterL aperture

F gray filter

MH

0D diffu

R

magnetichologram

objectreference

beamflectcd

exciter

beamplate

FIGURE 4 Experimental set-up for the optical investigationof the impeller by means of holographic interferometry.

FIGURE 5 Small test stand for investigating the vibrationbehavior of radial impellers at rest. Excitation by means of ashaker.


5 EXPERIMENTAL RESULTS

Measured Frequencies

A comparison between the measurements and theFE computations is given in Figs. 6 and 7, wherebyFig. 6 shows the strain gage measurements on a

blade while Fig. 7 shows the measurements on theimpeller disc. A in each figure indicates the resultsof the FE computations for the half-impeller withblade thickness variation whereas B indicates themeasurements.A difference between the measurements and

computations is immediately apparent. Whereas

the experiments yielded both the coupled naturalfrequencies as well as the corresponding ampli-tudes, the computations were unable to provide anyinformation concerning the amplitudes as these are

highly dependent on the excitation forces. In thecase of measurements, the amplifier voltage of theshaker was held constant over the entire frequencyrange. Bearing in mind that the strain gage on thenormal blade is unable to detect vibrations of thesplitter blade, relatively good agreement is obtainedbetween the computed and measured coupled nat-ural frequencies. Large phase shifts are apparent in

Fig. 6 only for the coupled natural frequency ranges

1 2s5 3s/.$7 10 5s 11

0 1000 2000 3000 4000 5000 6000 7000 Hzfrequency

FIGURE 6 Coupled vibration frequencies of the 28-bladed 90-impeller. Comparison between the FE computational results (A)for the part model with 14 blades and measurements (B) for the impeller at rest with a strain gage on the normal blade.

ls 2s5 6 3s.s7 10 5s 11

0 1000 2000 3000 z,O00 5000 6000 7000 Hzfrequency

FIGURE 7 Coupled vibration frequencies of the 28-bladed 90-impeller. Comparison between the FE computational results (A)for the part model with 14 blades and measurements (B) for the impeller at rest with a strain gage on the impeller disc.


/, 2 !..

impeller speed [lO00/min]

scale:

FIGURE 8 Blade vibrations of the 28-bladed 90-impeller depicted in the Campbell diagram. Results of measurements with astrain gage on the normal blade as well as computed coupled vibration natural frequencies corresponding to the normal blades.

3, 7 and 10. The 8th natural frequency is notregistered by the measurements.The representation in Fig. 7 also indicates larger

phase shifts at the natural frequencies 3 and 7whereas the remaining normal blade natural fre-quency bands as well as several splitter blade naturalfrequency bands are satisfactorily reproduced. Thefundamental frequency as well as the 6th naturalfrequency ofthe normal blade is not detected by thisstrain gage which is located on the impeller disc. It isnoticeable in the case of this measurement that themiddle and higher coupled natural frequencies inparticular are well reproduced whereas a betterreproduction of the lower frequencies is given bythe strain gage on the normal blade.

In addition to the tests with the impeller at rest,extensive blade vibration measurements were alsocarried out on the rotating impeller. In this case thesignals from the semiconductor strain gages appliedto the blades and the disc were transmitted fromthe rotating impeller to a fixed receiver by means ofthe above-described 8-channel telemetry unit andrecorded on magnetic tape. The vibration signalswere subsequently analyzed with the aid of afrequency analyzer.

Figure 8 shows the results of the analysis of thevibration signal for a normal blade during a test runpresented in a Campbell diagram. The vibrationloading with varying frequency is plotted in thefigure as a function of the rotor speed. Thisillustrates the frequency-dependent material load-ing of the normal blade at the position of theapplied strain gage for the overall speed rangerelevant to the operation of the compressor. As thestrain gage only measures the material loading at asingle location (in this case the stress maximum ofthe first mode shape), precise information con-

cerning the loading of the remaining blade regionscannot be deduced from this figure.

Moreover, the Campbell diagram presented isonly valid for one throttle position. For a differentthrottle position, i.e. in the part-load region, otherexcitation forces occur in part which give riseto a different amplitude distribution. Besides themeasured results, the computed coupled vibrationnatural frequencies of the 90-radial impeller modelwith 14 blades are also plotted in the diagram.These are based on the FE results with thicknessvariation. For the purpose of clarity only thefrequency bands corresponding to the normal


.0’/

ooo./scale:

impeller speed [1000/min]

FIGURE 9 Blade vibrations of the 28-bladed 90-impeller depicted in the Campbell diagram. Results of measurements with astrain gage on the impeller disc as well as computed coupled vibartion natural frequencies corresponding to the normal blades.

blades were considered. These are represented ashorizontal lines or shaded areas in the figures.Whereas good agreement was obtained betweenmeasurements and computations in the case of thefirst two natural frequencies, a large deviation wasobserved in the case of the third natural frequency.The same result was also apparent in the measure-ments with the impeller at rest. The small ampli-tudes measured in the case of the natural frequencybands 4, 5, 6 and 7 do not permit an exact

comparison. As far as is recognizable the 5th, 6thand 7th natural frequencies are reproduced wellby the computations whereas the 4th natural fre-quency is shifted downwards slightly. The moststriking feature is the high material loading mea-sured in the range of 5400-5800 Hz at a speed of18,000 rpm.The Campbell diagram presented in Fig. 9 shows

the measured and computed results for a straingage applied to the impeller disc in the outlet regionbetween two blades. As already noted in the caseof the stationary measurements, the lower fournatural frequencies of the normal blade are not

registered by this strain gage whereas the middleand higher natural frequencies, whose mode shapes

indicate increased vibration intensity at the impelleroutlet, are well registered. In overall terms, the twoCampbell diagrams together provide a relativelycomprehensive overview of the actual vibrationbehavior of the impeller.

Measured Mode Shapes

The computed mode shapes for the half-impellermodel with 14 blades were taken as a basis forcomparison with the holographic mode shapes. Theholographic interferogram illustrated in Fig. 10 wasrecorded at 790 Hz and shows the 28-bladed 90-impeller, whose 14 normal blades vibrate in theirfundamental mode shape.The interference fringe pattern indicates that the

largest amplitudes occur at the blade tips at theimpeller inlet. The blades with the more dense line

pattern vibrate at a larger amplitude than the bladeswith wide interference lines. The outlet region andthe impeller disc do not contribute towards thevibration mode shape. Computations for thecoupled system, as shown in Fig. 11, indicatenormal blade vibrations in the fundamental modeshape. As the blades partly overlap, the plot of the


FIGURE 10 Holographic interferogram of the 90-impellerwith 28 blades at a frequency of 790 Hz.

half-impeller is very unclear. For this reason, onlythe leading edges of the blades are plotted in thelower part of the figure. This representation clearlyshows that the normal blades vibrate in pairs in theopposite sense in their fundamental mode shapewhereas the splitter blades remain at rest. It is alsofound that the computed mode shapes for indivi-dual blades exhibit different vibration amplitudes.Of special interest are the mode shapes of the

impeller with a significant contribution from theouter portion of the impeller disc, i.e. for modeswith high coupling between blades and disc. Sucha mode shape is illustrated by the interferogramsshown in Fig. 12, which depict the impeller from thefront and back sides at a frequency of about3620Hz. Apart from the blade vibrations strongvibrations are also evident in the outlet regionbetween the blades, although not every interbladeregion is affected.

Regarding the aforementioned measurements onthe running impeller (see Campbell diagram inFig. 8), large vibration amplitudes of the 9th and10th normal blade mode shapes were registered at5400 and 5700Hz. Both vibration modes were

excited by coupling action of the 19-blade diffuserin the outlet region and exhibit high stresses at theposition of the applied strain gages at about half theblade height at the inlet.The hologram shown in Fig. 13, which was

recorded at 5400 Hz, reveals large vibrations of the

FIGURE ll Computed 1st mode shape of the part structureof the 90-radial impeller with 14 blades at 780 Hz.

inlet region. Antinodes are also apparent along theouter region of the impeller disc between the blades,although the amplitudes of the latter are very small.The computed mode shape at 5235 Hz is shown

in Fig. 14. The leading edge of the blade exhibitsthe same vibration mode as the hologram and theblades also vibrate with very different amplitudes.An absence of vibration was apparent in the caseof several blades. A view of the impeller disc alsoreveals large amplitude differences in the vibrationsbetween the blades.The interferograms recorded at 5680Hz are

shown in Fig. 15. In this frequency range theCampbell diagram also reveals large materialloading at the inlet due to vibration excitation viathe diffuser vanes. The recordings also indicatelarge vibrations at the inlet. The vibration pattern in


FIGURE 12 Holographic interferogram of the 90-impellerwith 28 blades. Recording at 3620Hz from the front (above)and the back (below).


this region is extremely complex. The vibrationamplitudes again vary from blade-to-blade and thevibration modes of the individual blades are non-uniform. This is reflected in different mode linecurves. Some blades vibrate in the 9th mode shapewhereas others vibrate in the 10th mode shape.

Antinodes observed on the impeller disc are partlyrestricted to the interblade region and also partlyoverlap.The computed mode shape at 5749 Hz presented

in Fig. 16 also reveals large vibration amplitudesof the blades at the inlet region as well as antinodes

COUPLED VIBRATION. PART

FIGURE 14 Computed 86th mode shape of the part struc-ture of the 90-radial impeller with 14 blades at 5235 Hz.

lll

on the impeller disc which extend over severalinterblade regions. The vibration behavior in theblade inlet region is highly complex and is againcharacterized by different amplitudes. For the twonormal blades on the left-hand boundary, whichexhibit only slight vibrations at the inlet, the uniquespecification of a mode shape is not possible. Theremaining normal blades, however, vibrate in their10th mode shape.At these high mode shapes the FE structure

attains the limits of its accuracy. In principle, a finerdiscretization of the blade computational meshas well as the impeller disc structure would benecessary to obtain more exact results. This cannotalways be realized, however, due to limited com-

puting capacity and cost considerations.


6 CONCLUSIONS

The experimental investigations, involving the use

of applied strain gages and data telemetry as wellas holographic interferometry, have made it pos-sible to determine coupled natural frequencies andcoupled mode shapes over a wide frequency range,


FIGURE 16 Computed 93rd mode shape of the part struc-ture of the 90-radial impeller with 14 blades at 5749 Hz.

thereby providing fundamental knowledge con-cerning the extremely complex vibration behaviorof radial impeller structures in practice.On the basis of the experimental results, it was

possible to validate the applicability of the FEmethod to problems of this nature. Despite thereduction of the impeller model to one half and thesomewhat coarse discretization of the models forinvestigating higher mode shapes, the FE compu-tations for the 90-impeller were found to agreeclosely with the experimental results with regard tofrequencies as well as mode shapes in most cases.As dangerous coupled blade vibrations are morepredominant in the middle and higher frequencyranges, finer discretization of the models should

be aimed at within the framework of increasedcomputer capacities in order to arrive at more exact

prognoses of the particular parts of the impellerstructure at risk. Despite this shortcoming, theFE model of the half-impeller used in the presentinvestigation was still capable of yielding relativelygood results.

Acknowledgments

The authors gratefully acknowledge the financialsupport ofthe German ResearchAssociation (DFG)throughout this research project. They would alsolike to thank Dr. Haupt and Dr. Jin for theircooperation as well as Mr. Tanneberg for runningthe tests and Mr. Wichmann for conducting themeasurements. The authors are also indebted toDr. Ian Westwood (Burgwedel, Germany) for hismeticulous translation of this paper.

References

Hasemann, H., Oberr6hrmann, A., Hagelstein, D. andRautenberg, M. (1995) Investigation of the solidity and theblade vibration behaviour of radial compressor impellers dueto a significant reduction of the hyperbolic undercut in theflankmilling process, Yokohama International Gas TurbineCongress, Yokohama, Japan, Oct 22-27.

Haupt, U. and Rautenberg, M. (1978) Zur Untersuchung vonSchaufelschwingungen an Laufrfidern hochbelasteter Radial-verdichter mittels Datentelemetrie, MTZ Motor-technischeZeitschrift 39, Bd. 4, S. 177-183.

Haupt, U. and Rautenberg, M. (1982a) Investigation of bladevibration of radial impellers by means of telemetry andholographic interferometry, ASME-Paper No. 82-GT-34,Int. Gas Turbine Conference of the ASME, London, England,April 18-22. Transactions of the ASME, Journal of Engi-neeringfor Power, Vol. 104, No. 4, October 1982, pp. 838/843.

Haupt, U. und Rautenberg, M. (1982b) Radialverdichter-Schaufelschwingungen, Forschungsvereinigung Verbrennun-gskraftmaschinen e.V., Frankfurt, FVV- Forschungs-bericht,Heft 315.

Haupt, U. und Rautenberg, M. (1982c) Untersuchung vonSchaufelschwingungen an hochbelasteten Radialverdichter-laufr/idern fortschrittlicher Technologie, Forschungs-vereinigung Verbrennungskraftmaschinen e.V., Frankfurt,FVV- Forschungsbericht, Heft R 425.

Haupt, U., Kreitlow, H. and Rautenberg, M. (1982) Bladevibration measurements by means of telemetry and holo-graphic interferometry on a radial impeller with thin blades,Paper No. V-55, Fourth International Conference forMechanical Power Engineering, Cairo, Egypt.

Haupt, U. (1984) Untersuchung des Schaufelschwingungsver-haltens hochbelasteter Radialverdichterlaufrfider, Disserta-tion, Universitfit Hannover, 1984.


Haupt, U., Rautenberg, M. and DiefenthS.ler, K. (1984)Beschleunigungsfeste 8-Kanal-Telemetrieanlage ftir Schau-felschwingungsmessungen am Radialverdichter, EuropS.ischeTelemetrie-Konferenz, ETC ’84, B6blingen, Mai 1984.Acceleration Proof 8-Channel-Telemetry-System for BladeVibration Measurements on a Centrifugal Compressor.European Telemetry Conference, 21-24. Mai 84, B6blingen,FRG.

Haupt, U., Bammert, K. and Rautenberg, M. (1985) Bladevibration on centrifugal compressors Fundamental consid-erations and initial measurements, ASME-Paper No. 85-GT-92, Int. Gas Turbine Conference of the ASME, Houston,Texas, USA, March 18-21, 1985.

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Coupled Vibration of Unshrouded Compressor Part I