Experimental in Ve 00 Iver

7/29/2019 Experimental in Ve 00 Iver

1/94


2/94

ay "HOOLCALIFORNIA 83943-5002


3/94


4/94


5/94

NAVAL POSTGRADUATE SCHOOLMonterey, California

THESISEXPERIMENTAL INVESTIGATION OF DAMPINGCHARACTERISTICS OF BOLTED STRUCTURALCONNECTIONS FOR PLATES AND SHELLSby

Jonathan C. IversonSeptember 1987

Thesis Advisor: Y. S. Shin

Approved for public release; distribution is unlimited.


6/94


7/94

REPORT DOCUMENTATION PAGEREPORT SECURITY CLASSIFICATIONUNCLASSIFIED lb. RESTRICTIVE MARKINGSSECURITY CLASSIFICATION AUTHORITYDECLASSIFICATION /OOWNGRAOlNG SCHEDULE

3 DISTRIBUTION/ AVAILABIUTY Of REPORTApproved for public release;distribution is unlimited

PERFORMING ORGANIZATION REPORT NUM8ER(S) S. MONITORING ORGANIZATION REPORT NUM9ER(S)

NAME OF PERFORMING ORGANIZATIONPostgraduate School

6b. OFFICE SYMBOL(I* iO&XaOl*)

697 4. NAME OF MONITORING ORGANIZATIONNaval Postgraduate School

AOORESS (Cry. Start, and ZIPCodt)California 93943-5000

fb. AOORESS(Cfy. Sr*r. and ZIP Cod*)

Monterey, California 93943-5000NAME OF FUNOING/ SPONSORINGORGANIZATION 8b. OFFICE SYMBOL(If apoiicabl*) 9 PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER

AOORESS (Gfy. Start, and ZIP Coo*) '0 SOURCE OF SUNOING NUMBERSPROGRAMELEMENT NO PROJECTNO TAS


8/94

Hnrl^sifiedSECURITY CLASSIFICATION OF THIS *AGe fWhmn Omm E*t;.


9/94

Approved for public release; distribution is unlimited

Experimental Investigation of Damping Characteristicsof Bolted Structural Connections for Plates and Shellsby

Jonathan C. IversonLieutenant, United States NavyB.S., University of Miami, 1979Submitted in partial fulfillment of therequirements for the degrees of

MASTER OF SCIENCE IN MECHANICAL ENGINEERINGandMECHANICAL ENGINEER

from theNAVAL POSTGRADUATE SCHOOLSeptember 1987r


10/94

1-r

ABSTRACTReducing the contact force in bolted structural

connections can reduce system vibration amplitudes byenhancing joint damping capacity. A test modelconsisting of two concentric circular cylindricalshells and four vanes connected by groups of bolts wastested and analyzed to investigate the relationshipbetween the contact force and the system damping. Aviscoelastic material was then introduced between thecontacting surfaces and its effect on systems dampingwere again investigated.

Experimental results show that resonantfrequencies of modes whose mode shapes provided themost differential motion at the joint connection wereshifted down in frequency and the damping increased.This damping increase and frequency shift continued ascontact force was reduced until the structural jointsmoved into the total slip regime where the responsebecomes nonlinear. The maximum damping and maximumfrequency shift were obtained just prior to this totalslip.

The greatest increase in damping was achieved withthe introduction of viscoelastic material betweencontact surfaces. This damping material also postponedthe transition from microslip to macroslip.


11/94

TABLE OF CONTENTSI. INTRODUCTION 7II. BACKGROUND 9III. THEORY AND METHOD 17IV. EXPERIMENTAL ARRANGEMENT 21

A. MODEL CONSTRUCTION 21B. IMPACT TESTING ARRANGEMENT 22C. VIBRATION GENERATOR TESTING ARRANGEMENT . 23D. VISCOELASTIC MATERIAL 24E. GENERAL TEST PLAN 2 5

V. RESULTS 2 9A. MODAL ANALYSIS 29B. VERIFICATION 30C. FRICTION JOINT ANALYSIS 33D. VISCOELASTIC JOINT ANALYSIS 36E. COMPARISON OF FRICTION JOINTS AND

VISCOELASTIC JOINTS 38VI. CONCLUSIONS 76VII. RECOMMENDATIONS 78LIST OF REFERENCES 79INITIAL DISTRIBUTION LIST 81


12/94

ACKNOWLEDGEMENTSThe author would like to express his appreciation

for the guidance and friendship extended by Prof. YoungShin. The technical and theoretical support for themodal analysis portion was provided by Dr. Kilsoo Kim,who made a complex subject much easier. Finally theauthor would like to gratefully acknowledge thecontinued support provided by Dr. Arthur Kilcullen andthe personnel at the Naval Research and DevelopmentCenter, Bethesda, Md . , who funded much of the researchcontained in the thesis.


13/94

I . INTRODUCTIONIn today's U.S. Navy design trends are tending

toward lighter, all-welded structures, since a lighterstructure decreases the total mass, and a weldedconstruction configuration increases the strength ofthe lighter structure. This technique, however,produces structures with low inherent damping, andproblems can occur under dynamic loading, which thestructure could encounter during its service life.Such problems include: structural noise, criticalalignment variations, dynamic stressing, and fatigue.Designs which enhance damping in a structure are,therefore, very desirable from the aspect of noisereduction and structural integrity.

Damping exists in all vibrating systems. There aremany different mechanisms which contribute to thedamping in a structure. Some of these mechanisms are:fluid resistance, the use of viscoelastic materials,internal friction (material damping), and friction atconnections. All of these mechanisms have been shownto be a function of many variables, including astructure's shape or geometry, its material properties,temperature, frequency, boundary conditions, anddifferent excitation energy levels.

Usually over ninety percent of the inherent dampingassociated with fabricated structures originates in themechanical Joints [Ref. 1]. These mechanical jointsare friction joints which dissipate energy during thevibration of a structure. This vibrational dampingoccurs when small relative movements take place betweenjoint interfaces. Effective use of this type ofdamping mechanism is very rarely utilized in the


14/94

mechanical engineering field. This is due to thecurrent design approach of preloading all bolted jointsto ninety percent of the bolting material's proofstrength. This design criteria is utilized to ensurestructural integrity and stiffness and to preventinterfacial slipping which would then lead tostructural wear. This design approach, however, isbased solely on the bolting material and not on thejoint's expected excitation energy. Use of thisengineering practice results in the joint dampingcapacity being kept to a minimum.

This investigation pursues possible dampingbenefits achievable by: (1) varying the contact forcebetween joint interfaces via bolt torque adjustments,(2) damping associated with the addition of aviscoelastic layer between the friction joints contactsurface, (3) a combination of both viscoelastic andvarying bolt torque, to obtain an optimum jointdamping, and (4) fluid loading variation by changingthe structures environment from air to water. Theinvestigation also includes the experimentalverification of the macroslip phenomena at the boltedjoints of the plate and shell structure.


15/94

II. BACKGROUNDUnderstanding of friction damping phenomena in

Joints has long been a significant research topic.Both analytical studies and experimental verificationhave pursued one of two analytical approaches,microslip or macroslip.

In the macroslip approach, the entire jointcontact surfaces interfaces is assumed to he eithertotally stuck (no movement) or totally slipping. Thefrictional energy dissipation mechanism associated withthe joints contact surfaces is assumed to be governedby some form of Coulomb's law of dry friction. In themicroslip approach, the joint interface progressivelymoves from stuck to total slip, with increasing extentof local slip between pairs of contacting points. Thisapproach produces a smoother transition from stick tototal slip but requires a relatively detailed analysisof the contact stress distribution at the interface.

Macroslip analytical analysis has been conductedon both single-degree-of-freedom ( SDOF ) systems, andmultimode systems. An exact solution for a SDOF systemat steady state stick/slip motion has been obtained byDen Hartog [Ref. 2]. Figure 2.1 indicates the type ofsystem analyzed which assumes a Coulomb friction typeresisting force (F),to the input excitation force with amplitude (P). DenHartog' s solution was limited by assuming thestick/slip motion achieve total lockup twice per cycle.His solution revealed that for forced vibration withdry friction, ratios of friction force to excitationamplitudes (F/P) of less than /4 result in resonanceresponse amplitudes becoming infinitely large (see

9


16/94

Figure 2.2). In Figure 2.2 wR is the resonancefrequency of the system. This analysis was extended tomultimode systems by Pratt and Williams [Ref. 3], withsimilar results.

A SDOF system with bilinear hysteresis tosinusoidal excitation was analyzed by Caughy [Ref. 4].This bilinear hysteresis behavior represented thepresence of Coulomb friction or elastoplast ic behaviorof the system material. His analysis showed that thereexists a critical value of excitation above which non-finite resonance amplitudes occur. The displacementsindicated by his analysis were also larger than thoseobtained from an equivalent linear system model. Asimilar analysis of a limited slip joint to sinusoidalexcitation was conducted by Iwan [Ref. 5]. Thisanalysis revealed that the system may possess suchfeatures as large jumps and/or discontinuous responsecurves which depend on the severity of the non-linearity induced by slip, the level of excitation, andthe amount of viscous damping.

Discrete models to characterize the dynamicresponses of a bladed disk system with dry frictiondampers, excited by harmonic forces was developed andexamined by Muszynska and his co-workers [Ref. 6 and7]. This model determined that two factors were highlyinfluential on the frictional damping realized. Thesefactors are: (a) the ratio of the friction force to theexcitation force, and (b) the blade-to-blade phaseangle of the exciting force. The frictional elementsalso introduced a coupling of the system components.

The origins of the microslip analysis can be foundhistorically in Mindlin's extension of Hertz's contactanalysis between two spheres. The major application ofmicroslip analysis on friction damping in joints can befound in contact analysis between flat surfaces.


17/94

The energy dissipation at an axial double lappedJoint under partial slip and then gross slip wasanalyzed by Earles and Philpot [Ref. 8]. This analysisindicated that the energy dissipated was proportionalto the cube of the load and inversely proportional tothe coefficient of friction for the partial slip case.Their experiments were conducted on plain stainlesssteel flat plates with the frictional damping occurringunder oscillating tangential loads. They obtained aclose agreement for the partial slip region obtainedpreviously by analytical means.

Most recent applications of this dry frictiondamping analysis have been applied to space structuresin which a truss structure is made of tubular members.Crawley et. al . [Ref. 9] considered a friction dampingmechanism consisting of segmented damping tubes placedend to end inside the tubular load carrying members. Asimple mircoslip Coulomb type friction model wasanalyzed to determine the energy loss per cycle andthen validated on a one dimensional friction dampingmodel. The resulting curves showed close agreementbetween theory and experiments.

Menq, Griffin and Bielak [Ref. 10] developed amicroslip model which allowed partial slip on thecontact interface. The model consisted of two elasticbars Joined by an elastoplastic shear layer as shown inFigure 2.3. The friction force in the shear layer, X,per unit length is given by,

kji, N


18/94

remains below the value! /k . As the load P increasesbeyond this value a region of slip is generated andthis region increases until the entire shear layerbecomes plastic.

This microslip model was used to simulate thevibration response of three sets of experiments [Ref.11]. In each case the microslip model could explainthe experimental results that could not be explained bythe macroslip model. Figure 2.4 displays the actualexperimental response obtained for a beam with platformarrangement. Figure 2.5 shows the results obtainedutilizing the numerical macroslip model and Figure 2.6illustrates the close agreement obtained from themicroslip model.

Beards and Williams [Ref. 12] constructed a testframe consists of a rectangular frame with a solidsteel bar bolted diagonally to it. The frequencyresponse of the structure was measured by exciting onecorner of the frame at a constant sinusoidal force anddetecting the response by an accelerometer at one ofthe other corners of the frame. They analyzed theresponse of the frame using a method that analyzes thevibration of a system, which is comprised of a linearundamped multi-degree-of-f reedom structure with asingle frictional damper [Ref. 13]. This experimentindicated that a useful increase in the damping in astructure could be achieved by fastening joints tightlyto prohibit translational slip but not tightly enoughto prohibit rotational slip.

An investigation of the effect of controlledfriction damping in Joints on the frequency response ofa frame excited by a harmonic force was preformed byBeards and Woodwat [Ref. 1]. They compared thefrequency response around the second mode of vibrationof the frame for various clamping forces at the joints.

12


19/94

It was observed that a maximum reduction in the frame'sresponse of 21 dB could be achieved. It was also shownthat a reduction in peak response of 10 dB occurred dueonly to microslip in the Joints.

Vibration damping associated with dry friction inturbine engines can occur at shroud interfaces ofblades and the platform of turbine blades fitted withplatform dampers. Srinivasan and Cutts [Ref. 14]studied the effect of these two sources of damping onblade vibration both experimentally and analytically.In the study of damping due to rubbing at shroudinterfaces, the macroslip analysis predicted an abrupttransition from a region of no friction damping to themacroslip region. However, the test results indicateda smoother transition indicating a region of partialslip or microslip conditions.

From all of these research papers and experiments,it is clear that the macroslip model is not enough toobtain an understanding of the damping associated withclamping forces. It is also clear that the excitationforce defines the region as micro or macroslip and thatthe current trend in the analytical approach should bethe development of a new model which exhibits the threemain characteristics of such contact problems. Thesecharacteristics are: elastic deformation at smallexcitation energies, followed by a region of partial ormicroslip, and finally a total slipping of the jointfor very large excitation forces.


20/94

P cos(o) t)

7777Tffl777T>^ f = n :iN

Figure 2.1 Single degree-of-f reedom system withCoulomb friction.

i=

2 5c

I I

Mmm'urn amu'tttt

! !


21/94

F A P1

A 1

SJp

F_ A 2


22/94

n 97 '.11 t


23/94

Ill . THEORY AND METHODOne of the important concepts in signal processing

is that of developing a clear understanding of time-frequency and Laplace domain transformations. Thesetransformations simply transform either data orexpressions from one in-dependent variable to another.The variables are time (t), frequency (w), or theLaplace operator (s).

The transformation process generates no newinformation but simply puts the data in a form which ismore easily interpretable or computationally simpler.

In this thesis work these transformations wereused extensively in the analysis of the data obtained.Fourier Transforms were used for computing frequencyresponse and coherence functions.

The frequency response of a system is defined asthe Fourier transform of the input to the systemdivided into the Fourier transform of the output of thesystem, or: H(Jw) = 0(jw) / I(jw)where H(jw) = frequency response

O(Jw) - Fourier transform of outputI(jw) = Fourier transform of input.

The transfer function is defined as the Laplacetransform of the system output divided by the Laplacetransform of the system input, or:

G(s) = 0(s) / 1(b)where G(s) = transfer function

0(s) = Laplace transform of output17


24/94

I(s) = Laplace transform of input.The frequency response and transfer function

supply essentially the same information about thesystem. The two terms are frequently usedinterchangeably in the literature. The frequencyresponse of a system is determined from the transferfunction by letting s = jw and by assuming that allinitial disturbances were either equal to zero orcompletely damped.

In the majority of present day vibrationalanalysis, the motion of the physical system is assumedto be adequately described by a set of simultaneoussecond-order linear differential equations of the form:

Mx(t) + Cx(t) + Kx(t) = f(t) equ 3.1where f(t) is the applied force vector, x(t), x(t), andx(t) are the resulting displacement, velocity, andacceleration vectors, and M, C, and K are called themass, damping, and stiffness matrices. If the systemhas n-dimensions (n-degrees-of -freedom ) then the abovevectors are n-dimensional and the matrices are (n x n).

Taking the Laplace transform of the system gives:B(s) * X(s) = F(s) equ 3.2

where F(s) is the Laplace transform of applied forcevector, X(s) is the Laplace transform of resultingdisplacement vector, B(s) = Ms 2 + Cs + K, and s is theLaplace variable, a complex number. B(s) is referredto as the system matrix. The transfer matrix H(s) isdefined as the inverse of the system matrix. Hence,the transfer matrix H(s) satisfies the followingequation

X(s) = H(s ) * F(s)18


25/94

which is equivalent to equation 3.2.This investigation assumes that the responses of

the model associated with microslip are linear innature. With this assumption it is possible todescribe the motion of the system as described above inequation 3.1.

The frequency response can be determined bysubstitution of jw for s in the transfer function or isalso define as:

1/mH(CO) =;co

2 - co ) + (2coco )

where2 k _ C C

CO = , 2co = , or =m n m V2kmThis result is for the slngle-degree-of-f reedom systembut is a simplification of the multi-degree systemsolution

The frequency response is a complex quantity andcontains both real and imaginary parts (rectangularcoordinates). It can also be presented in a polarcoordinates as magnitude and phase. Both systemsprovide the same information, however, the dB scaledtransfer function or Bode plot provides the mostinformation in one graphical presentation and used inthis paper.

Modal Analysis is a method by which the dynamicproperties of a system (damping, natural frequency, andmode shape) can be determined. There are threefundamental assumptions concerning the nature of thesystem upon which modal analysis is based. Theseassumptions are:

1. The system is linear. The response of the19


26/94

structure to a combination of forces,simultaneously applied, is the sum of theindividual responses to each of the forces actingalone

2. The structure is time-invariant or "stationary".The measured modal parameters are constants ofthe system.

3. The structure is observable. The force inputand acceleration output measurements takencontain enough information to generate anadequate behavioral model

The damping and frequency associated with aparticular mode of vibration are global properties ofthe structure under test and theoretically independentof where they are measured on the structure (assumingthe measurement is not performed at a nodal point).The mode shapes are a spatial description of theelastic response of the structure and also influencedby node point locations. To determine a mode shaperequires that sufficient measurements be taken suchthat when the modal analysis is preformed and the modeshape calculated the individual mode shapes accuratelydescribe the dynamic motion of the system under test.

A more detailed description of both modal analysisand transfer function are contain in References 15 and16.

20


27/94

IV. EXPERIMENTAL ARRANGEMENTA. MODEL CONSTRUCTION

A test model was constructed which consisted of twoconcentric cylindrical shells with a four vane intra-structure. All connections were by bolts, as shown inFigure 4.1. The outer shell was made of a standardcarbon steel, 0.25 inches in thickness and 18.0 incheswide. The remaining structural material was bronzewhich was also 0.25 inches thick and 18.0 inches wide(see Figure 4.1). Note that the inner shell is 0.5inches thick. High strength A325 bolts 0.75 inches indiameter and double washers were utilized throughoutthe structure to connect all structural piecestogether. Bolts were arranged in groups of six,uniformly spaced per row, each row being located onbolt lines as shown in Figure 4.1. Bolting hole weretapped such that the bolts had a 0.125 inch clearanceand were not in direct contact with the structure.This provided the bolts the ability to move relative tothe structure, which is similar to the standardengineering application. The other connections at thevane plates to support structures were full penetrationwelds

Maximum contact force was determined utilizing atypical machine design calculation:

Fi - 0.9 * Sp * Atwhere Fi is the proof load or contact force for eachbolt, Sp is the proof strength of the bolt material,and At is the tensile-stress area. This result canquickly be modified to obtain bolt torque by:T=0.2*Fi*Dwhere T is the torque for each bolt and D is the

21


28/94

diameter of the bolt. Values obtained for maximumtorque and contact force were 320.0 ft-lb and 3.06 X10" lb. For the continuation of the study all torquesand contact forces were taken as percentages of thesemaximum values.

Previous studies conducted at the NavalPostgraduate School have concluded that the optimumboundary condition is that of shock chord induced free-free support [Ref. 17]. This type of support wasutilized for the study and was found to limit thetransmission of random noise signals from the localenvironment to the structure.B. IMPACT TESTING ARRANGEMENT

Two different approaches were taken to determinethe best process in which to investigate the model'sresponse. The first was an impact-decay type analysis(see Figure 4.2), in which a PCB modally tuned impacthammer was used to excite the model and a miniatureENDEVCO accelerometer (model 2250A10) measured thestructures response. Each of 96 grid points wasexcited ten times and averaged to obtain input andoutput signals. These input and output signals wereamplified and filtered prior to analysis. The inputsignal was obtained from a force transducer located inthe head of the impact hammer. This signal was thenamplified by a PCB Power unit (model 480D06 ) with thegain value set at ten. The response signal wasamplified by an ENDEVCO signal conditioner (model4416A), which was also set with a gain factor of ten.These two signals were both pre-filtered by a HewlettPackard (HP) 5440A Low Pass Filter and analyzed by a HP5451C Fourier Analyzer.

The HP 5451C Fourier Analyzer utilizes a band-selectable Fourier analysis technique that makes it


29/94

possible to perform Fourier analysis over a frequencyband whose upper and lower frequencies areindependently selectable. It also provides a digitalfrequency domain analysis of complicated time signals.A modal analysis application package operates onmeasured transfer function data to determine modalproperties, this includes an animation of theparticular mode shape. From this analysis the firsteight mode shapes were determined.C. VIBRATION GENERATOR TESTING ARRANGEMENT

The second process (see Figure 4.3) employed aWilcoxon Research F7/F4 Vibration Generator as theinput force device. The vibration generator wasattached to one of the vanes on the structure, 5.5inches from the outside shell and six inches from thefront edge of the vane. This vibration generatorutilizes a combination electromechanical andpiezoelectric units which provide a controllable forceoutput in the range of 10 Hz to 15,000 Hz. An HP 3562ADynamic Signal Analyzer provided the driving signalwhich was amplified by a Wilcoxon Research PowerAmplifier (model PA7C ) . The driving signal was eithera frequency selected random noise or a swept sine.This amplified signal was then properly split into twosignals by a Wilcoxon Matching Network (model PA7C).The split is determined by the frequency of the drivingsignal. The lower the desired frequency the more poweris provided to the electromechanical (F7) vibrationgenerator. Similarly, when the high frequency signalis desired, power is sent to the piezoelectric (F4)vibration generator. This separation is to ensure asmooth transition from low frequency to the higherranges. Located at the base of this vibrationgenerator and before the attachment post was a force

23


30/94

transducer to measure the input excitation force. Thisforce signal was then amplified by a charge amplifierand fed to the HP 3562A Dynamic Signal Analyzer as aninput signal. An ENDEVCO accelerometer and signalconditioner were used to measure the structure'sresponse. This signal was also fed to the HP 3562AAnalyzer as the output signal. When the input signalwas random noise the output signal was subjected to aHanning window and utilized a 40 averaging analysis.Then the swept sine is utilized there is no requirementfor windowing, however a ten averaging analysis wastaken. The accelerometer was placed in ten differentgrid points, symmetrically oriented about the center ofthe structure. These grid points were both on theouter shell as well as the vane structures.

The HP 3562A Dynamic Signal Analyzer digitizedboth input and output signals, from this digitized datathe analyzer calculates frequency response, powerspectra, and coherence. Coherence shows the relativereliability of the data obtained. Its range is from1.0 to 0.0, or from exact data, to data fullycontaminated by noise.

For the underwater experimentation, a waterproofcase was utilized. The case was previously designed,constructed and tested at the Naval PostgraduateSchool. More information as to the construction andcheckout testing can be obtained from Reference 18.D. VISCOELASTIC MATERIAL

The viscoelastic material applied at the jointinterfaces was a 3M SJ-2015x ISD-112 viscoelasticcompound. This material was conveniently provided asthin sheets, approximately 10 mil. in thickness.Figure 4.4 shows the variation of the shear modulus andloss factor as functions of temperature and frequency


31/94

for the ISD-112 viscoelastic material alone. Theseplots are usually used for the design of constrainedlayer dampers. The stiffness, mass, resonance modeconfiguration, and geometry of the damper-substratecombination significantly affects the performance ofthe viscoelastic material. The ISD-112 viscoelasticmaterial was selected because of it's consistent lossfactor over a wide range of temperatures. This can beseen in Figure 4.4, that the loss factor is relativelyflat from 100 F to 50 F. The modulus of elasticitychanges significantly but this is characteristic of allviscoelastic materials.E. GENERAL TEST PLAN

The experimentation was broken down into fourareas. First a modal analysis was conducted todetermine the structures modes shapes and resonancefrequencies. Next a verification study to ensurerepeatability of the structural response and optimumtest equipment arrangements. The third area studiedwas the effects on structural damping associated withthe model by varying the contact force. The finalexamination was to observe the effects of aviscoelastic Joint and varying contact force.


32/94

Bolt (typical)

Shaker &WaterproofCase "

CO bsVco 2c tr

12 ? tf c :aa :

' ; ^""*912 ! 1 i / 1 y *fz . v

c 12 : N

Figure 4.4 3M ISD-112 specification plot.

28


35/94

V. RESULTSA. MODAL ANALYSIS

A modal analysis was conducted to determine theresonance frequencies and mode shapes for the structureup to 125 Hz. These mode shapes were examined in hopesof determining the best candidates to observe increaseddamping associated with the microslip phenomenon. Thismodal analysis and preliminary experimentation wasconducted utilizing an impact-decay response and the HP5451C system previously described in chapter IV. Themodal analysis application package operates on measuredtransfer function data to determine modal propertiesfor the structure. A grid structure was imposed overthe model and impact-response data was collected ateach grid point. All of this data was then used todetermine structural movements associated with eachparticular mode shape, which occurred at it'scharacteristic resonance frequency.

From this analysis the first eight mode shapeswere determined. Figure 5.1 and 5.2 shows theundeformed shape and grid structure that was utilizedfor the modal testing. The inner ring was not modeledfor the analysis due to the limitation of storagecapacity, which determined the maximum number of nodepoints. Figure 5.3 through 5.11 shows the eight modeshapes obtained by the modal analysis. These modeshapes as well as the resonance frequencies agreedclosely to a MSC/NASTRAN finite element analysispreviously conducted and reported in Reference 19.

The initial objective of the modal analysis was todetermine the optimum frequencies to conduct this study

29


36/94

on frictional damping. The optimum frequencies wouldprovide the most differential displacement associatedat the contacting surfaces of the joints. Thesedifferential displacements would then be used to obtainthe frictional damping desired to reduce the structuralresponse. The modal analysis, however, did not providea clear indication of these optimum frequencies / modeshapes. Due to this uncertainly, a broader lowfrequency analysis from 15 to 300 Hz was chosen for theremaining analyses.B. VERIFICATION

Preliminary experimentation was concentrated onensuring that repeatability could be achieved, bothfrom several input types as well as reestabl ishment ofapplied contact force, and minimizing any environmentaleffects on the model's response. These environmentaleffects included model orientation, added mass due to avibration generator versus impact, and boundaryconditions imposed by suspension by shock chord.

The vibration generator apparatus which waspreviously described in chapter IV was next used toconduct a frequency response analysis to compare withthe impact-response. The vibration generator processyielded the same resonance frequencies with very slightdifferences in frequency response amplitudes. Thesedifferences were determined to be a function of thefiltering utilized by each of the analyzers. When theHP 3562A was replaced by the HP 5451C in Figure 4.3,the frequency response obtained was exact, to thatobtained in the impact testing. The added massassociated with the vibration generator was concludedto have no effect on the resonance frequencies oramplitudes. This conclusion is believable due to thefact that the vibration generator and water-proof case


37/94

were less than 0.8 percent of the total weight of themodel. The orientation of the vibration generator inthe gravitational field was also determined to have noeffect on the structure's response as confirmed byfurther orientation experimentation.

Next the boundary condition associated with theshock cord were studied to determine if they had anyeffect on the structure's response. This investigationchanged the attachment location of the shock cordsupport as well as the length of the shock cord used.Figure 5.12 indicates that the support structureprovides no extraneous signals to the model on theorientations tested. This procedure was tested bothfor impact-response and vibration generator inputdevices

The repeatability study was then conducted, inwhich the entire structure was disassembled and thenreassembled again to the same contact force (same bolttorque). The results of this can be seen in Figures5.13 and 5.14 which indicate that the frequencyresponses for the grid point located on the vane in thesix o'clock position are repeatable. Several gridpoints were used to confirm the results for the entirestructure

During the repeatability study an interestingphenomenon was observed. A random noise driving inputforce was utilized because of its fast data samplingrate. However, upon comparison with the slower samplingrate, swept sine driving force, the random noise didnot achieve the same resolution. Therefore, the sweptsine driving input force was utilized for the rest ofthe investigation.

During the previously described testing, ten gridpoints were used to examine the symmetry of the modelwith respect to the frequency response of the total


38/94

structure. The ten grid points were located both onthe outer ring as well as the vanes. These locationswere chosen to observe the damping effects on the outerstructural Joints since these joints appeared to havemore relative motion across the joint interfaces atlower resonance frequencies. During all of the aboveexperiments, symmetric points produced similarfrequency response graphs. These plots were not exactbut the structure with the vibration generatorinstalled was not exactly symmetric.

Each swept sine data run was kept to a maximumspan of 100 Hz to increase the frequency resolution to0.5 Hz. Even at this resolution there were severaldata runs that yielded poor resolution and exactdamping calculations could not be obtained. Due to thetime required to obtain each data run, only two gridpoint were utilized for the continuation of this study.The first point was on the outer shell at a 15 degreerotation from the vane with the vibration generator onit and six inches from the front of the model. Theother grid point was located on the vane in which thevibration generator was attached, six inches from theback on the model and four inches in from the outershell. The same results were obtained on either sideof the vane joint and only the data obtained from thegrid point located on the vane are shown in the figuresto follow. All values of the coherence obtainedthroughout the experimentation were 0.9 or betterexcept in the frequency range of 15 to 23 Hz. This lowfrequency range is at the lower range of the F4/F7frequency generator making the reliability of the datahard to confirm.

The applicability of the data obtained in thisstudy was of concern so a vane to system couplingexperiment was conducted. This experiment started with


39/94

the outer cylinder removed and the four vanes installedat a uniform contact force at each joint. One vane wasthen removed at a time and the frequency responseobtained and compared to that of the four vane responseto determine the effects of the deletion of a vane.This type of analysis could be used to determine theeffects of the addition of a vane(s) to the structure,as in the case of a turbine compressor system. Theresults are presented in Figures 5.15 and 5.16. It canbe seen that the coupling associated by one vane isvery minimal. This is observed by the fact that onlyslight changes in the frequency response occurred whenthe vanes are removed (see Figures 5.15 and 5.16). Theonly significant change occurred when three of thevanes were removed (Figure 5.17). This indicates thatour test structure could model a structures with fouror more vanes without significant change in the overallresultsC. FRICTION JOINT ANALYSIS

The varying contact force analysis was thenconducted in which the bolts were torque to the maximumvalue, tested and then the torque reduced and testedagain

Figures 5.18 through 5.23 show the frequencyresponse of the model over the frequency range 15 to115 Hz. In all of these graphs the dotted line is thefrequency response of the structure at 100 percentcontact pressure, and the solid lines are at adifferent percentage as labeled with each figure.Figure 5.18 indicates that little or no change isobtained from 100 to 75 percent contact force. Theanomalies observed are similar to those obtained duringthe repeatability studies or were correctable byincreasing the resolution. However, due to the time


40/94

involved obtaining data, increasing the resolution wasnot deemed necessary for all resolution problems. Itcan be seen that the resonance peaks near 100 Hz beginto shift down in frequency at approximately 40 percentcontact force with still no indications of any shiftingat lower frequencies (see Figure 5.19). This frequencyshift is the first observable phenomena that can beobtained even before any damping changes take place.At twenty and again at ten percent the resonance peakscontinue to shift to the left or down in frequency (seeFigures 5.20 and 5.21). The results at ten percent(Figure 5.21) also indicates the beginning of the lowfrequencies to shift due to decreased contact force.These trends continue through five and 2.5 percentcontact force data runs (Figures 5.22 and 5.23). Fromthe data obtained there was a maximum frequency shiftof 8 Hz for the resonance frequencies at approximately100 Hz associated with the 2.5 percent contact force.

Figures 5.24 through 5.29 are the data obtainedfor the second 100 Hz frequency analysis. It can beseen that even at the 75 percent datum, there is anobservable shift In the frequencies at 127 and 137 Hz.These shift continue as the contact force decreases asbefore. These resonance frequency continue to shiftdown in frequency and are also associated with adecrease in resonance amplitudes. The maximumfrequency shift observed was 12 Hz, again at the 2.5percent contact force. Note also that the 100 Hz peakrepeats the previously observed effects obtained fromthe 15 to 115 Hz data runs.

The final frequency range analyzed was from 200 to300 Hz and is shown in Figures 5.30 through 5.35. Thisdata exhibited the same frequency shifts as before. Itwas also noted that the amount of frequency shift wasnot the same at each resonance frequency, this leads to

34


41/94

the possibilities of two resonance frequenciesoverlapping or adding together. This type phenomena isbelieved to cause the appearance of a new resonancepeak at approximately 256 Hz in Figure 5.31, and isclearly seen in Figure 5.33 at 252 Hz.

In Figure 5.35 the contact force is 2.5 percentand new resonances frequencies associated with totallynew mode shapes indicate that the structure has gonefrom the microslip to the macroslip (total slip)situation. An indication of when this transition takesplace can be estimated by when the response reaches itsminimum amplitude. This point is seen to be betweenten and five percent contact force (see Figures 5.33and 5.34). The amplitudes associated with 100, 123,132, 210, and 240 Hz all indicate this transition atthis particular contact force. Therefore, the maximumdamping should be achieved at this approximate contactforce

Figures 5.36 through 5.38 are plots of percentdamping factor versus frequency for each of thepreviously described data runs. The percent dampingfactor was determined via the half power point methodas described in Reference 17. The damping factor isvery sensitive to the frequency resolution and withonly a 0.5 Hz resolution the error bars would clearlyoverlap each consecutive data points and quantitativeconclusions from these results are not possible,however general trends in the damping can be observed.It can be seen that the damping increases until itachieves a maximum at the ten percent contact force aspreviously predicted from the frequency response plots.It is also noteworthy, that the damping factor seem toincrease across all resonance frequencies as thecontact force decreases instead of only at thoseparticular frequencies observed previously. The


42/94

greatest increase in damping factor is still associatedwith the above mentioned resonances frequencies. Theseparticular resonance frequencies are obviouslyassociated with mode shapes which exhibit thedeflections relative to each mating surface. Clearlyas a particular mode shape shifts in it's resonancefrequency, the damping increases until the mode shapeenters into the total slip regime.

Once this study was completed the contact forcerequired to bring the apposing joint surfaces togetherwas determined. This was done by slowly torquing thebolts until a one mil. filler gauge did not passthrough the joint clearance. This force was thensubtracted off the above contacting forces. Thevibration generator's weight was seven pounds and witha friction factor of 0.11 this then is equal to thecorrected normal contacting force for 8.8 percent.Clearly the ten percent contacting force is areasonable result for the force at which the modelenters the macroslip area.D. VISCOELASTIC JOINT ANALYSIS

The 3M ISD-112 viscoelastic material was thenintroduced between the contact surfaces of the matingjoints on the outer ring only. The viscoelasticmaterial was adhered to the outer surface of the vaneportion of the joint and the inner structure waslowered into the outer ring. The outer ring was thenbrought into contact with the material from one side ofthe joint to the other by torquing to 100 percenttorque, from one side of the joint to the other. Thetotal percentage of contact was questioned, andexamined upon removal . The actual percentage ofcontact was estimated at 70 percent, which was muchbetter then expected.

36


43/94

A similar investigational procedure was followedas with the bolt torque determination. Results can beseen in Figures 5.39 through 5.50 in which the dottedlines is the frequency response curve obtained from the100 percent contact force data run and the solid linesare the frequency response lines for the picturedcontact force. The effects of decreased joint contactforce are observed earlier than with the bolts onlystructure at the 75 percent bolt torque (compareFigures 5.18 and 5.39). This effect of shifting theresonance frequencies to the left or down in frequencyis accelerated as can be seen when comparing Figures5.40 and 5.41 with 5.20 and 5.21. However, thisshifting is reversed at the lower frequencies as can beobserved in the five percent plots (compare Figures5.42 with 5.22) .

Similar results can be observed in the secondfrequency analysis range from 100 to 200 Hz (seeFigures 5.43 through 5.46). The same reversal infrequency shift at about five percent is also observedin this series of plots.

In the final 100 Hz analysis the new resonancepeak is already observable in Figure 5.47 and continuesto increase in size down to the five percent plot. Inthe contact force study above this peak first becamenoticeable at the 20 percent torque and grew quickly,but in the viscoelastic study it was observed at the 75percent contact force and slowly grew.Again the percent damping factor versus frequencygraph were produced with similar results as thoseobserved previously with the exception that theviscoelastic joints appear not to have reached abreakaway torque where the model slips from themicroslip regime into the total slip area(see Figures5.51 and 5.52). It assumed that the viscoelastic

37


44/94

material provides a large coefficient of frictionbetween the mating surfaces and thus decreases thecontact forces required to hold the surfaces together.The graphs seem to indicate that the viscoelasticmaterial is reaching a maximum at approximately fivepercent, as can be seen in Figure 5.52, as the spacingbetween the lines become smaller with each decreasingcontact force.

The viscoelastic Joint plots indicated that adifferent manifestation is taking place at the jointwhen the viscoelastic material is added. Thismanifestation appears to start the shift of resonancefrequencies (and thus the damping) earlier and at afaster rate in the higher contact forces but decreasesthe amount of shift in the lower contact forces.E. COMPARISON OF FRICTION AND VISCOELASTIC JOINTS

To confirm the previous observation the plots ofthe same contact force but different jointconfiguration were graphed.

In Figures 5.53 through 5.67 the dotted lines are thefrequency response of the joints with no viscoelasticmaterial added and the solid lines are the frequencyresponse of the joints with viscoelastic materialadded. Each graph is at one particular contact forceas labeled.

Figure 5.53 shows the viscoelastic resonancefrequency at approximately 100 Hz to the right of thenon-viscoelastic peak, however as the contact pressuredecreases the viscoelastic peak shifts at a faster rateas can be seen in Figures 5.54 through 5.56. Then asthe non-viscoelastic peak slips into the macroslipregime, its peak slips at a faster rate and shows up tothe left of the viscoelastic peak at five percentcontact force (see Figure 5.57). This observation is

38


45/94

seen again in the second analysis band (100-200 Hz) at100 Hz, 126 Hz, and 136Hz (see Figures 5.58 trough5.61), however the peaks at 126 and 136 Hz start to theleft and increase their distant from the non-viscoelastic peaks until the ten percent contact force,then from ten to five percent the non-viscoelast icpeaks again shift at a faster rate and close back in onthe viscoelastic peaks (see Figure 5.62). Also notethat the viscoelastic resonance peaks have a decreasedamplitude as compared to that of the non-viscoelasticpeaks at 126 and 136 Hz.

The final analysis band produced the mostinteresting phenomenon, the resonance peaks associatedwith the viscoelastic Joints moved in both direction ascompared to its counterpart on the non-viscoelasticjoints (see Figure 5.63). However the trends mentionedabove still held true, both in frequency shifts andamplitudes (see Figures 5.63 through 5.67). Ofparticular note is the appearance of the third peak at256 Hz early at 75 percent contact force in theviscoelastic joints, which was mirrored at 20 percentby the non-viscoelastic joint.

The plots of the percent damping factor versusfrequency for the viscoelastic and non-viscoelasticjoints at a set contact force are shown in Figures 5.68through 5.71. The damping in the viscoelastic joints,at any resonance frequency, is either equal to orgreater than the damping associated with its non-viscoelastic resonance frequency. The smallest gapbetween the two joints appears to be at the ten percentcontact force situation or when the non-viscoelasticjoint reaches it maximum damping at just prior to theonset of macroslip.


46/94

I WMl .=3TCU0Uit 3D0a

Figure 5.1 Undeformed Shape and Grid S.ructure

Figure 5.2 Undeformed Shape, Front View.40


47/94

Figure 5.3 The First Free Vibration Mode Shape

wo. .=3Taauit sat ret aisau as en

Figure 5.4 The Second Free Vibration Mode Shape41


48/94

1mn. .ISiOOttlt X 1 1ST: CUSSii1

37.3 *ST!

Figure 5 . ihe Third Free Vibration Mode Shape(orthographic view)

w&KgnaiuEsin. isu nssu n.aien

Figure 5.6 The Third Free Vibration Mode Shape(front view)42


49/94

Figure 5./ The Forth Free Vibration Mode Shape

Figure 5.8 The Fifth Free Vibration Mode Shape43


50/94

WH. reTaiHf- sHtt [ 1ST: 313fiii ns ibu

Figure 5.9 The Sixth Free Vibration Mode Shape

11// 11\\\ J

**. .*ET3AaTt SHU 1 1ST: CT.SfiLl1

a.5atan

Figure 5.10 The Seventh Free Vibration Mode Shape44


51/94

Figure 5.11 The Eighth Free Vibration Mode Shape

FRSS RES?i--P.~.Z RESP

ACAvg CCvlp Hcnr4CAve C"Cv!s Hertr

SC H= change c..e:n"at:sm 3CC

Figure 5.12 Frequency Response Plots of Two DifferentFree-Free Boundary Conditions and Orientations.

45


52/94

-lOOFxd Y 50 HzC3HRENCrI. ~

Mag ma. 01

i"N"1

Fxd Y 50 Hz

4SAvg C~3vl3 Hor-in Ov2

6 CCLCCK VANE 2/240Aya C.13v 1 S HanntfTfrTWHi

3CCOv2

I

:k vane 2/2 SCOFigure 5.13 Frequency Response of Preliminary 1005bTorque.

e3

-1QOFxd Y 5C HzCCHEP.SNCE1. Qi

6 CCLCCK VANE 3/44CAve O'Cv 1 a Hon

MS f]^j! ., Ic irtr-Yi"Wirti ' i t . . , m HH ; I|J1,!1

o. o

! !

5C H-x. 6 CC'_CCK VANE 3/4. 3C~

Figure 5.14 Repeatability Frequency ResDonse, ModelDisassembled Then Reassemble to 100% Torque.46


53/94

FREO RESPHFRE3 RE5?

FxdXY 10 H= 3 VANES ONLY GP 58-# 3CO

Figure 5.15 Frequency Response of Three Vane StructurePlotted Over Four Vane Frequency Response.

HpRS- RESP12.5"

dS

Fxd Y lO H: 2 VANES QN1-Y GP S3-*

Figure 5.16 Frequency Response of Two Vane StructurePlotted Over Four Vane Frequency Response.47


54/94

FRE2 RE3PI-FRE3 RfS?40. "12. S

dS

dS

-87.-122

FxdXY 1C H= i VANE C.ML.Y CR Sa-n" 3CC

Figure 5.17 Frequency Response of One Vane StructurePlotted Over Four Vane Frequency Response.

dS

-ICO

WT7\Fxd Y IS 1 15

Figure 5 . 18 Frequency Response of Model at 75% Torqueand No Viscoelastic Material.(Dotted Line is 100% Torque)48


55/94

dS

-130~xcS Y 15

Figure 5.19 Frequency Response of Model at 40% Torqueand No Viscoelastic Material.(Dotted line is 100% Torque)

= s

-:ooFxd Y 15 Mz

Figure 5.20 Frequency Response of Model at 20% Torqueand No Viscoelastic Mater ial(Dotted line is 100% Torque)49


56/94

P^Ea RE3?2C. 3

dB

F^= Y IS 1 15

Figure 5.21 Frequency Response of Model at 10& torqueand No Viscoelastic Material.(Dotted line is 100$ Torque)

ic. a/Div

! 1 Ii

t1 , !

i 1i

i

! ^LX si1 '!'II 11 11 ! ji y i/fi9 / \ i1 i! J^nUri

1

i/fo> 4AT 1 ! ! /ii/-xaciM I i1 j || '' ii ii ii ( j ! j i

i|

! ?i

i i

1 Ll , ;

: i iiFxd Y 15

Figure 5.22 Frequency Response of Model at 5% Torqueand No Viscoelastic Material.(Dotted line is 100$ Torque)50


57/94

HPSS3 RESP-20. 3

da

1 : S

Figure 5.23 Frequency Response of Model at 2.5% Toraueind No Viscoelastic Material. queDotted line Is 100% Torque)!

d9

-93. CFxd Y XQC

Figure 5.24 o eqenY Response of Model at 75% Torque^Sd No Viscoelastic Material. 4'Dotted line is 100% Torque)51


58/94

dS

-SEFxc Y ICC 2CC

Figure 5.25 Frequency Response of Model at 40& Torqueind No Viscoelastic Material.Dotted line is 100& Torque)i

Fxd Y lOO 20C

Figure 5.26 Frequency Response of Model at 20& Torqueand No Viscoelast ic Mater ial(Dotted line is 100 Torque)52


59/94

r--^2 RES?-2-i. Oa. o

/Div

da

-as. oFxi Y ICC 2CC

Figure 5.27 Frequency Response of Model at 10* TorquefS d^,Alscoe Jastic Material. que(Dotted Line is 100* Torque)1-=- = !-2-.

a./o.

da

-aa.Fxd

:c PES.=I

1 ! 1 ! i !rLv,

aV

:: i *l]/ ' V

i JL*4t\ D/^JH^' 1 1 //H7\.1rw li/J i !/V 1 1 In!

',;i 1*H

K |

:: i

* i

i .1 :i i

i

l

! ! i

Ia1 1

!

i JY ICO 200Figure 5.28 Frequenc

fFrequency Response of Model at 5* Torquend No Viscoelastic Material. queDotted Line is 100* Torque)

53


60/94

dS

Figure 5.29 Frequency Response ofoH q ArenSY response of Model at 2.5% Torauef^ No Vl scoeIastic Material. que(Dotted Line is 100% Torque)

dS

-54. aFxd Y 2CC

Figure 5.30 Frequency Response of Model at 75% TorqueaS d No Viscoelastic Material. 4(Dotted Line is 100% Torque)54


61/94

i-F^EC RESPO. or

da

-6-a. a-xd Y 2CQ Hz 3c:

Figure 5.31 Frequency Response of Model at 40% Torqueand No Viscoelastic Materia^( Do - 'tted Line is 100% Torque )

d9

-5-i. O^xd Y 2QO

Figure 5.32 Frequency Response of Model at 20% Torqueind No Viscoelastic Material.Dotted Line is 100% Torque)i55


62/94

dS

d Y 2CC 3CC

Figure 5.33 Frequency Response of Model at 10 Torqueand No Viscoelastic Material.(Dotted Line is 100& Torque)

Fxd Y 2QC

Figure 5.34 Frequency Response of Model at 5$ Torqueand No Viscoelastic Material.(Dotted Line is 100& Torque)56


63/94

dB

-54. aFxd Y 2CC 3CC

Figure 5.35 Frequency Response of Model at 2.5$ Torque~ind No Viscoelastic Material.Dotted Line is 100% Torque)!

% DAMPING FACTOR VS. FREQ (VARYING BOLT TORQUE)

ccgo


64/94

% DAMPING VS. FREQ. (VARYING BOLT TORQUE)

ccO


65/94

rFSEO RESP-2c. O! r

d8

-xd Y 15 H: 1 1 5

Figure 5.39 Frequency Response of Model at 75% Torqueand Viscoelastic Material,(Dotted Line is 100% Torque)

Figure 5.40 Frequency Response of Model at 20% Torqueand Viscoelastic Material.(Dotted Line is 100% Torque)59


66/94

-23. a

d8

-ICGfd Y 15 1 1 5

Figure 5.41 Frequency Response of Model at 10%" Torqueand Viscoelastlc Material.(Dotted Line is 100% Torque)

Fxd Y 15

Figure 5.42 Frequency Response of Model at 5%" Torque.and Viscoelastic Material.(Dotted Line is 100% Torque)60


67/94

-24. O '

8. O/Div

dB

-38. C"xd Y lOO Hz 2CC

Figure 5.43 Frequency Response of Model at 75% Torque/ a Viscoelastic Material, 4(Dotted Line is 100% Torque)

dB

-88. OFxfi Y 1QC 2CO

Figure 5.44 Frequency Response of Model at 20% Torque^nL V i s ??elastlc Material. q e(Dotted Line is 100% Torque)61


68/94

dS

'xo y ice

Figure 5.45 Frequency Response of Model at 10% Torqueand Viscoelastic Material.(Dotted Line is 100% Torque)

-2-. Z '1

i iii

i

i

1 |

A. 1

I 1 1

s. o ,'i,'Div \'


69/94

dB

-84. a"xd Y 2CC M2 3CC

L 11^ 5.47 Frequency Response of Model at 75%" Torqueand Viscoelastic Material.(Dotted Line is 100% Torque).--^E- RE3 =

d9

-54.. aFxd Y 2CO Hz

Figure 5.48 Frequency Response of Model at 20* Torqueand Viscoelastic Material.(Dotted Line is 100% Torque)63


70/94

dS

-s-t. aFxd Y 2CC 3CC

Figure 5.49 Frequency Response of Model at 1056 Torqueand Viscoelastic Material. H(Dotted Line is 100* Torque)

"RES 9Ejo. a;

a9

-s-:. aPxc Y 23C 3CC

Figure 5.5 Frequency Response of Model atand Viscoelastic Material.(Dotted Line is 100% Torque)5% Torque

64


71/94

% DAMPING FACTOR VS. FREQ. (VARYING BOLT TORQUE)

ot5


72/94

2C. ClO. O/Dlv !

dB

~xci Y 15 H= 1 IS

Figure 5.53 Frequency Response of the ViscoelasticJoint at 100$ Torque.(Dotted line is Non-Viscoelastic Joint)

23. o:

o9

-iCOFxd Y 15 Hz US

Figure 5.54 Frequency Response of the ViscoelasticJoint at 75$ Torque.(Dotted line is Non-Viscoelastic Joint)66


73/94

2a. o

id. a/Div

dS

-1Q3Fxd Y IS Hz 1 15

Figure 5.55 Frequency ResDonse of the ViscoelasticJoint at 20% Torque.(Dotted line is Non-Viscoelast ic Joint)

!-~SE3 RESr-20. a

'

ee

-ICOFxd Y IS US

Figure 5.56 Frequency ResDonse of the ViscoelasticJoint at 10% Torque.(Dotted line is Non-Viscoelastic Joint)67


74/94

K-SE3 RESP-2c. a

dS

-laaFxii Y 15 1 15

Figure 5.57 Frequency Response of the ViscoelasticfT\~4.+ ^ -,? 0111 ? a 5 ^ Torque.(Dotted line is Non-Viscoelast ic Joint)

-24. C

C9

-aa. oFxd

Figure 5.58 Frequency Response of the Viscoelastic/n 4.* -,^ oln ? at 100 ^ Torque.(Dotted line is Non-Viscoelastic Joint)68


75/94

HPRE3 RES?-24. C

d9

-as:xd y ice

Figure 5.59 Frequency Response of the Viscoelastic. Joint at 75$ Torque.(Dotted line is Non-Viscoelastic Joint)

Hx 2CC

Figure 5.60 Frequency ResDonse of the Viscoelastic, , Joint at 20% Torque.(Dotted line is Non-Viscoelastic Joint)69


76/94

dB

-98.Fxd Y lOQ Hz zcz

Figure 5.61 Frequency ResDonse of the ViscoelasticJoint at 10% Torque.(Dotted line is Non-Viscoelast ic Joint)

c29

-as. aFxd y iao H= 2CC

Figure 5.62 Frequency ResDonse of the ViscoelasticJoint at 5% Torque.(Dotted line is Non-Viscoelastic Joint)70


77/94

l-FRa RESPa. a -

dS

3 i

Figure 5.63 Frequency Response of the Viscoelastic,_ Joint at 100& Torque.(Dotted line is Non-Viscoelastic Joint)

dB

-6-1.Fxd Y 2CO 300

Figure 5.64 Frequency ResDonse of the Viscoelastic. Joint at 75$ Torque.(Dotted line is Non-Viscoelastic Joint)

71


78/94

-=3 R3?

a. o

dB

-34. 3Fxd Y 2CC ac:

Figure 5.65 Frequency ResDonse of the Viscoelastic. Joint at 20


79/94

dB

-61. 3iFxd Y 2CC Hz 3CC

Figure 5.67 Frequency Response of the Viscoelastic,_ , Joint at 5& Torque.(Dotted line is Non-Viscoelastic Joint)

VISCOELASTIC VS NON-VISCOELASTIC

ccOO

Experimental in Ve 00 Iver

Documents

Transcript of Experimental in Ve 00 Iver