Enhanced ground-based vibration testing for aerodynamic environments

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Mechanical Systems and Signal Processing

Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]]

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Enhanced ground-based vibration testingfor aerodynamic environments$

P.M. Daborn a,b,n, P.R. Ind a, D.J. Ewins b

a Structural Dynamics, AWE Aldermaston, Reading, Berks RG7 4PR, UKb Bristol Laboratory for Advanced Dynamics Engineering (BLADE), Aerospace Engineering, University of Bristol,Queen's Building, University Walk, Bristol BS8 1TR, UK

a r t i c l e i n f o

Article history:Received 14 July 2013Received in revised form28 November 2013Accepted 16 April 2014

Keywords:AerodynamicCross spectral densityMIMOPiezoelectric patchPower spectral densityRandom vibration

x.doi.org/10.1016/j.ymssp.2014.04.01070/Crown Copyright & 2014 Published by E

ritish Crown Owned Copyright 2013/AWEocument is of United Kingdom origin andd in confidence and may not be copied, usedIPR-PL – Ministry of Defence, Abbey Wood, Besponding author at: Structural Dynamics, Aail addresses: [email protected], aepm

e cite this article as: P.M. Daborn, e. Syst. Signal Process. (2014), http:

a b s t r a c t

Typical methods of replicating aerodynamic environments in the laboratory are generallypoor. A structure which flies “freely” in its normal operating environment, excited over itsentire external surface by aerodynamic forces and in all directions simultaneously, is thensubjected to a vibration test in the laboratory whilst rigidly attached to a high impedanceshaker and excited by forces applied through a few attachment points and in one directiononly. The two environments could hardly be more different. The majority of vibrationtesting is carried out at commercial establishments and it is understandable that little hasbeen published which demonstrates the limitations with the status quo.

The primary objective of this research is to do just that with a view to identifyingsignificant improvements in vibration testing in light of modern technology. In this paper,case studies are presented which highlight some of the limitations with typical vibrationtests showing that they can lead to significant overtests, sometimes by many orders ofmagnitude, with the level of overtest varying considerably across a wide range offrequencies. This research shows that substantial benefits can be gained by “freely”suspending the structure in the laboratory and exciting it with a relatively small numberof electrodynamic shakers using Multi-Input–Multi-Output (MIMO) control technology.The shaker configuration can be designed to excite the modes within the bandwidthutilising the inherent amplification of the resonances to achieve the desired responselevels. This free-free MIMO vibration test approach is shown to result in substantialbenefits that include extremely good replication of the aerodynamic environment andsignificant savings in time as all axes are excited simultaneously instead of the sequentialX, Y and Z testing required with traditional vibration tests. In addition, substantial costsavings can be achieved by replacing some expensive large shaker systems with a fewrelatively small shaker systems.

Crown Copyright & 2014 Published by Elsevier Ltd. All rights reserved.

lsevier Ltd. All rights reserved.

contains proprietary information which is the property of the Secretary of State for Defence. It isor disclosed in whole or in part without prior written consent of Defence Intellectual Property Rightsristol BS34 8JH, England.WE Aldermaston, Reading, Berks RG7 4PR, UK. Tel.: þ44 118 982 [email protected] (P.M. Daborn).

t al., Enhanced ground-based vibration testing for aerodynamic environments,//dx.doi.org/10.1016/j.ymssp.2014.04.010i

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P.M. Daborn et al. / Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]]2

1. Introduction

Notwithstanding numerous advances in signal processing and measurement technology, our general methods ofvibration testing remain rooted in the 1960s and 1970s and we continue to test in the erroneous belief that the multi-directional vibration experienced by structures in the field can be effectively reproduced in the laboratory by shakingsequentially in the arbitrarily derived X, Y and Z directions [1–3]. In addition, we often find it surprising that service failuresare not replicated in the laboratory, or indeed, vice versa and critical examination of the processes we currently employshows that such discrepancies are actually to be expected and should come as no surprise.

Most environmental test engineers are aware that our vibration test methods are poor at replicating in-serviceenvironments. However, these methods were the best possible with the technology available in the early days of vibrationtesting and these early practices are continuing today, especially when employing industry or military standards. There isoften demand to carry out testing in a very similar manner to historical tests simply for continuity. This allows for directcomparison of the current results with all previous results of similar tests, even if it is known that the methodology is flawedor non-optimal. This methodology leads to poor practices enduring for long periods of time and restricts the evolution oftesting methodologies.

It has been shown in numerous publications that single-axis vibration tests are a poor representation of multi-axialexcitation environments [4,5]. The requirement to carry out multi-axis testing is imperative as greater pressures are placedupon test programs to reduce timescales and to create a better replication of the anticipated environment, allowing foroptimal structure designs. It should be noted that multi-axis testing is now integrated into military testing standards, suchas MIL-STD-810 G Method 527, and so will become more commonplace in the future [6]. There have been excitingdevelopments in the area of multi-axis testing facilities since the advent of Multi-Input–Multi-Output (MIMO) vibrationcontrol technology [7,8]. A few organisations have the ability to carry out multi-axial vibration tests, but these are relativelyexpensive and not easily accessible to most organisations [9,10]. Multi-axis testing is crucial for the future of dynamictesting, yet the capability is not easy to acquire for most organisations; it is with this background in mind that the researchdescribed in this paper has been undertaken.

This research focusses on one particular area of vibration testing – the replication of in-service aerodynamicenvironments in laboratory tests. Aerodynamic excitation is experienced by many aerospace structures in-flight, such asaircraft, rockets and missiles and is the environment which could yield substantial benefits from fresh insight. This paperfocusses on aerodynamic excitation but it should be noted that the details of this research could easily be transferred toother forms of distributed excitation.

This paper presents only test-based results but the techniques have been examined numerically prior to testing activitiesand these have been presented elsewhere [11]. One of the main findings from the numerical studies showed that thetraditional vibration test can lead to significant overtests, with the level of overtest varying considerably across thebandwidth. Another key conclusion was that the common practice of de-featuring the test specification, sometimes called“enveloping”, was a significant contributor to the overtest. The numerical studies demonstrated that significant improve-ments could be made by exciting the structure at multiple locations and controlling the vibration test at multiple responselocations using a MIMO controller. In addition, substantial improvements could be obtained by supporting the structure infree-free boundary conditions.

2. Vibration testing to replicate aerodynamic environments

When in flight, an aerial vehicle is excited over its external surface by normal and tangential fluid forces in all directions.In contrast, a laboratory vibration test often involves a single force applied in one direction by a high impedanceelectrodynamic shaker. It should be noted that attaching the structure to the shaker significantly alters the dynamics of thestructure. The vibration tests are generally controlled so as to meet a test specification but the scientific justification behindthe derivation of the test specification is questionable at best, especially when enveloping techniques are included. Often, afactor-of-safety is applied to the test specification. The factor-of-safety elevates the test specification by some constant valueacross the bandwidth, for instance 3 dB. This is to ensure robustness of design and to account for uncertainty and variabilityassociated with the structure and the flight environment. There is much evidence to show that the methodology fortraditional vibration tests often leads to overly severe tests [12–15]. For simplicity, no factors-of-safety have been appliedduring this research.

Ideally, a structure which is subjected to aerodynamic excitation in-flight should be subjected to a wind tunnel test in anattempt to replicate the environment in the laboratory. However, wind tunnels are not easily accessible to mostestablishments, are expensive to use and often cannot achieve the necessary full scale wind speeds, e.g. hypersonicconditions. Against this background, the use of shaker testing is still the most common method of qualifying a system foraerodynamic environments and is likely to remain so for the foreseeable future.

3. Objectives of the research

The overarching objective of this research was to make substantial improvements in the methods used to replicateaerodynamic environments in the laboratory. In order to achieve this, it was necessary to set the following three sub-strategic

Please cite this article as: P.M. Daborn, et al., Enhanced ground-based vibration testing for aerodynamic environments,Mech. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.04.010i




P.M. Daborn et al. / Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]] 3

objectives; (i) to develop a technique of representing a distributed excitation patternwith a small number of exciters, (ii) to applythe technique to a realistic structure, and (iii) to compare the results of the new technique against existing methods.

4. Using a small number of exciters to represent a distributed excitation pattern

4.1. Experimental setup

Previous research had numerically demonstrated that it is possible to replicate a distributed excitation pattern with asmall number of exciters [11]. It was hypothesised that this could be achieved in practice on a simple structure using acommercial MIMO random vibration controller. The simple structure used in this case study was an aluminium beam; theexperimental setup is shown in Fig. 1 and a list of the equipment used is given in Table 1. The beamwas made of aluminiumalloy of an unknown composition and was suspended using soft elastic at each end. Six equi-spaced piezoelectric patches(P1–P6) were attached to the top surface of the beam using adhesive. These patches were used to provide distributedexcitation to the beam and although they did not cover the top surface entirely, they covered a significant portion of it. Thepatches provided a convenient and controllable method of applying a distributed excitation environment, far more so than awind tunnel or flight environment could achieve. This distributed excitation pattern is called a “pseudo-flight trial” for theremainder of this paper as it replicates a real flight trial where the flight vibration levels are obtained.

To measure the acceleration along the beam, seven single-axis accelerometers (A1–A7) were attached using mountingwax at points equi-spaced along the top surface of the beam. It should be noted that the accelerometers and thepiezoelectric patches add significant mass and damping to the structure, but they were attached for all aspects of this casestudy and effectively become part of the structure.

The data acquisition and MIMO controller system was a Leuven Measurement Systems (LMS) Supervisory Control andData Acquisition System (SCADAS).

4.2. Experimental method

The experimental method can be broken into three steps;

(i)

TableExpe

Equ

DatAccPie

PleMe

Carry out a pseudo-flight trial and measure the acceleration response.
(ii) Specify target spectrums for a MIMO vibration test. (iii) Carry out a free-free MIMO vibration test in order to match the target spectrums.
The activities above mirror the standard practice of carrying out a flight trial, taking measurements to capture theenvironment, processing the measurements to derive target spectrums (often called a test specification) and carrying out alaboratory vibration test to meet the target spectrums. The main notable difference here is that the laboratory vibration testinvolved controlling multiple exciters instead of a single exciter.

Step I in the experimental method was to carry out the pseudo-flight trial by exciting the beam with distributed randomexcitation. To do this, all six piezoelectric patches were excited using white noise in the bandwidth 100–2000 Hz, to a level

Fig. 1. Experimental setup for the aluminium beam case study.

1rimental equipment used in the aluminium beam case study.

ipment description Relevant details

a acquisition and MIMO controller system LMS SCADAS Mobile 5-slot System. 8 channel input, 6 channel output (drive).elerometers Endevco 2250AM1-10zoelectric patches RS piezoelectric transducer, 27 mm dia, RS part no 724-3162

ase cite this article as: P.M. Daborn, et al., Enhanced ground-based vibration testing for aerodynamic environments,ch. Syst. Signal Process. (2014), http://dx.doi.org/10.1016/j.ymssp.2014.04.010i





of 5�10�4 V2/Hz. The voltage supplied to each patch was controlled using the MIMO controller and resulted in a timedomain root-mean-squared (rms) signal of nominally 1 Vrms. A high degree of control was achieved and is shown inAppendix A for P1 – similar results were obtained for P2–P6 but are not presented. It should be noted that for the purposesof clarity, some of the plots show data that has been down-sampled from the original high resolution data obtained. Thebeamwas excited by the patches for 5 min to allow sufficient time for a suitable number of averages to be taken. The voltagesignals to each patch were uncorrelated, i.e. there was very low coherence between any two signals. In aerodynamicenvironments there will almost certainly be some spatial correlation such that one excitation location will be highlycorrelated to its near neighbours but uncorrelated to distant points. It is beyond the scope of this paper to discuss in greatdetail the true nature of aerodynamic excitation, but uncorrelated inputs provide the greatest challenge to replicate as thereare more linearly independent inputs to the system.

Acceleration time histories were measured during the pseudo-flight trial by accelerometers A1–A7 and average powerspectral densities (PSDs) were calculated and are shown in Appendix B. It is only necessary to present the PSDs from A1–A4as the symmetry of the beam meant that the response PSDs for A5–A7 were almost identical to A1, A2 and A3, respectively.In this example, the A1–A7 response PSDs are the characterisation of the aerodynamic environment which is the target forany subsequent laboratory vibration test to reproduce. It should be noted that the four resonances within the bandwidth arethe first, second, third and fourth bending modes.

Step II in the experimental method was to generate a target spectrums based upon the acceleration response PSDs.At this stage it was important to make the target spectrums, and the subsequent MIMO test, as simple as possible. With thisin mind, only two acceleration response PSDs were used as target spectrums – these were the PSDs for A2 and A5. These

Fig. 2. Comparison of measured vibration response against target spectrums for the aluminium beam case study. The vibration test was carried out usingMIMO control, incorporating two piezoelectric patch exciters and two response locations. (a and b) PSD at accelerometer A2, and A5 and (c) CSD modulusand phase between accelerometers A2 and A5.






accelerometers were effectively selected as the control transducers for the subsequent laboratory vibration test.An important part of specifying the target spectrums for a MIMO test is the inclusion of the Cross Spectral Density (CSD)between the responses. In particular, the phase information contained in the CSD is critical as this will ultimately dictate theoperating deflection shape of the structure and therefore the stress field. The PSDs and the CSD form the target spectrumsfor the subsequent laboratory vibration test and are presented in Appendix C.

Step III in the experimental method was to carry out a laboratory vibration test to match the target spectrums. At leasttwo piezoelectric patches were needed to excite the structure and in order to keep the MIMO vibration test as simple aspossible only two were selected. There were many combinations of control accelerometers/exciters that could have beenselected and sensible combinations were those that did not result in a symmetrical excitation/measurement pattern.Numerous combinations were attempted with a similar outcome - only the results for P2 and P4 excitation and A2 and A5accelerometer locations are presented as they are a fair representation of all the sensible combinations attempted. Thelaboratory vibration test duration was 3 min to allow for a suitable number of averages to be taken, the results of which arepresented in the following section.

4.3. Results

The results presented in this section are for the MIMO vibration test only. The pseudo-flight trial control and responseplots are presented in the appendices.

The most important results to present are the acceleration response PSDs and CSD from the MIMO vibration testcompared to the target spectrums (Fig. 2). They demonstrate that the laboratory vibration test closely matched the targetspectrums, particularly above 200 Hz. In addition, the MIMO controller maintained the correct phasing between A2 and A5for a significant majority of the bandwidth. It may not be immediately obvious to the reader how two exciters canadequately recreate the required response when the initial excitation pattern was generated with six independent exciters.It can be explained by separating the bandwidth into two categories – the first category includes the spectral lines near theresonances, the second includes spectral lines far away from resonances. In the first category, the operating deflection shape(ODS) of the structure is usually dominated by the modeshape of the nearby resonance. In this situation, it is only necessaryto have one exciter provided that the exciter is not at a node of the associated modeshape. In the second category, theresponse is a combination of the significantly contributing modes. Often there are only a few modes dominating and inorder to recreate the desired response it is necessary to include enough exciters to adequately excite the dominant modesand in the correct proportion. For this case study, with well separated modes, a maximum of two modes contributesignificantly to the response at any spectral line, and hence only two exciters are required.

It is worth mentioning that the target spectrums used in the MIMO vibration test consisted of PSDs and CSDs with aresolution of 1.56 Hz and composed of 1218 breakpoints each; a breakpoint is a frequency/amplitude data point, a set ofwhich defines the outline of the target spectrum (or test specification) and typically consists of only tens of breakpoints in atraditional vibration test.

The aluminium beam case study has proven that, with the equipment available, it is possible to adequately replicate sixindependent exciters with two exciters. However, the method of exciting the structure in the vibration test was in the formof piezoelectric patches and at very low levels. The MIMO testing approach was not compared to the traditional method ofattaching the structure to a large electrodynamic shaker and the beam is effectively a one dimensional structure instructural dynamics terms. It was necessary to move onto a structure which was more realistic in nature, to elevate the testseverity levels and to compare the MIMO vibration test to the traditional vibration test – this was carried out for a dummymissile and is detailed in the next section.

5. The MIMO vibration test method applied to a realistic structure

5.1. Experimental setup

It was necessary to scale-up the MIMO vibration test technique to a realistic structure. The structure used in this casestudy is a dummy missile and is shown in Fig. 3 with relevant information detailed in Table 2. A plastic dummy payload wasmounted on a rod inside the missile and connected to the base of the missile. The missile was covered with protectivekapton tape and 44 piezoelectric patches. The patches were evenly distributed over the outer surface of the missile andwere attached using adhesive via plastic rapid prototype adaptors. The adaptors were required as the piezoelectric patcheswere brittle and needed to be stuck to a flat surface and the curvature of the missile was too great. A number of experimentswere carried out to ensure that the adaptors did not significantly filter any of the excitation bandwidth from the patches.The kapton tape, adaptors, piezoelectric patches and the associated wiring remained attached for all testing activities toensure structural consistency.

There were three different experimental setups; the pseudo-flight trial, the traditional laboratory vibration test and thefree-free MIMO vibration test. A list of the equipment used in the experimental setups for the dummy missile case study ispresented in Table 3.

The experimental setup for the pseudo-flight trial is displayed in Fig. 4. The dummy missile was suspended verticallyupside down from the base using soft elastic. One of the objectives of this case study was to excite the structure to higher





Fig. 3. The dummy missile displayed with the coordinate system and the attachment of piezoelectric patches.

Table 2Relevant details of the dummy missile structure.

Missile feature Details

Material Aluminium alloyMass 2.3 kgHeight 500 mmOuter diameter of cylinder 75 mmThickness of cylinder 4 mmPayload material PlasticPayload mass 0.1 kg

Table 3Experimental equipment used in the dummy missile case study.

Equipment description Relevant details

Data acquisition and MIMO controller system LMS SCADAS Mobile 5-slot System. 24 channel input,6 channel output (drive).

Accelerometers Single-axis: Endevco 2250AM1-10 ICP typeTri-axial: PCB 354C10 ICP type, PCB 356A01 ICP type

Piezoelectric patches RS piezoelectric transducer, 27 mm dia, RS part no 724-3162Power amplifiersa,c LDS PA25EPower amplifiersb LDS PA500LElectrodynamic shakersb LDS V406 98 N sine force peakForce transducersb,c B&K 8230-001 ICP TypeElectrodynamic shakersc LDS V201 17.8 N sine force peak

a Pseudo-flight trial.b Traditional laboratory vibration test.c Free-free MIMO vibration test.






Fig. 4. Experimental setup for the dummy missile pseudo-flight trial showing the missile suspended with soft elastic and instrumented withaccelerometers. The missile was excited by piezoelectric patches distributed over the outer surface.

Fig. 5. Experimental setup for the dummy missile traditional vibration test showing the missile attached to a high mechanical impedance shaker table.


vibration levels than the aluminium beam case study, and in order to do this, power amplifiers were used in the supplycircuit to the patches. Only two amplifiers were available, these were connected to the patches in a “checkerboard” fashionto ensure that only a limited number of adjacent patches were driven by the same voltage signal. Sixteen accelerometermeasurement channels, sensing in three orthogonal directions aligned with the missile axes (Fig. 3), were used in thepseudo-flight trial. The accelerometers were distributed around the missile including positions on the base, the maincylinder, the nose tip and the payload.

The experimental setup for a traditional vibration test is shown in Fig. 5. The dummy missile was mechanically attachedto a shaker table and an electrodynamic shaker was attached to the shaker table via a force transducer. The missile Y-axiswas aligned with the shaker excitation axis. Eleven accelerometer measurement channels were used in the traditionalvibration test sensing in the same three orthogonal axes and locations used in the pseudo-flight trial. An additional controlaccelerometer was placed on the shaker table, measuring in the missile Y-axis. Although the piezoelectric patches were leftattached for the traditional vibration test, they were not activated.





Fig. 6. Experimental setup for the MIMO vibration test with three shakers arranged orthogonally and attached via flexible drive rods.


The experimental setup for the MIMO vibration test can be seen in Fig. 6. The dummy missile was suspended verticallyupside down from the base using soft elastic. Three electrodynamic shakers were attached via force transducers andappropriate drive rods to the missile, with one shaker aligned to each of the three orthogonal missile axes. The locations ofthe shakers were selected by generating a finite element model and visualising the modeshapes and ensuring that thelocations were not at a node for any of the modes within the test bandwidth. The modes within the bandwidth included 1stand 2nd bending, axial, nose tip translating and numerous ovalling modes. No torsional modes were present in the testbandwidth. The same sixteen accelerometer measurement channels were used as the pseudo-flight trial, with ten beingused as control transducers for the MIMO control algorithm. Although the piezoelectric patches were left attached for theMIMO vibration test, they were not activated.

5.2. Experimental method

The experimental method can be broken into five steps;

(i)

PleMe

Carry out a pseudo-flight trial and measure the acceleration response.
(ii) Develop target spectrums for traditional vibration tests. (iii) Carry out traditional vibration tests to meet the target spectrums in (ii). (iv) Develop target spectrums for a MIMO vibration test. (v) Carry out a MIMO vibration test to meet the target spectrums in (iv).
Step I in the experimental method was to carry out the pseudo-flight trial by exciting the missile with distributedrandom excitation. To do this, all 44 piezoelectric patches were activated with constant voltage PSDs in the bandwidth 100–4000 Hz to a level of 5�10�4 V2/Hz. The pre-amplified supply voltages to the patches were controlled using the MIMOcontroller with the amplifier gain set to three. A high degree of control was achieved and is demonstrated in Appendix A.The rms values can be calculated from the PSD curves and are 1.40 Vrms for the two supply voltages and the reference. Themissile was excited by the patches for 1 min in order to allow sufficient time for a suitable number of averages to be taken.The voltage signals to each amplifier were uncorrelated, i.e. there was very low coherence between the two signals.Acceleration PSDs were calculated for all response measurements, a representative selection of which are presented inAppendix B.

Step II in the experimental method was to derive target spectrums for traditional vibration tests. It was decided to derivetwo target spectrums; the objective of the first target spectrum was to ensure that the base of the missile experienced thesame ride on the shaker table in the Y direction as it experienced during the pseudo-flight trial, this target spectrum will becalled the “high fidelity target spectrum”. The second test target spectrum imitates the typical enveloping procedure oftenemployed to simplify the target spectrum and will be called the “gross envelope target spectrum”. It was decided that onlyY direction excitation would be carried out for the traditional vibration test as it would give enough insight into thetechnique whilst saving a significant amount of time associated with three orthogonal tests. The target spectrums, alongwith two relevant pseudo-flight trial measurements are presented in Appendix C. The high fidelity target spectrum was






derived by taking the maximum of the two base measurement curves (Base 1 and Base 2 in Fig. C2) at every spectral line.Although the enveloping procedure used to generate the gross envelope target spectrum may be more severe than manyreal-life situations, its inclusion highlights the effect of enveloping on the quality of the test results.

Step III in the experimental method was to carry out two traditional vibration tests to meet the two target spectrumsderive in Step II. Traditional Vibration Test A was carried out to meet the high fidelity target spectrum and TraditionalVibration Test B was carried out to meet the gross envelope target spectrum. Vibration tests were executed for 1 min to

Fig. 7. Representative results from all vibration tests at MIMO control locations. (a) Nose tip PSDs (Y direction). (b) Missile cylinder PSDs (Y direction) and(c) CSD – Nose tip (Y direction)/missile cylinder (Y direction).






allow a suitable number of averages to be taken and a high degree of control was achieved at the shaker table controlaccelerometer (Appendix A).

Step IV in the experimental method was to derive target spectrums for the MIMO vibration test based on the pseudo-flight trial response. The objective of the target spectrums was to control points that adequately covered the exterior of themissile and in all three orthogonal directions. Ten locations/directions were selected and included positions on the nose tip,missile cylinder and base. The payload was not used as a control location as this could be used to determine howuncontrolled points respond in the test. The target spectrums consisted of ten PSDs from the pseudo-flight trial and the 45cross spectral densities between the ten locations. It should be noted that only the upper triangular portion of the 10�10spectral density matrix is required. Each of the PSDs and CSDs were in the bandwidth of 100–4000 Hz and with 1249spectral lines each, this totalled approximately 69,000 spectral lines for all target spectrums combined.

Step V in the experimental method was to carry out a MIMO vibration test to meet the target spectrums derived in Step IV.The MIMO vibration test was executed for 1 min to allow a suitable number of averages to be taken and a high degree of controlwas achieved for all PSDs and CSDs; a representative selection shall be presented in the results section.

5.3. Results

It is necessary to separate the results into three categories: (i) vibration response at locations controlled during the MIMOvibration test, (ii) vibration response at locations not controlled during the MIMO vibration test, and (iii) force PSDs.

It is not practical to display all of the PSDs/CSDs which were controlled during the MIMO vibration test. A representativeset of results are shown in Fig. 7, comprising nose tip PSDs (y direction), missile cylinder PSDs (y direction) and the CSDsbetween them. Fig. 7 demonstrates that the MIMO vibration test succeeding at replicating the pseudo-flight trial at controllocations. In contrast, the results show that the traditional vibration tests did not closely replicate the flight trial, particularlywhen using a gross envelope target spectrum. In addition, attaching the missile to the shaker table altered the dynamicssignificantly and resulted in unrealistic behaviour. This is apparent in Fig. 7 where resonance peaks were shifted significantlybetween the flight trial and the tradition vibration test B and new resonances introduced as shown in Fig. 7a. The resonanceintroduced at approximately 200 Hz is the missile acting as a cantilever off the shaker table and is only present because ofthe attachment of the missile to the shaker table and is dominated by the attachment region stiffness.

Similarly, it is not practical to present all of the PSDs/CSDs at locations not controlled during the MIMO vibration test, themost noteworthy result is that of the payload. The payload Y direction is the most appropriate result to present (Fig. 8) asthis is the only direction excited in the shaker table tests. The graph shows that the payload experienced a similar responsein the MIMO vibration test as it did during the pseudo-flight trial. This is a noteworthy result as this location was notincluded in the MIMO control strategy. On further reflection, this result stands to reason; by ensuring the outer surface getsa similar ride to the flight trial, the internal components will too.

In Figs. 7 and 8 the gross envelope target spectrum resulted in an overtest of many orders-of-magnitude at most spectrallines, while at other spectral lines an undertest was experienced (1000 Hz in Fig. 8). This discovery is rather worrying as thecurrent test philosophy is “by enveloping the target spectrumwe are definitely going to be overtesting the structure”. This is

Fig. 8. Payload Y acceleration PSDs from all vibration tests.





Fig. 9. Force PSDs from the all of the vibration tests.

Table 4Force root-mean-squared values from all of the vibration tests.

Vibration test Force root-mean-squared (Nrms)

MIMO sum 1.3Traditional vibration test A 20.5Traditional vibration test B 90.3


not necessarily true. By attaching the structure to a shaker table the resonances and anti-resonances shift significantly fromthose of the free structure and can cause a considerable disparity between the freely flying structure and the laboratoryconfiguration at some spectral lines. This disparity is so great that the envelope procedure can often provide nothing otherthan a false sense of security.

In all of the vibration tests, the force imparted to the structure was measured with force transducers and force PSDs werecalculated and are shown in Fig. 9. It should be noted that the force PSD presented from the MIMO test was the sum of threeindividual force PSDs. From an appropriately scaled PSD, it is possible to estimate the root-mean-squared (rms) value of the timedomain signal used to calculate the PSD. This is done by taking the square root of the area under the PSD curve and was calculatedfor the force PSDs resulting in Force root-mean-squared (Nrms) values which are shown in Table 4. It is apparent that the forcelevels required in the traditional vibration test are far greater than those for the MIMO test. This situation arises in the traditionalvibration test for two reasons: (i) To vibrate the shaker table, and (ii) to force the missile to behaviour unrealistically, i.e. to force it tobehave as if it were free, when it is not. As a general rule, it is an undesirable situation when considerably more force or energy isneeded in the test thanwould otherwise be expected in service. This is usually a natural warning that something is incorrect in thetest configuration – this is clearly the situation when replicating distributed excitation by attachment to a large shaker.

6. Discussion

The simple case study presented in section 4 demonstrates that it is possible to represent a distributed excitation patternwith a small number of exciters using a Multi-Input–Multi-Output (MIMO) controlled vibration test. In addition, the MIMOvibration test very closely matched the target spectrums specified at the outset of the test. The case study was carried outusing a small aluminium beam and it was necessary to assess the MIMO vibration testing technique on a more realisticstructure; a dummy missile was selected.

The case study presented in section 5 demonstrates that the MIMO vibration test technique was successful at replicatinga distributed excitation pattern on a realistic structure. In this case a dummy missile was used, but it could easily be appliedto service standard structures. Traditional single-axis shaker tests were carried out on the dummy missile and showed thatthe MIMO vibration test was far superior for numerous reasons. By attaching the dummy missile to a shaker table in thetraditional shaker test, the dynamics of the dummy missile were significantly altered and resulted in unrealistic behaviour.In the MIMO vibration test, the test configuration was designed to have a minimal effect on the dynamics of the missile by






suspending it using bungee and exciting it via drive rods. In addition, the traditional vibration test could only excite in oneaxis which has been shown in many publications to be a poor representation of multi-directional excitation. Single-axistesting also leads to cross-axis excitation and lengthy test durations should there be a requirement to test the other twoorthogonal axes. In contrast, the MIMO vibration test excited all axes simultaneously which is a far better representation ofthe multi-directional excitation present in aerodynamic environments.

It has been shown that the traditional vibration test can introduce resonances which would not be present in itsoperating environment. An example of this is a mode where the structure is cantilevered from the shaker table. This couldlead to failures in the laboratory which are very unlikely to occur in service conditions, resulting in lengthy and costlyinvestigations and subsequent overdesign and over engineering of future systems.

The traditional single-axis vibration test does not ensure the correct relative phase between response locations. Although notdemonstrated in this paper, it is apparent that this condition leads to operating deflection shapes in the laboratory being verydifferent to the service condition. In turn, this leads to a poor representation of the stress and strain patterns, which ultimatelycause failures and could potentially result in completely different failure mechanisms. This situation is exaggerated by the factthat testing is only carried out in one axis at a time in the traditional vibration test. In contrast, the MIMO vibration test aims tomatch the relative phase between numerous locations. This leads to similar operating deflection shapes to service conditions andhence similar stress and strain patterns which are far more likely to cause realistic failure mechanisms.

Test planning was carried out for the MIMO vibration test on the dummy missile by creating a finite element model andsolving for the modeshapes. By investigating these modeshapes, it was a relatively simple task to ensure that the exciters inthe MIMO test could excite all the relevant modes in the test bandwidth. In a traditional vibration test it is almost impossibleto excite all necessary modes and in the correct proportions.

It has been demonstrated that the force requirements of the traditional vibration test is far greater than for the MIMOvibration test. There are many reasons why the traditional vibration test requires far greater force levels, one of these beingthe requirement to vibrate the high-mass armature and shaker table. Another cause is the alteration of the dynamics of thestructure, often leading the laboratory test attempting to elevate the response of the structure to resonance levels, eventhough the structure is no longer at resonance at the original natural frequency. The “enveloping” procedure often employedon test specifications is a significant contributor to this grossly elevated force requirement. In nature, the low-energy or low-force solution is preferable, with the very high force option indicating something inherently wrong in the setup. This iscertainly the case for the traditional vibration test, particularly if “enveloping” techniques are employed.

It is worth discussing what the future holds for the MIMO vibration test. The benefits of the technique mean that itshould be developed and publicised as an enhanced method of replicating aerodynamic environments in the laboratory.In addition, early investigations show that the methodology can be successfully applied to other environments, such as roadtransport vibration, where the structure is a subcomponent of a larger system. One of the major advantages of the MIMOvibration test is that it utilises simple practices involving commercially available equipment and would not require a highlevel of resource to implement at most environmental test houses.

Substantial financial savings could be made by environmental test houses that employ MIMO vibration testing instead oftraditional large shaker tests for some of their environmental tests.

The cost of running a large shaker system is far greater than for the smaller shaker systems required in the MIMOvibration test. The most significant savings would be achieved when refurbishing or constructing new environmental testingfacilities. Large shaker systems require a significant footprint and often need specialist facility additions such as seismicfloors and cooling towers. The MIMO vibration test using smaller shakers would require none of these costly additions.

Further research is required to refine the MIMO vibration test before it becomes commonplace. One major area thatneeds addressing is the generation of adequate test specifications, especially the inclusion of cross spectra which may notalways be available. Another is scaling up the MIMO vibration test to larger structures and how to apply largerdisplacements, especially when considering the drive rod excitation method. This paper has detailed the application ofthe MIMO vibration test to structures that have been subjected to distributed excitation using piezoelectric patches. Thebenefits of the MIMO vibration test needs to be assessed on service standard structures that have been subjected to trueaerodynamic environments.

7. Conclusions

It is worth reiterating here the objectives set out for this research, these being; (i) to develop a technique of representinga distributed excitation pattern with a small number of exciters, (ii) to apply the technique to a realistic structure, and (iii) tocompare the results of the new technique against existing methods.

The following conclusions can be drawn from the findings described in this paper:

(i)

PleMe

A new technique has been developed which adequately represents a distributed excitation pattern with a small numberof exciters in the form of a MIMO vibration test.

(ii)
The MIMO vibration test has been applied to a realistic structure in the form of a dummy missile. (iii) The MIMO vibration test has been assessed against traditional single-axis shaker testing and has been shown to be
superior in many ways.






excites all axes simultaneously, there is minimal alteration of the dynamics and the MIMO control approach leads to a far
It has been demonstrated that the MIMO vibration test is superior to a traditional single-axis vibration test because it
better overall replication of the in-service aerodynamic environment.

Acknowledgements

The authors wish to acknowledge the following individuals for their help and insight during this research: HeleneBotevyle-Carter, Mark Carne, Richard Fieldhouse, Simon Futter, Mike Garrard, Steve Gubby, Dave Harrison, Jon Hieatt, BobHowden, Ross Lawrence, Dave Macknelly, Tony Moulder, Chris Roberts, Dave Swan, Brian Tyler.

The authors also wish to acknowledge Leuven Measurement Systems (LMS) International for their technical help withusing the MIMO control software and the LMS SCADAS system.

Appendix A. Control plots

See Figs. A1–A4.

Fig. A1. Control voltage PSD of P1 piezoelectric patch in the aluminium beam pseudo-flight trial.

Fig. A2. Control voltage PSDs (pre-amplified) in the dummy missile pseudo-flight trial.

Fig. A3. Control acceleration PSD in the dummy missile traditional vibration test A.





Fig. A4. Control acceleration PSD in the dummy missile traditional vibration test B.


Appendix B. Pseudo-flight trial response plots

See Figs. B1 and B2.

Fig. B1. Response PSDs from the pseudo-flight trial in the aluminium beam case study.

Fig. B2. A representative selection of response PSDs from the pseudo-flight trial in the dummy missile case study.






Appendix C. Target spectrums

See Figs. C1 and C2.

Fig. C2. Target spectrums for the dummy missile traditional vibration test derived from two pseudo-flight trial base measurements.

Fig. C1. Target spectrums for the aluminium beam MIMO vibration test derived from pseudo-flight trial (PSDs and CSD for A2 and A5).

References

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