Low-FrequencyVibrationTestingofHugeBucketWheel ...downloads.hindawi.com/journals/sv/2018/6182156.pdf2.TestMethod 2.1.Principle. Fornaturalfrequencytestingbyfreeingthe initialdisplacement,ifthereisaninitialdisplacementA,

Research ArticleLow-Frequency Vibration Testing of Huge Bucket WheelExcavator Based on Step-Decay Signals

Y Z Jiang C J Liu X J Li K F He and D M Xiao

Hunan Provincial Key Laboratory of Health Maintenance for Mechanical EquipmentHunan University of Science and Technology Xiangtan 411201 China

Correspondence should be addressed to Y Z Jiang jiangyz186126com

Received 30 August 2018 Accepted 30 October 2018 Published 2 December 2018

Academic Editor Salvatore Russo

Copyright copy 2018 Y Z Jiang et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e low-frequency vibration of the bucket wheel excavator has an important impact on the fatigue life of the structures Forconventional vibration testing methods it is difficult and expensive to excite the overall low-frequency vibration of the wholemachine Hence in this paper the excitation method that uses the belt-supporting rollers on the boom as an exciter is tried toexcite the low-frequency vibration so that the low natural frequencies can be identified by Fourier transforming the free decaysignals caused by the sudden power off By this method the first five natural frequencies are obtained and the results are verifiedthrough corresponding computational numerical model of the bucket wheel excavator It can be concluded that the proposedtesting method can achieve the same accuracy but is much more convenient and costs less than existing methods

1 Introduction

e bucket wheel excavator is a kind of efficient bulk ma-terial conveying equipment which is widely used in rawmaterials storage and transportation yards e buckedwheel boom is very important for the excavating operationIt weights up to hundreds of tons length up to tens ofmeters Due to the poor working conditions there exist anumber of complex excitations and it is easy to cause thelow-frequency vibration of the bucked wheel boom whichinduces fatigue cracks and even causes serious accidentssuch as collapse of the whole machine [1ndash6] It is for thisreason that bucked wheel excavator requires serving regu-larly and abnormal vibration diagnosis and repairments areoften performed on the bearing structures [7 8] which hasbrought huge losses to the plants erefore it is importantto study the vibration characteristics of the bucket wheelboom to improve its dynamic properties so that the fatiguelife of the structure can be prolonged

For the dynamic design of the structures obtaining thenatural frequencies is a key and fundamental need Usu-ally natural frequencies are based on calculations andnumerical simulations while designing and a lot of workhas been carried out on the dynamic modeling of structure

and mechanisms for bucket wheel excavators [9 10]However due to the complexity of structures the calcu-lated ones may differ from real natural frequencies as thecomputational numerical models do not exactly corre-spond with real structures and many details are impro-priety simplified So it is the quickest and most effectiveway to obtaining the natural frequency by testing methodsCurrently impulse excitation is a common vibration testmethod used for natural frequencies testing [11 12] butthe power of this kind of excitation is not enough to excitethe overall low-frequency vibration To solve this problemGottvald [13] designed a method that frees an initialdisplacement caused by hanging rope of 264 tons inweight at the far end of the bucked wheel boom so that thenatural frequencies can be obtained by Fourier transformof the decay signals caused by the sudden free of initialdisplacement Although this method is effective and ac-curate enough it is hard for widespread usage because thismethod is very difficult and expensive To find an easy andlow cost way in this paper the excitation method that usesthe belt-supporting rollers as exciter is tried for low-frequency vibration testing of the bucked wheel excava-tor and the results prove that this method is much simplercosts low and is also effective

HindawiShock and VibrationVolume 2018 Article ID 6182156 7 pageshttpsdoiorg10115520186182156

2 Test Method

21 Principle For natural frequency testing by freeing theinitial displacement if there is an initial displacement Awhen the initial enforced displacement is released themotional differential equation of a single-freedom systemcan be expressed in the form

eurox + 2n _x + ω2x

f(t)

m (1)

where 2n cm and ω km

radicin above expression Since

the external force f(t) equals zero in free decay vibrationthe solution of equation (1) is

x Aeminusnt sin

ω2 minus n2

radict + φ1113872 1113873 (2)

Obviously the vibration displacement x appears as a freedecay motion at the natural frequencies ω If the free decaysignal x is measured it will be easy to calculate the naturalfrequencies ω through Fourier transformation

For an n-freedom system the free decay signals arecomposed of n natural frequencies theoretically But prac-tically a lot of natural frequencies will be missing and onlyseveral apparent frequencies can be measured and identifiedHowmany and which frequencies can be identified from thetesting data depend mainly on the properties of excitationposition of sensors and so on [14ndash17] For measuring theoverall low-frequency vibration of the excavator boom theexcitation of initial displacement must be exerted on thewhole boom rather than local part Moreover the excitationof initial displacementmust be powerful enough to excite theoverall low-frequency vibration of the boom so that thesignals from the sensor are easy to identify

22 Excitation Strategy e bucket wheel excavator DQLZ1200 which is manufactured by Tidfore Heavy Industry CoLtd of China is used for natural frequency testing eexcavator DQLZ 1200 is 43 meters tall 1260 tons in totaland theoretical capacity is 7200m3 of bulk material ebucked wheel boom which is very important for the ex-cavating operation is a complex welded structure made upof numerous plates and beams It weighs up to eighty tonsand sixty meters of length and the vibration in work processis primary low frequency [18 19] For the low-frequencyvibration testing of this kind of huge structure the difficultyis providing suitable external excitations [20 21] It would beadvantageous provided that suitable excitation can be ob-tained from the internal of the machine rather than fromoutside ere are three potential internal excitations whichare the motor with rotation of 247Hz bucket wheel withrotation of 01Hz and the belt-supporting rollers with ro-tation of 667Hz respectively Among these three excita-tions the belt-supporting rollers are the most suitable as alow-frequency vibration exciter because there are manyrollers arrayed along the whole long boom (Figure 1) so thatit is powered enough to excite the overall structure vibrationAlso its rotation speed of 667Hz is the most proximate tothe low natural frequency of the boom

3 Test Process

In this paper the rotation of the belt-supporting rollers istried as the exciter for low-frequency vibration testing andthe experiment is designed as Figure 2 Bruel and Kjaervibration test and analysis system 3550 with 24 channels areadopted and there are totally five accelerometers withsensitivity of 100mVg mounted on the boom Two sensorsare mounted on the distal end of the boom for gathering y-direction acceleration signals and the other two aremounted on the near end of the boom for gathering y- and z-direction acceleration signals e last sensor is mountedvertically on the diagonal bar for measuring the verticalvibration signal

In a single test procedure the bucket wheel starts torotate at 58 rpm when the bucket wheel motor is turned onAt this time only a slight vibration can be felt After a fewseconds the conveyor belt began to rotate at 400 rpm(667Hz) so that obvious vibration occurs during this pe-riod After that the belt conveyor and the bucket wheelmotor are suddenly powered off leaving the boom vibrationdecay freely until it stops completely is test procedure isrepeated three times and the signals measured from the fivesensors are shown in Figure 3

4 Test Results

Figure 3(a) shows the in-time signal of acceleration mea-sured by sensor No 1 It clearly shows that the signal coversall the three periods which are the bucket wheel start periodbelt conveyor start period and the period of free decay afterthe sudden power off Figure 3(b) shows the partial en-largement of the free decay period after the first power offObviously the decay signal does not completely decrease tozero and the free decay signal shows a distinctive charac-teristic of multifrequency vibration For frequency identi-fication both the stable operation in-time signal and the freedecay in-time signal are converted into the frequency do-main by the fast Fourier transformation (FFT) and thetransformed results are shown as Figures 3(c) and 3(d)respectively Comparison of the two figures shows that thefrequency of the stable running is very rich which not onlyreflects the natural frequency of the boom but also reflectsthe motor rotation frequency (247Hz) and the electricalnoise frequency (498Hz) while the free decay periodconsists of only four frequencies of 01 176 202 and256Hz Since 01Hz comes from the inertial rotation of thebucket wheel the true natural frequencies of the boom are176 202 and 256Hz

Signals captured by the other four sensors are treatedsimilarly as the sensor No1 Finally five natural frequenciesin total can be obviously identified from the five sensorsey are 051 074 178 202 and 256Hz respectivelywhich are listed in Table 1

5 Results Verification

To verify the experiment results in this paper the finiteelement method is applied and a high precision FE model is

2 Shock and Vibration

built for comparison As for the powerful modeling capa-bility software HYPERMESH is chosen for the establish-ment and analysis of finite element model For modalanalysis the key to high accuracy of the FE model dependson the similarity of the structure mass and stiffness betweenthe model and the real object erefore to make sure the

accuracy of simulation model the weight shape andstructure of each component are strictly built to maximizeconsistency with the tested wheel excavator For simplifi-cation the pin supports are treated as rotational free beamelements with the same stiffness and mass hydraulic cyl-inder and suspensions are treated as spring and damping

No 1 Y direction

No 5 Z direction No 4 Y direction

No 2 Y directionNo 3 vertically on

the diagonal bar

Y

X

Z

Figure 2 e positions of five accelerometers

Counterweight arm Portal Tie-rods Boom Bucket wheel

(a)

Supporting roller Belt

(b)

Figure 1 Bucket wheel excavator DQLZ 1200 (a) components and structures (b) belt-supporting rollers

Shock and Vibration 3

elements with the same stiffness and damping After theprocess of geometric cleaning midsurface extractionmeshing mesh quality control and so on the finished high-quality simplified finite element model with mixed elementtypes is obtained and is shown in Figure 4(b)

In this study the block Lanczos method is used forsolving the dynamic equations and the solved results consistof the first thirty natural frequencies and the correspondingvibration forms in which nine modes in total are concernedwith the overall vibration of the excavator boom listed inTable 2 For comparison with the tested results the first fivesimulated natural frequencies and corresponding vibrationforms are presented in Figure 5 It clearly shows that all thefive tested frequencies correspond fairly closely with thesimulated resultsese prove that the test method proposedin this paper is very accurate

6 Conclusion

is paper aims to provide a better alternative method to testthe low-frequency vibration of the huge bucket wheel ex-cavator Since the difficulty of testing is providing effectiveand powerful excitation the strategy that uses the

Table 1 Measured natural frequencies

Frequencies (Hz) 051 074 178 202 256Axes x y z z x y z x y z x y z

003

0025

002

0015

001

0005

00 10 20 30 40 50

50 51 52 53 54 55ndash01

ndash005

0

005

01Free decay vibration

(177 202 257)Hz

(010 049)Hz

322Hz

249Hz

393Hz498Hz

FFT Time (s)

Frequency (Hz)

Mag

nitu

deStarting

bucket wheel 2

151

050

ndash05ndash1

ndash1520 40 60 80 100 120 1400

Power offStarting beltconveyer

e second time e third time

FFT Time (s)

(c) (d)

(a) (b)

Acc

eler

atio

n (m

s2 )

Acc

eler

atio

n (m

s2 )

00 2 4 6 8 10

0002

0004

0008

0006

001(010 176 202 256) Hz

Frequency (Hz)

Mag

nitu

de

Figure 3 Testing results (a) Signal of acceleration measured by sensor no 1 (b) partial enlargement of the free decay period (c) FFTresults of the stable operation period and (d) FFT results of the free decay period

(a)

(b)

Figure 4 Structure of bucket wheel excavator (a) real bucket wheelexcavator and (b) finite element model


Table 2 Selected simulated natural frequencies

Mode Frequency Vibration form1 0499 Overall y-direction swing2 0725 Overall z-direction swing3 1054 Overall x-axis rotation4 1761 x-axis torsion5 1982 Overall y-axis rotation6 2535 Overall z-axis rotation7 2831 Overall y-direction bending8 3079 Overall z-direction bending9 3848 Coupled bending and torsion

Contour plotEigen mode (mag)

Analysis system2338E ndash 01

2078E ndash 01

Mode no 1 051Hz vs 0499Hz1818E ndash 01

1559E ndash 01

1299E ndash 01

1039E ndash 01

7793E ndash 02

5195E ndash 02

5598E ndash 02

0000E + 00No result

Max = 2338E ndash 01Grids 77183Min = 0000E + 00Grids 411487

(a)Contour plot

Eigen mode (mag)Analysis system

Mode no 2 074Hz vs 0725Hz2485E ndash 012209E ndash 011933E ndash 011657E ndash 011381E ndash 011105E ndash 018285E ndash 025523E ndash 022762E ndash 020000E + 00No result


(b)

Mode no 4 178Hz vs 1761Hz



4452E ndash 01

3895E ndash 01

3339E ndash 01

2782E ndash 01

2226E ndash 01

1669E ndash 01

1113E ndash 01

5565E ndash 02

0000E + 00No result


(c)

Figure 5 Continued


belt-supporting rollers on the boom as exciter is tried eresults show that the proposedmethod is quite simple as wellas accurate for obtaining low natural frequencies of thebucked wheel excavator e detailed conclusions can besummed as follows

(1) As there is no need for adding extra devices theproposed method is much simpler and costs lowcompared to previous low natural frequencies testingmethods which obtained the frequencies through thesignals caused by the sudden free of initial displacement

(2) Since the bucket wheel excavator is a structure of vastbulk and great mass the difficulty of low-frequencyvibration testing is providing effective and powerfulexcitation In this paper the rotation of belt-supporting rollers is proposed as the excitationand it is proved that it is very suitable and powerfulenough for exciting the low-frequency vibration

(3) By starting the belt-supporting rollers and suddenlypowering off it is convenient to obtain the step-decay signal which is composed of stable runningand free decay vibration period Fast Fouriertransform results show that the frequency of thestable running is richer than the free decay period

(4) e measured five natural frequencies by the pro-posed method are respectively 051 074 178 202and 256Hz while the corresponding frequencies ofthe simulation are 0499 0725 1761 1982 and2533Hz is proves the proposed testing methodcan achieve the same accuracy but is much moreconvenient and costs less

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is study was funded by the National Natural ScienceFoundation of China (no 51705143) Hunan ProvincialNatural Science Foundation (no 2018JJ3164 and2017JJ1015)

References

[1] SM BosnjakMA Arsic N B Gnjatovic I L JMilenovic andD M Arsic ldquoFailure of the bucket wheel excavator bucketsrdquoEngineering Failure Analysis vol 84 pp 247ndash261 2018

[2] D Djurdjevic T Maneski V M Mitic N Andjelic andD Ignjatovic ldquoFailure investigation and reparation of a crackon the boom of the bucket wheel excavator ERS 1250 GackordquoEngineering Failure Analysis vol 92 pp 301ndash316 2018

[3] D Danicic S Sedmak D Ignjatovic and S Mitrovic ldquoBucketwheel excavator damage by fatigue fracturendashcase studyrdquoProcedia Materials Science vol 3 pp 1723ndash1728 2014

[4] S M Bosnjak S D Savicevic N B GnjatovicI L J Milenovic and M P Pantelic ldquoDisaster of the bucketwheel excavator caused by extreme environmental impactconsequences rescue and reconstructionrdquo Engineering Fail-ure Analysis vol 56 pp 360ndash374 2015

[5] E Rusinski P Harnatkiewicz M Kowalczyk and P MoczkoldquoExamination of the causes of a bucket wheel fracture in abucket wheel excavatorrdquo Engineering Failure Analysis vol 17no 6 pp 1300ndash1312 2010

[6] M Savkovic M Gasic D Petrovic N Zdravkovic andR Pljakic ldquoAnalysis of the drive shaft fracture of the bucketwheel excavatorrdquo Engineering Failure Analysis vol 20pp 105ndash117 2012

[7] E Rusinski M Kowalczyk P Odyjas and D PietrusiakldquoInvestigations of structural vibrations problems of highperformance machinesrdquo FME Transactions vol 41 pp 305ndash310 2013

[8] A ETH Brkic T Maneski D Ignjatovic P D Jovancic andV K S Brkic ldquoDiagnostics of bucket wheel excavator dis-charge boom dynamic performance and its reconstructionrdquoEksploatacja i Niezawodnosc-Maintenance and Reliabilityvol 16 pp 188ndash197 2014

[9] S Bosnjak N Zrnic and D Oguamanam ldquoOn the dynamicmodeling of bucket wheel excavatorsrdquo FME Transactionsvol 34 pp 221ndash226 2006

[10] E Rusinski J Czmochowski P Moczko and D PietrusiakldquoAssessment of the correlation between the numerical and


ZY

X

(d)


ZY

X

(e)

Figure 5 Comparison of results (a) mode no 1mdashoverall y-direction swing (b) mode no 2mdashoverall z-direction swing (c) mode no 4mdashx-axistorsion (d) mode no 5mdashoverall y-axis rotation (e) mode no 6mdashoverall z-axis rotation


experimental dynamic characteristics of the bucket wheelexcavator in terms of the operational conditionsrdquo FMETransactions vol 41 pp 298ndash304 2013

[11] E Rusinski S Dragan P Moczko and D PietrusiakldquoImplementation of experimental method of determiningmodal characteristics of surface mining machinery in themodernization of the excavating unitrdquo Archives of Civil andMechanical Engineering vol 12 no 4 pp 471ndash476 2012

[12] J Wang G Zhang X Gao and T Kong ldquoDynamic responseof bucket wheel stackerreclaimer under head shock excita-tionrdquo Hoisting and Conveying Machinery vol 1 pp 8ndash102012

[13] J Gottvald ldquoMeasuring and comparison of natural fre-quencies of bucket wheel excavators SchRs 1320 and K 2000rdquoin Proceedings of Wseas International Conference on Energyand Develepment-Environment-Biomedicine pp 335ndash340Corfu Island Greece July 2011

[14] A Bajric and J Hoslashgsberg ldquoIdentification of damping andcomplexmodes in structural vibrationsrdquo Journal of Sound andVibration vol 431 pp 367ndash389 2018

[15] J H Kang ldquoViscously damped free and forced vibrations ofcircular and annular membranes by a closed form exactmethodrdquo9in-Walled Structures vol 116 pp 194ndash200 2017

[16] J M Ramırez C D Gatti S P Machado and M Febbo ldquoAmulti-modal energy harvesting device for low-frequency vi-brationsrdquo Extreme Mechanics Letters vol 22 pp 1ndash7 2018

[17] L E anh Danh and N Vu Anh Duy ldquoLow-frequencyvibration isolator with adjustable configurative parameterrdquoInternational Journal of Mechanical Sciences vol 134pp 224ndash233 2017

[18] J Gottvald ldquoe calculation and measurement of the naturalfrequencies of the bucket wheel excavator SchRs 13204x30rdquoTransport vol 25 no 3 pp 269ndash277 2010

[19] D Pietrusiak T Smolnicki andM Stannco ldquoe influence ofsuperstructure vibrations on operational loads in the un-dercarriage of bulk material handling machinerdquo Archives ofCivil and Mechanical Engineering vol 17 no 4 pp 855ndash8622017

[20] P D Jovancic D Ignjatovic M Tanasijevic and T ManeskildquoLoad-bearing steel structure diagnostics on bucket wheelexcavator for the purpose of failure preventionrdquo EngineeringFailure Analysis vol 18 no 4 pp 1203ndash1211 2011

[21] X J Zhao and C Schindler ldquoEvaluation of whole-body vi-bration exposure experienced by operators of a compact wheelloader according to ISO 2631-11997 and ISO 2631-52004rdquoInternational Journal of Industrial Ergonomics vol 44 no 6pp 840ndash850 2014


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

2 Test Method

21 Principle For natural frequency testing by freeing theinitial displacement if there is an initial displacement Awhen the initial enforced displacement is released themotional differential equation of a single-freedom systemcan be expressed in the form

eurox + 2n _x + ω2x

f(t)

m (1)

where 2n cm and ω km

radicin above expression Since

the external force f(t) equals zero in free decay vibrationthe solution of equation (1) is

x Aeminusnt sin

ω2 minus n2

radict + φ1113872 1113873 (2)

Obviously the vibration displacement x appears as a freedecay motion at the natural frequencies ω If the free decaysignal x is measured it will be easy to calculate the naturalfrequencies ω through Fourier transformation

For an n-freedom system the free decay signals arecomposed of n natural frequencies theoretically But prac-tically a lot of natural frequencies will be missing and onlyseveral apparent frequencies can be measured and identifiedHowmany and which frequencies can be identified from thetesting data depend mainly on the properties of excitationposition of sensors and so on [14ndash17] For measuring theoverall low-frequency vibration of the excavator boom theexcitation of initial displacement must be exerted on thewhole boom rather than local part Moreover the excitationof initial displacementmust be powerful enough to excite theoverall low-frequency vibration of the boom so that thesignals from the sensor are easy to identify

22 Excitation Strategy e bucket wheel excavator DQLZ1200 which is manufactured by Tidfore Heavy Industry CoLtd of China is used for natural frequency testing eexcavator DQLZ 1200 is 43 meters tall 1260 tons in totaland theoretical capacity is 7200m3 of bulk material ebucked wheel boom which is very important for the ex-cavating operation is a complex welded structure made upof numerous plates and beams It weighs up to eighty tonsand sixty meters of length and the vibration in work processis primary low frequency [18 19] For the low-frequencyvibration testing of this kind of huge structure the difficultyis providing suitable external excitations [20 21] It would beadvantageous provided that suitable excitation can be ob-tained from the internal of the machine rather than fromoutside ere are three potential internal excitations whichare the motor with rotation of 247Hz bucket wheel withrotation of 01Hz and the belt-supporting rollers with ro-tation of 667Hz respectively Among these three excita-tions the belt-supporting rollers are the most suitable as alow-frequency vibration exciter because there are manyrollers arrayed along the whole long boom (Figure 1) so thatit is powered enough to excite the overall structure vibrationAlso its rotation speed of 667Hz is the most proximate tothe low natural frequency of the boom

3 Test Process

In this paper the rotation of the belt-supporting rollers istried as the exciter for low-frequency vibration testing andthe experiment is designed as Figure 2 Bruel and Kjaervibration test and analysis system 3550 with 24 channels areadopted and there are totally five accelerometers withsensitivity of 100mVg mounted on the boom Two sensorsare mounted on the distal end of the boom for gathering y-direction acceleration signals and the other two aremounted on the near end of the boom for gathering y- and z-direction acceleration signals e last sensor is mountedvertically on the diagonal bar for measuring the verticalvibration signal

In a single test procedure the bucket wheel starts torotate at 58 rpm when the bucket wheel motor is turned onAt this time only a slight vibration can be felt After a fewseconds the conveyor belt began to rotate at 400 rpm(667Hz) so that obvious vibration occurs during this pe-riod After that the belt conveyor and the bucket wheelmotor are suddenly powered off leaving the boom vibrationdecay freely until it stops completely is test procedure isrepeated three times and the signals measured from the fivesensors are shown in Figure 3

4 Test Results

Figure 3(a) shows the in-time signal of acceleration mea-sured by sensor No 1 It clearly shows that the signal coversall the three periods which are the bucket wheel start periodbelt conveyor start period and the period of free decay afterthe sudden power off Figure 3(b) shows the partial en-largement of the free decay period after the first power offObviously the decay signal does not completely decrease tozero and the free decay signal shows a distinctive charac-teristic of multifrequency vibration For frequency identi-fication both the stable operation in-time signal and the freedecay in-time signal are converted into the frequency do-main by the fast Fourier transformation (FFT) and thetransformed results are shown as Figures 3(c) and 3(d)respectively Comparison of the two figures shows that thefrequency of the stable running is very rich which not onlyreflects the natural frequency of the boom but also reflectsthe motor rotation frequency (247Hz) and the electricalnoise frequency (498Hz) while the free decay periodconsists of only four frequencies of 01 176 202 and256Hz Since 01Hz comes from the inertial rotation of thebucket wheel the true natural frequencies of the boom are176 202 and 256Hz

Signals captured by the other four sensors are treatedsimilarly as the sensor No1 Finally five natural frequenciesin total can be obviously identified from the five sensorsey are 051 074 178 202 and 256Hz respectivelywhich are listed in Table 1

5 Results Verification

To verify the experiment results in this paper the finiteelement method is applied and a high precision FE model is




No 1 Y direction



the diagonal bar

Y

X

Z



(a)


(b)





6 Conclusion




003

0025

002

0015

001

0005

00 10 20 30 40 50

50 51 52 53 54 55ndash01

ndash005

0

005


(177 202 257)Hz

(010 049)Hz

322Hz

249Hz

393Hz498Hz

FFT Time (s)

Frequency (Hz)

Mag

nitu

deStarting

bucket wheel 2

151

050

ndash05ndash1

ndash1520 40 60 80 100 120 1400



FFT Time (s)

(c) (d)

(a) (b)

Acc

eler

atio

n (m

s2 )

Acc

eler

atio

n (m

s2 )

00 2 4 6 8 10

0002

0004

0008

0006

001(010 176 202 256) Hz

Frequency (Hz)

Mag

nitu

de


(a)

(b)







2078E ndash 01


1559E ndash 01

1299E ndash 01

1039E ndash 01

7793E ndash 02

5195E ndash 02

5598E ndash 02

0000E + 00No result


(a)Contour plot




(b)




4452E ndash 01

3895E ndash 01

3339E ndash 01

2782E ndash 01

2226E ndash 01

1669E ndash 01

1113E ndash 01

5565E ndash 02

0000E + 00No result


(c)

Figure 5 Continued







Data Availability




Acknowledgments


References












ZY

X

(d)


ZY

X

(e)


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




No 1 Y direction



the diagonal bar

Y

X

Z



(a)


(b)





6 Conclusion




003

0025

002

0015

001

0005

00 10 20 30 40 50

50 51 52 53 54 55ndash01

ndash005

0

005


(177 202 257)Hz

(010 049)Hz

322Hz

249Hz

393Hz498Hz

FFT Time (s)

Frequency (Hz)

Mag

nitu

deStarting

bucket wheel 2

151

050

ndash05ndash1

ndash1520 40 60 80 100 120 1400



FFT Time (s)

(c) (d)

(a) (b)

Acc

eler

atio

n (m

s2 )

Acc

eler

atio

n (m

s2 )

00 2 4 6 8 10

0002

0004

0008

0006

001(010 176 202 256) Hz

Frequency (Hz)

Mag

nitu

de


(a)

(b)







2078E ndash 01


1559E ndash 01

1299E ndash 01

1039E ndash 01

7793E ndash 02

5195E ndash 02

5598E ndash 02

0000E + 00No result


(a)Contour plot




(b)




4452E ndash 01

3895E ndash 01

3339E ndash 01

2782E ndash 01

2226E ndash 01

1669E ndash 01

1113E ndash 01

5565E ndash 02

0000E + 00No result


(c)

Figure 5 Continued







Data Availability




Acknowledgments


References












ZY

X

(d)


ZY

X

(e)


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




6 Conclusion




003

0025

002

0015

001

0005

00 10 20 30 40 50

50 51 52 53 54 55ndash01

ndash005

0

005


(177 202 257)Hz

(010 049)Hz

322Hz

249Hz

393Hz498Hz

FFT Time (s)

Frequency (Hz)

Mag

nitu

deStarting

bucket wheel 2

151

050

ndash05ndash1

ndash1520 40 60 80 100 120 1400



FFT Time (s)

(c) (d)

(a) (b)

Acc

eler

atio

n (m

s2 )

Acc

eler

atio

n (m

s2 )

00 2 4 6 8 10

0002

0004

0008

0006

001(010 176 202 256) Hz

Frequency (Hz)

Mag

nitu

de


(a)

(b)







2078E ndash 01


1559E ndash 01

1299E ndash 01

1039E ndash 01

7793E ndash 02

5195E ndash 02

5598E ndash 02

0000E + 00No result


(a)Contour plot




(b)




4452E ndash 01

3895E ndash 01

3339E ndash 01

2782E ndash 01

2226E ndash 01

1669E ndash 01

1113E ndash 01

5565E ndash 02

0000E + 00No result


(c)

Figure 5 Continued







Data Availability




Acknowledgments


References












ZY

X

(d)


ZY

X

(e)


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






2078E ndash 01


1559E ndash 01

1299E ndash 01

1039E ndash 01

7793E ndash 02

5195E ndash 02

5598E ndash 02

0000E + 00No result


(a)Contour plot




(b)




4452E ndash 01

3895E ndash 01

3339E ndash 01

2782E ndash 01

2226E ndash 01

1669E ndash 01

1113E ndash 01

5565E ndash 02

0000E + 00No result


(c)

Figure 5 Continued







Data Availability




Acknowledgments


References












ZY

X

(d)


ZY

X

(e)


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







Data Availability




Acknowledgments


References












ZY

X

(d)


ZY

X

(e)


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia

















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

Low-FrequencyVibrationTestingofHugeBucketWheel ...downloads.hindawi.com/journals/sv/2018/6182156.pdf2.TestMethod 2.1.Principle. Fornaturalfrequencytestingbyfreeingthe initialdisplacement,ifthereisaninitialdisplacementA,