research article noise source identification of a ring...

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 875929 5 pageshttpdxdoiorg1011552013875929

Research ArticleNoise Source Identification of a Ring-Plate Cycloid ReducerBased on Coherence Analysis

Bing Yang1 and Yan Liu2

1 School of Mechanical Engineering Dalian Jiaotong University Dalian 116028 China2 School of Traffic and Transportation Engineering Dalian Jiaotong University Dalian 116028 China

Correspondence should be addressed to Bing Yang yangbing djtu126com

Received 16 November 2012 Revised 8 March 2013 Accepted 8 March 2013

Academic Editor Valentina E Balas

Copyright copy 2013 B Yang and Y Liu This 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

A ring-plate-type cycloid speed reducer is one of the most important reducers owing to its low volume compactness smoothand high performance and high reliability The vibration and noise tests of the reducer prototype are completed using the HEADacousticsmultichannel noise test and analysis systemThe characteristics of the vibration and noise are obtained based on coherenceanalysis and the noise sources are identified The conclusions provide the bases for further noise research and control of the ring-plate-type cycloid reducer

1 Introduction

Speed reducers are used in various fields for the purposesof speed and torque conversion Speed reducers have manykinds such as worm reducer crane reducer cycloid reducerplanetary gear reducer and ring-plate-type reducer A ring-plate-type cycloid speed reducer is one of the most impor-tant reducers owing to its low volume smooth and highperformance and high reliability The internal transmissionstructure of the ring-plate-type cycloid speed reducer isshown in Figure 1 [1ndash3] The input shaft equipped with adriving involute gear is supported by the reducer Two drivengears are mounted on two driven cranks Four ring plateswith pin gears are connected to the two driven cranks Twocranks have the same length Thus ring plate and two cranksbecome a parallel four-bar mechanismWhen the input shaftrotates it causes the two cranks to rotateThe four ring platesmounted to the cranks rotateThen the cycloidal gear rotatesThe output shaft rotates since the cycloidal gear is mountedto the output shaft [4]

At present the application of the reducer is limited tosome extent because of the noise level So it has practicalsignificance to research the vibration and noise of the reducer[5ndash10] The vibration and noise tests of the reducer arecompleted using the HEAD acoustics multichannel noise test

and analysis system The characteristics of the vibration andnoise are obtained based on coherence analysis and the noisesources of the double crank ring-plate-type pin-cycloid gearreducer are identified

2 Noise Source Identification Methods

Mechanical equipment noise control is mainly in threeareas sound source control transmission route control andrecipient protection And the control of the noise source isthe most fundamental and effective method The premiseis identifying the main sources of the equipment [11ndash13]There are many noise source identification methods such assubjective evaluation respectively run and lead cover Thefollowing are frequency spectrum and coherence analysismethods

21 Frequency Spectrum The data measured are time-do-main signal in general In order to obtain the frequency char-acteristics of the noise source frequency spectrum analysis isoften made The frequency spectrum can be generated via aFourier transform of the signal into a single harmonic com-ponent to study to thereby obtain the frequency structure ofthe signal and the amplitude and phase information of theharmonic and the resulting are usually presented as frequency

2 Mathematical Problems in Engineering

2

51 3

4 D

C

A

B119874119875

119881119875

119881119861

119890

119890

119874119862

(1) Crank(2) Ring plate(3) Crank

(4) Base(5) Cycloidal gear

Figure 1 Crank ring-plate-type cycloid speed reducer

ArtemisRing-plate-type cycloid gear Sensors SQLab IIreducer

Figure 2 Signal collection and analysis process

spectrum diagrams [14ndash16]The peak values of the frequencyspectrum diagrams are closely but not necessarily related tothe main source of noise A peak in the noise and vibrationfrequency spectrum diagram may come from several noisesources and sometimes a noise source may produce morethan one peak in the frequency spectrum diagram

22 Coherence Analysis A coherence function is the descrip-tion of the relevance of the two signals in a system [17 18] Let119909(119905) and 119910(119905) be the signals the Autocorrelation function isdefined as

119877119909(120591) = 119864 [119909 (119905 + 120591) 119909 (119905)] (1)

The cross-correlation function is defined as

119877119909119910(120591) = 119864 [119909 (119905 + 120591) 119910 (119905)] (2)

The correlation coefficient between 119909(119905) and 119910(119905) can beexpressed as

120588119909119910=

suminfin

119905=0119909 (119905) 119910 (119905)

[suminfin

119905=01199092(119905) suminfin

119905=01199102(119905)]05 (3)

The inputs of a system are the noise or vibration the onlylinear output is that 119910(119905) 119910(119905) is the sum of the linear outputsThe coherence function between an input and the output canbe expressed as

1205742

119894119910(120596) =

10038161003816100381610038161003816119866119894119910(120596)

10038161003816100381610038161003816

2

119866119894119894(120596) 119866119910119910(120596)

(4)

Figure 3 Test points position

3 Vibration and Noise Tests

31 Test Equipment The vibration and noise tests of thereducer prototype are completed using the HEAD acousticstest and analysis system in an ordinary laboratoryTheHEADacoustics multichannel noise test and analysis system isselected for the measurement The system is made of SQLabII data acquisition recorder G R A S microphones andKISTLER acceleration sensors and Artemis software Thedata collection and analysis process of the HEAD acousticsmultichannel noise test and analysis system is shown inFigure 2 The signals are collected from reducer throughsensors to the front end The analog signal is converted intoa digital signal through SQLab At last the digital signalsare analyzed by Artemis software with different analysismethods

32 Test Point Position The ring-plate cycloid reducer noisecomes mainly from structural noise Structural noise isgenerated by the imbalance the mechanical collision andstructural resonance and propagates to the space propagationthrough the shaft the bearing and the block Structural noisemainly comes from the following two sections The firstsection machinery parts produces sound when they rotateSuch as shaft gear motor and so onThe other section comesfrom components engagement and sound

The main noise sources of the ring-plate cycloid reducerare the following aspects through experiences (1) the noisegenerated by ring plates and cycloidal gear when theymesh (2) the noise generated by involute spur gears whenthey mesh (3) the noise caused by driving motor and(4) the noise caused unbalanced installation of ring platesAccording to the possible noise sources three vibration testpoints and one noise test point were positioned in the testprocedure Figure 3The location of the test points is shown inFigure 4 The detailed information of test points is shown inTable 1

4 Noise Source Identification

The double-crank four ring-plate-type cycloid reducer inter-nal-noise-source-related parameters can be expressed as

119896 =

119891

119891119904

(5)

Mathematical Problems in Engineering 3

Table 1 Test point location explanation

Pointname Test point location

1 Vibration test point near the input shafton the surface of the reducer

2 Vibration test point near the cycloid gearon the surface of the reducer

3 Vibration test point near the outputshaft on the surface of the reducer

5 Noise test point 1 meter above thereducer

1199091(119905)

1199092(119905)

1199093(119905)

1199091(119905)

119909119898(119905)

1198671(119891)

1198672(119891)

1198673(119891)

1198671(119891)

119867119898(119891)

sum (SPL)

Figure 4 Multi-input single-output linear system

0

0005

001

0015

002

0025

3 296 589 882 1175 1468 1761 2054 2347 2640 2933Frequency (Hz)

Vibr

atio

n ac

cele

ratio

n (g

)

Figure 5 Vibration acceleration of test point 1

where 119891 is the main frequency and 119891119904is the shaft frequency

and the shaft frequency can be expressed as

119891119904=

119899

60

(6)

where 119899 is the rotation speed of the gearsThe data collected from three vibrations test points are

supposed as 1199091(119905) 1199092(119905) 119909

3(119905) and the signal received from

the noise test point is 119910(119905) The multi-input single-outputlinear system model is shown in Figure 4 The collectedvibration acceleration signals 119909

1(119905) 1199092(119905) 1199093(119905) are the inputs

of the system the collected sound pressure level signal 119910(119905) isthe output of the linear outputs The four test point data are

0102030405060708090

104 584 1064 1544 2024 2504 2984

SPL

(dB)

Frequency (Hz)

Figure 6 SPL of test point 5

Auto

corr

elat

ion

(dB)

minus80

minus82

minus84

minus86

minus88

minus90

minus92

minus94

minus96

minus98

minus100

Frequency (Hz)4800 960 1440 1920 2400 2880

Figure 7 Autocorrelation of test point 1

Auto

corr

elat

ion

(dB)

Frequency (Hz)4800 960 1440 1920 2400 2880

minus84

minus86

minus88

minus90

minus92

minus94

minus96

minus98


collected synchronously through the front endThe collecteddata are analyzed through the Artemis software

In order to grasp the noise distributing laws of thereducer three different speeds and three different loads wereselected They are 750 rotations per minute 1000 rotationsperminute and 1250 rotations perminuteThe three differentloads are 40 60 and 80 of the full load Figure 5 showsthe vibration acceleration spectrum diagram of test point1 with the input shaft rotation of 1250 rpm The frequencyspectrum diagrams of the other speeds are not given here dueto limited space


Frequency (Hz)

0102030405060708090

3 296 589 882 1175 1468 1761 2054 2347 2640 2933

Cros

s-sp

ectr

um (d

B)

Figure 9 Cross-spectrum between 5 and 1

Frequency (Hz)

01020304050607080

0 293 586 879 1172 1465 1758 2051 2344 2637 2930

Cros

s-sp

ectr

um (d

B)

Figure 10 Cross-spectrum between points 5 and 2

Figure 5 shows that the vibration acceleration of test point1 shakes a little bit in the low frequency range Figure 6 showsthe noise frequency spectrum diagram of test point 5 withthe input shaft rotation of 1250 rpm Figure 6 shows that thesound pressure lever of test point 5 is 864 dBThe frequenciescorresponding to the four peaks are 584Hz 1168Hz 1744Hzand 2360Hz respectively

Figure 7 shows the Autocorrelation frequency spectrumdiagram of test point 1 The frequencies corresponding to thethree peaks are 584Hz 1768Hz and 2320Hz respectivelyFigure 8 shows the Autocorrelation frequency spectrum dia-gram of test point 2 The frequencies corresponding to thepeaks are 1752Hz and 2336Hz

Figure 9 shows the cross-spectrum analysis diagram ofbetween test point 5 and test point 1 Figure 10 shows thecross-spectrum analysis diagram of between test point 5and test point 2 From the analysis we know the followingconclusions The contribution of the noise from the positionof the ring plates is the biggest The involute spur gearsrsquocontribution to the noise is not too high So the noisereduction measures should be taken

5 Conclusions

Double-crank four ring-plate cycloid speed reducer is one ofthemost important reducers owing to its low volume smoothand high performance and high reliability In this paper the

characteristics of the vibration and noise are obtained afterthe vibration and noise tests The noise sources are identifiedas the ring plates To reduce the noise of the reducer thestructure of the ring plates or the unbalance of installationmay be taken into consideration

Acknowledgment

This work is supported by Key Laboratory of Modern Acous-tics Ministry of Education China (Project no 1108)

References

[1] WDHe X Li and L Li ldquoStudy on double crank ringplate-typecycloid driverdquo Journal of Mechanical Engineering vol 36 no 5pp 84ndash88 2000

[2] W D He X Li L Li and B Wen ldquoOptimum design andexperiment for reducing vibration and noise of double crankring-plate-type pin-cycloid planetary driverdquo Jixie GongchengXuebaoJournal of Mechanical Engineering vol 46 no 23 pp53ndash60 2010

[3] W D He Q Lu et al ldquoStudy on pin cycloid planetary gearreducer used in propeller pitch variator for 15MW windturbinerdquo Journal of Mechanical Transmission vol 36 no 7 pp1ndash4 2012

[4] X Li W D He L Li and L C Schmidt ldquoA new cycloid drivewith high-load capacity and high efficiencyrdquo ASME Journal ofMechanical Design vol 126 no 4 pp 683ndash686 2004

[5] N B Roozen J Van den Oetelaar A Geerlings and TVliegenthart ldquoSource identification and noise reduction of areciprocating compressor A case historyrdquo International Journalof Acoustics and Vibrations vol 14 no 2 pp 90ndash98 2009

[6] F Payri A Broatch X Margot and L Monelletta ldquoSoundquality assessment ofDiesel combustion noise using in-cylinderpressure componentsrdquo Measurement Science and Technologyvol 20 no 1 Article ID 015107 2009

[7] P Simon ldquoRetrieving the three-dimensionalmatter power spec-trum and galaxy biasing parameters from lensing tomographyrdquoAstronomy and Astrophysics vol 543 no 1 p 1 2012

[8] C C ZhuD TQin and SHong ldquoStudy on surface noise distri-bution of three-ring reducerrdquo Journal of Chongqing Universityvol 4 pp 18ndash21 2000

[9] T J Lin Y J Liao R F Li and W Liu ldquoNumerical simulationand experimental study on radiation noise of double-ring gearreducerrdquo Journal of Vibration and Shock vol 29 no 3 pp 43ndash472010

[10] J Prezelj and M Cudina ldquoQuantification of aerodynamicallyinduced noise and vibration-induced noise in a suction unitrdquoProceedings of the Institution ofMechanical Engineers C vol 225no 3 pp 617ndash624 2011

[11] Z Chu W Wang and X Xiao ldquoNoise source identificationand noise abatement of truck under idle speed conditionrdquoTransactions of the Chinese Society of Agricultural Engineeringvol 26 no 5 pp 153ndash158 2010

[12] A Ramachandran M C Reddy and R Moodithaya ldquoMin-imization and identification of conducted emission bearingcurrent in variable speed induction motor drives using PWMinverterrdquo Indian Academy of Sciences vol 33 no 5 pp 615ndash6282008

[13] R S Magalhaes C H O Fontes L A L Almeida andM Embirucu ldquoIdentification of hybrid ARXneural network


models for three-dimensional simulation of a vibroacousticsystemrdquo Journal of Sound and Vibration vol 330 no 21 pp5138ndash5150 2011

[14] X D Wu S G Zuo and Y Lu ldquoIdentifying noise source basedon application to partial coherence analysis in fuel cell carrdquoJournal of Noise and Vibration vol 3 pp 81ndash84 2008

[15] M L Chen and S M Li ldquoCoherence functions method forsignal source identificationrdquoChinaMechanical Engineering vol1 pp 95ndash100 2007

[16] K S Oh S K Lee and S J Kim ldquoIdentification and reductionof noise from axles in a passenger vehiclerdquo Noise ControlEngineering Journal vol 56 no 5 pp 332ndash341 2008

[17] F Dezelak ldquoEffective noise control through identification andranking of incoherent noise sourcesrdquoNoise Control EngineeringJournal vol 58 no 2 pp 212ndash221 2010

[18] H E Camargo P A Ravetta R A Burdisso and A K SmithldquoApplication of phased array technology for identification oflow frequency noise sourcesrdquo Journal of Low Frequency NoiseVibration and Active Control vol 28 no 4 pp 237ndash244 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


2

51 3

4 D

C

A

B119874119875

119881119875

119881119861

119890

119890

119874119862

(1) Crank(2) Ring plate(3) Crank

(4) Base(5) Cycloidal gear

Figure 1 Crank ring-plate-type cycloid speed reducer

ArtemisRing-plate-type cycloid gear Sensors SQLab IIreducer

Figure 2 Signal collection and analysis process

spectrum diagrams [14ndash16]The peak values of the frequencyspectrum diagrams are closely but not necessarily related tothe main source of noise A peak in the noise and vibrationfrequency spectrum diagram may come from several noisesources and sometimes a noise source may produce morethan one peak in the frequency spectrum diagram

22 Coherence Analysis A coherence function is the descrip-tion of the relevance of the two signals in a system [17 18] Let119909(119905) and 119910(119905) be the signals the Autocorrelation function isdefined as

119877119909(120591) = 119864 [119909 (119905 + 120591) 119909 (119905)] (1)

The cross-correlation function is defined as

119877119909119910(120591) = 119864 [119909 (119905 + 120591) 119910 (119905)] (2)

The correlation coefficient between 119909(119905) and 119910(119905) can beexpressed as

120588119909119910=

suminfin

119905=0119909 (119905) 119910 (119905)

[suminfin

119905=01199092(119905) suminfin

119905=01199102(119905)]05 (3)

The inputs of a system are the noise or vibration the onlylinear output is that 119910(119905) 119910(119905) is the sum of the linear outputsThe coherence function between an input and the output canbe expressed as

1205742

119894119910(120596) =

10038161003816100381610038161003816119866119894119910(120596)

10038161003816100381610038161003816

2

119866119894119894(120596) 119866119910119910(120596)

(4)

Figure 3 Test points position

3 Vibration and Noise Tests

31 Test Equipment The vibration and noise tests of thereducer prototype are completed using the HEAD acousticstest and analysis system in an ordinary laboratoryTheHEADacoustics multichannel noise test and analysis system isselected for the measurement The system is made of SQLabII data acquisition recorder G R A S microphones andKISTLER acceleration sensors and Artemis software Thedata collection and analysis process of the HEAD acousticsmultichannel noise test and analysis system is shown inFigure 2 The signals are collected from reducer throughsensors to the front end The analog signal is converted intoa digital signal through SQLab At last the digital signalsare analyzed by Artemis software with different analysismethods

32 Test Point Position The ring-plate cycloid reducer noisecomes mainly from structural noise Structural noise isgenerated by the imbalance the mechanical collision andstructural resonance and propagates to the space propagationthrough the shaft the bearing and the block Structural noisemainly comes from the following two sections The firstsection machinery parts produces sound when they rotateSuch as shaft gear motor and so onThe other section comesfrom components engagement and sound

The main noise sources of the ring-plate cycloid reducerare the following aspects through experiences (1) the noisegenerated by ring plates and cycloidal gear when theymesh (2) the noise generated by involute spur gears whenthey mesh (3) the noise caused by driving motor and(4) the noise caused unbalanced installation of ring platesAccording to the possible noise sources three vibration testpoints and one noise test point were positioned in the testprocedure Figure 3The location of the test points is shown inFigure 4 The detailed information of test points is shown inTable 1

4 Noise Source Identification

The double-crank four ring-plate-type cycloid reducer inter-nal-noise-source-related parameters can be expressed as

119896 =

119891

119891119904

(5)








1199091(119905)

1199092(119905)

1199093(119905)

1199091(119905)

119909119898(119905)

1198671(119891)

1198672(119891)

1198673(119891)

1198671(119891)

119867119898(119891)

sum (SPL)


0

0005

001

0015

002

0025

3 296 589 882 1175 1468 1761 2054 2347 2640 2933Frequency (Hz)

Vibr

atio

n ac

cele

ratio

n (g

)




119891119904=

119899

60

(6)


supposed as 1199091(119905) 1199092(119905) 119909



1(119905) 1199092(119905) 1199093(119905) are the inputs


0102030405060708090

104 584 1064 1544 2024 2504 2984

SPL

(dB)

Frequency (Hz)


Auto

corr

elat

ion

(dB)

minus80

minus82

minus84

minus86

minus88

minus90

minus92

minus94

minus96

minus98

minus100

Frequency (Hz)4800 960 1440 1920 2400 2880


Auto

corr

elat

ion

(dB)

Frequency (Hz)4800 960 1440 1920 2400 2880

minus84

minus86

minus88

minus90

minus92

minus94

minus96

minus98





Frequency (Hz)

0102030405060708090

3 296 589 882 1175 1468 1761 2054 2347 2640 2933

Cros

s-sp

ectr

um (d

B)


Frequency (Hz)

01020304050607080

0 293 586 879 1172 1465 1758 2051 2344 2637 2930

Cros

s-sp

ectr

um (d

B)





5 Conclusions



Acknowledgment


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















1199091(119905)

1199092(119905)

1199093(119905)

1199091(119905)

119909119898(119905)

1198671(119891)

1198672(119891)

1198673(119891)

1198671(119891)

119867119898(119891)

sum (SPL)


0

0005

001

0015

002

0025

3 296 589 882 1175 1468 1761 2054 2347 2640 2933Frequency (Hz)

Vibr

atio

n ac

cele

ratio

n (g

)




119891119904=

119899

60

(6)


supposed as 1199091(119905) 1199092(119905) 119909



1(119905) 1199092(119905) 1199093(119905) are the inputs


0102030405060708090

104 584 1064 1544 2024 2504 2984

SPL

(dB)

Frequency (Hz)


Auto

corr

elat

ion

(dB)

minus80

minus82

minus84

minus86

minus88

minus90

minus92

minus94

minus96

minus98

minus100

Frequency (Hz)4800 960 1440 1920 2400 2880


Auto

corr

elat

ion

(dB)

Frequency (Hz)4800 960 1440 1920 2400 2880

minus84

minus86

minus88

minus90

minus92

minus94

minus96

minus98





Frequency (Hz)

0102030405060708090

3 296 589 882 1175 1468 1761 2054 2347 2640 2933

Cros

s-sp

ectr

um (d

B)


Frequency (Hz)

01020304050607080

0 293 586 879 1172 1465 1758 2051 2344 2637 2930

Cros

s-sp

ectr

um (d

B)





5 Conclusions



Acknowledgment


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Frequency (Hz)

0102030405060708090

3 296 589 882 1175 1468 1761 2054 2347 2640 2933

Cros

s-sp

ectr

um (d

B)


Frequency (Hz)

01020304050607080

0 293 586 879 1172 1465 1758 2051 2344 2637 2930

Cros

s-sp

ectr

um (d

B)





5 Conclusions



Acknowledgment


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article noise source identification of a ring...

Documents