research article noise source identification of a ring ...mathematicalproblems in engineering...

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013, Article ID 875929, 5 pageshttp://dx.doi.org/10.1155/2013/875929

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 [email protected]

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

Academic Editor: Valentina E. Balas

Copyright © 2013 B. Yang and Y. Liu. This is an open access article distributed under the Creative Commons Attribution License,which 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 system.The 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 reducer,planetary 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 [1–3]. 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 mechanism.When the input shaftrotates, it causes the two cranks to rotate.The four ring platesmounted to the cranks rotate.Then the cycloidal gear rotates.The 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[5–10]. 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 [11–13].There are many noise source identification methods such assubjective evaluation, respectively run, and lead cover. Thefollowing are frequency spectrum and coherence analysismethods.

2.1. 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

B𝑂𝑃

𝑉𝑃

𝑉𝐵

𝑒

𝑒

𝑂𝐶

(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 [14–16].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.

2.2. Coherence Analysis. A coherence function is the descrip-tion of the relevance of the two signals in a system [17, 18]. Let𝑥(𝑡) and 𝑦(𝑡) be the signals; the Autocorrelation function isdefined as

𝑅𝑥(𝜏) = 𝐸 [𝑥 (𝑡 + 𝜏) 𝑥 (𝑡)] . (1)

The cross-correlation function is defined as

𝑅𝑥𝑦(𝜏) = 𝐸 [𝑥 (𝑡 + 𝜏) 𝑦 (𝑡)] . (2)

The correlation coefficient between 𝑥(𝑡) and 𝑦(𝑡) can beexpressed as

𝜌𝑥𝑦=

∑∞

𝑡=0𝑥 (𝑡) 𝑦 (𝑡)

[∑∞

𝑡=0𝑥2(𝑡) ∑∞

𝑡=0𝑦2(𝑡)]0.5. (3)

The inputs of a system are the noise or vibration; the onlylinear output is that 𝑦(𝑡). 𝑦(𝑡) is the sum of the linear outputs.The coherence function between an input and the output canbe expressed as

𝛾2

𝑖𝑦(𝜔) =

𝐺𝑖𝑦(𝜔)

2

𝐺𝑖𝑖(𝜔) 𝐺𝑦𝑦(𝜔)

. (4)

Figure 3: Test points position.

3. Vibration and Noise Tests

3.1. Test Equipment. The vibration and noise tests of thereducer prototype are completed using the HEAD acousticstest and analysis system in an ordinary laboratory.TheHEADacoustics 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.

3.2. 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 first,section, machinery parts produces sound when they rotate.Such as shaft, gear, motor and so on.The 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 plates.According to the possible noise sources, three vibration testpoints and one noise test point were positioned in the testprocedure Figure 3.The 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

𝑘 =

𝑓

𝑓𝑠

, (5)

Mathematical Problems in Engineering 3

Table 1: Test point location explanation.

Pointname Test point location

1 Vibration test point, near the input shaft,on the surface of the reducer

2 Vibration test point, near the cycloid gear,on 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

𝑥1(𝑡)

𝑥2(𝑡)

𝑥3(𝑡)

𝑥1(𝑡)

𝑥𝑚(𝑡)

𝐻1(𝑓)

𝐻2(𝑓)

𝐻3(𝑓)

𝐻1(𝑓)

𝐻𝑚(𝑓)

∑ (SPL)

Figure 4: Multi-input single-output linear system.

0

0.005

0.01

0.015

0.02

0.025

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 𝑓 is the main frequency and 𝑓𝑠is the shaft frequency,

and the shaft frequency can be expressed as

𝑓𝑠=

𝑛

60

, (6)

where 𝑛 is the rotation speed of the gears.The data collected from three vibrations test points are

supposed as 𝑥1(𝑡), 𝑥2(𝑡), 𝑥

3(𝑡), and the signal received from

the noise test point is 𝑦(𝑡). The multi-input single-outputlinear system model is shown in Figure 4. The collectedvibration acceleration signals 𝑥

1(𝑡), 𝑥2(𝑡), 𝑥3(𝑡) are the inputs

of the system; the collected sound pressure level signal 𝑦(𝑡) 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)

−80

−82

−84

−86

−88

−90

−92

−94

−96

−98

−100

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

−84

−86

−88

−90

−92

−94

−96

−98

Figure 8: Autocorrelation of test point 2.

collected synchronously through the front end.The 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 perminute.The 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.

4 Mathematical Problems in Engineering

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 86.4 dB.The frequenciescorresponding to the four peaks are 584Hz, 1168Hz, 1744Hz,and 2360Hz, respectively.

Figure 7 shows the Autocorrelation frequency spectrumdiagram of test point 1. The frequencies corresponding to thethree peaks are 584Hz, 1768Hz, and 2320Hz, respectively.Figure 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 gears’contribution 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] W.D.He, X. Li, and L. Li, “Study on double crank ringplate-typecycloid drive,” Journal of Mechanical Engineering, vol. 36, no. 5,pp. 84–88, 2000.

[2] W. D. He, X. Li, L. Li, and B. Wen, “Optimum design andexperiment for reducing vibration and noise of double crankring-plate-type pin-cycloid planetary drive,” Jixie GongchengXuebao/Journal of Mechanical Engineering, vol. 46, no. 23, pp.53–60, 2010.

[3] W. D. He, Q. Lu et al., “Study on pin cycloid planetary gearreducer used in propeller pitch variator for 1.5MW windturbine,” Journal of Mechanical Transmission, vol. 36, no. 7, pp.1–4, 2012.

[4] X. Li, W. D. He, L. Li, and L. C. Schmidt, “A new cycloid drivewith high-load capacity and high efficiency,” ASME Journal ofMechanical Design, vol. 126, no. 4, pp. 683–686, 2004.

[5] N. B. Roozen, J. Van den Oetelaar, A. Geerlings, and T.Vliegenthart, “Source identification and noise reduction of areciprocating compressor; A case history,” International Journalof Acoustics and Vibrations, vol. 14, no. 2, pp. 90–98, 2009.

[6] F. Payri, A. Broatch, X. Margot, and L. Monelletta, “Soundquality assessment ofDiesel combustion noise using in-cylinderpressure components,” Measurement Science and Technology,vol. 20, no. 1, Article ID 015107, 2009.

[7] P. Simon, “Retrieving the three-dimensionalmatter power spec-trum and galaxy biasing parameters from lensing tomography,”Astronomy and Astrophysics, vol. 543, no. 1, p. 1, 2012.

[8] C. C. Zhu,D. T.Qin, and S.Hong, “Study on surface noise distri-bution of three-ring reducer,” Journal of Chongqing University,vol. 4, pp. 18–21, 2000.

[9] T. J. Lin, Y. J. Liao, R. F. Li, and W. Liu, “Numerical simulationand experimental study on radiation noise of double-ring gearreducer,” Journal of Vibration and Shock, vol. 29, no. 3, pp. 43–47,2010.

[10] J. Prezelj and M. Čudina, “Quantification of aerodynamicallyinduced noise and vibration-induced noise in a suction unit,”Proceedings of the Institution ofMechanical Engineers C, vol. 225,no. 3, pp. 617–624, 2011.

[11] Z. Chu, W. Wang, and X. Xiao, “Noise source identificationand noise abatement of truck under idle speed condition,”Transactions of the Chinese Society of Agricultural Engineering,vol. 26, no. 5, pp. 153–158, 2010.

[12] A. Ramachandran, M. C. Reddy, and R. Moodithaya, “Min-imization and identification of conducted emission bearingcurrent in variable speed induction motor drives using PWMinverter,” Indian Academy of Sciences, vol. 33, no. 5, pp. 615–628,2008.

[13] R. S. Magalhães, C. H. O. Fontes, L. A. L. Almeida, andM. Embiruçu, “Identification of hybrid ARXneural network

Mathematical Problems in Engineering 5

models for three-dimensional simulation of a vibroacousticsystem,” Journal of Sound and Vibration, vol. 330, no. 21, pp.5138–5150, 2011.

[14] X. D. Wu, S. G. Zuo, and Y. Lu, “Identifying noise source basedon application to partial coherence analysis in fuel cell car,”Journal of Noise and Vibration, vol. 3, pp. 81–84, 2008.

[15] M. L. Chen and S. M. Li, “Coherence functions method forsignal source identification,”ChinaMechanical Engineering, vol.1, pp. 95–100, 2007.

[16] K. S. Oh, S. K. Lee, and S. J. Kim, “Identification and reductionof noise from axles in a passenger vehicle,” Noise ControlEngineering Journal, vol. 56, no. 5, pp. 332–341, 2008.

[17] F. Deželak, “Effective noise control through identification andranking of incoherent noise sources,”Noise Control EngineeringJournal, vol. 58, no. 2, pp. 212–221, 2010.

[18] H. E. Camargo, P. A. Ravetta, R. A. Burdisso, and A. K. Smith,“Application of phased array technology for identification oflow frequency noise sources,” Journal of Low Frequency NoiseVibration and Active Control, vol. 28, no. 4, pp. 237–244, 2009.

Submit your manuscripts athttp://www.hindawi.com

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttp://www.hindawi.com

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com

Volume 2014 Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Stochastic AnalysisInternational Journal of

research article noise source identification of a ring ...mathematicalproblems in engineering...

Documents