基于小波理论和混沌理论的轴承故障信号判别

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Sep．2013机 床 与 液 压Hydromechatronics Engineering VoI．41 No．18DOI：10．3969／j．isn．1001-3881．2013．18．013Detection of Bearing Fault Signal Based on the W aveletand Chaos TheoryREN Xueping，LIU TongtongMechanwal Enginering School，Inner Mongolia University of Science&Technology，Baotou 014010，China1．IntroductionAbstract：Based on the knowledge of wavelet packet and chaos theory，a new approach is pro-posed to determine the bearing fault signa1．Through a large number of numerical simulationtests，it has been shown that the proposed method is very good for the real industrial applica-tions．An example of the detection of bearing outer ring fault signal was conducted in this paper
，and the results have shown that this method is capable to detect the fault of bearing．Therefore
.

it has been confirmed that the proposed method is an accurate and efective way to detect thebearing fault signa1.

Key words：wavelet packet de-noising，dufing oscilator，bearing fault，signal detectionBearing is one of the most common parts in me—chanical equipments and the running state directly af-fects the function of the equipment．Since the preci—sion of modern mechanical equipment is geting high—er and higher，any slight fault or disturbance maycause a great error to the product and it will bringhuge economic losses．Detection of the fault bearingat the first time is an important way to improve thequality of products．Therefore，it is necessary to findan efective method to judge the failure of bearings.

During the practical application process of me—chanical equipment，the characteristic signal of bear.

ing failure is very weak at the beginning time of bear—ing failure due to the complexity of equipment whichcontains all kinds of spare parts and different spareparts have different vibration ~equency and ampli—tude．Therefore，the signal of bearing failure is oftensubmerged in other interfering signals and how to i-dentify this weak signal from the background strongReceived：2013—01—22LIU Tongtong．E—mail：liuxiaohangl314277### 126．connoise is very important for the signal processing andfault diagnosis[1].

2．The basic theory2．1．wavelet packet de-noisingThe signals collected at the workplace are alsothe mixture of other signals．It always contains somebandwidth of the signals． If the Dufing oscilator isdirectly adopted to process the original signal，it willnot only waste a lot of processing time，but also willaffect the accuracy．Therefore．it is necessary to de.

noise the original signals before these signals are ana-lyzed．The conventional way to denoise the signalscan only give us a given frequency of the signal whichmay not what we want． However， if the waveletpacket of de—noising is adopted，any band of signalscould be obtained．Therefore，the wavelet packet ofde—noising will become one of the main methods toreduce the noise signals in the future.

The wavelet packet of de．noising could be divid.

ed into the folowing four steps[2]：① The waveletpacket，② Calculate the champion tree and determinethe optimal basis of wavelet packet，(~)Threshold thedecomposition coeficients of wavelet packet，④ Re.

construction of wavelet packet.

REN Xueping，et al：Detection of Bearing Fault Signal Based on the W aveletand Chaos Theory 67lyzed that the bearing outer ring faults of 6502 2RSSKF bearing could be detected when the rotationspeed was 1 750r／min．In this case，the faults was atiny Found pit with 0．007 made by EDM method，the rol diameter is 8 mm，pitch circle diameter is 40mm，number is 9，roller contact angle is 0，the sam—pling frequency is 1 2 000 Hz， sampling point is5 050，calculated engine speed is 1 750 r／min．Thebearing components fault frequencies are shown inTab．1.

1 51 O0 50- 0 5． 1 O． 1 5Fig．3 The system phase track diagramTab．1 Frequency of each position fault of bearingFirstly，the fault signal was denoised by thewavelet packet，and the obtained wave patterns areshown0 ．=△ 目0．-=鲁2figure 4J I J 』 I l1 f l 1 『O 1 000 2 000 3 000 4 000 5 000 6 000Sample serial number n0 1 UUU 2 000 3 000 4 UUU 5 000 6 000Sample serial number／,／(b)Fig．4 Be~re and after the wavelet packet de-noisingthe bearing outer ring fault signal waveformAs shown in Fig．5，the power spectrum are pre—liminarily analyzed by the wavelet packet． The ob—tained failure frequency of signal mainly appears be-tween 80 Hz and 150 Hz as shown the power spec-trum in Figure 5(b).

． According to the various characteristics parame—ter of bearing outer ring，the Dufing oscilator equa·tion could be designed as shown in equation 5.

= 105yly =105(一0．5y+ 一 +frCOS(105t)+input)(5)To evaluate the maximum lyapunov index ofDufing oscilator equation，the maximum lyapunovindex is shown in Fig．6． From this figure，it couldbe seen that the Duffing oscillator equation of thecritical threshold，i．e．fr．iS 0．737.

0 之 0 4 3 2 0 0 4CJ【 O I 5 O ) ) O b ( 5 0 _0 -5 -68 Hydromechatronics Engineering一 竺竺!!竺!竺竺 j0 2 000 4 000 6 000一 囤 匦 ]0 2 000 4000 6 000圈曼丑圈圈疆归 0 2 000 4000 6 000?O．O《匿圈受受受町 0 2000 4000 6 000一 o{臣要曼勇匦曼受0 2 000 4 000 6 000一 o《圈圈圉臣受受豳 ]0 2 000 4 000 6 000?O 0}—I．．．．r+-—7 r-- 10 2 000 4 000 6 000一ulul墨受曼璺圈圈曼]． O 4o 200．020．010420一；匝 ]0 2 000 4 000 6 000． 巨三曼旦堕 曼 ]0 2 000 4 000 6 000一 巨 受三三三虽 ]o 2 000 4 000 6 000一i匝巫匝砸受圈受 ]0 2 000 4 000 6 000．}巨至 三至 妇 ‘
0 2 000 4000 6 000一 圈亟圈匝 受豳[]0 2 000 4000 6 000哑 亟 三 ]0 2 000 4 000 6 000一i圈砸殛匝塑巫0 2 000 4 000 6000 0original signalO 08O 060 04言詈 o 02导0_O 02． 0 O4(a)O 01一 o o52 000 4 000 6 000trouble signa1． I .

(c)0 350 30O 250 20O l 50 1O0 O5O0．20 10420O 40．20420L Li_ _ _ ● ● l 一 ■ lL0 200 400 600 0 200 400 600The power spectrum oforinal signa~ The power spectrum offault signals0 200 400 600(b)0 4O 201 0O 5O200 400 6000 2O0 400 6000 20O 400 600The power spectrum of S23。 The power spectrum of S 3Fig．5 the signal power spectrum diagram with wavelet packet transform0 725 0 73O O 735 0 740 0 745 0 750 0 755 0 760Fig．6 The maximum lyapunov index ofthe bearing outer ringIn order to further analyze the bearing fault sig—nal after wavelet packet de—noising by using Duffingoscillator equation， the phase track diagram werepresented in Figure 7.

From Fig．7，it could be seen that the phasetrajectory of system mutations only when the fault sig—nal of bearing outer ring is added．If other signals areadded，the phase trajectory of system could be also inchaos states． Consequently，a conclusion could bedrawn that the system is only sensitive to some specK-ic frequency of fault signal and then the location ofthe fault could be determined．Therefore，these re—suits confirmed that the proposed method in this pa-per could be used to diagnose the rolling bearingfa11t4 2 O 8 6 4 2 0 REN Xueping，et al：Detection of Bearing Fault Signal Based on the W aveletand Chaos Theory 691．51 00．5S 0． 0．5． 1．0． 1．5． 1．5 一l 0 一O．5 0 O．5 1．O 1．5(f)(a)the phase track diagram without the test signal1 51．00．5S 0· 0．5一 1．0． 1．51．51．00．5S 0- 0 5- 1．0． 1．5一 l 5 —1．O 一0．5 0 0．5 1．0 l 5(f)(b)the phase track diagram with the normal signal1．51．00．5S 0一 0．5— 1 0． 1．5． 1．5 ．1．0 ．0．5 0 0．5 1．0 1 5 -1．5 -1．0 -0 5 0 0．5 1．0 1．5x(t) (f)(c)the phase track diagram with the fault signal (d)the phase track diagram with the fault signalofbearing outer ring ofbearing rolling elementFig．7 The phase track diagram of Dufing oscilator equation4．C：onclusionsIn this paper，the combination of wavelet packetde—-noising and chaos theory was adopted to distin-guish the fault signal of bearing outer ring．The basictheory and feasibility have been comprehensively ana—lyzed.

Through the real application of experimental da—ta，it has been confirmed that the proposed methodhas high accuracy and it is capable to distinguishlarge SNR of beating fault signa1．Furtherm ore，thismethod is comparatively simple and effective and itcould be applied to detect the fault of the bearing inthe future.

References：[1][2][3][4][5][6][7]GUO Yuxiu，NI Xiaohong，WANG Yutian．Study on the [8]fault diagnosis of roling mils based on the chaos weaksignal detection method[J]．Journal of Engineering De—sign，201I，18(3)：218—221.

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Case Western Reserve University Bearing Data CenterWebsite[EB／OL]．[2013—02—19]．http：／／www．ee-as．case．edu／laboratory／beating／.

(Continued from 108 page)108 Hydromechatronics Engineering[2][3]VEY OF ADVANCED PID PARAMETeR TUNINGMETHODS【J I．ACTA AUTOMAT ICA SINICA，2000，26(3)：343—355． 『4]JIANG Yaping，LI Tao，LIANG Gang，et a1．An Im—mune—based Model for Solving TSP[J]．Computer Engi—neering，2006，32(15)：165—167.

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de A1meida G M，e Silva V V R．．Nepomuceno E G，eta1．Application of Genetic Programming for Fine TuningP1D Controler Parameters Designed Through Ziegler—Nichols Technique lJ}．IJEC rURE NOTES IN COMPUT—ER SCIENCE．2005．3612：313.

摘要：PID控制系统的技术性能取决于系统控制器的控制参数。针对控制参数整定过程中各个技术指标之间的要求难以兼容的难题 ，提 出了一种基于免疫原理的 PID控制器参数整定方法。讨论了协调各技术指标关系的目标函数，描述了人体免疫系统与控制 系统的对应关系，构建 了基于免疫原理的控制参数整定模型，研究了具体的免疫控制算法。以二阶大滞后过程为控制对象，采用不同整定方法的仿真实验响应对比研究显示，基于免疫方法整定的控制参数，其 系统响应时间快，系统调节时间短，系统超调量小，技术指标之间兼容性能比较好。研究结果表明，所提 出方法是一种优化的 PID控制参数整定算法。

关键词：免疫原理；PID控制器；控制参数；参数整定方法中图分类号：TP273(Continued on 69 page)基于小波理论和混沌理论的轴承故障信号判别任学平，刘桐桐内蒙古科技大学 机械工程学院，内蒙古 包头 014010摘要 ：分析了小波包理论和混沌理论的基本理论知识．给出了将小波包降噪和 Dufing方程相结合来判断轴承故障信号的新方法。通过对仿真信号进行大量模拟，得 出该方法具有很好的应用效果。

最后将该方法应用到轴承外圈故障信号检测中，能准确地检测出轴承的故障所在，验证 了该方法的可行性 。

关键词：小波包降噪；Dufing振子；轴承故障；信号检测中图分类号：TH13