滾動(dòng)軸承缺陷振動(dòng)建模及沖擊特征提取*

李祥陽(yáng)，陳萬(wàn)強(qiáng)（西安航空學(xué)院陜西省泵類裝備工程研究中心 西安，710077）

滾動(dòng)軸承缺陷振動(dòng)建模及沖擊特征提取*

李祥陽(yáng)，陳萬(wàn)強(qiáng)
（西安航空學(xué)院陜西省泵類裝備工程研究中心 西安，710077）

以SKF6205-2RS深溝球軸承為研究對(duì)象，運(yùn)用Hertzian接觸理論、彈性力學(xué)及滾動(dòng)軸承幾何學(xué)，建立了可預(yù)測(cè)滾動(dòng)軸承不同損傷位置和程度的狀態(tài)模型，并通過(guò)Runge-Kutta數(shù)值方法獲取了系統(tǒng)響應(yīng)。計(jì)算結(jié)果表明：徑向負(fù)荷作用下，模型對(duì)內(nèi)圈、外圈、鋼球局部損傷所激勵(lì)的頻率及其諧波成分可進(jìn)行良好預(yù)測(cè)；闡述不同狀態(tài)下軸承振動(dòng)規(guī)律，論證連續(xù)Haar小波變換周期性；利用連續(xù)Haar小波變換在時(shí)間-尺度域上所特有的周期性結(jié)合自相關(guān)消噪，提出了一種滾動(dòng)軸承早期損傷特征提取的自相關(guān)連續(xù)Haar小波方法。診斷實(shí)例證明，這種方法能夠有效消除信號(hào)的噪聲，提取信號(hào)的弱沖擊成分。

滾動(dòng)軸承；預(yù)測(cè)模型；連續(xù)Haar小波；自相關(guān)消噪；弱沖擊成分

引 言

航空發(fā)動(dòng)機(jī)和航空燃?xì)鉁u輪機(jī)等重大裝備的核心技術(shù)問(wèn)題之一就是軸承，它對(duì)整個(gè)飛機(jī)制造業(yè)的發(fā)展水平有著舉足輕重的作用。對(duì)滾動(dòng)軸承進(jìn)行狀態(tài)評(píng)估可以提高裝備的可靠性，實(shí)現(xiàn)由“事后維修”到“預(yù)知維修”的轉(zhuǎn)變，提高飛機(jī)設(shè)備的管理水平，保證產(chǎn)品質(zhì)量；同時(shí)又為航空軸承可靠性增長(zhǎng)設(shè)計(jì)和服役性能控制奠定了方法基礎(chǔ)［1-2］。預(yù)測(cè)模型是一種有效的工具，它可以幫助深入理解產(chǎn)生損傷的機(jī)理，還可以用來(lái)檢驗(yàn)各種評(píng)估方法的實(shí)效性。文獻(xiàn)［3-4］從數(shù)字信號(hào)角度出發(fā)，用周期性脈沖序列來(lái)模擬單點(diǎn)和多點(diǎn)損傷對(duì)軸承的沖擊激勵(lì)，并給出了軸承損傷響應(yīng)模型，在研究軸承載荷分布基礎(chǔ)上采用脈沖序列模擬瞬態(tài)沖擊力。文獻(xiàn)［5］提出了一種數(shù)學(xué)模型，用來(lái)描述當(dāng)軸承通過(guò)損傷點(diǎn)時(shí)內(nèi)部軸承力的變化，并且采用VB編制了載荷影響及譜圖分析程序。文獻(xiàn)［6］分析了外負(fù)荷和損傷位置對(duì)振動(dòng)行為的影響，確定了外載荷作用下振動(dòng)的周期性與力傳遞的途徑。文獻(xiàn)［7］論證了滾動(dòng)軸承局部損傷信號(hào)的統(tǒng)計(jì)量具有近似循環(huán)平穩(wěn)性，指出由于離心力、陀螺力矩和潤(rùn)滑形態(tài)的影響，會(huì)導(dǎo)致接觸角的不斷變化和軸承部件的相對(duì)滑動(dòng)，從嚴(yán)格意義上講，軸承損傷信號(hào)是非平穩(wěn)信號(hào)，但仍然可以將其視為近似循環(huán)平穩(wěn)信號(hào)。文獻(xiàn)［8-9］研究了球軸承的自然振動(dòng)，拾取了外圈的徑向、軸向的振動(dòng)，對(duì)拾取信號(hào)進(jìn)行FFT譜分析和模態(tài)分析，導(dǎo)出了外圈自然振動(dòng)表達(dá)式、平面內(nèi)自然振動(dòng)頻率表達(dá)式和平面外自然振動(dòng)頻率表達(dá)式，分析了3種振動(dòng)頻率公式的精度。研究了單個(gè)和多個(gè)缺陷對(duì)應(yīng)的沖擊響應(yīng)特點(diǎn)，給出了損傷頻率的計(jì)算公式，但并沒(méi)有在時(shí)、頻域進(jìn)行分析，只是認(rèn)為損傷對(duì)軸承的沖擊可以用矩形波、三角波和半余弦波等脈沖序列來(lái)描述。以上研究從動(dòng)力學(xué)響應(yīng)的角度進(jìn)行統(tǒng)計(jì)模擬，沒(méi)有涉及軸承本身的建模問(wèn)題。文獻(xiàn)［10］提出考慮接觸-變形域的軸承仿真模型，討論了故障位置對(duì)振動(dòng)的影響。文獻(xiàn)［11］采用兩自由度方程模擬了內(nèi)、外圈和滾動(dòng)體故障，分析了軸承周期、準(zhǔn)周期和混沌運(yùn)動(dòng)。文獻(xiàn)［12］用有限元法研究了不平衡力作用下?lián)p傷軸承的動(dòng)特性。

筆者對(duì)已有的狀態(tài)模型作了改進(jìn)。在Fukata二自由度方程［13］基礎(chǔ)上引入了套圈-鋼球-支座的振動(dòng)耦合作用，綜合考慮了局部損傷的位置和程度，建立了可預(yù)測(cè)不同損傷位置和損傷程度的滾動(dòng)軸承狀態(tài)分析模型，揭示了不同狀態(tài)下的振動(dòng)規(guī)律。要獲得軸承服役的準(zhǔn)確信息，信號(hào)處理至關(guān)重要。FFT變換通過(guò)構(gòu)造不同類型的濾波器來(lái)滿足消噪的需要，卻無(wú)法消除遍布于整個(gè)頻域范圍內(nèi)的噪聲。應(yīng)用匹配濾波器時(shí)，如果輸入信號(hào)的信噪比較低，濾波器將輸出多峰，造成特征失效［14］。筆者在對(duì)預(yù)測(cè)響應(yīng)信號(hào)處理的基礎(chǔ)上，分析了連續(xù)Haar小波所特有的時(shí)間-尺度周期性，指出這種特性可以充分展示滾動(dòng)軸承損傷振動(dòng)信號(hào)中的周期性沖擊成分。已有的小波技術(shù)在軸承信號(hào)處理中的應(yīng)用往往從基函數(shù)相似性匹配的角度出發(fā)，筆者進(jìn)一步發(fā)掘小波基函數(shù)在滾動(dòng)軸承振動(dòng)信號(hào)中的應(yīng)用。結(jié)合自相關(guān)預(yù)處理，提出了一種自相關(guān)連續(xù)Haar小波變換方法用來(lái)識(shí)別軸承早期損傷模式。理論和實(shí)踐證明，這種方法能夠有效消除損傷信號(hào)中的干擾，使得在消除干擾信號(hào)的同時(shí)保留信號(hào)中的弱沖擊成分。

1 滾動(dòng)軸承預(yù)測(cè)模型

滾動(dòng)軸承受載接觸時(shí)，鋼球與滾道之間將發(fā)生非線性彈性變形，由Hertzian理論，點(diǎn)接觸彈性恢復(fù)力［15］為

其中：δ為彈性趨近量；K為總接觸剛度系數(shù)。

內(nèi)外圈分別為Ki，Ko，由以下兩式求的

其中：∑-ρ為接觸點(diǎn)的曲率和；γ*為變形系數(shù)，其值的計(jì)算參見(jiàn)文獻(xiàn)［15］。

圖1為滾動(dòng)軸承坐標(biāo)示意圖，第i個(gè)鋼球-套圈接觸變形δi為內(nèi)圈在x，y方向位移（xs，ys），鋼球位置角θi和游隙c的函數(shù)

圖1 滾動(dòng)軸承示意圖Fig.1 The reference axes of the rolling bearing

設(shè)（xb，yb）為鋼球的坐標(biāo)，由于振動(dòng)傳遞作用，考慮到鋼球自身的振動(dòng)，局部接觸變形為

其中：θi為軸承第i個(gè)鋼球的位置角。

其中：ωc為軸承公轉(zhuǎn)速度即保持器轉(zhuǎn)速；N為鋼球個(gè)數(shù)。

設(shè)軸的轉(zhuǎn)速為ω，則，其中：Db為鋼球直徑；Dp為軸承節(jié)圓直徑。

同理，設(shè)（xo，yo）為支座處的運(yùn)動(dòng)坐標(biāo)，接觸變形就可表示為

圖2為內(nèi)圈-鋼球-支座振動(dòng)耦合作用示意圖。根據(jù)Lagrange方程，動(dòng)力學(xué)方程為

其中：ms，mb，mo分別為內(nèi)圈與軸的質(zhì)量、鋼球質(zhì)量、外圈與支座質(zhì)量；cs為軸承內(nèi)阻尼；ko，co為支座剛度與阻尼。

圖2 滾動(dòng)軸承振動(dòng)系統(tǒng)坐標(biāo)圖Fig.2 The reference axes of the rolling bearing vibration system

2 局部損傷模型及響應(yīng)分析

2.1 軸承損傷建模

軸承長(zhǎng)期服役由于交互應(yīng)力作用會(huì)出現(xiàn)疲勞剝落等局部損傷，在損傷接觸域θd中，載荷作用會(huì)激發(fā)短時(shí)沖擊，沖擊可以表示為

對(duì)內(nèi)圈處的局部損傷誘發(fā)振動(dòng)可表示為

設(shè)kd為動(dòng)荷系數(shù)，其大小與損傷類型、形狀及尺寸等因素有關(guān)，通過(guò)調(diào)整kd的值可以模擬不同損傷程度；ε為載荷分配系數(shù)；β為外圈局部損傷角位置，根據(jù)文獻(xiàn)［15］則有

內(nèi)圈接觸角為

外圈處局部損傷誘發(fā)沖擊序列可表示為

滾動(dòng)體自轉(zhuǎn)時(shí)損傷處會(huì)與內(nèi)、外圈作用而激發(fā)兩個(gè)序列，同內(nèi)、外圈作用時(shí)產(chǎn)生的脈沖大小不同，表達(dá)式為

軸承外圈與支座固定，因此外圈接觸角為

2.2 軸承預(yù)測(cè)響應(yīng)分析

上述軸承損傷建模方法可以根據(jù)設(shè)計(jì)參數(shù)預(yù)測(cè)各種損傷信號(hào)，表現(xiàn)在模型上相當(dāng)于把式（5），（7）中的游隙c增加損傷激勵(lì)沖擊序列，使得

鋼球損傷總的振動(dòng)沖擊序列為

軸承診斷首要的任務(wù)是根據(jù)軸承損傷信號(hào)的特點(diǎn)選擇可行的處理方法。預(yù)測(cè)模型從動(dòng)力學(xué)角度描述了軸承損傷的內(nèi)在涵義，這對(duì)時(shí)序方法的選擇十分有益。以SKF6205-2RS深溝球軸承為研究對(duì)象進(jìn)行算例分析，有關(guān)參數(shù)為：轉(zhuǎn)軸質(zhì)量ms=5.5 kg，軸承阻尼cs=877.6 Ns/m，內(nèi)圈直徑為25.001 mm，外圈直徑為51.998 mm，厚度為0.5906 mm，鋼球直徑Db= 7.94 mm，節(jié)圓直徑Dp=39.039 mm，支座質(zhì)量mo= 12.638 kg，支座阻尼co=1796 Ns/m，支座剛度ko= 12.3×106N/m，軸承游隙e=0.1um，鋼球個(gè)數(shù)N= 9，轉(zhuǎn)速為1796 r/min，徑向載荷Fx=650 N，F(xiàn)y= 500 N，軸承為普通軸承鋼制。式（8）非線性很強(qiáng)，難以得到解析解，通過(guò)Runge-Kutta數(shù)值方法獲取系統(tǒng)響應(yīng)。

軸承從正常演化為異常，在波形和譜圖上會(huì)顯示一定的規(guī)律。圖3對(duì)應(yīng)正常狀態(tài)軸承的振動(dòng)，顯然從波形中看不出沖擊成分，這時(shí)軸承的振動(dòng)主要由轉(zhuǎn)頻fs和變?nèi)岫日駝?dòng)頻率［13］及其諧波組成。這是因?yàn)樵趶较蜉d荷的作用下，各鋼球的受力情況是不一樣的，隨著鋼球上的某一點(diǎn)的運(yùn)動(dòng)位置不同受力情況亦不一樣。隨著鋼球相對(duì)于徑向載荷作用線的移動(dòng)，軸承剛度以數(shù)倍于鋼球沿靜止套圈轉(zhuǎn)動(dòng)的頻率呈周期性變化。文獻(xiàn)［13］研究證明，當(dāng)轉(zhuǎn)速遠(yuǎn)離臨界轉(zhuǎn)速時(shí)，軸承振動(dòng)頻率表現(xiàn)為變?nèi)岫日駝?dòng)頻率振動(dòng)和它的諧波。

圖3 正常狀態(tài)波形與譜圖Fig.3 Waveform and spectrum of normal signal

以外圈為例進(jìn)行損傷模擬，圖4為模擬信號(hào)波形和功率譜圖。與正常狀態(tài)相比，其特點(diǎn)是時(shí)域?yàn)橐幌盗杏幸欢〞r(shí)間間隔的周期性沖擊波形，循環(huán)周期T=1/fo與損傷頻率相對(duì)應(yīng)，這是由于損傷接觸產(chǎn)生沖擊能量所致。譜圖主要為轉(zhuǎn)頻fs，損傷特征頻率fo=0.5 N 1-d/D（）

pfs=105.8 Hz及其高次諧波與調(diào)制成分。在承受來(lái)自鋼球方向的接觸載荷作用下，軸承支座處產(chǎn)生彎曲變形，并與滾動(dòng)體一起旋轉(zhuǎn)而產(chǎn)生振動(dòng)。Fukata二自由度方程實(shí)質(zhì)上描述了轉(zhuǎn)軸處的運(yùn)動(dòng)，缺乏式（8）耦合效應(yīng)，因此振動(dòng)頻率表現(xiàn)為低頻成分，反映不出損傷的循環(huán)周期沖擊與鋼球-支座振動(dòng)的高頻調(diào)制。圖4中，因?yàn)闆_擊能量較弱，低頻處譜線被軸承其他振動(dòng)成分壓制。同時(shí)，損傷接觸區(qū)產(chǎn)生的脈沖沖擊力受到載荷分布的調(diào)制，沖擊響應(yīng)為一種單邊振蕩衰減波形，是局部化的，通過(guò)圖5可以明顯看出特征頻率的各次諧波。

圖4 外圈損傷信號(hào)波形與譜圖Fig.4 Waveform and spectrum of outer ring damage signal

圖5 外圈損傷信號(hào)包絡(luò)譜圖Fig.5 Envelope spectrum of outer ring damage signal

3 自相關(guān)Haar小波原理

使用與信號(hào)波形最相似的基函數(shù)對(duì)信號(hào)分解，提取隱含異常特征是特征波形混合基分解的精髓［16］。小波函數(shù)中Haar小波在支撐域上是單位矩形波，標(biāo)準(zhǔn)的Haar小波為

Haar小波在時(shí)域中不連續(xù)，且為方形波，如圖6所示。連續(xù)Haar小波特有的時(shí)間（平移）和尺度的周期性可以充分展示信號(hào)中的周期性沖擊成分及其特點(diǎn)，用這種小波來(lái)分析由滾動(dòng)軸承局部損傷而誘發(fā)的周期性沖擊振動(dòng)有著其他小波不具備的特定優(yōu)勢(shì)。

圖6 Haar小波波形Fig.6 Waveform of Haar wavelet

3.1 連續(xù)Haar小波變換周期性

與二進(jìn)離散小波相比，連續(xù)小波具有以下兩個(gè)方面的優(yōu)勢(shì)［14］：a.連續(xù)小波變換的分割是使窗長(zhǎng)按尺度減低方向逐漸減少的，在尺度劃分上比二進(jìn)小波更加精細(xì)，信息冗余度高，對(duì)時(shí)間-尺度特性體現(xiàn)更加直觀，適合瞬態(tài)成分檢測(cè)；b.二進(jìn)小波要求基函數(shù)正交并且不具有“時(shí)不變”特性，對(duì)不確定時(shí)刻信號(hào)檢測(cè)時(shí)，則要求小波的時(shí)不變性。對(duì)于標(biāo)準(zhǔn)Haar小波，幅值變化最大倍數(shù)為2，設(shè)軸承損傷信號(hào)為s（ t），因此s（ t）的Haar小波變換在時(shí)間b上是以T為周期，在尺度j上以2T為周期的［17］，即

其中：n為自然數(shù)。

圖7為損傷信號(hào)局部放大圖，可以清晰看出周期性沖擊分量和軸承阻尼作用使沖擊波形衰減?？梢?jiàn)，對(duì)一個(gè)固定的尺度，當(dāng)Haar小波沿時(shí)間移動(dòng)整周期時(shí)，內(nèi)積是不變的，形成了時(shí)間上的周期性。同理，尺度整周期變化時(shí)由于整周期部分的內(nèi)積互相抵消，總的內(nèi)積仍保持不變，從而形成了尺度上的周期性。對(duì)損傷信號(hào)連續(xù)Haar小波變換正是利用時(shí)間-尺度上的周期性，將滾動(dòng)軸承周期沖擊衰減模式提取出來(lái)。

圖7 損傷信號(hào)時(shí)間周期性表示Fig.7 Time periodic expression of damage signal

3.2 連續(xù)Haar小波自相關(guān)分析及應(yīng)用

診斷實(shí)踐表明，滾動(dòng)軸承正常信號(hào)峭度值約為3，近似為高斯信號(hào)。除了軸承自身轉(zhuǎn)頻和變?nèi)岫日駝?dòng)外，還有許多隨機(jī)性干擾，有效去除可以大幅提高診斷的準(zhǔn)確性［14-16］。利用Haar小波變換提取周期性沖擊成分，利用自相關(guān)消噪可以預(yù)除噪聲干擾，兩者結(jié)合可對(duì)軸承早期損傷進(jìn)行精確識(shí)別。

時(shí)間序列（）s t按時(shí)間平均計(jì)算的各態(tài)歷經(jīng)隨機(jī)過(guò)程的自相關(guān)函數(shù)［1］為

s（ t），Rs（τ）中包含損傷信息，由于噪聲與噪聲之間的不相關(guān)性會(huì)隨著時(shí)間延遲而很快衰減為0，并且不需要任何關(guān)于信號(hào)與噪聲的譜分布和概率分布的先驗(yàn)知識(shí)。

自相關(guān)連續(xù)Haar小波處理流程如圖8所示，對(duì)圖4外圈損傷信號(hào)加強(qiáng)噪聲干擾來(lái)模擬軸承早期損傷，圖9為波形和譜圖?？梢?jiàn)，沖擊成分被大量噪聲掩蓋，直接進(jìn)行譜分析難以提取出特征譜線。將信號(hào)進(jìn)行連續(xù)Haar小波變換，如圖10所示。可以看出，兩圖中均有等間隔的脈沖成分，但是噪聲干擾使圖10（a）分辨率不高，自相關(guān)處理后圖10（b）的等間隔沖擊成分顯示清晰，周期約為0.009 5 s與損傷頻率一致。為了譜分析的需要，需要計(jì)算尺度與頻率的對(duì)應(yīng)關(guān)系［16］

圖8 連續(xù)自相關(guān)Haar小波流程圖Fig.8 The flow of autocorrelation-Continuous Haar wavelet

圖9 模擬信號(hào)波形與譜圖Fig.9 Waveform and spectrum of simulation signal

圖10 模擬信號(hào)Haar小波時(shí)間-尺度圖Fig.10 Haar wavelet time-scale map of simulation signal

其中：fj為尺度j對(duì)應(yīng)的頻率；fc為小波的中心頻率；δt為采樣周期。

選擇沖擊特征明顯的尺度進(jìn)行包絡(luò)譜分析如圖11所示。轉(zhuǎn)頻fs=ω/2π=29.5 Hz以及損傷頻率與其高次諧波清晰可辨?？梢?jiàn)，自相關(guān)連續(xù)Haar小波變換在提取淹沒(méi)在強(qiáng)大背景噪聲中的微弱周期性沖擊成分是有效的，且Haar小波形式簡(jiǎn)單，運(yùn)算方便，非常適合于基于圖像的在線監(jiān)測(cè)系統(tǒng)。

4 實(shí) 驗(yàn)

實(shí)驗(yàn)數(shù)據(jù)來(lái)源于美國(guó)凱斯西儲(chǔ)大學(xué)軸承研究中心［18］。該中心提供了深溝球軸承正常與內(nèi)外圈、鋼球損傷的實(shí)驗(yàn)數(shù)據(jù)，并設(shè)置了軸承的不同損傷程度以供研究者使用。實(shí)驗(yàn)裝置如圖12所示，實(shí)驗(yàn)軸承支承電動(dòng)機(jī)轉(zhuǎn)軸，電動(dòng)機(jī)風(fēng)扇端和驅(qū)動(dòng)端的軸承座上方各放置一個(gè)加速度傳感器來(lái)采集軸承的振動(dòng)加速度信號(hào)。分析的為6205-2RS JEM SKF深溝球軸承，轉(zhuǎn)速為1 772 r/min，采樣頻率為12 k Hz，結(jié)構(gòu)參數(shù)見(jiàn)文獻(xiàn)［18］。圖13為軸承早期損傷信號(hào)的時(shí)域波形。由于在確定尺度下連續(xù)Haar小波整周期移動(dòng)的內(nèi)積不變，對(duì)不同的信號(hào)連續(xù)Haar小波沿一個(gè)周期移動(dòng)內(nèi)積變化不同，因此導(dǎo)致不同信號(hào)在其時(shí)間-尺度圖上具有不同的特征。圖14為各種狀態(tài)的自相關(guān)連續(xù)Haar小波時(shí)間-尺度圖?？梢钥吹剑鞣N狀態(tài)在圖形中得到了明顯區(qū)分，正常情況主要表現(xiàn)為諧波形式；損傷狀態(tài)下均有等間隔的沖擊產(chǎn)生，其余信號(hào)成分的能量在圖形上產(chǎn)生了發(fā)散。這樣利用連續(xù)Haar小波所特有的時(shí)間-尺度周期性加之自相關(guān)消噪就可以分離弱沖擊。

圖11 自相關(guān)連續(xù)Haar小波處理后譜圖Fig.11 Spectrum of autocorrelation-continuous Haar wavelet processing

當(dāng)滾動(dòng)軸承在轉(zhuǎn)速為1 772 r/min時(shí)，鋼球內(nèi)外圈損傷頻率分別為139.205，159.928和105.871 Hz。從圖15可以看出，表征鋼球輕微故障的特征信息已被完全淹沒(méi)在振動(dòng)信號(hào)中，即使145.9 Hz附近都沒(méi)有明顯的譜峰，自相關(guān)連續(xù)Haar小波處理后選擇相應(yīng)尺度譜分析可以清楚地觀察到軸承鋼球損傷特征頻率139.2 Hz。利用自相關(guān)連續(xù)Haar小波對(duì)內(nèi)、外圈損傷進(jìn)行識(shí)別［19-20］，如圖16，17所示?？梢?jiàn)，特征頻率非常明顯，譜峰突出，與實(shí)際損傷類型相符。

圖12 實(shí)驗(yàn)裝置Fig.12 Experimental apparatus

圖13 典型型號(hào)時(shí)域波形Fig.13 Typical time domain waveform

圖14 實(shí)驗(yàn)信號(hào)自相關(guān)連續(xù)Haar小波時(shí)間-尺度圖Fig.14 Haar wavelet time-scale map of test signal

5 案例分析

滾動(dòng)軸承的服役性能是復(fù)雜工況下運(yùn)動(dòng)行為的綜合體現(xiàn)，貫穿于設(shè)計(jì)、制造、裝調(diào)和服役整個(gè)壽命周期。出廠前的全壽命周期實(shí)驗(yàn)是軸承企業(yè)掌握軸承服役行為的重要途徑。ABLT-1A型全壽命軸承實(shí)驗(yàn)機(jī)可以測(cè)試到軸承從正常到失效的全壽命周期振動(dòng)信號(hào)，實(shí)驗(yàn)現(xiàn)場(chǎng)如圖18所示。ABLT-1A型試驗(yàn)機(jī)一次能實(shí)驗(yàn)4個(gè)軸承，4個(gè)測(cè)試軸承都為6309深溝球軸承，實(shí)驗(yàn)機(jī)轉(zhuǎn)速為3 kr/min，振動(dòng)信號(hào)由探針傳感器直接接觸軸承外圈測(cè)量，采樣頻率為32 k Hz。

圖15 鋼球損傷頻譜Fig.15 Spectrum of the ball damage signal

圖16 內(nèi)圈損傷頻譜Fig.16 Spectrum of the inner ring damage signal

圖17 外圈損傷頻譜Fig.17 Spectrum of the outer ring damage signal

圖19（a）為監(jiān)測(cè)到的振動(dòng)信號(hào)。由于測(cè)試過(guò)程中噪聲很大，因此監(jiān)測(cè)到的振動(dòng)信號(hào)雜亂無(wú)章，沖擊特征信號(hào)基本被完全淹沒(méi)，得不到有用的失效信息。經(jīng)自相關(guān)-連續(xù)Haar小波消噪后，大量噪聲被剔除，可以觀察到多個(gè)明顯的沖擊且具有一定周期，如圖19（b）和（c）所示。對(duì)濾波后的信號(hào)進(jìn)行包絡(luò)譜分析，譜圖中特征頻率及其倍頻分量突出，這與外圈故障頻率相吻合，因此可以認(rèn)定實(shí)驗(yàn)軸承的外圈已經(jīng)損傷，結(jié)果與現(xiàn)場(chǎng)實(shí)際情況相吻合。

圖18 實(shí)驗(yàn)現(xiàn)場(chǎng)Fig.18 Experimental site

圖19 使用提取方法測(cè)得信號(hào)的消噪結(jié)果Fig.19 De-noising measured results of signal using the extraction method

6 結(jié) 論

1）在已有的二自由度方程基礎(chǔ)上建立了滾動(dòng)軸承局部損傷的預(yù)測(cè)模型，該模型可預(yù)測(cè)不同狀態(tài)下軸承振動(dòng)響應(yīng)。分析了預(yù)測(cè)響應(yīng)及其規(guī)律，指出滾動(dòng)軸承正常信號(hào)是由轉(zhuǎn)頻和變?nèi)岫日駝?dòng)頻率及其諧波組成，沒(méi)有沖擊特征；損傷振動(dòng)信號(hào)本質(zhì)上為循環(huán)的周期性脈沖序列，是損傷特征頻率及其高次諧波的組合和調(diào)制。

2）論證了連續(xù)Haar小波變換在時(shí)間-尺度上的周期性，運(yùn)用這種特定優(yōu)勢(shì)有效提取了滾動(dòng)軸承周期性沖擊模式。在基函數(shù)相似匹配的基礎(chǔ)上揭示了小波選擇深層次的理論，豐富了小波選擇的思路。

3）沖擊振蕩信號(hào)在時(shí)間-尺度域的圖形特征便于在諧波干擾下突出沖擊成分。自相關(guān)處理不需要任何關(guān)于信號(hào)與噪聲的譜分布和概率分布的先驗(yàn)知識(shí)，就能高效去除噪聲，用于信號(hào)預(yù)處理，增強(qiáng)了連續(xù)Haar小波時(shí)間-尺度圖的沖擊特征。實(shí)踐表明，該方法在滾動(dòng)軸承弱沖擊提取方面有較好的應(yīng)用前景。

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Abstract A cone-shaped MDOF-USM（multi-degree-of-freedom ultrasonic motor）is designed for research and application.The single-foot drive mode is adopted on the stator.A four-quadrant piezoelectric stack is employed as the exciting element to generate two-dimensional linear motion，and its movement mechanism is analyzed.The parametric model of the MDOF-USM is set up in ANSYS，and the finite element model is imported into the Optimus（a multi-disciplinary optimization software）.Optimization results indicate that the design requirements of the MDOF-USM are fulfilled.Finally，a MDOF-USM is successfully manufactured and applied to an x-y platform.

Keywords ultrasonic motors；multi-degree of freedom；optimal design；Optimus；x-y platform

Abstract To provide a real loading environment for structural design，product life estimation and health assessment，it is important to correctly identify the dynamic load and its position.In this paper，the fre-

quency domain method is used to study dynamic load position determination，and an equivalent load error method based on the vibration characteristic of the linear elastic system is proposed.This method constructs an object function with equivalent load error values at the same location from different measuring points.The actual position is where the equivalent load error is the smallest.Simulation on the tablet is perfect with both single point drive and double points one，and the method is still valid when noise is added.It provides the basis for complex structures and the determination of multiple loading locations.The experimental verification on a simply supported beam shows that this method can correctly identify the dynamic load location，is not sensitive to noise，and has good prospects for engineering applications.

Keywords load identification；position determination；equivalent load；frequency domain method

Abstract The floor of a car body experiences an abnormal vibration when a metro accelerates and brakes，which significantly deteriorates riding comfort.Theoretical analysis and field experiments are conducted to study this abnormal vibration，with resolution promoted and validation measurements.The short-time Fourier transform（STFT）time-frequency method is applied to tested data.It shows that the excitation of the abnormal floor vibration comes from the twice frequency of motor rotation.A mathematical model consisting of the motor shaft and gear rotor connected by a coupler is built to study the rotary dynamics of the traction system of the railroad vehicle＇s powered bogie.Analysis illustrates that the dynamics in the traction system experience a shaft misalignment between the motor shaft and gear rotor.The output torque of the gear rotor is obtained and shows that this misalignment can result in even frequencies oscillation of motor shaft rotation with the twice frequency dominated.The measurement is explained by the analysis，and it is shown that the abnormal vibration can be alleviated by eliminating this misalignment.Validation measurements are conducted after eliminating the misalignment and show that the twice frequency vibration of motor rotation dropp significantly，which reduces the root mean square and amplitude of acceleration of the car body floor by 41％and 53％，respectively.The measurements agree with the theoretical analysis，and a high level of riding comfort is obtained.

Keywords metro；car body；coupler；misalignment

Abstract The dispersion and multimode nature of a guided wave makes the analysis and identification of guided wave echoes complex.This paper proposes an echo identification method based on the frequency domain phase tracking.First，the frequency domain phase of the analyzed signals is extracted and normalized to the referenced signals of the direct propagation wave-packet.Then，the normalized values are pres-ented in an order spectrum.Finally，the location and recognition of each echo is determined with the analysis of the propagation path in the propagation medium.Simulation analysis and experimental results demonstrate the applicability and effectiveness of the proposed method.

Keywords Ultrasonic guided waves；dispersion characteristic；phase shift tracking；echo identification

Abstract Aiming at the end effect and mode mixing of empirical mode decomposition（EMD）in practical applications，an improved EMD method consisting of the following techniques is proposedafter analyzing several solutions.First，short signals are extended with genetic support vector regression，then an ensemble EMD combined with an alternative envelope for the sifting procedure is employed to process the extended signals.The simulation results of two nonlinear and one simulated fault signals，as well as comparisons with other EMD methods，verify the capability of the proposed method to alleviatethe end effect and mode mixing.Applying the proposed method and envelope analysis to fault diagnosis of the ball bearing with an inner raceway defect，the results demonstrate the superiority of the method in extracting fault characteristic information for engineering applications.

Keywords empirical mode decomposition；end effect；genetic support vector regression；mode mixing；envelope fitting；fault diagnosis

Abstract Variable predictive model based class discrimination（VPMCD）is a pattern recognition method that utilizes the inner relations among characteristic values extracted from the original data.In this paper，VPMCD and independent component analysis（ICA）are combined with the correlation coefficient in order to diagnosis the rolling bearing fault.First，the ICA is used to analyze vibration signals with different fault categories，and the independent components are extracted from each category.Second，the correlation coefficients are extracted from the samples and independent components of each category.The sum of the absolute values of the correlation coefficients is used as a characteristic value.Finally，the VPMCD classifier is used to recognize and classify the faults.The experimental results show that this method can be effectively applied to rolling bearing fault diagnosis.

Keywords variable predictive model based class discriminate；independent component analysis；correlation coefficient；rolling bearing；fault diagnosis

Abstract In the fault diagnosis of a hydro-turbine generating unit（HGU），kernel clustering is a valid non-supervised learning method.In order to solve the problems of kernel parameter selection and cluster center calculation，a novel electromagnetism-like artificial bee colony weighted kernel clustering（EAWKC）is proposed.First，after considering the influence of different symptoms，the data is weighted，and the clustering model is built based on the kernel Xie-Beni clustering index.Then，the electromagnetism-like artificial bee colony（ELABC）method is proposed and introduced in order to solve the objective function to realize the synchronized optimization of the clustering center，symptom weight and kernel parameter.The classification accuracy of EAWKC is checked by three of the UCI testing data sets and the HGU fault samples，and compared with the traditional method.The experimental results show that EAWKC has higher accuracy and can effectively complete the fault diagnosis.

Keywords hydroelectric generating unit；fault diagnosis；mercer kernel；weighted kernel clustering；electromagnetism-like artificial bee colony（ELABC）

Abstract In order to diagnose the abnormal noise of a certain type of diesel generating set，a new method of empirical mode decomposition（EMD）and Hilbert transform is proposed to analyze the non-stationary vibration signals of the generator main bearing，which can effectively extract the time-frequency characteristics of main bearing vibration signals.Comprehensive analyses are made based on the signals of diesel generating set noise，generator main bearing vibration and shaft system torsional vibration.The diagnostic results show that the torsional vibration amplitude values of the shaft system are too high，with diesel engine excitation causing the relative motion of pin coupling rubber parts surfaces.This procedure can produce dry friction force，which leads to the intermittent abnormal vibration noise of the shaft system.This method has reference value for the abnormal vibration noise diagnosis caused by friction of the rotary shaft system components.

Keywords vibration noise；empirical mode decomposition（EMD）；Hilbert transform；time-frequency characteristic；diagnosis

Abstract A novel method is proposed for finite element model updating and structural damage identification.The second generation wavelet is used as a platform for the multi-resolution representation of the updating information.This method reduces the uncertainty of the model updating process.At the lower level of resolution，the updating curve of stiffness is represented by a limited number of scaling and wavelet coefficients，which are realized with the generic algorithm（GA）.The complex finite element model is simplified by matching a number of modal parameters for easy manipulation in the updating process.Then，damage identification is carried out based on the simplified model.An example of a box girder with variable cross-sections is given for varying sectional properties to show the effectiveness of the proposed method.The results indicate that the proposed method is stable against variations in crack depth and changes in the number of concentrated cracks.The method is also suitable for the identification of multiple groups of cracks.

Keywords model updating；damage identification；multi-resolution analysis；wavelet

Abstract The rotor inter-turn short circuit fault is one of the main electrical faults of turbo-generators.It can cause the unbalanced electromagnetic force to act on the rotor，leading to rotor vibration and even greatly affecting the security of the generator and power system.The accurate calculation of the electromagnetic force is significant for the stability of the generator and power system.By establishing the generator finite element model，the operation of the generator under a rotor winding short-circuit fault is simulated.The changes of magnetic field lines and air-gap field density are analyzed for the impacts of short position，short circuit number of turns and excitation current on the electromagnetic force.The equivalent magnetic flux method and the magnetomotive force superposition method are compared and come up with some improvements for the equivalent magnetic flux method.The calculation results of the unbalanced electromagnetic force by the two methods are compared with the results of the finite element method，and reasons for the difference are pointed out.

Keywords rotor inter-turn short circuit fault；unbalanced electromagnetic force；the finite element method；the equivalent magnetic flux method；the magnetomotive force superposition method

Abstract In order to analyze the multi-component and multi-modulation characteristics of a gearbox fault signal，an optimal wavelet demodulation method based on singular value decomposition（SVD）is proposed.In this method，Morlet wavelet transform is used as an adaptive band-pass filter to extract the impact component in the geabox vibration signal.The minimum Shannon entropy is used as the wavelet timescale resolution index to optimize the Morlet wavelet parameters.Based on SVD，the optimal wavelet coefficient is utilized to determine the parameters.The new method can extract transient information better，reduce noise，effectively extract the signal period，and assure the validity of the fault feature recognition.The experimental results show that the proposed method can more accurately and effectively extract the fault characteristic hidden in the gearbox vibration signal.

Keywords singular value decomposition；continuous wavelet transform；parameter selection；feature extraction

Abstract Shaft orbit recognition is an important approach for the vibration state judgment of steam turbines.Extracting the features of shaft orbit images is not an easy task，and the traditional feature extraction methods are not perfect in comprehensiveness，accuracy and stability.In order to overcome these problems，a feature extraction method based on imitating human eyes is proposed for the steam turbine.This method imitates human eyes to extract the most important information of the image structure，boundary and region，and realizes the shape characterization comprehensively and accurately through full integration of the information.Three intelligent classification methods are used to test the effectiveness of the proposed method，and the experimental results prove that this feature extraction method for steam turbine is simple，efficient and accurate.

Keywords steam turbine；shaft orbit；condition monitoring；feature extraction；imitating human eyes

Abstract This paper presents a neural sliding mode control method for the mechanical arm with a non-singular inversion terminal in order to realize the trajectory tracking of a multi-joint robot arm with external

interference and modeling errors.First，an inversion-sliding-mode controller with a non-singular terminal sliding surface is designed based on the inversion method and the principle of sliding mode control.Then，the radial basis function（RBF）neural network adaptive law is designed against the uncertainty in the inversion sliding mode control system due to its modeling errors and external interference.The upper bound of this uncertainty is estimated online.Finally，the stability of the control system is proved using the Lyapunov Theorem.Simulation analysis and experimental results show that the proposed method can not only eliminate the chattering phenomenon in the system，but also improve its tracking performance and robustness.

Keywords inversion of control；neural network；sliding mode control；non-singular terminal

Abstract In environmental shaker testing applications，sigma clipping of the shaker drive signal is used to protect the test system.However，the clipped signal spectrum will no longer correspond exactly to the given power spectral density（PSD）.This may cause reduced vibration test reliability and even the wrong results，especially for modal tests.Both the power spectrum equalization control algorithm and PID control strategy are presented in order to compensate for the difference between certain spectra and the clipped specification.The results show that，in the case of Gaussian random signals，the two methods show almost the same compensation effect in terms of minimum error and iterative steps.For non-Gaussian random signals，however，the PID control strategy obtained fewer iterative steps and minor errors.

Keywords clipping；Gaussian signal；Non-Gaussian signal；power spectrum equalization；PID control

Abstract It is of great importance to useany prior information effectively and reasonably in the evaluation of small samples.Therefore，a new testability evaluation method based on mixed Beta prior distribution is presented，while considering both the credibility and the importance of prior information as well as the testability evaluation of complex equipment in small samples.The results show that，according to classical methods using small binomial samples，the lowerconfidence limits of product testability are conservative.Most of the measurements for the credibility of the prior information are based on data.The evaluation results are aggressive due to the missing sources of prior information.Thus，the conclusion is reasonable，and this method is promising for engineering applications.

Keywords testability evaluation；small sample；credibility；importance；mixed Beta distribution

Abstract In the processing of fault vibration signals，an improved CBI-LMD（cubic B-spline interpolation local mean decomposition）method based on self-adaptive waveform matching and an orthogonality criterion is proposed to combat the low decomposition accuracy of the cubic spline interpolation-based local mean decomposition（CSI-LMD）method.First，the raw vibration signal is extended with a self-adaptive waveform matching technique.Next，instead of CSI，the CBI is used to calculate the local means and envelope functions.Finally，the orthogonality criterion is used to set a stopping criterion for the product function.Simulation and experimental results show that the proposed method can effectively extract more accurate feature information in less time than CSI-LMD.

Keywords local mean decomposition；cubic B-spline interpolation；orthogonality criterion；fault rotor；vibration analysis

Abstract Aiming at the multi-functional properties of Pb-based lanthanumdoped zirconate titanates（PZT）sensors in concrete for structural health monitoring，which enable the sensors to simultaneously receive signals with different functions，a method for extracting the signals for variant purposes in the multi-functional PZT sensors is proposed.Because there is a difference in frequency ranges from different function signals，the vibration signal related to the overall structure performance and the acoustic emission signal associated with local damages are acquired based on the Mallat algorithm.The correctness of the extracted signals is verified by comparing with those from accelerometers and acoustic emission sensors.In addition，the proposed method is applied to the seismic damage experiment of a reinforced concrete frame-shear structure.The experimental results show that the vibration signal acquired by the proposed method can abstract the frequency of the structure.Meanwhile，the acoustic emission signal abstracted from PZT sensors can monitor the released energy caused by local damage.It can be concluded that the vibration signals and acoustic emission signals can be extracted using the proposed method，and the evaluation of the overall dynamic performance and local damage can be realized.

Keywords PZT sensors；wavelet analysis；acoustic emission；vibration test

Abstract Based on wavelet packet analysis and wavelet packet energy，the sum square of the wavelet packet energy change rate（WPERSS）damage index is proposed.The wavelet packet is applied to extract the damage index from both healthy and damaged structures for damage detection.A simply supported beam example is simulated in different damage and noise conditions.In addition，a double pylon cablestayed bridge model is tested in three damage conditions.The results are analyzed and prove the effectiveness of the WPERSS damage index.

Keywords wavelet packet；damage detection；damage index；sum square of energy change rate

Abstract To improve the impeller milling efficiency，the zero-order analytical method to construct the milling stability lobe diagram is investigated，which is used to determine parameter optimization of the FV520B material milling.The appropriate number of revolutions and the cutting depth processing can be selected，and the chatter occurrence can be avoided.By using this method，the required accuracy and surface quality for the workpiece can be achieved，and tool safety and machine reliability can be maintained.Through experimental data analysis，the parameters to construct the lobe diagram can be obtained.Different testing points in the constructed lobes are used to verify the method＇s correctness.This method has great significance in the actual impeller manufacturing process.

Keywords milling chatter；stability lobes；modal analysis；FV520B

Abstract A method for realizing tool wear condition monitoring using multi-feature of the cutting sound is presented.Based on empirical mode decomposition and Hilbert transformation theories，the cutting sound signal is analyzed.The energies of intrinsic modes and Hilbert spectrum in different frequency ranges are extracted as candidatefeatures of the monitoring signal.To solve the feature selection problem，the sup-port vector machine is selected as the classifier，and the multiple population genetic algorithm is used to optimize its input features.Then，the interference features are eliminated from the candidate features.After the classifier parameters are also optimized with the multiple population genetic algorithm，the test samples are classified with the optimized classifier，and the performances of the classifiers before and after optimization are compared.The results show that the performance of the optimized classifier is significantly improved，and the method can be used effectively for identification of the tool wear condition.

Keywords empirical mode decomposition；Hilbert transformation；cutting sound；support vector machine；multiple population genetic algorithm

Abstract The mode shape functions of the elastic beams with concentrated mass and stiffness and their frequency equations under typical boundary conditions are derived with Laplace transform.Using these equations，the inherent characteristics of a cantilever beam with a spring and lumped mass are obtained.Then，its modal parameters are recognized using the NEx T-ERA（eigen system realization algorithm based on the natural excitation technique）method.The analytic and experimental results show that modal parameters change with the stiffness and location of the mass and spring.

Keywords elastic beams；concentrated masses；lumped springs；NEx T-ERA；modal identification

Abstract The dynamic responses of a light-weight，high-speedplanar parallel robot are studied based on elastodynamics and experiments.First，according to the geometric and inertial nonlinearities of the mechanism，a set of linear ordinary differential equations of motion is built，and the dynamic responses of two typical configurations are analyzed.Second，an experimental setup that includes the test-bed mechanism of a 3-RRR light-weight parallel robot and a control system is developed.Finally，the experimentally measured residual vibrations of the manipulator are compared with the numerical results.It turns out that the experimental results agree with the numerical ones at configuration two，but differ at configuration one，where the experimentally measured dynamic response is self-excited vibrationand the simulation result is damped vibration.This shows that the robot has different dynamic responses at different configurations.

Keywords planar parallel robot；high-speed；elasto-dynamic；residual vibration

Abstract In order to effectively minimize the harmful vibration caused by rotor unbalance and to monitor the balance state in real time，an embedded on-line automatic balance system for a magnetic balancer is designed based on a modular design concept.First，an embedded controller is constructed using the combination of digital signal processing（DSP）and field-programmable gate array（FPGA）.At the same time，a mathematical model of an adaptive control algorithm is established based on the traditional influence coefficient method.Multithreaded balance control software and a user interface are developed using C and C# language，respectively.Lastly，the experiment is conducted on a domestic electric spindle to verify the function of the whole system.The experimental results show that the unbalance-induced vibration can decrease by 43％at 3 000 r/min.

Keywords rotor unbalance；online automatic balance；embedded control system；adaptive control；digital signal processing

Abstract While the existing de-noising algorithm requires prior knowledge of vibration signals，a new adaptive de-noising algorithm is proposed based on sparse coding and dictionary learning（DLSDF）.Depending on the essential attribute of different signals，the optimal dictionary of data-driving is learned from the raw data.The orthogonal matching pursuit algorithmworks out the sparsest coefficients.Then，the de-noised signal is reconstructed using sparse coding and the optimal dictionary.Simulation and experimental results show that the algorithm based on sparse coding and dictionary learning is adaptive，and denoising is stronger than the existing one.

Keywords dictionary learning；sparse coding；adaptive de-nosing；vibration signal

Abstract Multiscale entropy has begun to play an increasingly important role in the analysis of non-sta-tionary and nonlinear vibration signals.Changes in the sample entropy of different scales can reflect changes in the transformer windings of different runnings.In this paper，a novel feature extraction is proposed，and a new and effective feature parameter is provided to efficiently and quantitatively describe faulty signals of the transformer winding.The results of analyzing the experimental data of the winding vibration show that compared to sample entropy，multiscale entropy can efficiently realize the feature extraction of faulty signals.Therefore，it is feasible to introduce the effective feature parameter into the use of transformer winding vibration signal analysis.

Keywords multiscale entropy；transformer winding；vibration signal；feature extraction；effective feature parameter

Abstract To analyze milling chatter stability lobes and surface location error with worn tools，the cutting force coefficients under different worn conditions are identified using the full-discrete method.The stable critical cutting depth of the milling system increases after normal wear，and gradually declines as the work piece surface hardness increases.Then，the difference in the critical cutting depth between the normal wear tool and the wear free tool flank gradually becomes small.In addition，surface location error appears in some stable regions.Experimental results prove that the theoretical model can effectively optimize machining parameters with varying wear loss of the milling cutter.

Keywords milling cutter wear；full-discrete method；chatter stability lobes；surface location error

Abstract This paper proposes a method based on singular value decomposition technology in order to solve the hard target penetration overload signals de-noising problem.First，the signal reconstruction submatrix is established based on the principle of stability of the main singular components.Second，the″dominant of the former K singular values energy″rule is used to extract the effective order of singular value.Penetration signals are then decomposed based on the previous steps.Finally，the signal is reconstructed using the extracted effective singular values.Experiments show that the proposed method can effectively eliminate the vibration and noise hiding in the penetration process.The proposed method can get a better signal to noise ratio than when using the wavelet transform，as well as the exact penetration depths of the experiments.Ultimately，the proposed method is a feasible new method on penetration fuse signals processing.

Keywords penetration overload signals；singular value decomposition；signal reconstruction；signal to noise ratio

Abstract A method for flood discharge structure in the time domain is proposed in order to identify the operating modal parameters of high dams.First，useful information of the vibration signals is obtained by filtering the white noise and flow fluctuating noise using the wavelet threshold empirical mode decomposition filtering method.Then，the natural frequency and damping ratio of the system are identified using Hilbert-Huang transform（H HT）.Finally，the modal orders and operating modal parameters of the flood discharge structure are determined using the singular entropy increment theory.Simulation results show that this method has strong robustness and superior precision，and can effectively avoid frequency confounding.Its successful use on the No.5 overflow section of the Three Gorges gravity dam provides the basis of the safe operation and online dynamic non-destruction monitoring of the high dam flood discharge structure.

Keywords flood discharge excitation；operating modal；parameter identification；wavelet threshold-empirical mode decomposition filtering；Hilbert-Huang transform

Abstract The state models of the SKF6205-2RS deep groove ball bearing are set to predict the location and degree of its damage based on the Hertzian contact deformation theory，elastic theory and the geometry of the rolling bearing.Next，the system response is obtained using the Runge-Kutta numerical method.The calculation results prove that the frequency and harmonic components of the local damages of the inner ring，outer ring and ball under radial loads are well predicted.Moreover，the bearing vibration laws under different conditions are introduced to prove the periodicity of the continuous Haar wavelet transform.Finally，an autocorrelation continuous Haar wavelet method is proposed for early damage signals exacting of rolling bearings.The proposed approach is successfully applied to noise reduction and weak impulse feature extraction of bearing signals.

Keywords rolling bearing；prediction model；continuous Haar wavelet；autocorrelation denoising；weak impulse component

Advance in Electrokinetic Phenomena and Theory

Guo Wanlin1，2，F(xiàn)ei Wenwen1，2
（1.State Key Laboratory of Mechanics and Control of Mechanical Structures，Nanjing University of Aeronautics and Astronautics Nanjing，210016，China）
（2.Key Laboratory for Intelligent Nano Materials and Devices of the MOE，Nanjing University of Aeronautics and Astronautics Nanjing，210016，China）

Electrokinetic phenomena are a family of dynamic phenomena that occur commonly in the interfaces of solids and ionic liquids.All the electrokinetic phenomena originate from the same source of the electrical double layer formed at the interface，and are widely used in areas such as separation of mass and protein，purification of water，detection of molecules and particles and gene sequencing.A brief historical review of the discovery of electrokinetic phenomena is firstly given here，and the development of the electrical double layer theory is described in details.The important classical electrokinetic phenomena are introduced.Especially，the newly discovered electrokinetic phenomena in graphene are introduced and compared with the classical phenomena.The review is aimed to deepen our understanding of the physical mechanisms of electrokinetic phenomena and enhance their applications.

electrokinetic phenomena；solid/liquid interfaces；electrical double layer；graphene

Optimization of a Multi-degree of Freedom Ultrasonic Motor and Its Application on a x-y Platform

Zhu Hua，Wu Wencai，Liu Weidong，Pan Song
（State Key Laboratory of Mechanics and Control of Mechanical Structures，Nanjing University of Aeronautics and Astronautics Nanjing，210016，China）

The Equivalent Load Error Method of Dynamic Load Position Determination

Jiang Qi1，2，Zhang Fang1，2，Jiang Jinhui1，2，Zhu Dechun1，2，Xu Jing1，2，Pu Yuxue1，2
（1.State Key Laboratory for Strength and Vibration of Mechanical Structures，Nanjing University of Aeronautics and Astronautics Nanjing，210016，China）
（2.Institute of Vibration Engineering Research，Nanjing University of Aeronautics and Astronautics Nanjing，210016，China）

Car Body Vibration Analysis Subject to Coupling Misalignment in Traction System of Metro Vehicle

Shi Huailong，Wang Jianbin，Dai Huanyun，Wu Pingbo
（Traction Power Skate Key Laboratory，Southwest Jiaotong University Chengdu，610031，China）

Echo Identification of Phase Shift Tracking for Ultrasonic Guided Waves

Bo Lin，Liu Xiaofeng，F(xiàn)u Libin
（The State Key Laboratory of Mechanical Transmission，Chongqing University Chongqing，400044，China）

Applications of Improved Empirical Mode Decomposition in Machinery Fault Diagnosis

Ma Wenpeng1，2，Zhang Junhong1，3，Ma Liang1，3，Liu Yu1，Jia Xiaojie1
（1.State Key Laboratory of Engines，Tianjin University Tianjin，300072，China）
（2.School of Mechanical Engineering，Tianjin University of Technology Tianjin，300384，China）
（3.Renai College，Tianjin University Tianjin，301636，China）

The Rolling Bearing Fault Diagnosis Method Based on Correlation Coefficient of Independent Component Analysis and VPMCD

Cheng Junsheng，Ma Xingwei，Yang Yu
（State Key Laboratory of Advanced Design and Manufacture for Vehicle Body，Hunan University Changsha，410082，China）

Fault Diagnosis for Hydroelectric Generator Unit Based
on Electromagnetism-Like Artificial Bee Colony Weighted Kernel Clustering

Xiao Han1，2，F(xiàn)u Junfang1，Cai Daquan1，Zhou Jianzhong2，Xiao Jian2，F(xiàn)u Wenlong2
（1.Henan Electric Power Survey and Design Institute Zhengzhou，450000，China）
（2.School of Hydropower and Information Engineering，Huazhong University of Science and Technology Wuhan，430074，China）

Abnormal Vibration Noise Diagnosis for Rubber Pin Coupling of Diesel Generating Set

Wen Huabing，Peng Zilong，Meng Fanlin
（School of Energy and Power Engineering，Jiangsu University of Science and Technology Zhenjiang，212003，China）

Finite Element Model Updating and Damage Identification Based on the Second Generation Wavelet Analysis

Zhang Xin，Liu Yang，Gao Danying
（School of Civil Engineering，Zhengzhou University Zhengzhou，450001，China）

Contrast of Calculation Method for Unbalanced Electromagnetic Force Under Rotor Inter-Turn Short Circuit Faults

Wan Shuting，Dou Longjiang，Zhang Yu，Zhang Chengjie，Zhou Guowei
（Department of Mechanical Engineering，North China Electric Power University Baoding，071003，China）

The Feature Extraction Method of Non-Stationary Vibration Signal Based on SVD-Complex Analytical Wavelet Demodulation

Zhao Ling1，Liu Xiaofeng2，Lou Lu1
（1.The College of Information Science and Engineering，Chongqing Jiaotong University Chongqing，400074，China）
（2.The State Key Laboratory of Mechanical Transmission，Chongqing University Chongqing，400044，China）

A Shaft Orbit Identification Method Imitating Human Eyes for Steam Turbine

Chen Xiaoyue1，2，Zhou Jianzhong2，Xiao Jian2，F(xiàn)u Wenlong2，Zhang Weibo2，
Xia Xin2，Li Chaoshun2，Zhang Yongchuan2
（1.School of Electrical and Electronic Engineering，East China Jiaotong University Nanchang，330013，China）
（2.College of Hydropower and Information Engineering，Huazhong University of Science and Technology Wuhan，430074，China）

Manipulator Inversion of Non-Singular Terminal Neural Sliding Mode Control

Jia Yuqin1，2，Hu Xiaoxiong2
（1.Department of Mining Engineering，Lüliang University Lüliang，033001，China）
（2.School of Mechanical Engineering，Taiyuan University of Science and Technology Taiyuan，030024，China）

Power Spectral Density Compensation Algorithm for Signal Clipping in Vibration Test

Yan Lutao，Yang Zhipeng，Gao Fei，Liu Jie
（Beijing Institute of Structure and Environment Engineering Beijing，100076，China）

Evaluation of Complex Equipment Testability Based on Mixed Prior Distribution

Zhang Xishan1，Huang Kaoli2，Yan Pengcheng2，Lian Guangyao2，Wang Shaoguang2
（1.Four Department，Ordnance Engineering College Shijiazhuang，050003，China）
（2.One Research Room，Ordnance Technological Research Institute Shijiazhuang，050003，China）

Vibration Analysis of Fault Rotor Based on the Improved Local Mean Decomposition

Deng Linfeng，Zhao Rongzhen，Jin Wuyin
（School of Mechanical and Electronical Engineering，Lanzhou University of Technology Lanzhou，730050，China）

The Analysis and Application of Multi-functional PZT Sensors for Health Monitoring of Concrete Structures

Li Xu1，Huo Linsheng1，Li Hongnan1，Bai Fenglong2
（1.Faculty of Infrastructure Engineering，Dalian University of Technology Dalian，116023，China）
（2.Dalian Building Scientific Research＆amp；Design Stock Co.，LTD Dalian，116021，China）

Wavelet Packet Energy Based Damage Detection Index for Bridge

Zhu Jinsong1，2，Sun Yadan1
（1.School of Civil Engineering，Tianjin University Tianjin，300072，China）
（2.The Ministry of Education Key Laboratory of Coast Civil Structure Safety，Tianjin University Tianjin，300072，China）

Milling Stability Lobe Diagram Construction on FV520B Stainless Steel and Experimental Testing Investigation

Li Hongkun，Zhao Pengshi，Li Jingzhong，Dong Lei
（School of Mechanical Engineering，Dalian University of Technology Dalian，116023，China）

Tool Wear Condition Monitoring Based on Cutting Sound Signal and Optimized SVM

Zhang Kaifeng1，2，Yuan Huiqun1，Nie Peng2
（1.School of Mechanical Engineering＆amp；Automation，Northeastern University Shenyang，110819，China）
（2.School of Mechanical＆amp；Electrical Engineering，Shenyang Aerospace University Shenyang，110136，China）

Analytical Study and Modal Identification Experiment on Free Vibration of Beams Carrying Concentrated Masses and Springs

Wang Zhuang1，2，Hong Ming2，Xu Junchen2，Cui Hongyu2
（1.China Ship Development and Design Center Wuhan，430064，China）
（2.School of Naval Architecture Engineering，Dalian University of Technology Dalian，116024，China）

Dynamic Analysis and Experiment of High-Speed Planar Parallel Robots

Gao Mingwang1，Zhang Xianmin2
（1.School of Mechanical Engineering，Shandong University of Technology Zibo，255049，China）
（2.School of Mechanical and Automotive Engineering，South China University of Technology Guangzhou，510641，China）

Development and Validation of Embedded Control System for Rotor Online Automatic Balance

Fan Hongwei1，2，Jing Minqing1，Zhi Jingjuan1，Xin Wenhui3，Li Meng1，Liu Heng1
（1.School of Mechanical Engineering，Xi＇an Jiaotong University Xi＇an，710049，China）
（2.School of Mechanical Engineering，Xi＇an University of Science and Technology Xi＇an，710054，China）
（3.School of Mechanical and Precision Instrument Engineering，Xi＇an University of Technology Xi＇an，710048，China）

Adaptive De-noising for Vibration Signal Based on Dictionary Learning and Sparse Coding

Guo Liang1，Yao Lei2，Gao Hongli1，Huang Haifeng1，Zhang Xiaochen1
（1.School of Mechanical Engineering，Southwest Jiaotong University Chengdu，610031，China）
（2.Air-Breathing Hypersonic Technology Research Center，China Aerodynamics Research and Development Center Mianyang，621000，China）

Feature Research of Vibration Signal of Power Transformer Using Multiscale Entropy

Li Li1，Zhu Yongli2，Song Yaqi1
（1.School of Control and Computer Engineering，North China Electric Power University Baoding，071003，China）
（2.State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources，North China Electric Power University Beijing，102206，China）

The Influence of Wear Loss of Milling Cutter on Milling Stability and Surface Location Error

Wu Shi，Liu Xianli，Song Shenggang，Qu Da
（School of Mechanical and Power Engineering，Harbin University of Science and Technology Harbin，150080，China）

Research of the Penetration Overload Signals De-noising Method Based on Singular Value Decomposition

Zhao Haifeng1，2，3，Zhang Ya1，Li Shizhong1，Guo Yan1，2
（1.Faculty of Mechanical and Electrical Engineering，North University of China Taiyuan，030051，China）
（2.School of Mechatronics，Nanjing College of Information Technology Nanjing，210023，China）
（3.Department of Mechanical Engineering，University of Ottawa Ottawa，K1N 6N5，Canada）

Research on Operating Modal Parameter Identification for High Dam Discharge Structure Based on the Hilbert-Huang Transform

Zhang Jianwei，Zhu Lianghuan，Jiang Qi，Zhao Yu，Guo Jia
（College of Water Conservancy，North China University of Water Conservancy and Electric Power Zhengzhou，450011，China）

Vibration Modeling of Rolling Bearing Defect and Impulse Feature Extraction

Li Xiangyang，Chen Wanqiang
（Pump Equipment Engineering Research Center of Shaanxi Province，Xi＇an Aeronautical College Xi＇an，710077，China）

TB17；TH133.3

10.16450/j.cnki.issn.1004-6801.2015.04.030

李祥陽(yáng)，男，1972年10月生，講師。主要研究方向?yàn)闄C(jī)械設(shè)計(jì)及理論。曾發(fā)表《Rolling bearing fault diagnosis based on physical model and one-class support vector machine》（《ISRN Mechanical Engineering》2014，No.4）等論文。

E-mail：lxygyl@163.com

*科技部創(chuàng)新基金資助項(xiàng)目（13C26216105730）；陜西省自然科學(xué)基礎(chǔ)研究計(jì)劃資助項(xiàng)目（2014JM2-5069）

2014-12-03；

2015-03-01