孫 斌， 梁 超， 尚 達(dá)

(1．東北電力大學(xué)能源與動(dòng)力工程學(xué)院 吉林,132012) (2.吉林省電力科學(xué)研究院有限公司 長春，130021)

基于遞歸復(fù)雜網(wǎng)絡(luò)的滾動(dòng)軸承故障診斷*

孫 斌1， 梁 超1， 尚 達(dá)2

(1．東北電力大學(xué)能源與動(dòng)力工程學(xué)院 吉林,132012) (2.吉林省電力科學(xué)研究院有限公司 長春，130021)

針對(duì)滾動(dòng)軸承振動(dòng)信號(hào)的非線性、非平穩(wěn)的特征，提出了一種基于遞歸復(fù)雜網(wǎng)絡(luò)(recurrence complex network,簡稱RCN)的軸承故障診斷方法。首先，利用相空間重構(gòu)的理論將一維時(shí)間序列擴(kuò)展到高維相空間中，構(gòu)建遞歸矩陣；然后，研究了基于遞歸思想的定量遞歸分析方法；最后，采用遞歸復(fù)雜網(wǎng)絡(luò)的方法提取故障軸承振動(dòng)信號(hào)的非線性特征參數(shù)，對(duì)軸承正常狀態(tài)、內(nèi)圈故障、滾動(dòng)體故障和外圈故障振動(dòng)信號(hào)進(jìn)行分析。研究結(jié)果表明，RCN方法可以對(duì)滾動(dòng)軸承故障進(jìn)行較為準(zhǔn)確的診斷，與傳統(tǒng)方法相比具有較好的診斷效果。

遞歸復(fù)雜網(wǎng)絡(luò); 振動(dòng)信號(hào); 故障診斷; 波動(dòng)模態(tài)

引 言

滾動(dòng)軸承廣泛應(yīng)用于旋轉(zhuǎn)機(jī)械中，軸承失效是機(jī)械產(chǎn)生故障的重要原因之一；因此，對(duì)其故障進(jìn)行診斷識(shí)別具有重要的實(shí)際意義。滾動(dòng)軸承包括內(nèi)圈、外圈和滾動(dòng)體，當(dāng)其中的某一組件表面發(fā)生故障時(shí)，就會(huì)導(dǎo)致軸承與相鄰組件發(fā)生共振頻率，進(jìn)而對(duì)旋轉(zhuǎn)機(jī)械的正常運(yùn)行產(chǎn)生一定的影響。滾動(dòng)軸承的性能不僅與它的材料有關(guān)，日常的維護(hù)和及時(shí)的診斷也是其長期正常工作的有力保障[1-3]。目前，人們已經(jīng)提出了多種軸承故障診斷的方法，如儀器檢測和參數(shù)比較識(shí)別等方法。

復(fù)雜網(wǎng)絡(luò)是一種天然的結(jié)構(gòu)，代表了許多真實(shí)世界的系統(tǒng)[4]。近年來，復(fù)雜網(wǎng)絡(luò)在醫(yī)學(xué)、社會(huì)學(xué)等很多領(lǐng)域已經(jīng)有了蓬勃的發(fā)展。復(fù)雜網(wǎng)絡(luò)有著很好的靈活性和通用性，能代表所有的自然結(jié)構(gòu)，包括那些發(fā)生動(dòng)態(tài)變化的拓?fù)浣Y(jié)構(gòu)[5-8]。

軸承的振動(dòng)信號(hào)更多呈現(xiàn)出的是非線性及非平穩(wěn)的特性[9-10]。傳統(tǒng)的統(tǒng)計(jì)特征量分析方法僅能進(jìn)行粗略判斷，如頻譜分析法雖可以進(jìn)行精確的故障診斷，但首先要了解診斷對(duì)象的故障機(jī)理。近年來，人們更多地將非線性時(shí)間序列分析方法應(yīng)用于故障診斷[11]。例如，用基于遞歸定量分析(recurrence quantification analysis, 簡稱RQA)的方法對(duì)軸承的故障進(jìn)行診斷分析，但RQA方法只能提取相空間中時(shí)間相關(guān)的特征，且當(dāng)故障成分較為復(fù)雜時(shí)，診斷效果并不理想，對(duì)于這類問題用空間結(jié)構(gòu)信息如遞歸復(fù)雜網(wǎng)絡(luò)(recurrence complex network, 簡稱RCN)方法更為有效。筆者將遞歸復(fù)雜網(wǎng)絡(luò)的方法應(yīng)用于滾動(dòng)軸承的故障診斷中，從應(yīng)用的結(jié)果可以看出，RCN為滾動(dòng)軸承故障診斷提供了一種有效可靠的方法。

1 遞歸圖定量分析

1.1 遞歸圖的算法及原理

遞歸性是很多動(dòng)力系統(tǒng)最基本的特性，指系統(tǒng)的某些狀態(tài)在特定的時(shí)間具有的相似性質(zhì)[12]。Eckmannd等提出了遞歸圖的概念，將一維時(shí)間序列擴(kuò)展到二維相空間，能夠更清楚地認(rèn)識(shí)系統(tǒng)的遞歸性質(zhì)。Maizel提出以像素點(diǎn)0和1的方式將一維空間擴(kuò)展到二維平面空間，進(jìn)而顯示時(shí)間序列內(nèi)部的結(jié)構(gòu)特征。Zbilut等[13]提出了基于遞歸圖的定量遞歸分析的方法，對(duì)非線性動(dòng)力學(xué)系統(tǒng)的研究有積極的作用。

遞歸圖采用Takens提出的相空間重構(gòu)的思想，將一維時(shí)間序列重構(gòu)到高維相空間中，具體算法如下。

1) 對(duì)于m維相空間的嵌入矢量從時(shí)間序列uk(k=1,2，…，N)以延遲時(shí)間τ重構(gòu)得到的動(dòng)力系統(tǒng)為

(1)

2) 計(jì)算重構(gòu)相空間i和j兩點(diǎn)的距離

(2)

3) 計(jì)算遞歸值

(3)

其中：H(·)為heaviside函數(shù)；‖·‖為范數(shù)(這里采用Euclidean范數(shù))；ε為參考閾值。

1.2 實(shí)驗(yàn)數(shù)據(jù)的采集

實(shí)驗(yàn)數(shù)據(jù)采用美國凱斯西儲(chǔ)大學(xué)電氣工程實(shí)驗(yàn)室[14]的軸承實(shí)驗(yàn)數(shù)據(jù)進(jìn)行滾動(dòng)軸承故障的特征提取和智能診斷。圖1為滾動(dòng)軸承振動(dòng)實(shí)驗(yàn)臺(tái)，用來模擬軸承的振動(dòng)信號(hào)。實(shí)驗(yàn)所采用的滾動(dòng)軸承型號(hào)為SKF6205，裝置包括瑞恩電動(dòng)機(jī)、加速度傳感器、控制電子裝置以及計(jì)算機(jī)等。軸承的狀態(tài)為正常、內(nèi)圈故障、滾動(dòng)體故障和外圈故障4種，而軸承的故障損傷狀況為單一損傷，是由電火花在軸承內(nèi)圈、滾動(dòng)體和外圈人為加工的，損傷的直徑均為0.178 mm，深度為0.279 mm。測試軸承連接在電機(jī)上，電機(jī)的負(fù)荷為0～2.2 kW，額定轉(zhuǎn)速為1 797 r/min。當(dāng)傳感器位置變化時(shí)軸承幾種狀態(tài)下的振動(dòng)信號(hào)都隨之變化，但都呈現(xiàn)出非線性非平穩(wěn)的特性。因此，筆者在研究中將加速度傳感器垂直固定于感應(yīng)電機(jī)輸出軸支撐軸承上方的殼上，這與水平方向放置有著相同的診斷結(jié)果。

圖1 軸承振動(dòng)實(shí)驗(yàn)臺(tái)Fig.1 Experimental platform for the bearing

實(shí)驗(yàn)裝置由電機(jī)帶動(dòng)輸入軸，輸出軸帶動(dòng)負(fù)載。為了獲得最大負(fù)荷下的振動(dòng)信號(hào)，故障信號(hào)在驅(qū)動(dòng)端工作轉(zhuǎn)速下進(jìn)行采樣。采樣頻率為12 kHz，每種故障信號(hào)采集10組數(shù)據(jù)，采樣點(diǎn)數(shù)為10 000點(diǎn)。

2 振動(dòng)信號(hào)復(fù)雜網(wǎng)絡(luò)的拓?fù)湫再|(zhì)

2.1 度及度的分布

度是復(fù)雜網(wǎng)絡(luò)中單獨(dú)節(jié)點(diǎn)屬性中簡單而又重要的性質(zhì)。若v代表網(wǎng)絡(luò)中的某一節(jié)點(diǎn)，kv表示節(jié)點(diǎn)v的度，網(wǎng)絡(luò)的平均度對(duì)應(yīng)于RQA中的遞歸度

(4)

網(wǎng)絡(luò)的度分布可以表示為

(5)

其中：xv表示網(wǎng)絡(luò)中度為k的節(jié)點(diǎn)的個(gè)數(shù)。

度的大小描述了各種振動(dòng)模態(tài)之間的短程相關(guān)的關(guān)系，一個(gè)節(jié)點(diǎn)的度越大表明在實(shí)際中某種意義越重要。

2.2 聚類系數(shù)

聚類系數(shù)是刻畫復(fù)雜網(wǎng)絡(luò)結(jié)構(gòu)統(tǒng)計(jì)特性的一個(gè)重要概念。局部的聚類系數(shù)是網(wǎng)絡(luò)中各個(gè)節(jié)點(diǎn)的聚類系數(shù)，全局的聚類系數(shù)為網(wǎng)絡(luò)中所有節(jié)點(diǎn)局部聚類系數(shù)的平均值

(6)

(7)

其中：Ev為與節(jié)點(diǎn)v相連的閉合三角形結(jié)構(gòu)的數(shù)目；kv(kv-1)/2為與節(jié)點(diǎn)v相連的三元組的總數(shù)。

聚類系數(shù)反映網(wǎng)絡(luò)頂點(diǎn)間的緊密程度，聚類系數(shù)越大說明振動(dòng)信號(hào)之間的關(guān)系越緊密，反之則越稀疏。

2.3 平均最短路徑

網(wǎng)絡(luò)中兩節(jié)點(diǎn)i和j之間的距離dij定義為連接這兩個(gè)節(jié)點(diǎn)之間最短路徑的邊數(shù)，而網(wǎng)絡(luò)中的平均最短路徑則表示任意兩節(jié)點(diǎn)之間距離的平均值

(8)

其中：N為網(wǎng)絡(luò)中的頂點(diǎn)數(shù)；i和j分別為網(wǎng)絡(luò)中的任意兩個(gè)節(jié)點(diǎn)。

平均最短路徑反應(yīng)的是網(wǎng)絡(luò)中一種振動(dòng)信號(hào)向另一種振動(dòng)信號(hào)變化時(shí)所經(jīng)歷的過程，平均最短路徑越大，則變化的過程越復(fù)雜。

2.4 復(fù)雜網(wǎng)絡(luò)的探索

網(wǎng)絡(luò)中的模塊度可定義為

(9)

其中：‖e2‖表示矩陣e2的各元素之和。

物理意義如下：網(wǎng)絡(luò)中連接兩種同類型節(jié)點(diǎn)的邊的比例，減去同樣社團(tuán)結(jié)構(gòu)下任意連接這兩個(gè)節(jié)點(diǎn)的邊的比例的期望值。若社團(tuán)內(nèi)部邊的比例不大于任意連接時(shí)的期望值，則Q=0，而Q最大為1。通過定義可知，Q越大，所對(duì)應(yīng)的網(wǎng)絡(luò)越復(fù)雜，因此模塊度Q可以作為衡量網(wǎng)絡(luò)結(jié)構(gòu)的有效標(biāo)準(zhǔn)。

3 故障特征分析

3.1 遞歸定量特性分析

筆者采取以下幾種參數(shù)進(jìn)行遞歸定量特征分析。

1) 遞歸率(recurrence rate)指遞歸圖中遞歸點(diǎn)在圖中所占有的比率

(10)

2) 確定率(determinism)指平行對(duì)角線線段數(shù)量與總的遞歸點(diǎn)數(shù)的比值

(11)

其中：l為平行對(duì)角線線段的長度；p(l)表示線段長度為l的頻率，這里lmin取2。

3) 平均對(duì)角線長度指對(duì)角線方向線段長度的加權(quán)平均值

(12)

4) 遞歸熵(entropy)反應(yīng)了遞歸圖中對(duì)角線長度的熵分布

(13)

根據(jù)遞歸矩陣的定義，分別以i和j作為橫、縱坐標(biāo)繪出遞歸矩陣R所得到的圖形即為遞歸圖(RP圖)，該方法反映到圖形上的實(shí)質(zhì)就是采用黑白圖形來刻畫時(shí)間序列。圖2為軸承在4種狀態(tài)振動(dòng)信號(hào)下的遞歸圖。從RP圖中可以看出，正常狀態(tài)的RP圖是均勻布滿的，不存在與主對(duì)角線平行直線的點(diǎn)，表明振動(dòng)信號(hào)是平穩(wěn)隨機(jī)的。幾種故障圖則存在不規(guī)則的圖案，且存在與主對(duì)角線平行的點(diǎn)，這說明振動(dòng)信號(hào)不是平穩(wěn)的，系統(tǒng)存在不確定成分。

圖3是軸承4種狀態(tài)下的遞歸參數(shù)分布圖。從圖中可知，遞歸參數(shù)圖中外圈的幾個(gè)參數(shù)值都比較大，說明在遞歸圖中沿對(duì)角線的線條紋理比較明顯，系統(tǒng)的結(jié)構(gòu)清晰完整，確定性較強(qiáng)，這與圖2中的RP圖是一致的。內(nèi)圈和滾動(dòng)體與正常的比變化較為復(fù)雜，整體表現(xiàn)為：內(nèi)圈>正常>滾動(dòng)體。幾種遞歸參數(shù)都有不同趨勢的變化，基于遞歸定量特性分析，僅僅從遞歸圖中的線段分布情況量化軸承的動(dòng)力學(xué)特性，只能對(duì)其故障進(jìn)行大致的判別，但不能進(jìn)行較為準(zhǔn)確的故障分析，診斷效果不是很理想。

圖2 軸承4種狀態(tài)振動(dòng)信號(hào)遞歸圖Fig.2 Recurrence plot of vibration signal of four differential type bearings

圖3 軸承4種狀態(tài)振動(dòng)信號(hào)的遞歸參數(shù)分布圖Fig.3 Recurrence parameter of vibration signal of four differential type bearings

3.2 網(wǎng)絡(luò)特性的空間分布特征

鄰接矩陣是復(fù)雜網(wǎng)絡(luò)研究分析的基礎(chǔ)，而從時(shí)間序列映射到復(fù)雜網(wǎng)絡(luò)，構(gòu)造出相應(yīng)的鄰接矩陣又是復(fù)雜網(wǎng)絡(luò)應(yīng)用于時(shí)間序列分析的關(guān)鍵。Donner等[15]研究發(fā)現(xiàn)，可直接將遞歸矩陣視為網(wǎng)絡(luò)的鄰接矩陣，提出了遞歸復(fù)雜網(wǎng)絡(luò)的概念。其優(yōu)點(diǎn)在于直接將時(shí)間序列定義為網(wǎng)絡(luò)結(jié)構(gòu)，且能從相空間中遞歸矩陣的空間角度量化動(dòng)力學(xué)系統(tǒng)，克服了其他構(gòu)造方法在概念上的限制，為動(dòng)力系統(tǒng)中的非線性時(shí)間序列分析提供了統(tǒng)一的概念和實(shí)際框架。

圖4為軸承4種狀態(tài)下一組數(shù)據(jù)通過相空間重構(gòu)得到的遞歸點(diǎn)所構(gòu)建的復(fù)雜網(wǎng)絡(luò)。從圖中可看出，軸承不同狀態(tài)所對(duì)應(yīng)的復(fù)雜網(wǎng)絡(luò)有著明顯的不同。圖中周圍的數(shù)字表示遞歸矩陣的遞歸節(jié)點(diǎn)，復(fù)雜網(wǎng)絡(luò)中一個(gè)節(jié)點(diǎn)與另一個(gè)節(jié)點(diǎn)間有連接，反映在振動(dòng)信號(hào)中是一種振動(dòng)模態(tài)向另一種振動(dòng)模態(tài)的轉(zhuǎn)變，即為振動(dòng)信號(hào)的波動(dòng)模態(tài)。不同的波動(dòng)模態(tài)說明不同的振動(dòng)特征，通過波動(dòng)模態(tài)的轉(zhuǎn)變，對(duì)軸承振動(dòng)信號(hào)的變化有了更清晰的認(rèn)識(shí)， 從而能夠更好地對(duì)其故障進(jìn)行診斷分析。如圖4(a)中節(jié)點(diǎn)13指向節(jié)點(diǎn)33，表示軸承正常狀態(tài)下這兩個(gè)節(jié)點(diǎn)代表的波動(dòng)模態(tài)之間的轉(zhuǎn)換。不同狀態(tài)下不同振動(dòng)信號(hào)連接的緊密程度不同，反應(yīng)出各種信號(hào)在網(wǎng)絡(luò)中的強(qiáng)弱不同，從而造成網(wǎng)絡(luò)的空間結(jié)構(gòu)不同。從網(wǎng)絡(luò)圖中直接得到了相空間中軌跡遞歸的幾何拓?fù)浣Y(jié)構(gòu)，為研究動(dòng)力學(xué)系統(tǒng)提供了更加豐富的信息。

圖4 軸承4種狀態(tài)復(fù)雜網(wǎng)絡(luò)Fig.4 Complex network of four differential type bearings

當(dāng)軸承發(fā)生故障時(shí)，振動(dòng)信號(hào)呈現(xiàn)非線性、非平穩(wěn)的特性，對(duì)應(yīng)的復(fù)雜網(wǎng)絡(luò)也是不同的，而網(wǎng)絡(luò)中的參數(shù)也呈現(xiàn)出不同的變化特征。表1～表4分別給出了軸承4種狀態(tài)下，基于RCN參數(shù)平均度k、聚類系數(shù)C、平均最短路徑L和模塊度Q的診斷結(jié)果。

如表1所示，幾種狀態(tài)下振動(dòng)信號(hào)呈現(xiàn)出不同的度值，整體表現(xiàn)為滾動(dòng)體的度值相對(duì)較小，內(nèi)圈和外圈故障也呈現(xiàn)出不同的變化，說明在軸承故障點(diǎn)撞擊其他的部件時(shí)導(dǎo)致振動(dòng)信號(hào)發(fā)生了變化。內(nèi)圈故障中，度值比正常的略大，滾動(dòng)體中度值略小，而外圈中度值則比較大。說明各個(gè)故障振動(dòng)信號(hào)所對(duì)應(yīng)的網(wǎng)絡(luò)模態(tài)會(huì)出現(xiàn)一定概率的波動(dòng)，網(wǎng)絡(luò)中模態(tài)間有一定的相互轉(zhuǎn)變(中間不需要經(jīng)過其他模態(tài)的直接轉(zhuǎn)變)。一種模態(tài)與另一種模態(tài)間的短程相關(guān)性越強(qiáng)，這種模態(tài)的度越大，則說明這種模態(tài)越重要，度小的波動(dòng)模態(tài)較少發(fā)生。軸承不同的狀態(tài)反映出的頻發(fā)或不頻發(fā)的振動(dòng)模態(tài)種類是不同的。

表2是基于參數(shù)C的診斷結(jié)果，整體呈現(xiàn)的是正常狀態(tài)的聚類系數(shù)大于故障狀態(tài)。這是由于在正常狀態(tài)下軸承具有較好的聚類性質(zhì)。內(nèi)圈的聚類系數(shù)較大，滾動(dòng)體和外圈的則較小。在軸承旋轉(zhuǎn)過程時(shí)，故障表面撞擊軸承其他的部位，使得振動(dòng)信號(hào)發(fā)生變化，從而對(duì)網(wǎng)絡(luò)的聚類性質(zhì)有一定的影響。

表1 基于參數(shù)k的診斷結(jié)果

表2 基于參數(shù)C的診斷結(jié)果

表3 基于參數(shù)L的診斷結(jié)果

表4 基于參數(shù)Q的診斷結(jié)果

如表3所示，內(nèi)圈和外圈的平均最短路徑大于正常情況下的，說明內(nèi)圈和外圈振動(dòng)信號(hào)比較復(fù)雜，而滾動(dòng)體的則整體小于正常情況，說明其振動(dòng)信號(hào)所對(duì)應(yīng)的波動(dòng)網(wǎng)絡(luò)的復(fù)雜性較小。平均最短路徑體現(xiàn)了網(wǎng)絡(luò)的任意兩種模態(tài)之間轉(zhuǎn)換所經(jīng)歷的時(shí)間，借此反映振動(dòng)信號(hào)變化的復(fù)雜性。平均最短路徑越大，說明網(wǎng)絡(luò)中一種模態(tài)向另一種模態(tài)轉(zhuǎn)換時(shí)所經(jīng)過的中間模態(tài)越多，軸承振動(dòng)信號(hào)變換越復(fù)雜。

由圖5可知，幾種故障所對(duì)應(yīng)的網(wǎng)絡(luò)累計(jì)節(jié)點(diǎn)度與度分布雙對(duì)數(shù)關(guān)系較為復(fù)雜，整體表現(xiàn)為度值比較集中，度值較高和較低的比較少，且分布曲線能基本擬合為一條直線，即符合冪律分布。說明軸承的每種波動(dòng)模態(tài)出現(xiàn)的次數(shù)在一個(gè)較長的時(shí)間段內(nèi)遵循較多的模態(tài)出現(xiàn)的概率較少，而較小的模態(tài)出現(xiàn)的概率則較大。故障振動(dòng)信號(hào)出現(xiàn)這種變化規(guī)律可能是由于所承受的載荷不均造成的，這又從側(cè)面反映出軸承復(fù)雜的動(dòng)力學(xué)特征，也反映出其網(wǎng)絡(luò)模態(tài)隨時(shí)間的變化是非線性的特征。每種故障網(wǎng)絡(luò)中都有一定概率產(chǎn)生較大的波動(dòng)模態(tài)，而這種波動(dòng)模態(tài)對(duì)應(yīng)著不同的故障典型振動(dòng)變化信號(hào)。通過對(duì)不同故障典型振動(dòng)信號(hào)的分析，量化軸承的動(dòng)力學(xué)特征，從而對(duì)軸承故障進(jìn)行準(zhǔn)確的診斷。

圖5 軸承故障網(wǎng)絡(luò)累計(jì)節(jié)點(diǎn)度與度分布Fig.5 Degree distribution of the bearing fault complex network

表4為幾種狀態(tài)下網(wǎng)絡(luò)的模塊度，從表中可知，滾動(dòng)體的模塊度較大，外圈的較小，而模塊度越大的對(duì)應(yīng)的網(wǎng)絡(luò)也越復(fù)雜，這與上文的復(fù)雜網(wǎng)絡(luò)一致。通過模塊度的變化對(duì)復(fù)雜網(wǎng)絡(luò)社區(qū)進(jìn)行較為精確的探索，對(duì)網(wǎng)絡(luò)的社團(tuán)結(jié)構(gòu)進(jìn)行準(zhǔn)確的分析，從而對(duì)故障軸承進(jìn)行較為準(zhǔn)確的診斷識(shí)別。

4 討 論

軸承內(nèi)圈發(fā)生故障時(shí)，分布到故障點(diǎn)的靜態(tài)載荷密度隨內(nèi)圈的旋轉(zhuǎn)發(fā)生周期性的變化，內(nèi)圈隨著軸承的轉(zhuǎn)動(dòng)發(fā)生旋轉(zhuǎn)，因此其損傷點(diǎn)有時(shí)位于載荷區(qū)內(nèi)，有時(shí)位于載荷區(qū)外，振動(dòng)信號(hào)變化較為復(fù)雜，對(duì)應(yīng)網(wǎng)絡(luò)中的平均最短路徑、聚類系數(shù)較大，網(wǎng)絡(luò)比較稀疏。滾動(dòng)體故障中，損傷點(diǎn)與內(nèi)圈接觸時(shí)產(chǎn)生的脈沖力要通過滾動(dòng)體及滾動(dòng)體與外圈界面?zhèn)鞑ズ蟛抛饔糜谕馊Γ跐L動(dòng)體內(nèi)及通過界面?zhèn)鞑r(shí)的能量有損失，其振動(dòng)信號(hào)的復(fù)雜性較小，對(duì)應(yīng)于網(wǎng)絡(luò)中聚類系數(shù)和平均最短路徑較小，而網(wǎng)絡(luò)較為復(fù)雜。外圈故障中，分布到故障點(diǎn)的靜態(tài)載荷密度不變，聚類系數(shù)和模塊度相應(yīng)較小，網(wǎng)絡(luò)較為稀疏，但由于傳感器位于徑向載荷密度最大的地方，振動(dòng)信號(hào)比較復(fù)雜，因此其對(duì)應(yīng)的平均最短路徑比較大。從以上的網(wǎng)絡(luò)參數(shù)分析中可以看出，軸承的振動(dòng)信號(hào)表現(xiàn)出較小的平均節(jié)點(diǎn)度、較高的聚類系數(shù)和平均最短路徑。隨著度值的不同，聚類系數(shù)、平均最短路徑和模塊度變化比較復(fù)雜，度值大的聚類系數(shù)不一定大，而度值小的聚類系數(shù)可能較大，說明軸承網(wǎng)絡(luò)特性既不是隨機(jī)的，也不同于小世界網(wǎng)絡(luò)。振動(dòng)信號(hào)中的波動(dòng)模態(tài)大多呈現(xiàn)出短程相關(guān)性，因此軸承振動(dòng)信號(hào)的波動(dòng)并不是無關(guān)聯(lián)的隨機(jī)過程，識(shí)別這些具有拓?fù)浣y(tǒng)計(jì)重要性的節(jié)點(diǎn)模態(tài)對(duì)于準(zhǔn)確發(fā)現(xiàn)軸承的故障有積極的意義。

5 結(jié)束語

軸承的信號(hào)呈現(xiàn)的是非線性、非平穩(wěn)的特性。筆者首先采用傳統(tǒng)的遞歸定量特性分析的方法對(duì)軸承的故障進(jìn)行診斷，但由于此方法是基于遞歸圖上水平方向、垂直方向和對(duì)角線方向的遞歸性質(zhì)的研究，因此診斷效果并不理想。與傳統(tǒng)的診斷方法相比，采用遞歸復(fù)雜網(wǎng)絡(luò)的方法，從網(wǎng)絡(luò)的角度量化軸承的動(dòng)力學(xué)特性，研究了幾種狀態(tài)下的振動(dòng)信號(hào)間的變化規(guī)律，從空間的角度更好地解讀系統(tǒng)的幾何結(jié)構(gòu)。結(jié)果表明，基于RCN的方法比基于RQA的方法更能揭示軸承的遞歸性質(zhì)和空間拓?fù)浣Y(jié)構(gòu)，可對(duì)軸承振動(dòng)故障進(jìn)行較為準(zhǔn)確的診斷分析。

[1] 蘇連成，李興林，李小俚，等.風(fēng)電機(jī)組軸承的狀態(tài)監(jiān)測和故障診斷與運(yùn)行維護(hù)[J].軸承，2012(1)：47-53.

Su Lianchen, Li Xinglin, Li Xiaoli, et al. Condition monitoring and fault diagnosis and operating maintenance systems for wind turbine bearings[J]. Bearing, 2012(1):47-53. (in Chinese)

[2] Arabian-Hoseynabadi H, Oraee H, Tavner P J. Wind turbine productivity considering electrical subassembly reliability[J]. Renewable Energy, 2010,35(1):190-197.

[3] 范光輝，何加群.再論風(fēng)電軸承的技術(shù)和市場[J].軸承，2012(3)：56-59.

Fan Guanghui, He Jiaqun. Further discussion on technology and market of wind turbine bearings[J]. Bearing, 2012(3):56-59. (in Chinese)

[4] 周磊，龔志強(qiáng)，支蓉，等.基于復(fù)雜網(wǎng)絡(luò)研究中國溫度變化的區(qū)域特征[J].物理學(xué)報(bào)，2009，58(10)：7351-7357.

Zhou Lei, Gong Zhiqiang, Zhi Rong, et al. Study on the regional characteristics of the temperature changes in China based oncomplex network[J]. Acta Physica Sinica, 2009,58(10):7351-7357. (in Chinese)

[5] André R B, Dalcimar C, Odemir M B. Texture analysis and classification: a complex network-based approach[J]. Information Sciences, 2012,219:168-180.

[6] Mendes G A, da Silva L R, Herrmann H J. Traffic gridlock on complex networks[J]. Physica A, 2012,391(2):362-370.

[7] Wang Na, Li Dong, Wang Qiwen. Visibility graph analysis on quarterly macroeconomic series of China based on complex network theory[J]. Physica A, 2012,391(24):6543-6555.

[8] 孫斌，尚達(dá).復(fù)雜網(wǎng)絡(luò)在轉(zhuǎn)子故障診斷中的應(yīng)用[J].振動(dòng)、測試與診斷，2012，32(6)：1-6.

Sun Bin, Shang Da. The complex network in application of rotor fault diagnosis[J]. Journal of Vibration, Measurement & Diagnosis, 2012,32(6):1-6. (in Chinese)

[9] 李輝，鄭海起，唐立偉.基于階次跟蹤和變換時(shí)頻譜的軸承故障診斷[J].振動(dòng)、測試與診斷，2010，30(2)：138-142.

Li Hui, Zheng Haiqi, Tang Liwie. Bearing fault diagnosis based on order tracking and Teager-Huang transform[J]. Journal of Vibration, Measurement & Diagnosis, 2010,30(2):138-142. (in Chinese)

[10]Andrew K, Anoop V. Analyzing bearing faults in wind turbines: a data-mining approach[J]. Renewable Energy, 2012,48:110-116.

[11]白寶丹，汪源源，楊翠微.基于遞歸復(fù)雜網(wǎng)絡(luò)的房顫術(shù)后檢測[J].儀器儀表學(xué)報(bào)，2012，33(4)：809-815.

Bai Baodan, Wang Yuanyuan, Yang Cuiwei. Predicting recrudescence of atrial fibrillation based on recurrence complex network[J]. Chinese Journal of Scientific Instrument, 2012,33(4):809-815. (in Chinese)

[12]趙鵬，周云龍，孫斌.遞歸定量分析在離心泵故障診斷中的運(yùn)用[J].振動(dòng)、測試與診斷，2010，30(6)：612-616.

Zhao Peng, Zhou Yunlong, Sun Bin. Application of recurrence quantification analysis to fault diagnosis of centrifugal pump[J]. Journal of Vibration, Measurement & Diagnosis, 2010,30(6):612-616. (in Chinese)

[13]Zbilut J P, Webber J, Charles L. Embeddings and delays as derived from quatification of recurrence plots[J]. Physics Letters A, 1992,171(3-4):199-203.

[14]The Case Western Reserve University Bearing Data Center. Bearing data center fault test data[EB/OL]. [2012-11-02]. http:∥www.eecs.cwru.edu/laboratory/bearing/.

[15]Donner R V, Zou Yong, Donges J F, et al. Recurrence networks a novel paradigm for nonlinear time series analysis[J]. New Journal of Physics, 2010,12(3):1-41.

Research on Dynamic Measurement Technology of Fiber Optic Sensors

and Their Development

ZhangXiaodong1，2，XieSiying2，NiuHang2，ZhangPing3，JiaBinghui4

(1.Key Laboratory of Education Ministry for Modern Design and Rotor-Bearing System,

Research on Design and Dynamics for Common Berthing Mechanism

ChenJinbao1，ChengMei2,NieHong3，YangMingbo2

(1 .College of Aeronautics Engineering, Nanjing University of Aeronautics and Astronautics Nanjing, 210016, China)

(2.Shanghai Institute of Satellite Engineering Shanghai, 201100, China)

(3.College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics Nanjing, 210016, China)

Abstract Based on international space station(ISS) mission requirements, this paper puts forward the development of a common berthing mechanism (CBM) with a large passageway. First, three typical docking mechanisms are surveyed and summarized. Second, by comparing it with the mechanism configuration of existing mechanisms, the configuration of the CBM′s main component is determined, a CAD model is presented, and the performance of the alignment guide and capture latch are analyzed. Third, a contact dynamics modeling is presented in detail as the key technological design aspect, and a virtual prototype of CBM is analyzed for the design of CBM. Finally, the modal analysis of CBM is studied, andthe natural frequencies and vibration modes are given. Through these analyses, this paper provides some scientific basis for reducing the structural vibration and improving the reliability of the CBM. This work has value for the design of CBMs and the development of China′s space berthing mechanism.

Keywords berthing mechanism; contact; dynamics; modal analysis

Method of Potential Fault Identification Based on the Projection Pursuit for

Rotary Equipment

ChengXiaohan,WangAiming,ChenYulin,LiWei,MengGuoying

(School of Mechanical Electronic & Information Engineering, China University of Mining

and Technology (Beijing) Beijing, 100083, China)

Abstract In order to solve the problems of a weak characteristic signal of the potential failure stage and the difficulty of extracting effective information, a method of potential fault identification for large equipment is put forward. Twenty-four characteristic indexes are calculated to describe the equipment running status. In order to avoid one-sidedness of disclosed information in a single projection direction, these 24 characteristic indexes of different states (including normal state and abnormal state) are projected into two-dimensional space under the best projection direction matrix, and an evaluation index system is established by virtue of distribution features of the projection value. By comparing the distribution of these 24 indexes under one status to be evaluated with the established evaluation index system, it can be judged whether the equipment state is abnormal or in the failure mode. Analysis of the test data shows that this method is feasible, reliable, and highly sensitive in capturing the early fault signal.

Keywords 24 characteristic indexes; the projection pursuit method; the best projection direction matrix; evaluation index system; status identification and early warning

Milling Vibration Suppression of Thin-Walled Structure Based on

Electromagnetic Induction

YangYiqing，GongJiwen

(School of Mechanical Engineering and Automation, Beihang University Beijing, 100191, China)

Abstract There are many thin-walled structures in aircraft. Due to the low flexibility of structures, workpiece deformation and deflection occur easily during the machining, which causes low precision and low surface quality. Therefore, much has been done to investigate the machining process, deflection prediction and control technology of thin-walled structure machining. However, real application in the industry is still a challenge. In this paper, a vibration suppression device for the thin-walled structure is investigated and designed based on electromagnetic induction. The workpiece vibration is utilized in order to cause a change in the magnetic flux through the closed circuit, so the resulting magnetic force can contribute to the suppression of workpiece vibration. The magnetic force resulting from the movement of the magnet inside the copper tube is formulated. It is shown to vary linearly with workpiece velocity in the opposite direction. Impact tests show that the device can sharply attenuate the oscillation time, and the chatter stability simulation shows that the stability limit of the thin-walled workpiece is increased from 0.4mm to 5.1mm. Cutting tests are carried out to verify the final vibration suppression effect.

Keywords thin-walled structure; electromagnetic induction; milling; vibration suppression

Fault Diagnosis of Service Robot Based on Multi-PCA Models

and SVM-DS Fusion Decision

YuanXianfeng1,SongMumin1,ZhouFengyu1,ChenZhumin2

(1.School of Control Science and Engineering, Shandong University Jinan, 250061, China)

(2.School of Computer Science and Technology, Shandong University Jinan, 250101, China)

Abstract To solve the fault diagnosis problem of the wheeled service robot driving system, a novel fault diagnosis method based on multi-principle component analysis (multi-PCA) models is proposed, which compounds with support vector machine (SVM) and Dempster-Shafer evidence theory(DS) . Multiple PCA models are established using sensor data sampled in the normal and fault states, respectively. The normal state PCA model is used to accomplish fault detection. During the fault isolation process, the multi-PCA models are used to carry out feature extraction from sensor data, and the processed data are taken as the input vectors of SVM classifiers, which achieves preliminary fault isolation. The global and local confidence values of the SVM classifiers are defined based on the confusion matrixes. To realize the effective combination of SVM and DS, the basic probability assignment (BPA) is appointed by the integration of the confidence values and the preliminary fault isolation results. Experimental results indicate that sensitive faults in the robot driving system can be detected, with an average fault isolation accuracy of 92.6%. Compared with the traditional single PCA model method, the proposed method has better performance in accuracy and stability.

Keywords service robot; fault diagnosis; principle component analysis(PCA); support vector machine(SVM); Dempster-Shafer evidence theory

Experimental and Analytical Study of Dynamic Response of Structure Controlled

by Active-Passive Hybrid Tune Mass Damper

LiuYanhui1,2,3,TanPing1,ZhouFulin1,2,YanWeiming2

(1.State Key Laboratory for Seismic Reduction /Control & Structural Safety (Cultivation),

Guangzhou University Guangzhou, 510405, China)

(2.College of Architecture and Civil Engineering, Beijing University of Technology Beijing, 100124, China)

(3.Department of Civil Engineering, University of Toronto Toronto, M5S1A4, Canada)

Abstract For the vibration control of structures under earthquake and wind excitation, the active-passive hybrid tune mass damper (HMD) is presented and the realization tactic of the control device is proposed, which adopts active mass damper (AMD) driven by linear motors, hollow rubber bearings as restoring force springs of the tune mass damper(TMD), and guide rails as supported structure. Then, the control effect and damping mechanism of the HMD for the dynamic response of the structure are analyzed under external excitations. Meanwhile, the influence of feedback response on control effect, control force and displacement AMD are discussed. Finally, the shaking table test of the structure controlled by HMD is carried out based on linear-quadratic-gaussian(LQG) and control algorithm. Simulation and experimental results show that HMD can effectively suppress the dynamic response of the structure and improve the performance of TMD. In order to solve the problem of AMD shifting, the displacement of AMD should be chosen as a control object and feedback vector when the AMD driven by linear motors is taken as the active control device. The control effect of the LQG control algorithm is better than that of thecontrol algorithm, and the feasibility of the HMD′s hardware system is experimentally proven, which supports the application of the HMD control system to pure engineering.

Keywords hybrid tune mass control; vibration control; active mass damper; tune mass damper; control algorithm

Experimental Study on the Vibration Fatigue Failure Confirmation Method

of the Structure Under Multi-axial Random Excitation

HeGuangzong1,2,ChenHuaihai1,HeXudong1

(1.College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics Nanjing, 210016, China)

(2.School of Transportation and Vehicle Engineering, Shandong University of Technology Zibo, 255049, China)

Abstract The fatigue failure characteristics of a structure under multi-axial random excitation presented in this paper have been researched, and two methods of determining the vibration-fatigue-life experiment are presented. A laser vibrometer and dynamic signal analyzer (35670A) are used to monitor the first order natural frequency, and the dynamic strain of the gap position on the structure is monitored using the dynamic strain measurement system in real time. Based on the investigation results, the relationship between the crack growth and the first order natural frequency as well as the strain variation are analyzed, two criteria for fatigue failure are determined, and the applicability of these two methods is discussed. This method lays the foundation for the multi-axial vibration fatigue experiment.

Keywords multi-axial random excitation; vibration fatigue; fatigue life; the first order natural frequency; dynamic strain

Characteristics Analysis and Extraction Method for Electrostatic

Monitoring Signal in Aero-engines Gas Path

WenZhenhua1,HouJunxing1,ZuoHongfu2

(1.School of Mechatronics Engineering, Zhengzhou Institute of Aeronautical Industry Management Zhengzhou, 450015, China)

(2.College of Civil Aviation, Nanjing University of Aerospace and Astronautics Nanjing, 210016, China)

Abstract The charge mechanism of aero-engine particles and the action mechanism between charged particles and the electrostatic sensor are analyzed, then the influence factors on the frequency property of the electrostatic monitoring signal are explored. Based on the difference in frequency spectrum caused by the flow features of particles, the energy distribution characteristics extraction from the frequency domain is proposed, and the wavelet analysis method is employed to calculate the energy distribution characteristics. The effectiveness of the characteristics is verified using simulated experiments and a turbo-shaft engine. The experimental results show that the electrostatic monitoring technology can detect the rapid change of aero-engine output power. The signals caused by continuous particles contain more high frequency content. The even distribution of energy can be applied to identify whether the particles are continuous or not, and the change in energy distribution can effectively reflect the small change in the output power of an engine. These results are helpful in promoting the airborne electrostatic technology and improving the ability to diagnose the work condition and track performance of parts in the aero-engines gas path.

Keywords aero-engines; electrostatic monitoring; characteristics extraction; electrostatic sensor

Self Adjusting Composite Cascade Morphology Filter

Algorithm and Its Application

ZhangPing1,2，ZhangXiaodong2DongXiaoni2,HeLile1,NiuHang2

(1.School of Mechanical and Electrical Engineering, Xi′an University of Architecture and Technology Xi′an, 710055, China)

(2.School of Mechanical Engineering, Xi′an Jiaotong University Xi′an, 710049, China)

Abstract In order to eliminate the pulse and random noise interference of the lubricant film thickness signal obtained by the optic fiber displacement sensor, a filtering algorithm based on self adjusting composite cascade mathematical morphology is proposed. The triangular and semi-circular structural elements are adopted in the filter. The composite cascade morphology filtering algorithm is built with cascading open-close and close-open combinational filters. The simulation results show that the algorithm improves the signal-to-noise ratio (SNR). Meanwhile, in order to avoid a low SNR, which is caused by the random selection of structural element parameters, a self adjusting method for the structural element parameters is proposed. Both experimental and simulation analysis results show that the filtering algorithm based on the self adjusting composite cascade mathematical morphology can effectively eliminate the pulse interference and random noise interference of the lubricant film thickness signal.

Keywords optical fiber; lubricant film; morphology filtering algorithm; structural element

Vibration Analysis of IC Trimming and Forming Mechanisms Based on

Rapid Chirplet Matching Pursuit

ChenZhong1,2,HuangMian1,2,ZhangXianmin1,2,ZhangQingchun3

(1.Guangdong Province Key Laboratory of Precision Equipment Manufacturing Technology,

South China University of Technology Guangzhou, 510641, China)

(2.School of Mechanical and Automotive Engineering, South China University of Technology Guangzhou, 510641, China)

(3.Dongguan Langcheng Microelectronic Equipment Co., Ltd Dongguan, 523945, China)

Abstract Aiming at the die-cutting precision of integrated circuit (IC) trimming and forming mechanisms, the rapid chirplet matching pursuit is used to analyze the vibration of a trimming and forming mechanism. Based on the fast matching pursuit of gaussian chirps, an algorithm is used to decompose the vibration signals of the key parts of the mechanism and obtain the chirp spectrograms. According to the characteristics of the atoms, the intrinsic frequency and other features can be identified from these spectrograms. The experiments indicate that the algorithm based on the fast matching pursuit of gaussian chirps, which has fine time-frequency resolution, can extract vibration characteristics from massive nonstationary signals, precisely reflect the work condition of the mechanisms, and lay a reliable basis for fault diagnosis.

Keywords chirplet； matching pursuit； trimming and forming； vibration analysis

Effect of Key Parameters on the Dynamic Performance

of the Multi-mesh Gear Systems

HuPeng,WangQibin,ZhangYimin

(School of Mechanical Engineering & Automation, Northeastern University Shenyang, 110819, China)

Abstract A nonlinear dynamic model and relative dimensionless equations focusing on time-varying stiffness and backlash are developed to study the steady state of the dynamic gear drive system of the computer numerical control (CNC) turret. The time-varying stiffness is obtained, considering the effect of the modification coefficient on stiffness values. The piecewise displacement functions caused by the backlash are simplified into an expression containing a hyperbolic tangent to avoid the complex judging in the iterative process. The equations are solved by employing the fourth-order Runge-Kutta method in Matlab programming. The influence of the alternating mesh stiffness amplitudes, transmitted static torque and backlash are investigated. Results show that smaller amplitudes of harmonic stiffness benefit the system′s stability. Stability is also improved under heavy loads, since working speed is smaller than critical speed, which increases due to the jumping phenomenon. Double-sided impact occurs more easily with small backlash and leads to noise.

Keywords time-varying mesh stiffness; gear backlash; nonlinear model; multi-mesh gear; jump phenomenon

Experimental Study of Caudal-Fin-Like Piezoelectric-Bimorph

Valveless Pump with Flexible-Rigid Structure

HuXiaoqi1,2,FangYamin1,ZhangRuihua1,YeXiaoping1,ChenXiaoyuan1,LüYongchang1

(1.College of Engineering and Design, Lishui University Lishui，323000，China)

(2.State Key Laboratory of Mechanics and Control of Mechanical Structures,

Nanjing University of Aeronautics and Astronautics Nanjing, 210016, China)

Abstract Compared to the traditional valveless pump working principle based on structural asymmetry, unidirectional flow produced by swing vibration has the advantages of being easy to realize miniaturization, high efficiency, little flow pulsation, no back flow, etc. The key part of the pump is the flexible caudal-fin structure configured on the tip of the swing vibrator. First, the relationship between the pressure head and excitation frequency is obtained by the pressure head test method, in which the length of the flexible caudal-fin is within the range of 2～18 mm. Second, the vibration mode is scanned by laser doppler vabrimeter with the swing vibrator immersed in water, and the corresponding relation between the maximum pressure head and vibrator mode is established after comparison with the experiment. Finally, the relationship between the flexible caudal fin and main part is discussed, and the fluctuation phenomenon of the optimum working frequency is explained. The results show that the pressure head can be observed in the first three vibration modes when the vibrator works in the approximate infinite water domain. The pressure head reaches 55 mm when the length of the flexible caudal-fin is 4 mm or 6 mm. The optimum working frequencies of the series vibrator fluctuate around the second bending mode frequency of the main part, without the caudal fin.

Keywords piezoelectric-bimorph; caudal-fin structure; valve-less pump; weak coupling

A Gyromagnetic Piezo-cantilever Generator Used for RWMS

KanJunwu,LiShengjie,WangShuyun,LiYang,YanMengjia,ZengPing

(Institute of Precision Machinery, Zhejiang Normal University Jinhua, 321004, China)

Abstract A gyromagnetic piezo-cantilever generator (GPG) is presented to meet the demand of the railway wheelset monitoring system (RWMS) for self-power. The influence of the magnetic force and rotating speed on GPG energy generation, in terms of the number and configuration of the magnets, is experimentally investigated. The results show that there are 9 optimal rotating speeds for the GPG to achieve peak voltages in the speed range of 0～1 360 r/min. The increasing number of rotating magnets exerts no influence on optimal rotating speeds, but leads to increasing output voltage when the magnets on the piezo-cantilever are fixed. The peak voltages of GPG with 2, 4, 8, and 12 rotating magnets are 13.2, 16.6, 23.8, and 27.8V respectively at the rotating speed of 1 042.5 r/min. The optimal speeds decrease and the responding voltage rises with an increasing number of magnets fixed on the piezo-cantilever when the number of rotating magnets is constant. In the case of two rotating magnets, the 9thoptimal rotating speeds and the peak voltages of the GPG with 1, 3, 5, and 7 magnets fixed on the piezo-cantilever are 1 056.4, 861.8, 750.6, and 611.6 r/min and 13.2, 34.4, 48, and 64 V, respectively. Moreover, the generated energy in terms of the voltage and wave number produced by one excitation depends on the magnets′ rotating speed. The wave number generated at the lower rotating speed (264.1 r/min) and higher rotating speed (1 024.5 r/min) is 1 and 4, respectively.

Keywords piezoelectric； energy generation； rotating excitation； magnetic coupling

Research on Vibration Suppression for Magnetic Suspension Motor Based on

Repetitive Control Method

HanBangcheng1,2,LiuYang1,2,ZhengShiqiang1,2

(1.Science and Technology on Inertial Laboratory, Beihang University Beijing, 100191, China)

(2.Fundamental Science on Novel Inertial Instrument & Navigation System Technology Laboratory Beijing, 100191, China)

Abstract Aiming at the suppression of unbalance vibration in rotors suspended by magnetic bearings, a plug-in repetitive controller is presented. The model of the unbalance vibration is proposed with emphasis on its periodicity. The stability and the abilities of error tracking and disturbance elimination are analyzed with the repetitive controller. The experiment is conducted with a 4kW magnetic suspension motor at the rotating speed of 10 kr/min. The rotor′s peak-to-peak position is reduced by 33% in thex-direction and 37% in they-direction, and the maximum amplitude of vibration at the rotating frequency is reduced by 42.1% in thex-direction and 45.4% in they-direction. The results demonstrate that the repetitive controller has good effect on the suppression of the unbalance vibration, and the control precision and stability of the magnetic bearing system are effectively improved.

Keywords magnetic suspension motor; magnetic bearings; unbalance vibration; repetitive control

Distinguishing Spurious Modes Obtained from PRCE Based on

Modal Similarity Index

ZhangGuowen1,MaJinghua2,ChenZhuo3

(1.College of Life Information Science & Instrument Engineering, Hangzhou Dianzi University Hangzhou, 310018, China)

(2.State Key Laboratory of Mechanical Transmission, Chongqing University Chongqing, 400044, China)

(3.State Key Laboratory of Bridge Structure Dynamics, Chongqing Communication

Research & Design Institute Chongqing, 400067, China)

Abstract A new method based on the modal similarity index is introduced to distinguish spurious modes. The method mainly focuses on the effect of spurious modes in the poly-reference complex exponential method on the results. First, two sets of results can be obtained by imposing different constraints on the coefficient matrix, in which the system poles appear at the same point, yet the mathematical poles are randomly distributed. Then, the mode similarity index (MSI) is proposed to measure the degree of similarity between the two sets of results. Spurious modes resulting from the noise or model redundancy can be removed according to the fact that the modal similarity index of physical modes is much larger than that of the spurious modes. Finally, parameter estimation of a linear time-invariant system of 3 degrees of freedom and the Chaotianmen bridge in Chongqing are presented. Results show that the proposed method can remove spurious modes effectively without losing physical modes.

Keywords modal analysis; polyreference complex exponential; spurious modes; stabilization diagram

Bearing Fault Diagnosis Based on Generalized S-Transform

and Two-Directional 2DPCA

LiWeihua,LinLong,ShanWaiping

(School of Mechanical Automotive Engineering, South China University of Technology Guangzhou, 510640, China)

Abstract The problem of bearing fault diagnosis can be solved by time-frequency image recognition. A two-directional, two-dimensional principal component analysis (TD-2DPCA) method is proposed to extract features from a time-frequency image matrix. First, features are extracted with TD-2DPCA using the generalized S-transform to transform fault signals into images in the time-frequency domain. The bearing fault experiments are carried out on a bearing test-bed, and vibration signals are collected under the normal condition, inner ring fault condition and outer ring fault condition. The proposed method is adopted to extract image features of three bearings from time-frequency spectrums, and the assembled matrix distance (AMD) is calculated for image classification. Experimental results show that TD-2DPCA combined with the generalized S-transform has good diagnostic performance and can effectively improve the computational speed.

Keywords generalized S-transform; two-dimensional principle component analysis(2DPCA); image recognition; feature extraction; fault diagnosis

Vibration Performance of the Cutter During Cutting Large Welded Cylinder

ChengYaonan,LiuLi,GongYa′nan,WuMingyang,QianJun,YanFugang

(The Key Laboratory of National and Local United Engineering for High-Efficiency Cutting & Tools,

Harbin University of Science and Technology Harbin, 150080, China)

Abstract The mechanism of cutting vibration is analyzed to research the dynamic characteristics of the cutter for cutting a large welded cylinder. The dynamic model of the cutting process of a large welded cylinder is established and solved. The cutting experiment is carried out under the real condition, and the vibration model is amended according to the changing of models. Thus, the feasibility and stability of the model in practical applications are verified. Finally, the critical condition of dynamically cutting a large welded cylinder is determined, which provides theoretical support to the further study of unstable vibration laws of large structure processing.

Keywords large welded cylinder; cutter vibration; dynamical model; numerical analysis

Compound Fault Diagnosis of Rolling Bearing Based on Dual-tree

Complex Wavelet Packet Transform and ICA

XuYonggangMengZhipengLuMing

(Beijing Engineering Research Center of Precision Measurement Technology and Instruments,

Beijing University of Technology Beijing, 100124, China)

Abstract A new fault diagnosis method is proposed based on the dual-tree complex wavelet packet transform (DT-CWPT) and independent component analysis (ICA), aiming at separating fault information from the compound rolling bearing fault signal. First, the non-stationary and complex signal of the compound fault is decomposed into several different frequency band components through dual-tree complex wavelet packet decomposition. Then, ICA is used to separate the mixed signal consisting of each component to eliminate the frequency aliasing as much as possible. Finally, independent signal components separated from the mixed signal are processed by Hilbert demodulation. The results show that the fault feature of rolling bearing can be effectively separated and extracted, and the method′s feasibility and effectiveness are verified.

Keywords dual-tree complex wavelet packet transform (DT-CWPT)； independent component analysis (ICA)； blind source separation； frequency aliasing；compound fault

The Probability Imaging Algorithm of Composite T-joint Damage Monitoring

LiuBin1,2,QiuLei1,YuanShenfang1,ShaoHuixue1,ZhangHua1

(1.The State Key Lab of Mechanics and Control of Mechanical Structures, Nanjing University of

Aeronautics and Astronautics Nanjing, 210016, China)

(2.Department of Air Force Military Transportation, Air Force Logistics College Xuzhou, 221006, China)

Abstract The T-joint is an important part of damage monitoring. However, it is difficult to accurately monitor T-joint′s damage with the PZT sensors array and Lamb wave based on structural health monitoring imaging methods because of its complex structures. The probability imaging algorithm independent of the signal propagation velocity, which is the base of traditional methods, is studied for engineering applications. The affected areas of each channel′s damage index (DI) are confirmed with the elliptical orbit method based on the DI of the piezoelectric excitation-sensor network. Then, the accurate monitoring of the T-joint damage is realized through the integration and imaging of all channels′ affected areas. The results are verified with the ultrasonic C-scan. The study reveals that the DI is able to monitor the T-joint of the composite material online and alert to the damage. Thus, damage locating can be implemented with the probability imaging algorithm.

Keywords composites; T-joint; structural health monitoring; damage index; probability imaging

Nonlinear Dynamics Characteristics of Dual-cylinder Opposed Compressor

Driven by Linear Motor

QinZhaoju1,2，GaoYuguo1,YuanYanpeng2,SongLiye2

(1.School of Mechanical Engineering, North China University of Water Resources and Electric Power Zhengzhou, 450045, China)

(2.School of Mechanical and Vehicular Engineering, Beijing Institute of Technology Beijing, 100081, China)

Abstract A nonlinear dynamics model of the compressor is established based on thermodynamics equations and the electromagnetic force equation, in order to study the dynamics characteristics of the piston in a free-piston compressor driven by a linear motor. The approximate solution of the nonlinear model is solved by the energy equilibrium method based on the oscillation theory. The stability and frequency characteristics of the piston in the linear compressor are discussed in terms of the solution of the nonlinear model. The results show that the movement principle of the linear compressor is a single degree vibration system with self-excited force. The initial movement does not affect the final operation of the compressor, and the piston motion tends to be stable. Piston motion frequency is influenced by the compressor′s physical structure, the linear motor thrust and the intake pressure. The electromagnetism force determines the piston′s movement amplitude and has a serious impact on the piston′s vibration frequency. The piston motion frequency increases with intake pressure, and is mainly decided by the inlet pressure under larger load conditions.

Keywords dynamics; nonlinear model; frequency characteristics; linear compressor; piston

Investigation on Uncertain Factors Affecting the Joint Stiffness of

Some Rubber Isolator

ChenXueqian，ShenZhanpeng，LiuXin′en,WangYujun

(Institute of Systems Engineering, China Academy of Engineering Physics Mianyang, 621999, China)

Abstract Two types of modal tests are designed to separate the uncertain resources in some rubber isolation systems. Repeated multi-test cases are conducted in each type of test. According to the test results, the joint stiffness of the isolation system is identified based on the traditional finite element (FE) model updating. The probability density functions of the joint stiffness are established by combining the Bayesian method with the Markov chain Monte Carlo (MCMC). Moreover, the effect of the uncertain resources on joint stiffness is quantified by the operation of random variables. Lastly, the uncertain model of the joint stiffness is validated with other validation tests. Results show that the effect of the assembling uncertainty on joint stiffness is only one tenth of that of the rubber material dispersion.

Keywords rubber isolator; uncertain resource; Bayesian method; uncertainty quantification

Localization of Delamination in Plate Structures Using

Natural Frequency Measurement

ChengXinlei1,2,XiaoGuanghong1,KennedyD2,ChengPeijiang3

(1.School of Civil and Architecture, Chongqing Jiaotong University Chongqing， 400074， China)

(2.School of Engineering, Cardiff University Cardiff, CF24 3AA, United Kingdom)

(3.Department of Civil Engineering, Logistic Engineering University Chongqing， 401311， China)

Abstract Delamination is regarded as one of the most serious defect in composite materials, which reduces the structural capacity and will spread to cause a catastrophic collapse. Based on the simplicity and high accuracy of measurement for natural frequency, a new type of non-destructive measurement is proposed to determine the delamination location in composite plate structures by using normalized natural frequencies. The predicted location by this method can be used before applying the quantitative detection, which can be considered as a preliminary work to improve the detection efficiency. The validity of this method is demonstrated by comparing the predicted location of a delaminated plate modelling with experimental data. The results show the procedure simplicity and accuracy of this method.

Keywords natural frequency； plate structure； delamination； location prediction

Self-Synchronous Theory of No-Swing Vibrating Machine Driven by Dual-motor

LiHe,LiuDan,ZhaoChunyu,WenBangchun

(School of Mechanical Engineering and Automation, Northeastern University Shenyang, 110819, China)

Abstract The self-synchronous theory of a no-swing vibrating machine driven by dual-motor is researched. The vibrating machine comprises an inner plastidium and an outer plastidium. The rotational centers of two eccentric rotors are in line with the inner plastidium′s center of mass along a vertical axis. Therefore, the moments generated by the inertial force of the eccentric rotors to the vertical axis are zero, thus eliminating the swing of the vibrating machine. First, the differential motion equations of the vibrating machine are established using the Lagrange equation, and the conditions of self-synchronization and motion stability are obtained. Moreover, numerical simulations are carried out to verify the correctness of the theoretical analysis. It can be shown that the capability of self-synchronization is positively correlated with the mass ratio of the two exciters and negatively related to the frequency ratio along the vertical direction, the angle of the resonant excitation, and the mass ratio between the material box and the vibrating system.

Keywords self-synchronous motion; vibrating mechanism; stability; vibratory synchronization transmission

Experimental Isolation Effect Analysis of Two-Stage Vibration Isolation System

SunYuhua1,DongDawei2,YanBing2,WangYuanwen2,WuJunda2

(1.College of Engineering and Technology, Southwest University Chongqing, 400715, China)

(2.School of Mechanical Engineering, Southwest Jiaotong University Chengdu, 610031, China)

Abstract Aiming at analyzing the isolation effect of a two-stage vibration isolation system that is used in exported internal combustion motor car, a ground platform experiment of the power train′s two-stage vibration isolation system is carried out according to the optimized two-stage vibration isolation system stiffness. By using the acceleration values of unit vibration intensity measuring points and each vibration isolator′s upper and lower measuring points, the isolation effect of the system is systematically analyzed from the unit vibration intensity, vibration level difference and dynamic dimpling force of each primary and secondary vibration isolator. The results show that the isolation effect of the system′s optimized stiffness is good, which can completely meet practical engineering needs.

Keywords two-stage vibration isolation system; vibration intensity;dynamic damping force; transmissibility

Analysis and Application of Deep Hole Drilling Straightness Error

Influenced by Cutting Fluid

ChenZhenya1,2,ShenXingquan1,2,XinZhijie1,2,PangJunzhong1,2,GuoTingting1

(1.School of Mechanical Engineering, North University of China Taiyuan, 030051, China)

(2.Shanxi Province Research Center of Deep-Hole Machining Engineering Technology Taiyuan, 03005l, China)

Abstract The equation for deep hole straightness error is established by using the cutting fluid Reynolds equation, bar bending deformation theory and drill bar angle equation, which reveals relationships between cutting fluid inlet pressure, drill rotation, whirl, squeezing feed and deep hole straightness. In the condition of cutting stability, deep hole straightness can be improved by reducing the cutting fluid inlet pressure, increasing the drill rotation speed or decreasing drill whirl speed and extrusion speed. A new type of multi-injection device is designed that can effectively reduce the deep hole straightness error through an additional shunt cavity and injection series to reduce the inlet pressure. Squeeze film dampers (SFD) are designed, and extruding whirl and extrusion of the deep hole drill pipe are decreased by using oil film resistance, which improves the deep hole straightness. Testing deep hole straightness error under the action of the multi-stage injection device and SFD, and drill in the lower cutting fluid inlet pressure and small whirl and extrusion have a better deep hole drilling straightness is verified. New ideas and a design scheme are given to control the deep hole processing straightness error.

Keywords deep hole drilling; straightness error; multi-injection device; squeeze film dampers(SFD)

Mixed-basis Superposition Method for Eigenvector Reanalysis

of Large Modified Structures

LiuZhijun,DengZhaoxiang

(The State Key Laboratory of Vehicle NVH and Safety Technology, China Automotive Engineering

Research Institute Chongqing, 400039, China)

Abstract In order to extend the application range of the structure reanalysis method based on the matrix perturbation theory in engineering practice, and to improve the calculation precision of reanalysis, an improved mixed-basis superposition method of dynamical reanalysis is proposed for large modified structures without complete modal space. The known modes are used to construct a new mixed-basis of the modal space, and the changes in the stiffness matrix and mass matrix reflecting the changes of structural physical parameters are represented as the incremental form of higher order. The present method is as simple and easy to operate as the classical perturbation method. The numerical results show that the presented method yields high precision for dynamical reanalysis of large modified structures.

Keywords structural dynamical reanalysis; large modifications of structures; matrix perturbation method; mixed-basis superposition method

Dynamic Characterization Analysis of Flexible Multibody Manipulator

with Joint Clearance

RenWu1，2,WuYunxin1,ZhangZhaowei1

(1.State Key Laboratory of High Performance Complex Manufacturing, Central South University Changsha, 410083, China)

(2.School of Biomedical Engineering , Xinxiang Medical University Xinxiang, 453003, China)

Abstract The long manipulator of ground machinery is typical multi-body system, the existing research on the kinematic relationship and dynamic characterization are generally concerned on the flexible booms with the ideal joint whereas the dynamics of joint clearance isn′t ignored. Firstly, a flexible multi-body boom model is established. Then, the first cylinder and boom joint clearance is considered. Next numerical simulation is done on the tip trajectory and vibration characteristic of ideal and clearance joint models. The simulation results show that the tip displacement of the flexible multi-body model with joint clearance is larger than that of ideal joint model. Meanwhile the hydraulic cylinder force also increases. And the first natural frequency is lower than that of ideal joint model. Finally an experiment is done on a flexible multi-body boom structure. The result provides a design reference for such machinery.

Keywords flexible multibody; manipulator； joint clearance； dynamic； natural frequency

Test Study on Adaptive Control Wavelet De-noising of the Semi-active

Air Suspension

WangRuochen,ChenXin,QianJingang,LiJiaojiao,ChenLong

(School of Automobile and Traffic Engineering, Jiangsu University Zhenjiang, 212013, China)

Abstract In order to eliminate the noise interference of the semi-active air suspension system caused by nonlinearity of the system, time-variation of parameters and uncertainty of the model, the working principle of wavelet de-noising of the semi-active air suspension is studied. In addition, the wavelet de-noising neuron adaptive controller of the semi-active air suspension is designed, the dynamic model of the semi-active air suspension is established based on wavelet de-noising, and the effectiveness of wavelet de-noising is analyzed using simulation and bench tests. The result shows that the semi-active air suspension based on wavelet de-noising neuron adaptive controller improves the centroid acceleration and pitching angular acceleration of the vehicle and ameliorates the comprehensive performance of the vehicle.

Keywords semi-active air suspension; adaptive control; wavelet de-noising; bench test

Conversion Method for Loss Factor of Unconstrained Damping Structures

ZhangAnfu1,YanXiaowei2,ShengMeiping1,WuQingqing1

(1.School of Marine Science and Technology, Northwestern Polytechnical University Xi′an, 710072, China)

(2.China State Shipbuilding Corporation Systems Engineering Research Institute Beijing, 100094, China)

Abstract Based on theoretical loss factor′s formula of damping structure, a conversion method for the loss factor of different unconstrained damping structures is proposed. The damping tests are carried out on a damping plate and damping shell. The experimental results are compared with the results from the conversion method in order to prove the effectiveness of the conversion process. The conversion coefficient change with thickness ratio and error amplification factor are both analyzed in the process of loss factor calculation. The simulation results show that the conversion coefficient change with height ratio is bigger for damping material with a small elastic modulus than for damping material with a large elastic modulus, and the conversion data is more accurate for damping material with a larger elastic modulus. In order to improve precision, the thickness of damping materials should be bigger than that of the target backing material, and the thickness of conversion backing should be smaller than twice thickness of target backing. The unmeasured loss factor of the structure can be obtained through the conversion method. It achieves the goal of acquiring the loss factor of the damping structure, which is difficult to be measured in practice. This method provides a referable solution to acquisition of the loss factor of large damping cylindrical shells and vibration suppression effect comparison of various damping layers on large damping cylindrical shells.

Keywords damping materials; loss factor; conversion method; error amplification factor

Rolling Bearings Fault Diagnosis Based on Recurrence Complex Network

SunBin1,LiangChao1,ShangDa2

(1.School of Energy and Power Engineering, Northeast Dianli University Jilin, 132012, China)

(2.Jilin Electric Power Research Institute Co.,Ltd Changchun, 130021, China)

Abstract In the case of the non-stationary and non-linear vibration signal of a rolling bearing with faults, a bearings fault diagnosis method based on the recurrence complex network (RCN) is put forward. First, a one dimension time series is extended to high dimension phase space by using the phase space reconstruction method, and a recurrence matrix is built. Then, recurrence quantification analysis (RQA) is discussed. Finally, the recurrence complex network (RCN) method is employed to extract nonlinear characteristic parameters of the vibration signals, which yield the feature vectors. The analysis results of the vibration signals acquired from the bearings with normal, outer track fault, ball fault and inner track fault, respectively, show that the RCN method has better diagnosis effect than the RQA method.

Keywords recurrence complex network; vibration signal; fault diagnosis; fluctuation modal

Xi′an Jiaotong University Xi′an, 710049, China)
(2.School of Mechanical Engineering, Xi′an Jiaotong University Xi′an, 710049, China)

(3.School of Mechanical Engineering, Xi′an University of Architecture and Technology Xi′an, 710055, China)

(4.School of Mechanical Engineering, Nanjing Institute of Technology Nanjing, 211100, China)

The fiber optic sensor is a new kind of measurement sensor that can detect various physical quantities, such as displacement, vibration, strain, and flow, by studying the modulating characteristic of the optical wave inside the fiber optic under the influence of the quantities to be measured. Based on fundamental theoretical knowledge of fiber optic measurement technology, the reflective displacement sensor and light-transmission fiber optic motion sensor are introduced as two typical transmission-type optical fiber sensors in order to elaborate the operational principle of the transmission-type optical fiber sensor and its applications in the dynamic measurement of lubricating oil film inside journal bearings, rotor vibration in rotating machinery, blade tip clearance in aircraft engines, fluid flow in aircraft engines and movement detection in the human body. Discussion on the innovative design of and the research on these measurement systems is presented. Then, another kind of fiber optic sensor, the functional-type optical fiber sensor, is discussed by introducing two typical sensors, the curvature optical fiber sensor and fiber Bragg grating sensor, as well as their measurement principles and applications in measuring casing deformation, and the measurement of dynamic stress on planet gear. Lastly, the development of this new technology is summarized and prospected.

fiber optic sensor; dynamic measurement technology; rotating machinery; engineering parameters

10.16450/j.cnki.issn.1004-6801.2015.03.030

2013-03-21；

2014-04-08

TH133.33

孫斌,男，1972年1月生,博士、教授。主要研究方向?yàn)榉蔷€性信號(hào)處理、故障診斷等。曾發(fā)表《基于等距特征映射和支持矢量機(jī)的轉(zhuǎn)子故障診斷方法》(《機(jī)械工程學(xué)報(bào)》2012年第48卷第9期)等論文。 E-mail: sunbin@mail.nedu.edu.cn