喜歡這個資料需要的話就充值下載吧。。。資源目錄里展示的全都有預(yù)覽可以查看的噢，，下載就有,,請放心下載，原稿可自行編輯修改=【QQ：11970985 可咨詢交流】====================喜歡就充值下載吧。。。資源目錄里展示的全都有，，下載后全都有,,請放心下載，原稿可自行編輯修改=【QQ：197216396 可咨詢交流】====================
Procedia Engineering 35 ( 2012 ) 176 181 1877-7058 2012 Published by Elsevier Ltd. doi: 10.1016/j.proeng.2012.04.178 International Meeting of Electrical Engineering Research ENIINVIE-2012 Experimental characterization of mechanical vibrations and acoustical noise generated by defective automotive wheel hub bearings Eduardo Rubio * , Juan C. Juregui CIATEQ A.C.,Centro de Tecnologa Avanzada Cto. Aguascalientes Norte 135, P.I.V.A., Aguascalientes, Ags., C.P. 20358, Mexico Abstract Wheel hub bearing faults in passenger cars cause chattering at the corresponding wheel, increase chassis vibration and generate high noise levels inside the car cabin. In this paper a series of in-situ test with defective and healthy wheel hub bearings were conducted. Mechanical vibrations and sound were measured and data were analyzed with a number of signal processing methods in frequency and time-frequency domains. Additionally, a statistical signal processing method was also performed. The results of the various methods are compared and it was found that most of the methods used in this work are well suited for the analysis. Some methods, however, show certain limitations with respect to their informative value and their ability of implementation. 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Organizing Committee of the ENIINVIE-2012. Keywords: Instrumentation; vibrations analysis; faulty bearing; automotive parts 1. Introduction Bearings play an important role in any rotary machinery. Not only do bearings influence the quality of the machinerys accuracy, but also do they directly impact the engines life span. Defects in bearings cause recurrent impacts on the rotating part degrading its performance. Therefore, a lot of research has * Corresponding author. Tel.: +52-449-9731060 E-mail address: eduardo.rubiociateq.mx. Available online at Open access under CC BY-NC-ND license. Open access under CC BY-NC-ND license. 177 Eduardo Rubio and Juan C. Juregui / Procedia Engineering 35 ( 2012 ) 176 181 been conducted to the detection of bearing defects at early stages of failure development, especially because early detection decreases production machinery downtime and maintenance costs. There are a number of measurement, analyses and detection schemes which are widely recognized. It appears that the state of the art is to measure acceleration directly on the bearing casing by means of piezoelectric accelerometers 1, 2. Furthermore, acoustic measurement methods have been proposed by means of acoustic transducers 3. Time-domain analyses and detection methods have been proposed, such as phase diagrams 4 and threshold counters 5. However, the frequency-domain analysis is the most ubiquitous method found in the literature. Pure frequency analyses or time-frequency methods such as the Short-Term Fourier Transform (STFT) have been investigated. In addition, statistical signal processing methods have been published as well. Among these methods are Crest Factor, Kurtosis and Beta Function 6, probability prediction and scatter plots 7 and autocorrelation together with the probability density function 8. Most research has been done with respect to rotating production machinery bearings, rarely car wheel hub bearings. In this paper in-situ measurements of mechanical vibrations produced by a defective wheel hub bearing and sound transmitted to the chassis cabin, under normal car usage conditions were conducted and various vibration analysis techniques were applied. 2. Autocorrelation The autocorrelation function displays information about a signals self-similarity. More formally speaking, it gives the correlation between two signal points separated by a time lag. For continuous, finite energy signals the autocorrelation function is + = dttstsR )()()( * (1) and for discrete-time signals = n nxnxR * (2) In both cases 2 is the lag between two observation points whereas * is the complex conjugate. R(0) and R0, respectively, are the maximum of the function and, furthermore, the autocorrelation is normalized so that the latter points equal unity. Real signals autocorrelation is an even symmetric function with respect to zero. It gives information about a signals stationarity, e.g. a clearly pronounced pointy correlation indicates weak stationarity whereas a wide correlation corresponds to a strongly stationary signal. In addition, periodic signals produce periodic autocorrelation functions with the same period as the time signal 3. Experimental setup In order to acquire the desired data for further processing and analysis, a passenger car was equipped with measurement devices and signal processing hardware. The experiment, as depicted in Fig. 1, was conducted on a conventional highway. During the first measurement series, the left rear wheel hub was equipped with a faulty bearing. Then it was replaced with a healthy bearing. Consequently, two series of measurements were conducted, with the faulty and the good bearing, respectively. To begin with, a solid-state accelerometer was mounted on the relevant wheel hub. The mounted accelerometer was sensible to acceleration forces perpendicular with respect to the road. All consecutive 178 Eduardo Rubio and Juan C. Juregui / Procedia Engineering 35 ( 2012 ) 176 181 measurement modules were installed inside the vehicle cabin. The acquired acceleration data were voltages proportional to the gravitational constant and passed first through a conditioner stage whose output terminal held the acceleration data. Furthermore, the obtained acceleration data were sent through two integrator stages. The outputs of the latter held the velocity and the displacement, respectively. Ultimately, all four data streams were connected to a data acquisition device. Fig. 1 Experimental setup. Not only is vibration information of interest, but also acoustic noise perception inside the car cabin. To this end, an electret condenser microphone was mounted onto the inner hull of the cabin. A high-end data acquisition board NI PCMCIA 6062E was used. For measurement series, all five data streams were sampled at 20 kHz and sent to a control center in a laptop computer for storage. Hence, all the data were available for off-line signal processing. The bearing in use was of the type double-rowed ball bearing for non-driven wheels. A perspective view with a lateral cut is shown in Fig. 2. As depicted, the inner race is stationary whereas the outer race revolves. The latter is connected to the wheel and the former to the vehicle body. Fig. 2 Wheel hub bearing. 4. Results As the experiment was conducted with rising vehicle velocity, a proportional increase in the measured vibrations acceleration at the bearing was expected. The corresponding ramp was expected to be of lower 179 Eduardo Rubio and Juan C. Juregui / Procedia Engineering 35 ( 2012 ) 176 181 inclination with a healthy bearing as opposed to the faulty one. Fig. 3 shows two acceleration surface spectrogram plots for both defective and healthy bearings. 4.1. Acceleration Analysis Fig. 3 shows the frequency analysis for a defective bearing and a healthy bearing. Interestingly, both spectra have a similarity which could, to some extent, be approximated by a factor. However, it is clearly visible where most of the energy caused by a defective bearing is located in the measured data. Those cumulated peaks evolve at around 4750 Hz with a bandwidth of roughly 2000 Hz. Added to that, a further accumulation of peaks caused by the bad bearing is located at frequencies below 500 Hz (see Fig. 5 for a more detailed view). Both trends are a clear indicator of a defective component in the wheel hub. Bearings show a resonance frequency band in the upper frequencies. Published works, as in 5, stated that low-frequency impulses created by defective bearing parts excite a resonance frequency band in the upper frequencies of the bearing vibration. This resonance can clearly be seen in the spectrogram. The detection technique using this resonance property is called High Frequency Resonance Technique and has been implemented together with envelope detection schemes 9,10. Fig. 3 Surface spectrogram of acceleration data. Good bearing (left), faulty bearing (right). Statistical signal processing methods were applied to the data. The autocorrelation function results can be seen in Fig. 4 and are surprisingly clear and similar in shape for the good bearing as in 8. The dominating low frequency components in the healthy bearing result in a smooth autocorrelation. On the other hand, the high frequency resonance conglomerate of the bad bearing produces strong jittering with respect to the lag in the autocorrelation. 4.2. Acoustic Noise Analysis As a huge amount of the signal energy of the acceleration data were located around 4750 Hz, a similar conglomerate was expected in the acoustic noise measurements. However, Fig. 5 shows clearly that the audio signal of a defective bearing carries hardly any energy above 500 Hz. Most likely the chassis natural frequencies lie far below the high frequency conglomerate of the acceleration data. Molisani et al. 11 stated that car cabin noise below 400 Hz is mainly structural borne, meaning that it gets translated into the cabin by physical connections, which apparently do omit higher frequencies. On that account, only a partial energy amount initiated by the chattering of the bad bearing was transformed into acoustic waves inside the vehicle cabin. 180 Eduardo Rubio and Juan C. Juregui / Procedia Engineering 35 ( 2012 ) 176 181 Fig. 4 Statistical analysis. Plots shown in Fig. 5 indicate the correlation between the acceleration and noise measurements below 500 Hz. Three clearly pronounced peaks in the acceleration data of the bad bearing distinguish it from the good bearing, where such peaks remain unobserved. The peak at 200 Hz translates unequivocally into the noise measurement, where a notable amount of energy is located around 200 Hz, as well. Post experimental subjective tests confirmed that the most important audible part, which distinguishes the audio signals, is indeed the 200 Hz peak. The same phenomenon was audible while conducting the measurements inside the vehicle cabin, it equaled a booming sound. 5. Conclusions From our analyses the following conclusions can be established: The FFT and STFT are powerful and meaningful instruments for off-line analysis of accelerometer measurements of bearings. And whats more, healthy from faulty bearings can be distinguished, observing the upper frequency resonance band, even when the measurements were conducted in a raw environment such as a regular highway road. Statistical signal processing of acceleration data can also be used. Especially because the computed data are nearly self-explanatory and easy to interpret. Measurements can be used to identify good and bad bearings, respectively. Noise measurements inside the vehicle cabin are only significant at low frequencies, as higher frequencies are virtually non-existent. Nevertheless, clearly audible frequencies caused by a faulty bearing prove noise perception to be a potent means of evaluating a bearings state in a moving vehicle. Acknowledgements The authors wish to acknowledge financial assistance from the Mexican National Council for Science and Technology (CONACyT) and the Government of Aguascalientes. 181 Eduardo Rubio and Juan C. Juregui / Procedia Engineering 35 ( 2012 ) 176 181 Fig. 5 Correlation between audio (top) and acceleration (bottom) data, good bearing (left) and faulty bearing (right). References 1 He W, Jiang ZN, Feng K. Bearing fault detection based on optimal wavelet filter and space code shrinkage. Measurement 2009;42:1092-1102. 2 Wang GF, Li YB, Luo ZG. Fault classification of rolling bearing beased on reconstructed phase space and gaussian mixture model. J. Sound Vib.2009;323:1077-89. 3 Li CJ, Li SY. Acoustic emission analysis for bearing condition monitoring. Wear 1995;185:67-74. 4 Jauregui JC, Gonzalez O, Rubio E. The application of time-frequency and phase diagram analyses for the early detection of faulty roller bearing. Proc. ASME Turbo Expo 2009: Power for Land, Sea and Air; 2009, p. 1-10. 5 Tandon N, Choudhury A. A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings. Tribol. Int. 1999;32:469-480. 6 Heng RBW, Nor MJM. Statistical analysis of sound and vibration signals for monitoring rolling element bearing condition. Appl. Acoust. 1998;53:211-226. 7 Masuike H, Ikuta A. Statistical signal processing by using the higher-order correlation between sound and vibration and its application to fault detection of rotational machine. Adv. Acoust. Vib. 2008;2008:1-7. 8 Sturm A, Kinsky D. Diagnostics of rolling-element bearing condition by means of vibration monitoring under operating conditions. Measurement 1984;2:58-62. 9 McFadden PD, Smith JD. Vibration monitoring of rolling element bearings by the high-frequency resonance technique-a review. Tribol. Int. 1984;17:3-10. 10 Sheen YT. An envelope detection method based on the first-vibration-mode of bearing vibration. Measurement 2008; 41:797-809. 11 Molisani LR, Burdisso RA, Tsihlas D. A coupled tire structure/acoustic cavity model. Int. J. Solids Struct. 2003;40:5125-38. Y
Design of 10t Hydraulic Hoist
10噸液壓卷揚機設(shè)計
資料來源： SciVerse ScienceDirect
設(shè)計題目： 10噸液壓卷揚機設(shè)計
學(xué)生姓名：
學(xué)院名稱：
專業(yè)名稱：
班級名稱：
學(xué) 號：
指導(dǎo)教師：
教師職稱：
完成時間：
在線提供 Procedia Engineering 35（ 2012） 176 - 181 ENIINVIE-2012電氣工程研究國際會 議 由有缺陷的汽車輪轂軸承產(chǎn)生的機械振動和聲學(xué) 噪聲的實驗表征 愛德華多 愛德華 Rubio*, 胡安賈雷吉 CIATEQ AC,Centro de Tecnologa Avanzada CTO。 Aguascalientes Norte 135， PIVA， Aguascalientes， Ags。， CP 20358， Mexico 摘要 乘用車中的輪轂軸承故障會導(dǎo)致相應(yīng)車輪顫動，增加底盤振動并在車廂內(nèi)產(chǎn)生高噪音。在本文中，進行了一 系列有缺陷和健康的輪轂軸承的現(xiàn)場測試。測量機械振動和聲音，并使用頻率和時頻域中的多種信號處理方 法分析數(shù)據(jù)。另外，還執(zhí)行統(tǒng)計信號處理方法。比較了各種方法的結(jié)果，發(fā)現(xiàn)本工作中使用的大多數(shù)方法都 非常適合分析。然而，一些方法在其信息價值和實施能力方面顯示出某些限制。 2011 Elsevier Ltd.出版的 ENIINVIE-2012組委會負責(zé)的選拔和 /或同行評審。 CC下的開放訪 問 BY-NC-ND許可證 。 關(guān) 鍵詞：儀器儀表 ;振動分析 ;軸承故障 ;汽車部 件 1. 介紹 軸承在任何旋轉(zhuǎn)機械中都起著重要作用。軸承不僅會影響機器的精度，而且會直接影響發(fā)動機 的使用壽命。軸承的缺陷會導(dǎo)致旋轉(zhuǎn)部件的反復(fù)沖擊，從而降低其性能。因此，很多研究都有 *通訊作者。電話： + 52-449-9731060 電子郵件地址： eduardo.rubiociateq.mx。 1877-70582012 Elsevier Ltd.出版開放獲 取 CC BY-NC-ND許可證 。 doi:10.1016/j.proeng.2012.04.178 Eduardo Rubio and Juan C. Juregui / Procedia Engineering 35 (2012) 176 181 177 在故障發(fā)展的早期階段進行軸承缺陷檢測，特別是因為早期檢測可以減少生產(chǎn)機器的停機時間 和維護成本。 有許多被廣泛認可的測量，分析和檢測方案?，F(xiàn)有技術(shù)似乎是通過壓電加速度計直接測量軸承 套管上的加速度 1,2。此外，已經(jīng)通過聲換能器 3提出了聲學(xué)測量方法 。 已經(jīng)提出了時域分析和檢測方法，例如相圖 4和閾值計數(shù)器 5。然而，頻域分析是文獻中最 常用的方法。已經(jīng)研究了純頻率分析或諸如短期傅里葉變換（ STFT）的時頻方法。此外，還公布 了統(tǒng)計信號處理方法。這些方法包括波 峰因數(shù)，峰度和 Beta函數(shù) 6，概率預(yù)測和散點圖 7以及 自相關(guān)和概率密度函數(shù) 8。大多數(shù)研究都是針對旋轉(zhuǎn)生產(chǎn)機械軸承，很少是汽車輪轂軸承 。 在本文中，在正常的汽車使用條件下進行了由有缺陷的輪轂軸承產(chǎn)生的機械振動和傳遞到底盤 艙的聲音的原位測量，并且應(yīng)用了各種振動分析技術(shù)。 2. 自相關(guān) 自相關(guān)函數(shù)顯示有關(guān)信號自相似性的信息。更正式地說，它給出了由時滯分隔的兩個信號點之 間的相關(guān)性。對于連續(xù)的有限能量信號，自相關(guān)函數(shù)是 對于離散時間信號 R () s*(t (1) R n xn x n * (2) 在兩種情況下， T是兩個觀察點之間的滯后，而 *是復(fù)共軛。 R（ 0）和 R 0分別是函數(shù)的最大 值，此外，自相關(guān)被歸一化，使得后者指向相等的單位。實信號的自相關(guān)是相對于零的偶對稱函 數(shù)。它給出關(guān)于信號的平穩(wěn)性的信息，例如明顯明顯的尖性相關(guān)性表示弱平穩(wěn)性，而寬相關(guān)性對 應(yīng)于強靜止信號。另外，周期信號產(chǎn)生周期性自相關(guān)函數(shù)，其周期與時間信號相 同 3. 實驗裝置 為了獲得用于進一步處理和分析的期望數(shù)據(jù)，乘用車配備有測量裝置和信號處理硬件。如圖 1 所示，該實驗是在傳統(tǒng)的高速公路上進行的。在第一個測量系列中，左后輪轂配備了故障軸承。 然后用健康的軸承代替。因此，分別進行了兩個系列的測量，分別具有故障和良好 的軸承 。 首先，將固態(tài)加速度計安裝在相關(guān)的輪轂上。安裝的加速度計對垂直于道路的加速力是敏感的。 全部連續(xù) 178 Eduardo Rubio and Juan C. Juregui / Procedia Engineering 35 (2012) 176 181 測量模塊安裝在車廂內(nèi)。所獲取的加速度數(shù)據(jù)是與重力常數(shù)成比例的電壓，并首先通過其輸出端 保持加速度數(shù)據(jù)的調(diào)節(jié)器級。此外，獲得的加速度數(shù)據(jù)通過兩個積分器級發(fā)送。后者的輸出分別 保持速度和位移。最終，所有四個數(shù)據(jù)流都連接到數(shù)據(jù)采集設(shè)備。 圖 1實驗裝置 。 不僅是感興趣的振動信息，還有車廂內(nèi)的聲學(xué)噪聲感知。為此，將駐極體電容式麥克風(fēng)安裝在 機艙的內(nèi)殼上。 使用高端數(shù)據(jù)采集板 NI PCMCIA 6062E。對于測量系列，所有五個數(shù)據(jù) 流都以 20kHz采樣并發(fā)送 到膝上型計算機中的控制中心進行存儲。因此，所有數(shù)據(jù)都可用于離線信號處理。使用的軸承是 用于非驅(qū)動輪的雙列滾珠軸承。在圖 2中示出了具有橫向切口的透視圖。如圖所示，內(nèi)圈是靜止的 而外圈是旋轉(zhuǎn)的。后者連接到車輪，前者連接到車身 。 圖 2輪轂軸承 。 4. 結(jié)果 由于實驗是在車速上升的情況下進行的，因此預(yù)計軸承處測得的振動加速度會成比例增加。相 應(yīng)的坡道預(yù)計會更低 Eduardo Rubio and Juan C. Juregui / Procedia Engineering 35 (2012) 176 181 179 傾向于健康的方位而不是錯誤的方位。圖 3顯示了有缺陷和健康軸承的兩個加速表面譜圖 。 4.1. 加速度分析 圖 3顯示了有缺陷的軸承和健康軸承的頻率分析。有趣的是，兩種光 譜都具有相似性，在某種 程度上可以用一個因子來近似。然而，在有缺陷的軸承引起的大部分能量位于測量數(shù)據(jù)中的情況 下，清晰可見。這些累積的峰值在 4750Hz附近發(fā)展，帶寬約為 2000Hz。除此之外，由不良軸承引 起的峰值的進一步累積位于 500Hz以下的頻率（更詳細的視圖見圖 5）。這兩種趨勢都是輪轂缺陷 部件的明確指標。軸承在較高頻率中顯示共振頻帶。已發(fā)表的作品，如 5所述，由有缺陷的軸承 零件產(chǎn)生的低頻脈沖激發(fā)了軸承振動的高頻中的共振頻帶。在頻譜圖中可以清楚地看到這種共振。 使用這種共振特性的檢測技術(shù)稱為高頻共振技術(shù)，并 與包絡(luò)檢測方案一起實施 9,10。 圖 3加速度數(shù)據(jù)的表面譜圖。良好的軸承（左），軸承故障（右） 。 統(tǒng)計信號處理方法應(yīng)用于數(shù)據(jù)。自相關(guān)函數(shù)結(jié)果可以在圖 4中看到，并且在形狀方面令人驚訝 地清晰且類似于 8中的良好軸承。健康軸承中主導(dǎo)的低頻分量導(dǎo)致平滑的自相關(guān)。另一方面，壞 軸承的高頻共振礫巖相對于自相關(guān)中的滯后產(chǎn)生強烈的抖動 。 4.2. 聲學(xué)噪聲分析 由于加速度數(shù)據(jù)的大量信號能量位于 4750Hz附近，因此在聲學(xué)噪聲測量中預(yù)期有類似的聚集體。 然而，圖 5清楚地表明，有缺陷的軸承的音頻信號幾乎不承載 500Hz以上的任何能量。底盤的固有 頻率很可能遠低于加速度數(shù)據(jù)的高頻集團。 Molisani等。 11指出，低于 400赫茲的車廂噪音主要 是結(jié)構(gòu)性的，這意味著它通過物理連接轉(zhuǎn)換到機艙，顯然省略了更高的頻率。因此，僅由不良軸 承的抖動引發(fā)的部分能量量被轉(zhuǎn)換成車廂內(nèi)的聲波 。 180 Eduardo Rubio and Juan C. Juregui / Procedia Engineering 35 (2012) 176 181 圖 4統(tǒng)計分析 。 圖 5中所示的曲線表示低于 500Hz的加速度和噪聲測量值之間的相關(guān)性。在不良軸承的加速度數(shù) 據(jù)中，三個明顯明顯的峰值將其與良好的軸承區(qū)分開來，其中這樣的峰值仍未被觀察到。 200 Hz 處的峰值明確地轉(zhuǎn)換為噪聲測量，其中顯著量的能量位于 200Hz附近 。 后實驗主觀測試證實，區(qū)分音頻信號的最重要的可聽部分確實是 200Hz的峰值。在車廂內(nèi)進行 測量時聽到同樣的現(xiàn)象，它等于轟鳴聲 。 5. 結(jié)論 根據(jù)我們的分析，可以建立以下結(jié)論： FFT和 STFT是用于離軸分析軸承加速度計測量的強大而有意義的儀器。而且，即使在諸如常規(guī) 公路的原始環(huán)境中進行測量，也可以區(qū)分出有缺陷的軸承的健康，觀察上頻率共振帶 。 也可以使用加速度數(shù)據(jù)的統(tǒng)計信號處理。特別是因為計算的數(shù)據(jù)幾乎是不言自明的并且易于解 釋。測量可分別用于識別好軸承和壞軸承。 車廂內(nèi)的噪聲測量僅在低頻時很重要，因為更高頻率幾乎不存在。然而，由軸 承故障引起的明 顯可聽頻率證明噪聲感知是評估移動車輛中軸承狀態(tài)的有效手段 。 致謝 作者希望得到墨西哥國家科學(xué)技術(shù)委員會（ CONACyT）和阿瓜斯卡連特斯政府的財政援助 。 Eduardo Rubio and Juan C. Juregui / Procedia Engineering 35 (2012) 176 181 181 圖 5音頻（上）和加速（下）數(shù)據(jù)，良好軸承（左）和軸承故障（右）之間的相關(guān)性 。 參考 1 何 W，姜志恩，馮 .基于最優(yōu)小波濾波和空間碼收縮的軸承故障檢測。測 量 2009;42:1092-1102. 2 王 GF，李 YB，羅志剛。基于重構(gòu)相空間和高斯混合模型的滾動軸承故障分類。 J. Sound Vib.2009; 323： 1077-89。 3 Li CJ， Li SY。軸承狀態(tài)監(jiān)測的聲發(fā)射分析。穿 1995; 185： 67-74。 4 Jauregui JC， Gonzalez O， Rubio E.應(yīng)用時頻和相圖分析來早期檢測故障滾子軸承。 PROC。 2009年 ASME渦輪博覽 會：陸地，海洋和空中力量 ;2009年， p。 1-10。 5 Tandon N， Choudhury A.回顧用于檢測滾動軸承中缺陷的振動和聲學(xué)測量方法。 TRIBOL。詮釋。 1999; 32： 469- 480。 6 Heng RBW， Nor MJM。用于監(jiān)測滾動軸承狀態(tài)的聲音和振動信號的統(tǒng)計分析 。 申請聲量。 1998; 53： 211-226。 7 Masuike H， Ikuta A.利用聲音和振動之間的高階相關(guān)性進行統(tǒng)計信號處理及其在旋轉(zhuǎn)機械故障檢測中的應(yīng)用。進 階聲量。顫音。 2008; 2008： 1-7。 8 Sturm A， Kinsky D.通過在運行條件下的振動監(jiān)測來診斷滾動軸承的狀態(tài)。測量 1984; 2： 58-62。 9 McFadden PD， Smith JD。高頻共振技術(shù)對滾動軸承的振動監(jiān)測 - 綜述。 TRIBOL。詮釋。 1984; 17： 3-10。 10 Sheen YT。一種基于軸承振動的第一振動模式的包絡(luò)線檢測方法。測量 2008; 41:797-809. 11 Molisani LR， Burdisso RA， Tsihlas D.耦合輪胎結(jié)構(gòu) /聲腔模型。詮釋。 J. Solids Struct。 2003;40:5125-38.