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附 錄A1
Dynamic Modeling of Vehicle Gearbox for Early
Detection of Localized Tooth Defect
ABSTRACT
Dynamic modeling of the gear vibration is a useful tool to study the vibration response of a geared system under various gear parameters and operating conditions. An improved understanding of vibration signal is required for early detection of incipient gear failure to achieve high reliability. However, the aim of this work is to make use of a 6-degree-of-freedom gear dynamic model including localized tooth defect for early detection of gear failure. The model consists of a gear pair, two shafts, two inertias representing load and prime mover and bearings. The model incorporates the effects of time-varying mesh stiffness and damping, backlash, excitation due to gear errors and modifications. The results indicate that the simulated signal shows that as the defect size increases the amplitude of the acceleration signal increases. The crest factor and kurtosis values of the simulated signal increase as the fault increases. Though the crest factor and kurtosis values give similar trends, kurtosis is a better indicator as compared to crest factor.
KEYWORDS：Vibration acceleration, system modeling, Crest Factor, Kurtosis value, defect size, gear meshing, pinion, gear
INTRODUCTION
Much of the past research in the dynamic modeling area has concluded that an essential solution to the problem is to use a comprehensive computer modeling and simulation tool to aid the transmission design and experiments. These have been two major obstacles to such an approach: (1) Progress in understanding of the basic gear rattle phenomenon has been limited and slow. This is because the engine-clutch-transmission system involves some strong nonlinearities including gear backlash, multi-valued springs, dry friction, hysteresis, and the like. (2)The gear rattle is a system problem and not only problem of gear teeth. Even through the research and industrial community has discussed the difficulties in varies stages of the problem, yet no thorough frame work covering the entire investigation process of such problem currently exists. This is largely due o the complexity of the power train system, which may make a computer analysis tool inefficient, in particularly when many different elements and clearances are encountered (e.g., gears, bearings, splines, synchronizers, and clutch).
A comprehensive review of mathematical models used in gear dynamics, published before 1986, has been presented by. In this review, gear dynamic models without defects have been discussed. In the past few years, researchers have been working on the gear dynamic models which include defects like pitting, spalling, crack and broken tooth.
A single-degree-of-freedom model is used which include the e4ffects of variable mesh stiffness, damping, gear errors, profile modifications and backlash. The effect of time-varying meshing damping is also included in this case, The solution is obtained by using the harmonic balance methods. A method of calculated the optimum profile modification has been proposed in order to obtain a zero vibration of the gear pair. They also proposed a linear approximate equation to mode the gear pair by using a single-degree-of freedom model
Gear rattle vibration is a undesirable vibration for passenger cars and light trucks equipped with manual transmissions. Unlike automatic transmissions, manual transmission do not have the high viscous damping inherent to a hydrodynamic torque converter to suppress the impacting of gear teeth oscillating through their gear backlash. Therefore a significant level of vibration an be produced by the gear rattle and transmitted both inside the passenger compartment and outside the vehicle. Gear rattle, idle shake, and other vibration generated in the automobile driveline have become an important concern to automobile manufactures in their pursuit of an increased level of perception of high vibration quality. The torsional vibration o driveline is a major source of gear rattle vibration. The manual transmission produces gear rattle by the impacting of gear oscillating through their gear backlash. The impact collisions are transmitted to the transmission housing via shafts and bearings.
The gear pair dynamic models including defects have been done by. The study suggests that little work has been done on modeling of gear vibration with defect and an accurate analytical procedure to predict gear vibrations in the presence of local tooth fault has yet to be developed.However, the purpose of this paper is to develop a multidegree-of-freedom nonlinear model for a gear pair that can be used to study the effect of lateral-torsional vibration coupling on vibration response in the presence of localized tooth defect. A typical fault signal is assumed to be impulsive in nature because of the way it is generated. The simulation artificially introduced pitting in gears in multi-stage automotive transmission gearbox at different operation conditions (load, speed, etc). The processing of simulated and experimental signals is also introduced.
SIGNAL-PROCESSING TECHNIQUE
Among various signal-processing techniques, crest factor and kurtosis analysis have been used for analyzing the whole vibration signal for the early detection of fault. In this section, crest factor and kurtosis value have been explained.
MATHEMATICAL MODEL FORMULATION
Helical gears are almost always used in automotive transmissions. The meshing stiffness of a helical tooth pair is time-varying, and was modeled as a series of suggested spur gears so that the simulation techniques for spur gears can be applied. where M is Module (mm), b is Face width (mm), is pressure angle (deg), is helix angle (deg) and D1 is pitch diameter (mm).
附 錄A2
汽車變速箱動(dòng)態(tài)建模輪齒局部缺陷的早期檢測
摘要：
在研究齒輪系統(tǒng)中各種齒輪參數(shù)的振動(dòng)響應(yīng)和操作條件時(shí)，齒輪振動(dòng)的動(dòng)態(tài)建模是一個(gè)非常有用的工具。對早期的齒輪檢測提出了一種改進(jìn)理解的振動(dòng)信號，但還沒達(dá)到高的可靠性。但是，這項(xiàng)工作的目的是利用一個(gè)6自由度的齒輪動(dòng)力學(xué)模型對齒輪輪齒缺陷故障的早期檢測。該模型包括一對齒輪副、兩個(gè)軸、兩個(gè)慣性負(fù)載、動(dòng)力傳動(dòng)裝置和軸承。由于齒輪的誤差和變動(dòng)，該模型被采用時(shí)受到時(shí)變嚙合剛度、阻尼、反彈和勵(lì)磁的影響。模擬信號顯示的結(jié)果表明，隨著缺陷尺寸的增加加速度信號的振幅增加。模擬信號的波峰因素和峰值隨著缺陷的增加而增加。雖然波峰因素和峰值做同樣的趨勢，但和波峰因素相比峰值是一個(gè)比較好的指標(biāo)。
關(guān)鍵詞：振動(dòng)加速度、系統(tǒng)建模、波峰因素、峰值、缺陷大小、齒輪嚙合、齒輪
引言：
在大多數(shù)過去的動(dòng)態(tài)建模研究領(lǐng)域中，解決問題的重要辦法是全面使用計(jì)算機(jī)建模和仿真工具來輔助變速器的設(shè)計(jì)和實(shí)驗(yàn)。這種方法有兩種主要的障礙：（1）對齒輪傳動(dòng)中噪聲基本認(rèn)識的進(jìn)展是有限的和緩慢的。這是因?yàn)榘l(fā)動(dòng)機(jī)離合器傳動(dòng)系統(tǒng)中包括齒輪側(cè)隙、多值彈簧、非線性滯后等等。（2）齒輪發(fā)出的噪聲是一個(gè)系統(tǒng)問題，并不是齒輪的唯一問題。既使是工業(yè)研究領(lǐng)域已經(jīng)討論了這個(gè)問題在不同階段所出現(xiàn)的不同問題，但并沒有徹底覆蓋工作的框架，整個(gè)研究過程中的問題依然存在。這主要是由于列車電力系統(tǒng)的復(fù)雜性，可能導(dǎo)致你的計(jì)算機(jī)的分析工具效率不高，尤其是工作中遇到許多不同的因素和間隙（例如：齒輪、軸承、花鍵、同步器和離合器）。
在1986年出版之前，對齒輪動(dòng)力學(xué)中提出的齒輪動(dòng)態(tài)建模進(jìn)行了審查。這次審查中，對不存在齒輪缺陷的齒輪動(dòng)力學(xué)模型進(jìn)行了討論。在過去的幾年里，研究人員對齒輪的動(dòng)態(tài)模型缺陷進(jìn)行了研究，其中包括點(diǎn)蝕、剝落、裂縫和齒輪折斷等。
單自由度系統(tǒng)模型中，對嚙合剛度的影響包括4個(gè)方面的因素，阻尼、齒輪誤差、輪廓變動(dòng)和齒側(cè)間隙，時(shí)變嚙合阻尼效應(yīng)也包含在這種情況中。解決問題的方法是利用諧波平衡的方法。為了實(shí)現(xiàn)齒輪副的零振動(dòng)，提出了一種最優(yōu)化的計(jì)算方法。他們還利用齒輪副單自由度模型提出了一個(gè)近似的線性方程模型。
齒輪噪聲振動(dòng)是轎車和輕型貨車手動(dòng)變速箱中的不良振動(dòng)。不同于自動(dòng)變速箱的是，手動(dòng)變速箱沒有一個(gè)固有的高粘性阻尼液力變矩器以制止通過齒輪側(cè)隙造成的齒輪擺動(dòng)的影響。因此，無論是在車廂內(nèi)外由齒輪振動(dòng)和傳動(dòng)產(chǎn)生的噪聲，對車輛振動(dòng)的影響都非常大。隨著人們對汽車高性能振動(dòng)的追求，齒輪松動(dòng)、振動(dòng)以及其他汽車傳動(dòng)系產(chǎn)生的噪聲已成為人們關(guān)注的重點(diǎn)。傳動(dòng)系統(tǒng)中的扭轉(zhuǎn)振動(dòng)是齒輪振動(dòng)的一種主要噪聲來源。手動(dòng)變速箱產(chǎn)生的齒輪噪聲是由于齒輪受到齒輪間隙振動(dòng)的影響。通過軸和軸承把碰撞產(chǎn)生的影響傳輸?shù)阶兯傧錃んw。
對齒輪副的動(dòng)態(tài)模型缺陷的研究結(jié)果表明，對齒輪副動(dòng)態(tài)模型缺陷已做了大量工作，用準(zhǔn)確的分析方法對齒輪振動(dòng)的檢測在當(dāng)時(shí)輪齒故障方面還沒得到發(fā)展。然而，本研究的目的是建立一個(gè)多自由度非線性模型用于研究，結(jié)果表明輪齒局部缺陷的扭轉(zhuǎn)振動(dòng)是耦合振動(dòng)的響應(yīng)。由于他的產(chǎn)生一個(gè)典型的故障信號被假設(shè)為自然的脈沖信號。在不同操作條件下（負(fù)荷、轉(zhuǎn)速等），模擬人工對多級汽車變速器齒輪缺陷進(jìn)行了介紹。同時(shí)也對信號的仿真和實(shí)驗(yàn)處理進(jìn)行了介紹。
信號處理技術(shù)：
在各種各樣的信號處理技術(shù)中，波峰因素、峰值已用于分析整個(gè)振動(dòng)信號的早期故障。在本節(jié)中，波峰因素和峰值已被解釋。
數(shù)學(xué)模型：
汽車變速器中的齒輪大都是斜齒圓柱齒輪。被視為一系列齒輪仿真技術(shù)適用于螺旋狀的輪齒時(shí)變嚙合剛度。其中m是模數(shù)(毫米),b齒面寬(毫米),是壓力角(度),是螺旋角(度)，D1是直徑(毫米)。
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