The Correlation of Vibration Signal Features to Cutting Tool
鲁棒性峭度图方法的研究与应用39...
旋转机械轴承振动信号分析方法研究重庆大学博士学位论文学生姓名:彭*指导教师:柏林教授专业:机械电子工程学科门类:工学重庆大学机械工程学院二O一四年三月Vibration signal analysis of bearings in therotating machineryA Thesis Submitted to Chongqing Universityin Partial Fulfillment of the Requirement for theDoctor‟s Degree of EngineeringByPeng ChangSupervised by Prof. Bo LinSpecialty:Mechatronics EngineeringCollege of Mechanical Engineering of Chongqing University,Chongqing, ChinaMarch 2014中文摘要摘要轴承作为旋转机械中广泛使用的关键零部件之一,其运行状态直接关系整台机械设备的工作性能,开展基于振动信号分析的轴承状态监测与故障诊断的相关研究并及时准确地识别故障萌发与演变,对确保设备平稳运行、减少甚至避免重大安全事故具有相当重要的意义。
本课题以滚动轴承及滑动轴承故障振动信号为研究对象,针对滚动轴承故障信号易受噪声干扰的影响拓展并丰富了峭度图理论在振动信号降噪以及故障特征提取中的应用,并基于定向循环平稳分析理论研究了滑动轴承在油膜失稳状态下的故障信号特征,最后开发了虚拟式旋转机械轴承测试诊断系统实现了理论创新成果在工程实践中的应用。
本文的具体研究内容介绍如下:本文首先介绍了峭度图理论中涉及的峭度统计理论、谱峭度系数等数学基础,并详细阐述了传统峭度图算法以及基于COT的阶比峭度图算法在故障信号降噪和最优解调频带参数确定方面的优势。
针对传统四阶矩累积量谱峭度系数易受信号奇异点影响而不能真实估计信号峰态程度水平的问题,定义了Moors谱峭度、Hogg 谱峭度以及Crow-Siddiqui谱峭度等三种鲁棒性谱峭度系数,并提出了能消除信号奇异点干扰的鲁棒性峭度图算法。
滚动轴承和齿轮振动信号分析与故障诊断方法
2.3 滚动轴承的振动类型及故障特征分析 .................................9
2.3.1 滚动轴承的旋转机构 ..................................................................9 2.3.2 滚动轴承的振动类型 ................................................................10 2.3.2.1 滚动轴承的固有振动频率 ...............................................11 2.3.2.2 滚动轴承的缺陷特征频率 ...............................................11 2.3.2.3 滚动轴承的振动及其故障特征 ........................................12
Keywords: Rolling-Element bearing Hilbert transform
Gears
Fault Diagnosis
Envelope Analysis
Correlation-Envelope Analysis
- II -
西北工业大学硕士学位论文
目
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目
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第一章 绪
论 ................................................................... 1
3.4 齿轮振动信号的特征 ........................................................ 25
3.4.1 啮合频率及其各次谐波 .............................................................26 3.4.2 隐含成分 ..................................................................................26 3.4.3 调制效应产生边频带 ................................................................26 3.4.3.1 幅值调制 ........................................................................27 3.4.3.2 调频效应 ........................................................................27 3.4.4 轴速频率及其低次谐波 .............................................................27 3.4.5 啮合频率及其各次谐波的分析 ..................................................27 3.4.6 边带分析 ..................................................................................28
NVH相关术语定义
白噪声(white noise),整个音频频率范围内,功率密度谱均匀分布且等比例宽度的能量相等的一种噪声,换句话说,此信号在各个频段上的功率是一样的,由于白光是由各种频率(颜色)的单色光混合而成,因而此信号的这种具有平坦功率谱的性质被称作是“白色的”,此信号也因此被称作白噪声。
一般用于测试音响设备的频率响应等特性。
粉红噪声(Pink Noise),是一种频率覆盖范围很宽的声音,低频能下降到接近0Hz(不包括0Hz)高频端能上到二十几千赫,而且它在等比例带宽内的能量是相等的(误差只不过0.1dB 左右)。
比如用1/3oct带通滤波器去计算分析,我们会发现,它的每个频带的电平值都是相等的(2/3oct、1/6oct、1/12oct也是一样),这就是为什么在测试声场频率特性中要用粉红噪声作为标准信号源的原因。
也是一种随机测试信号。
这种信号随着频率每升高一个八度,信号强度就衰减3dB,由于人耳对音量的感受是对数型的,所以“粉红噪声”这种每升高一个八度、强度就衰减3dB的特性,在人耳里听起来反而感觉每个频段的音量大小都是一致的。
振动:The oscillatory (back and forth) motion of a physical object.噪声:Any component of a transducer signal which does not represent the variable intended to be measured.固有频率(振动中最重要的概念):The frequency of free vibration of a mechanical system at which a specific natural mode of the system elements assumes its maximum amplitude.强迫振动:The response vibration of a mechanical system due to a forcing function (exciting force). Typically, forced vibration has the same frequency as that of the exciting force.自由振动:Vibration response of a mechanical system following an impulse-like initial perturbation (change of position, velocity or external force). Depending on the kind of perturbation, the mechanical system responds with free vibrations at one or more of its natural frequencies.绝对振动:Vibration of an object as measured relative to an inertial (fixed) reference frame. Accelerometers and velocity transducers measure absolute vibration typically of machine housings or structures; thus they are referred to as seismic transducers or inertial transducers.简谐振动:Sinusoidal vibration with a single frequency component.赫兹:(Hz) Unit of frequency measurement in cycles per second.频率:The repetition rate of a periodic vibration per unit of time. Vibration frequency is typically expressed in units of cycles per second (Hertz) or cycles per minute (to more easily relate to shaft rotative speed frequency). In fact, since many common machine malfunctions produce vibration which has a fixed relationship to shaft rotative speed, vibration frequency is often expressed as a function of shaft rotative speed. 1X is a vibration with a frequency equal to shaft rpm, 2X vibration is at twice shaft rpm, 0.5X vibration with a frequency equal to one-half shaft rpm, etc.振幅:The magnitude of periodic dynamic motion (vibration). Amplitude is typically expressed in terms of signal level, e.g., millivolts or milliamps, or the engineering units of the measured variable, e.g., mils, micrometres (for displacement), inches per second (for velocity), etc. The amplitude of a signal can bemeasured in terms of peak to peak, zero to peak, root mean square, or average.相位角:The timing relationship, in degrees, between two vibration signals, such as a Keyphasor® pulse and a vibration signal; also, the phase difference between two signals, such as the input force signal and output response signal. The "lag" corresponds to "minus" in mathematical formulations.加速度:The time rate of change of velocity. For harmonic motion, this is often expressed as g or a. Typical units for acceleration are feet per second per second (ft/s2) pk, meters per second per second (m/s2) pk, or more commonly g pk (= acceleration of earths gravity = 386.1 in/s2 = 32.17 ft/s2 = 9.81 m/s2). Acceleration measurements are generally made with an accelerometer and are typically used to evaluate high frequency vibration of a machine casing or bearing housing due to blade passing, gear mesh, cavitation, rolling element bearing defects, etc.速度:The time rate of change of displacement. Typical units for velocity are inches/second or millimetres/second, zero to peak. Velocity measurements are used to evaluate machine housing and other structural response characteristics. Electronic integration of a velocity signal yields displacement, but not position.位移:The change in distance or position of an object relative to a reference. Machinery vibration displacement is typically a peak to peak measurement of the observed vibrational motion or position, and is usually expressed in units of mils or micrometres. Proximity probes measure displacement directly. Signal integration is required to convert a velocity signal to displacement, but does not provide the initial displacement (distance from a reference) measurement.分贝:A numerical expression of the ratio of the power or voltage levels of electrical signals.dB = 10 log P1/P2 = 20 log V1/V2.共振:The condition in which the frequency of an external force coincides with a natural frequency of the system. A resonance typically is identified by an amplitude peak, accompanied by a maximum rate of change of phase lag angle.频谱:Commonly a presentation of the amplitudes of a signal's frequency components versus their frequencies. Or the frequency content of a signal.信噪比:The number formed by dividing the magnitude of the signal by the magnitude of the noise present in the signal. A low noise signal has a high Signal-to-Noise Ratio, while a high noise signal has a low Signal-to-Noise Ratio. The noise can originate from many different sources and is considered to be any part of the signal which does not represent the parameter being measured.比例阻尼:proportional damping传递矩阵法:transfer matrix method颤振:flutter 喘振:surge功率谱密度函数:power spectral density function功率谱密度矩阵:power spectral density matrix互谱密度函数:cross-spectral density function互谱密度函数:cross-spectral density matrix互相关函数:cross-correlation function混沌振动:chaotic vibration简正模态函数:normal modal function简正模态矩阵:normal modal matrix模态截断法:mode truncation method模态综合法:component modal synthesis method均值Mean value方差Variance机械阻抗Mechanical impedance位移阻抗Displacement impedance速度阻抗Speed impedance加速度阻抗Acceleration impedance声学基础知识扫盲帖(原创)1、人耳能听到的频率范围是20—20KHZ2、把声能转换成电能的设备是传声器3、把电能转换成声能的设备是扬声器4、声频系统出现声反馈啸叫,通常调节均衡器5、房间混响时间过长,会出现声音混浊6、房间混响时间过短,会出现声音发干1477、唱歌感觉声音太干,当调节混响器8、讲话时出现声音混浊,可能原因是加了混响效果9、声音三要素是指音强、音高、音色10、音强对应的客观评价尺度是振幅11、音高对应的客观评价尺度是频率12、音色对应的客观评价尺度是频谱13、人耳感受到声剌激的响度与声振动的频率有关14、人耳对高声压级声音感觉的响度与频率的关系不大15、人耳对中频段的声音最为灵敏16、人耳对高频和低频段的声音感觉较迟钝17、人耳对低声压级声音感觉的响度与频率的关系很大18、等响曲线中每条曲线显示不同频率的声压级不相同,但人耳感觉的响度相同19、等响曲线中,每条曲线上标注的数字是表示响度级20、用分贝表示放大器的电压增益公式是20lg(输出电压/输入电压)21、响度级的单位为phon22、声级计测出的dB值,表示计权声压级23、音色是由所发声音的波形所确定的24、声音信号由稳态下降60dB所需的时间,称为混响时间25、乐音的基本要素是指旋律、节奏、和声26、声波的最大瞬时值称为振幅27、一秒内振动的次数称为频率28、如某一声音与已选定的1KHz纯音听起来同样响,这个1KHz纯音的声压级值就定义为待测声音的响度29、人耳对1~3KHZ的声音最为灵敏30、人耳对100Hz以下,8K以上的声音感觉较迟钝31、舞台两侧的早期反射声对原发声起加重和加厚作用,属有益反射声作用32、观众席后侧的反射声对原发声起回声作用,属有害反射作用33、声音在空气中传播速度约为340m/s34、要使体育场距离主音箱约34m的观众听不出两个声音,应当对观众附近的补声音箱加0.1s延时35、反射系数小的材料称为吸声材料36、透射系数小的材料称为隔声材料37、透射系数大的材料,称为透声材料38、全吸声材料是指吸声系数α=139、全反射材料是指吸声系数α=040、岩棉、玻璃棉等材料主要吸收高频和中频41、聚氨酯吸声泡沫塑料主要吸收高频和中频42、薄板加空腔主要吸收低频43、薄板直接钉于墙上吸声效果很差44、挂帘织物主要吸收高、中频45、粗糙的水泥墙面吸声效果很差46、人耳通过声源信号的强度差和时间差,可以判断出声源的空间方位,称为双耳效应47、两个声音,一先一后相差5ms--50ms到达人耳,人耳感到声音是来自先到达声源的方位,称为哈斯效应48、左右两个声源,声强级差大于15dB,听声者感到声源是在声强级大的声源方位,称为德波埃效应49、一个声音的听音阈因为其它声音的存在而必须提高,这种现象称为掩敝效应50、厅堂内某些位置由于声干涉,使某些频率相互抵消,声压级降低很多,称为死点51、声音遇到凹的反射面,造成某一区域的声压级远大于其它区域称为声聚焦52、声音在室内两面平行墙之间来回反射产生多个同样的声音,称为颤动回声。
encyclopediaofvibration
Encyclopedia of VibrationBraun, Simon GISBN-13: 9780122270857Table of ContentsAbsorbers, VibrationValder Steffen, Jr, and Domingo Rade, Federal University of Uberlandia, BrazilActive Control of Civil StructuresT T (Larry) Soong, MCEER, SUNY Buffalo, USA, and B F Spencer, Jr, USAActive Control of Vehicle VibrationMehdi Ahmadian, Virginia Polytechnic Institute & State University, USAActive IsolationSteve Griffin, AFRL/VSSV, USA, and Dino Sciulli, Virginia, USAActive Vibration SuppressionDaniel Inman, Virginia Polytechnic Institute & State University, USAActuators and Smart StructuresVictor Giurgiutiu, University of South Carolina, USAAdaptive FiltersStephen J Elliott, University of Southampton, UKAeroelastic ResponseJ E Cooper, University of Manchester, UKAveragingSimon Braun, Technion - Israel Institute of Technology, IsraelBalancingR Bigret, Drancy, FranceBasic PrinciplesGiora Rosenhouse, Technion City, IsraelBeamsRichard A Scott, University of Michigan, USABearing DiagnosticsK McKee and C James Li, Rensselaer Polytechnic Institute, USABearing VibrationsR Bigret, Drancy, FranceBeltsL Zhang and J W Zu, University of Toronto, CanadaBlades and Bladed DisksR Bigret, Drancy, FranceBoundary ConditionsGiora Rosenhouse, Technion City, IsraelBoundary Element MethodsFriedel Hartmann, University of Kassel, GermanyBridgesSingiresu S Rao, University of Miami, USACablesNoel C Perkins, University of Michigan, USACepstrum AnalysisBob Randall, University of New South Wales, AustraliaChaosPhilip J Holmes, Princeton University, USAColumnsIsaac Elishakoff, Florida Atlantic University, USA, and C W Bert, University of Oklahoma, USACommercial SoftwareGuy Robert, Liege, BelgiumComparison of Vibration Properties: Comparison of Spatial PropertiesMircea Rades, University Politechnica of Bucharest, RomaniaComparison of Vibration Properties: Comparison of Modal PropertiesMircea Rades, University Politechnica of Bucharest, RomaniaComparison of Vibration Properties: Comparison of Response PropertiesMircea Rades, University Politechnica of Bucharest, RomaniaComputation for Transient and Impact DynamicsDavid J Benson, University of California, San Diego, USA, and John Hallquist, Livermore Software Technology Corporation (LSTC), USAContinuous MethodsC W Bert, University of Oklahoma, USACorrelation FunctionsSimon Braun, Technion - Israel Institute of Technology, IsraelCrashVictor H Mucino, West Virginia University, USACritical DampingDaniel Inman, Virginia Polytechnic Institute & State University, USADamping in FE ModelsGeorge A Lesieutre, Pennsylvania State University, USADamping MaterialsEric E Ungar, Acentech, Inc, USADamping MeasurementD J Ewins, Imperial College of Science, Technology and Medicine, UKDamping ModelsDaniel Inman, Virginia Polytechnic Institute & State University, USADamping MountsJian-Qiao Sun, University of Delaware, USADamping, ActiveAmr Baz, University of Maryland, USAData AcquisitionBob Randall and M J Tordon, University of New South Wales, AustraliaDiagnostics and Condition Monitoring, Basic ConceptsM Sidahmed, Université de Compiegne, France, and Giorgio Dalpiaz, University of Bologna, Italy Digital FiltersTony Constantinides, Imperial College of Science, Technology and Medicine, UKDiscrete ElementsSingiresu S Rao, University of Miami, USADisksD J Ewins, Imperial College of Science, Technology and Medicine, UKDisplays of Vibration PropertiesMircea Rades, University Politechnica of Bucharest, RomaniaDynamic StabilityA Steindl, Vienna University of Technology, Austria, and Hans Troger, Vienna, Austria Earthquake Excitation and Response of BuildingsFarzad Naeim, John A Martin & Associates, Inc, USAEigenvalue AnalysisOliver Bauchau, Georgia Institute of Technology, USAElectrorheological and Magnetorheological FluidsR Stanway, The University of Sheffield, UKElectrostrictive MaterialsKenji Uchino, Pennsylvania State University, USA, and H S Tzou, University of Kentucky, USA Environmental Testing, ImplementationP S Varoto, Escola de Engenharia de Sao Carlos, USP, BrazilEnvironmental Testing, OverviewDavid Smallwood, Sandia National Laboratories, USAFatigueAlbert Kobayashi and M Ramula, University of Washington, USAFeed Forward Control of VibrationChristopher R Fuller, Virginia Polytechnic Institute & State University, USAFinite Difference MethodsSingiresu S Rao, University of Miami, USAFinite Element MethodsSingiresu S Rao, University of Miami, USAFluid/Structure InteractionSabih Hayek, Pennsylvania State University, USAFlutterJan Wright, University of Manchester, UKFlutter, Active ControlFrank H Gern, Virginia Polytechnic Institute & State University, USAForced ResponseN A J Lieven, Bristol University, UKFriction DampingRaouf Ibrahim, Wayne State University, USAFriction Induced VibrationsRaouf Ibrahim, Wayne State University, USAGear DiagnosticsC James Li, Rensselaer Polytechnic Institute, USAGround Transportation SystemsA K W Ahmed, Concordia University, CanadaHand-transmitted VibrationM Griffin, University of Southampton, UKHelicopter DampingNorman M Wereley, University of Maryland at College Park, USAHilbert TransformsM Feldman, Technion - Israel Institute of Technology, IsraelHybrid ControlKon-Well Wang, Pennsylvania State University, USAHysteretic DampingH T Banks, North Carolina State University, USA and G A Pinter, North Carolina State University, USA Identification, Fourier-based MethodsSimon Braun, Technion - Israel Institute of Technology, IsraelIdentification, Model Based MethodsSpilios D Fassois, University of Patras, GreeceInverse ProblemsY M Ram, Louisiana State University, USAKrylov-Lanczos MethodsRoy Craig, University of Texas, USALaser Based MeasurementsP Castellini, E P Tomasini, and G M Revel, Università di Ancona, ItalyLinear AlgebraCharbel Farhat, University of Colorado, USA, and Daniel Rixen, Delft, BelgiumLinear Damping Matrix MethodsFai Ma, University of California, Berkeley, USALiquid SloshingRaouf Ibrahim, Wayne State University, USALocalizationChristophe Pierre, University of Michigan, USAMagnetostrictive MaterialsAlison Flatau, National Science Foundation, USAMembranesArthur W Leissa, Ohio State University, USAMEMs ApplicationsI Stiharu, Concordia University, CanadaMEMs, Dynamic ResponseI StiharuMEMs, General PropertiesI StiharuModal Analysis, Experimental: Basic PrinciplesD J Ewins, Imperial College of Science, Technology and Medicine, UKModal Analysis, Experimental: Measurement TechniquesJ M Silva, Institute Superior Technico, PortugalModal Analysis, Experimental: Parameter Extraction MethodsN M Maia, Institute Superior Technico, PortugalModal Analysis, Experimental: Construction of Models from TestsN M Maia, Institute Superior Technico, PortugalModal Analysis, Experimental: ApplicationsD J Ewins, Imperial College of Science, Technology and Medicine, UKMode of VibrationD J Ewins, Imperial College of Science, Technology and Medicine, UKModel Updating and ValidatingM Link, Universität Gesamthoschule Kassel, GermanyMotion SicknessM Griffin, University of Southampton, UKNeural Networks, Diagnostic ApplicationsM Zacksenhouse, Technion - Israel Institute of Technology, IsraelNeural Networks, General PrinciplesB Dubuisson, La Croix Saint Ouen, FranceNoise, Noise Radiated from Elementary SourcesMichael Peter Norton and J Pan, University of Western Australia, AustraliaNoise, Noise Radiated by Baffled PlatesMichael Peter Norton and J pan, University of Western Australia, AustraliaNondestructive Testing, SonicScott Doebling and Charles Farrar, Los Alamos National Laboratory, USANondestructive Testing, UltrasonicL W Schmerr Jr, Iowa State University, USANonlinear Normal ModesAlexander Vakakis, University of Illinois, USANonlinear System IdentificationB F Feeny, Michigan State University, USANonlinear System Resonance PhenomenaAnil Bajaj and Charles M Krousgrill, Purdue University, USANonlinear Systems AnalysisAnil Bajaj, Purdue University, USANonlinear Systems, OverviewNoel C Perkins, University of Michigan, USAObject Oriented Programming in FE AnalysisIgor Klapka, Université de Liège, Belgium, Alberto Cardona, INTEC, Argentina, and Philipee Devloo, Universidade Estadual de Campinas, BrazilOptimal FiltersStephen J Elliott, University of Southampton, UKPackagingJorge Marcondes, San Jose University, USAParallel ProcessingDaniel Rixen, Delft, BelgiumParametric ExcitationAlexandra David and Subhash Sinha, Auburn University, USAPerturbation Techniques for Non-linear SystemsSteve Shaw, Michigan State University, USAPiezoelectric MaterialsH S Tzou, University of Kentucky, USA, and M C Natori, Institute of Space & Astronautical Science, JapanPipesSingiresu S Rao, University of Miami, USAPlatesArthur W Leissa, Ohio State University, USARandom ProcessesMikhail F Dimentberg, Worcester Polytechnic Institute, USARandom Vibration, Basic TheoryMikhail F Dimentberg, Worcester Polytechnic Institute, USAResonance and AntiresonanceMircea Rades, University Politechnica of Bucharest, RomaniaRobot VibrationsWayne Book, Georgia Institute of Technology, USARotating Machinery, Essential FeaturesR Bigret, Drancy, FranceRotating Machinery, Model CharacteristicsR Bigret, Drancy, FranceRotating Machinery, MonitoringR Bigret, Drancy, FranceRotor DynamicsR Bigret, Drancy, FranceRotorstator InteractionsR Bigret, Drancy, FranceSeismic Instruments, Environmental FactorsKenneth McConnell, Iowa State University, USASensors and ActuatorsH S Tzou, University of Kentucky, USA, and C S Chou, National Taiwan University, Republic of ChinaShape Memory AlloysM Baz, University of Maryland, USAShellsW Soedel, Purdue University, USAShip VibrationsWilliam S Vorus, University of New Orleans, USAShockJorge Marcondes, San Jose University, USAShock Isoloation SystemsMircea Rades, University Politechnia of Bucharest, RomaniaSignal Generation Models for DiagnosticsGiorgio Dalpiaz, University of Bologna, Italy, and M Sidahmed, Université de Compiegne, FranceSignal Integration and DifferentiationStuart Dyne, University of Southampton, UKSignal Processing, Model Based MethodsSimon Braun, Technion - Israel Institute of Technology, IsraelSpectral Analysis, Classical MethodsSimon Braun, Technion - Israel Institute of Technology, IsraelStandards for Vibrations of Machines and Measurement ProceduresJohn Niemkiewicz, Maintenance and Diagnostic (M&D) LLC, USAStochastic Analysis of Nonlinear SystemsY K Lin and C Q Cai, Florida Atlantic University, USAStochastic SystemsMikhail F Dimentberg, Worcester Polytechnic Institute, USAStructural Dynamic ModificationsA Sestieri, Universita Degli Studi di Roma, Italy, and W D'Amorogio, Universita Be L'Aquila, ItalyStructure-Acoustic Interaction, High FrequenciesA Sestieri, Universita Degli Studi di Roma, ItalyStructure-Acoustic Interaction, Low FrequenciesA Sestieri, Universita Degli Studi di Roma, ItalyTesting, Non-linear SystemsAlan Haddow, Michigan State University, USATheory of Vibration, FundamentalsBingen Yang, University of Southern California, USATheory of Vibration, SuperpositionM G Prasad, Stevens Institute of Technology, USATheory of Vibration, Duhamel's Principle and ConvolutionG Rosenhouse, Technion - Israel Institute of Technology, IsraelTheory of Vibration, Energy MethodsSingiresu S Rao, University of Miami, USATheory of Vibration, Equations of MotionJonathan Wickert, Carnegie Mellon University, USATheory of Vibration, SubstructuringMehmet Sunar, King Fahd University of Petroleum and Minerals, Saudi ArabiaTheory of Vibration, Impulse Response FunctionRakesh Kapania, Virginia Polytechnic Institute & State University, USATheory of Vibration, Variational MethodsSingiresu S Rao, University of Miami, USATime-Frequency MethodsPaul White, University of Southampton, UKTire VibrationsG D Shteinhauz, The Goodyear Tire & Rubber Company, USATool Wear MonitoringM Sidahmed, Université de Compiegne, FranceTransducers for Absolute MotionKenneth McConnell, Iowa State University, USATransducers for Relative MotionKenneth McConnell, Iowa State University, USA, Simon Braun, Technion - Israel Institute of Technology, Israel, and Gene E Maddux, Tipp City, USATransform MethodsSimon Braun, Technion - Israel Institute of Technology, IsraelTransforms, WaveletsPaul White, University of Southampton, UKUltrasonicsM J S Lowe, Imperial College of Science, Technology and Medicine, UKVibration Generated Sound, FundamentalsMichael Peter Norton and S J Drew, University of Western Australia, AustraliaVibration Generated Sound, Radiation by Flexural ElementsMichael Peter Norton and S J Drew, University of Western Australia, AustraliaVibration IntensitySabih Hayek, Pennsylvania State University, USAVibration Isolation, Applications and CriteriaE Rivin, Wayne State University, USAVibration Isolation TheoryE Rivin, Wayne State University, USAVibration TransmissionSabih I Hayek, Pennsylvania State University, USAVibro-impact SystemsF Peterka, Academy of Sciences of the Czech Republic, Czech RepublicViscous DampingFarhan Gandhi, Pennsylvania State University, USAWave Propagation, Waves in an Unbound MediumM J S Lowe, Imperial College of Science, Technology and Medicine, UKWave Propagation, Interaction of Waves with BoundariesM J S Lowe, Imperial College of Science, Technology and Medicine, UKWave Propagation, Guided Waves in StructuresM J S Lowe, Imperial College of Science, Technology and Medicine, UKWhole-body VibrationM Griffin, University of Southampton, UKWind-Induced VibrationsAhsan Kareem, University of Notre Dame, USAWindowsSimon Braun, Technion - Israel Institute of Technology, Israel。
纳米固体的声子硬化和光子软化
Size-induced acoustic hardening and optic softening of phonons in CdS, InP, CeO2, SnO2, and Si nanostructuresChang Q SunSchl EEE, NTU, Singaporeecqsun@.sg; .sg/home/ecqsun/It has been puzzling that the Raman optical modes shift to lower frequency (or termed as optical mode softening) associated with creation of Raman acoustic modes that shift to higher energy (or called as acoustic hardening) upon nanosolid formation and size reduction. Understandings of the mechanism behind the size-induced acoustic hardening and optic softening have been quite controversial. On the basis of the recent bond order-length-strength (BOLS) correlation [Phys. Rev. B 69 045105 (2004)], we show that the optical softening arises from atomic cohesive energy weakening of surface atoms and the acoustic mode hardening is predominated by intergrain interaction. Agreement between predictions and observations has been reached for Si, CdS, InP, TiO2, CeO2, and SnO2 nanostructures with elucidation of vibration frequency of the corresponding isolated dimers. Findings further evidence the impact of bond order loss to low-dimensional systems and the essentiality of the BOLS correlation in describing the behavior of nanostructures.PACS: 61.46.+w; 78.30.-j; 78.67.-n; 63.22.+mKeywords: nanostructures; Raman shift; BOLS correlation; surface bond contraction; interparticle interaction- 1 -- 2 -I IntroductionAtomic vibration is of high interest because the behavior of phonons influence directly on the electrical and optical properties in solid materials and devices such as electron-phonon coupling in photoabsorption and photoemission, and phonon scattering in device transport dynamics.1 It has been long surprising that with structural miniaturization down to nanometer scale the transverse and the longitudinal optical (TO/LO) Raman modes shift towards lower frequency (or called as optical mode softening)2 accompanied with generation of low-frequency Raman (LFR) acoustic modes at wave numbers of a few or a few tens cm -1. The LFR peak shifts up (or called as acoustic mode hardening) towards higher frequency upon the solid size being reduced.3,4 Generally, the size dependent Raman shifts follow a scaling relation: 2,4κωωj f j K A K +∞=)()(where A f and κ are adjustable parameters for data fitting. K j , the dimensionless form of size, is the number of atoms with diameter d lined along the radius (R j ) of a spherical dot. For optical red shift, A f < 0. For Si example, ω(∞) = 520 cm -1 corresponds to wavelength of 2×104 nm and the index κ varies from 1.08 to = 1.44 or even 2.0, varying from source to source.5 For the LFR blue shift, A f > 0, κ = 1, and ω(∞) = 0. Therefore, the LFR disappears for large particles.The underlying mechanism behind the Raman shift is under debate with numerous theories. Theoretical studies of phonon frequency shift are often based on continuum dielectric mechanism.6,7 Sophisticated calculations have been carried out using models of correlation length,8 bulk phonon dispersion,9 lattice-dynamic matrix,10 associated with microscopic valence force field,4 phonon confinement,11 and bond polarization.2The mechanism of quadrupolar vibration taking the individual nanoparticle as a whole was assumed to be responsible for the LFR acoustic modes. The phonon energies are size dependent and vary with materials of the host matrix. The LFRscattering from silver nanoclusters embedded in porous alumina 12 andSiO 213 was suggested to arise from the quadrupolar vibration modes that are enhanced by the excitation of the surface plasmas of the encapsulated Ag particles. The selection of modes by LFR scattering is suggested to arise from the stronger plasmon-phonon coupling for these modes. For an Ag particle smaller than four nanometers, the size dependence of the peak frequency can be explained using Lamb’s theory 14 that gives vibrational frequencies of a homogeneous elastic body with a spherical form. On the other hand, lattice strain was suggested to be another possible mechanism for the LFR blue shift as size-dependent compressive strain has been observed from CdS x Se 1-x nanocrystals embedded in a borosilicate (B 2O 3-SiO 2) glass matrix.15 The lattice strain enhances the surface stress when the crystal size is reduced. Therefore, the observed blue shift of acoustic phonon energies was suggested to be consequence of thecompressive stress that overcomes the red shift caused by phonon confinement. Liang et al 16 presented a model for the Raman blue shift by relating the frequency shift to the bond length and bond strength that are functions of entropy latent heat of fusion and the critical temperature for solid-liquid transition.- 3 -The high-frequency Raman shift has ever been suggested to be activated by surface disorder,17 surface stress,18,19 and phonon quantum confinement,20,21 as well as surface chemical passivation.22 The phonon confinement model attributes the red shift of the Raman line to the relaxation of the wave-vector selection rule (∆q = 0) for the excitation of the Raman active phonons due to their localization. The relaxation of the selection rule arises from the finite crystalline size and the diameter distribution of nanosolid in the films. When the size is decreased the rule of momentum conservation will be relaxed and the Raman active modes will not be limited at the center of the Brillouin zone.18 A Gaussian-type phonon confinement model 21 indicates that strong phonon damping presents whereas calculations 23 using the correlation functions of the local dielectric constant ignores the role of phonon damping in the nanosolid. The large surface-to-volume ratio of a nanodot strongly affects the optical properties because of introducing surface polarization and surface states.24 Using a phenomenological Gaussian envelope function of phonon amplitudes, Tanaka et al.25 showed that the size dependence of optic red shift originated from the relaxation of the ∆q = 0 selection rule based on the phonon confinement argument with negative phonon dispersion. The phonon energies for all the glasses are reduced and the values of the phonon energies of CdSe nanodots are found to be quite different for different host glasses. A sophisticated analytical model of Hwang et al.5 indicates that the effect of lattice strain must be considered in explaining the optical red shift for CdSe nanodots embedded in different glass matrices. For a free surface, it has been derived that the red shift follows the relation:()()2−=∞∆jjBK K ωω (1)The value of B in eq (1) is a competition between the phonon negative dispersion and the size-dependent surface tension. Thus, a positive value of B indicates that the phonon negative dispersion exceeds the size-dependent surface tension and consequently causes the red shift of phonon frequency, and vice versa. In case of balance of the two effects, i.e. B = 0, the size dependence disappears. There are still some difficulties to use this equation, as remarked by Hwang et al.5It is noted that currently available models for the optical red shift are based on assumptions that the materials are homogeneous and isotropic which is valid only in the long-wavelength limit. When the size of the nanosolid is in the range of a few nanometers the continuum dielectric models exhibit limitations. Therefore, the discussed models could hardly reproduce with satisfactory the Raman frequency shifts at the lower end of the size limit. The objective of this work is to show that derivatives of the recent BOLS correlation mechanism 26,27,28 could reproduce the size induced Raman shifts leading to deeper and consistent insight into the mechanism behind with information about the vibration frequency of the corresponding dimers, which is beyond the scope of other sophisticated models.- 4 -II Principle2.1 Vibration modesRaman scattering is known to arise from the radiating dipole moment induced in a system by the electric field of incident electromagnetic radiation. The laws of momentum and energy conservation govern the interaction between a phonon and the incident photon. When we consider a solid containing numerous Bravais unit cells, and each cell contains n atoms, there will be 3n modes of vibrations. Among the 3n modes, there will be three acoustic modes, LA, TA 1, and TA 2, and 3(n-1) optical modes, LO and TOs. The acoustic modes represent the in-phase motion of the mass center of the unit cell or the entire solid as a whole. The long-range Coulomb interaction is responsible for the intercluster interaction. Therefore, the acoustic LFR should arise from the vibration of the entire nanosolid interacting with the host matrix or with other neighboring clusters. Therefore, it is expected that the LTR mode approaches zero if the particle size is infinitely large. The optical modes arise from the relative motion of the individual atoms in a complex unit cell. For elemental solids with a simple crystal structure such as the fcc of Ag, only acoustic modes present. Silicon or diamond is an interlock of two fcc unit cells that contain each cell two atoms in nonequivalent positions, there will be three acoustic modes and three optical modes.2.2 Optical phonon frequencyThe total energy E causing lattice vibration consists of the component of short-range interactions E S and the component of long-range Coulomb interaction E C 4.C S E E E +=(2)The long-range part corresponds to the LFR mode and represents the weak interaction between nanosolids. The short-range energy E S arising from nearest bonding atoms, which is composed of two parts. One is the lattice thermal vibration E V (T) and the other is interatomic binding energy at zero K, E b (r). The E S for a dimer can be expressed in a Taylor’s series, 26()()()()()()()()()()()()()T E d E d r k d r k d E d r dr r u d d r dr r u d d u d r dr n r u d T r E V b b d d n dr n n n S +=+−+−+=−+−++=−⎟⎟⎠⎞⎜⎜⎝⎛==∑ (6)'2!3!20!,32333222K(3)The term with index n = 0 corresponds to the minimal binding energy at T = 0 K, E b (d ) < 0. The term n = 1 is the force [()d r r u ∂∂= 0] at equilibrium and the terms n ≥ 2correspond to the thermal vibration energy, E V (T). By definition, the thermal vibration energy of a single bond is- 5 -()()()()()()222222!22d r d r dr n r u d d r k d r T E d n n n n v V −⎟⎟⎠⎞⎜⎜⎝⎛−=−=−=∑≥−µω(4)where r-d = x is the magnitude of lattice vibration. µ is the reduced mass of the dimer of concern. The k v = µω22/d E b ∝ is the force constant for lattice harmonic vibration with an angular frequency of ω. High-order terms correspond to nonlinear contribution that can be negligible in the first order approximation.For a single bond, the k v is strengthened because of the bond order loss induced bond contraction and bond strength gain.26-29 For a single atom, we have to count contribution from all the neighboring bonds. For a lower-coordinated atom the resultant k v could be lower because of the bond order loss. Considering the vibration amplitude x << d, it is convenient and reasonable to take the mean contribution from each coordinate to the force constant and to the magnitude of dislocation as the first order approximation:221ωµi z k k k ====L and z d r x x x z )(21−====L .Therefore the total energy of a certain atom with z coordinates is the sum over all the coordinates,()()()...!2...2,22222+−+=⎥⎥⎦⎤⎢⎢⎣⎡+⎟⎠⎞⎜⎝⎛−+=∑d r dr r u zd zE z d r E T d E d b z b S µω (5)This relation leads to the expression for phonon frequency as a function of bond energy and atomic CN, and bond length, ()d zE dr r u d z b d 212122∝⎥⎥⎦⎤⎢⎢⎣⎡×=µω(6)According to the BOLS correlation,26-29the bond order loss of a surface atom causes the remaining bonds of the lower-coordinated atoms to contract spontaneously (d i = c i d ) associated with bond strength gain (E i = c i –m E b ). The index m recognizes the nature of the bond involved. Such a BOLS correlation and its consequence modify not only the atomic cohesive energy (atomic CN multiplies the single bond energy) but also the Hamiltonain due to the densification of binding energy in the relaxed region. A physically detectable quantity that depends on the atomic cohesive energy or the Hamiltonian for a nanosolid can be expressed as Q (K j ) in a shell structure: ⎪⎪⎩⎪⎪⎨⎧∆=∞∞−−+=∑≤300)()()()()(i i j S S j q q Q Q K Q q q N Nq K Q γ- 6 -(7)where Q (∞) = Nq 0 is for a bulk solid. q 0 and q S correspond to the Q value per atomic volume inside the bulk and in the surface region, respectively. N S = ΣN i is the number of atoms in the surface atomic shells. Combining eqs. (6) and (7) gives the size-dependent optic red shift (where ()∞Q =())1(ωω−∞):()()()∑∑≤⎟⎠⎞⎜⎝⎛+−≤<∆=⎥⎥⎦⎤⎢⎢⎣⎡−=⎥⎦⎤⎢⎣⎡−=−∞∞−3123011)1(i p m i b i i i b i i c z z R γωωγωωωω where ())[]{}()⎪⎪⎪⎪⎩⎪⎪⎪⎪⎨⎧==−=−+=⎪⎩⎪⎨⎧≤≈==12;6)75.01(4812exp 12,3,1321z z spherical K z z z c else K c K V V N N j i i i j i j i i i τγ(8)ω(1) is the vibrational frequency of an isolated dimer which is the reference point for the optical red shift upon nanosolid and bulk formation. γi is the portion of atoms in the i th atomic layer over the total number of atoms of the entire solid of different shapes(τ = 1–3 correspond to a thin plate, a rod, and a spherical dot, respectively). The index i is counted up to three from the outmost atomic layer to the center of the solid as no atomic CN imperfection is justified at i > 3.III Results and discussion3.1 Optical modes and dimer vibrationIn experiment, one can only measure ()∞ω and ()j K ω in eq (8). However, with the known m value derived from measurement of other quantities such as the melting point or core level energy,26-29 one can determine )1(ω or the bulk shift ()∞ω-)1(ω by matching the measured data represented below to the predicted line in eq (8) without needing any other assumptions,()()()[]⎪⎩⎪⎨⎧−∞∆=−=∆)(,1)(,'Theory t Measuremen K A K R j j ωωωκ (9)Hence, the frequency shift from the dimer bond vibration to the bulk value,()()κωωj R K A ∆−≡−∞')1(, can be obtained. The matching of prediction with- 7 -measurement indicates that k ≡ 1, because 1−∝∆j R K .Figure 1 shows that the BOLS predictions match exceedingly well with the theoretically calculated or the experimentally measured optical red shift of a number of samples. Derived information about the corresponding dimer vibration is given in Table 1.3.2 A coustic modes and intercluster interactionFigure 2 shows the least-square-mean-root fitting of the size dependent LFR frequency for different nanosolids. The LFR frequency depends linearly on the inverse K j()()j j K A K '−=∞−ωω(10)The zero intercept at the vertical axis, ()∞ω= 0, indicates that when the K j approaches infinity the LFR peaks disappear, which implies that the LFR modes and their blue shifts originate from vibration of the individual nanoparticle as a whole. It seems not essential to involve the quadruple motion or the bond strain at the interface. However, the current derivative gives information about the strength of interparticle interaction, as summarized in Table 2.3.3 Surface atom vibration According to Einstein’s relation, it can be derived that T k z x c B =2)(2ωµ. At a given temperature, the vibrational amplitude and frequency of a given atom is correlated as: 121−∝ωz x , which is CN dependent. The frequency and magnitude of vibration for an surface atom at the surface (z = 4) or a metallic monatomic chain (MC with z = 2) can be derived as()()()()⎪⎪⎪⎩⎪⎪⎪⎨⎧========−−−+−1,2846.0670.01,404.0388.088.4,517.0388.0232344.3111m MC m Metal m Si c z m ib b ωω and()()()()()()⎪⎪⎩⎪⎪⎨⎧=×=×=×===+MC Metal Si c z z z z x x m b b b b43.170.0643.188.0309.188.0332344.31212111111ωω(11)The vibrational amplitude of an atom at the surface or a MC is indeed greater thanthat of a bulk atom while the frequency is lower. The magnitude and frequency are sensitive to the m value and varies insignificantly with the curvature of a spherical dot when K j > 3. This result verifies for the first time the assumption30,31 that the vibration amplitude of a surface atom is always greater than the bulk value and it keeps constant at all particle sizes.IV SummaryIn summary, a combination of the BOLS correlation and the scaling relation has enabled us to correlate the size-created and the size-hardened LFR acoustic phonons to the intergrain interaction and the optic phonon softening to the CN-imperfection reduced cohesive energy of atoms near the surface edge. The optic softening and acoustic hardening is realized in a K j-1 fashion. Decoding the measured size-dependence of Raman optical shift has derived vibrational information of Si, InP, CdS, CdSe, TiO2, CeO2, and SnO2 dimers and their bulk shifts, which is beyond the scope of direct measurement. As the approach proceeds in a way from bond-by-bond, atom-by-atom, shell-by-shell, no other constraints developed for the continuum medium are applied. One striking significance is that we are able to verify the correlation between the magnitude and the frequency of vibration of the lower-coordinated atoms. Consistency between the BOLS predictions and observations also verify the validity of other possible models that incorporate the size-induced Raman shift from different perspectives.Table and Figure captionsTable 1 Vibration frequencies of isolated dimers of various nanosolids and their red shift upon bulk formation derived from simulating the size dependent red shift of Raman optical modes as shown in Figure 1.Material d(nm)A′ω(∞)(cm-1) ω(1)(cm-1)ω(∞)-ω(1)(cm-1)CdS0.65Se0.35 0.286 23.9 203.4 158.8 44.60.28624.3 303 257.7 45.3CdSe 0.2947.76 210 195.2 14.8CeO20.22 20.89 464.5 415.1 49.4SnO20.20214.11 638 602.4 35.6InP 0.2947.06 347 333.5 13.5Si 0.26325.32520.0502.317.7Table 2 Linearization of the LFR acoustic modes of various nanosolids gives information about the strength of interparticle interaction for the specific solids.Sample A′Ag-a & Ag-b 23.6 ± 0.7Ag-c 18.2 ± 0.6TiO2-a TiO2-b 105.5 ± 0.1SnO2-a 93.5 ± 5.4- 8 -CdSe-1-a 146.1 ± 6.27CdSe-1-b 83.8 ± 2.8CdSe-1-c 46.7 ± 1.4CdSSe-a 129.4 ± 1.2CdSSe-b 58.4 ± 0.8Si-LA 97.77Si-TA1 45.57Si-TA2 33.78Figure 1 (link) Comparison of the BOLS predictions (lines for different shapes) with theoretical and experimental observations (scattered data) on the size-dependent optic phonon softening of nano-solid. (a) data labeled Si-1 was calculated using correlation length model,8 Si-3 (dot) and Si-4 (rod) were calculated using the bulk dispersion relation of phonons, 9 Si-5 was calculated from the lattice-dynamic matrix,4 Si-7 was calculated using phonon confinement model,11 and Si-8 (rod) and Si-9 (dot) were calculated using bond polarizability model.2 Data for Si-2,32 Si-6,33and Si-10, and Si-1118 are measured data. (b) CdS0.65Se0.35-1, CdS0.65Se0.35 (in glass)-LO2,CdS0.65Se0.35-2, CdS0.65Se0.35 (in glass)-LO1,34CdSe-1, CdSe(in B2O3SiO2)-LO, CdSe-2, CdSe(in SiO2)-LO, and CdSe-3 CdSe(in GeO2)-LO, CdSe-4, CdSe(inGeO2)-LO,25 (c) CeO2-1,35 SnO2-1,36 SnO2-2,17 and InP37 are all measurement. Figure 2 (link) Generation and blue shift of the LFR acoustic modes where the solid dotted and dashed lines are the corresponding results of the least squares fitting. (a) the Si-a, Si-b, and Si-c were calculated from the lattice-dynamic matrix by using a microscopic valence force field model,4 the Si-d and Si-e are the experimental results.3 (b) Ag-a (Ag in SiO2)38Ag-b (Ag in SiO2)13 Ag-c (Ag in Alumina).12 (c) TiO2-a39 TiO2-b39 SnO2-a.17 (d)CdSe-a (l = 0 n = 2) CdSe-b (l = 2 n = 1) and CdSe-c (l = 0 n = 1).40 (e) CdS0.65Se0.35-a [CdS0.65Se0.35 (in glass)-LF2] and CdS0.65Se0.35-b [CdS0.65Se0.35 (in glass)-LF1]34 are all measured data.- 9 -- 10 -R a m a n S h i f t (%)K j R a m a n S h i f t (%)R a m a n S h i f t (%)Fg-1RamanShift(cm-1)RamanShift(cm-1)1/R (nm-1)1/R (nm-1)RamanShift(cm-1)RamanShift(cm-1)RamanShift(cm-1)Fg-2- 11 -1 T. Takagahara, Phys. Rev. Lett.71, 3577 (1993).2 J. Zi, H. Büscher, C. Falter, W. Ludwig, K. M. Zhang, and X. D. Xie, Appl. Phys. Lett.69, 200(1996).3 M. Fujii, Y. Kanzawa, S. Hayashi, and K. Yamamoto, Phys. Rev. B 54, R8373 (1996).4 W. Cheng and S. F. Ren, Phys. Rev. B 65, 205305 (2002).5 Y.-N. Hwang, S. Shin, H. L. 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糖尿病周围神经病变震动感觉阈值测定与分析
作者简介:郑映芳,女,主管护理师,研究方向:糖尿病足感觉阀值的测定。
670
新疆医学
第51卷
感神经障碍,致使局部充血,进而引起髓大神经纤 维受损,致使震动感觉减退叫数字震动感觉阈值 检查仪是一种测量震动感觉阈值(VPT)的设备,能 够应用于身体各个部位。该仪器震动头的振幅能够 慢慢提高,继而让人感觉到明显感觉到震动31。与 其相反,振幅减弱也可让人感觉到感觉消失不见。 检查期间的全部振幅均能够精确获得叫该仪器既 比音叉检测震动感觉阈值更加精密、更加准确,又 操作简单冋。为对比不同病程及不同年龄糖尿病患 者震动感觉阈值测定结果,本次研究选取2019年 3月~ 2020年3月期间本院收治的糖尿病患者80 例作为研究对象,详细报道如下。 1.资料与方法 1.1 一般资料
右下肢 14.97 ± 3.54 17.65 ± 3.68 23.76 ±5.56 29.76 ±4.63
不同年龄段间左下肢及右下肢VPT对比具有 明显差异(P<0.05),年龄越大,VPT越大,右下肢 及左下肢对比无明显差异(P>0.05),详见表lo
机械毕业设计英文外文翻译47部分频谱与齿轮缺陷发现相互关系的实际应用
附录一英文参考文献Application of slice spectral correlation density to gear defect detectionG Bi, J Chen, F C Zhou, and J HeThe State Key Laboratory of Vibration, Sound, and Noise,Shanghai Jiaotong University, Shanghai,People’s Republic of ChinaThe manuscript was received on 16 October 2005 and was accepted after revision for publication on 3 May 2006.DOI: 10.1243/0954406JMES206 Abstract: The most direct reflection of gear defect is the change in the amplitude and phase modulations of vibration. The slice spectral correlation density (SSCD)method presented in this paper can be used to extract modulation information from the gear vibration signal; amplitude and phase modulation information can be extracted either individually or in combination.This method can detect slight defects with comparatively evident phase modulation as well as serious defects with strong amplitude modulation. Experimental vibration signals presenting gear defects of different levels of severity verify to its character identification capability and indicate that the SSCD is an effective method, especially to detect defects at an early stage of development.Keywords: slice spectral correlation density, gear, defect detection, modulation1 INTRODUCTIONA gear vibration signal is a typical periodic modulation signal. Modulation phenomena are more serious with the deterioration of gear defects. Accordingly, the modulation sidebands in the spectrum get incremented in number and amplitude.Therefore, extracting modulation information from these sidebands is the direct way to detect gear defects. A conventional envelope technique is one of the methods for this purpose. It is sensitive to modulation phenomena in amplitude, but not in phase. A slight gear defect often produces little change in vibration amplitude, but it is always accompanied by evident phasemodulation. Employing the envelopetechnique for an incipient slight defect does not produce satisfactory results.In recent years, the theory of cyclic statistics has been used for rotating machine vibration signal and shows good potential for use in condition monitoring and diagnosis [1–3]. In this article, spectral correlation density (SCD) function in the second-order cyclostationarity is verified to be a redundant information provider for gear defect detection. It simultaneously exhibits amplitude and phase modulation during gear vibration, which is especially valuable for detecting slight defects and monitoring their evolution.The SCD function maps signals into a two-dimensional function in a cyclic frequency (CF) versus general frequency plane (a–f). Considering its information redundancy [4] and huge computation,the slice of the SCD where CF equals the shaft rotation frequency is individually computed for defect detection,which is named slice spectral correlation density (SSCD). The SSCD is demonstrated to possess the same identification capability as the SCD function. It can be computed directly from a time-varying autocorrelation with less computation and, at the same time, has clear representation when compared with a three-dimensional form of the SCD.2 SECOND-ORDER CYCLIC STATISTICSA random process generally has a time-varying autocorrelation[5]Where is the mathematic expectation operator and t is the time lag. If the autocorrelation is periodic with a period T0, the ensemble average can be estimated with time averageThe autocorrelation can also be written in the Fourier series because of its periodicityWhere Combining with equation(2), its Fourier coefficients can be given as [5]Where is the time averaging operation, is referred to as the cyclic autocorrelation (CA),and a is the CF. SCD can be obtained by applying Fourier transform of the CA with respect to the time lag tThe SCD exhibits the characteristics of the signal in a–f bi-frequency plane. All non-zero CFs characterize the cyclostationary (CS) characters of the signal.3 THE GEAR MODELThe most important component in gearbox vibration is the tooth meshing vibration, which is due to the deviations from the ideal tooth profile. Sources of such deviations are the tooth deformation under load or original profile errors made in the machining process. Generally, modulation phenomena occur when a local defect goes through the mesh and generates periodic alteration to the tooth meshing vibration in amplitude and phase. To a normal gear, the fluctuation in the shaft rotation frequency and the load or the tiny difference in the teeth space also permits slight amplitude modulation(AM) or phase modulation (PM). Therefore, the general gear model can be written as [6, 7]where fx is the tooth meshing frequency and fs is the shaft rotation frequency. am(t) and bm(t) denote AM and PM functions, respectively. The predominant component of the modulation stems from the shaft rotation frequency and its harmonics; other minute modulation components can be neglected.AM and PM, either individually or in combination,cause the presence of sidebands within the spectrum of the signal. Band-pass filtering around one of the harmonics of the tooth meshing frequency is the classical signal processing for the detailed observation of the sidebands. The filtered gear vibration signal can be expressed as followswhere fh denotes one of the harmonics of the tooth meshing frequency. The subscript m is ignored for simplification in this equation and in the following discussion. The study emphasis of this paper is the filtered gear vibration signal model in equation (7),and its carrier is a single cosine waveform and modulated parts are period functions.4 CS ANALYSIS OF THE GEAR MODELAccording to the analysis mentioned earlier, the gear vibration signal can be simplified as a periodic signal modulated in amplitude and phase. The modulation condition reflects the severity extent of potential defect in gear. In this section, AM and PM cases are studied individually, and the CS analysis of the gear model is developed on the basis of their results.4.1 AM caseThe model of AM signal is derived from equation (7)The analytic form of x(t) in equation (8) can be written asSubstitution of ^x(t) into equation (4) can deduce the CA of xˆ(t)Where is the envelope ofis equal to as a provider of modulation information.It is theFourier transform of according to equation (11). Inaddition, the Fourier transform of with respect to the time lag is thecorresponding SCD .thus can be computed using twice Fouriertransform of with respect to time t and time lag t,respectivelyAccording to integral transform, becomeswhere H(v) is the Fourier transform of a(t)After substituting H(v) into equation (13) and uncoupling f and a using theproperties of d function, the final expression of an be obtainedhas a totally symmetrical structure in four quadrants. Equation (15) is just a part of it in the first quadrant, and others are ignored for simplification. Accordingto equation (15), is composed of some discrete peaks. In addition, these peaks regularly distribute on the a–f plane. Despite the comparatively complexexpression, the geometrical description of is simple. These peaks nicelysuperpose the intersections of the cluster of lines.Then, these lines can also be considered as the character lines of .4.2 PM casePM signal derived from equation (7) isThe CA of its analytic form can be represented asThe CA in the PM case also has the envelope–carrier form, as in the AM case. Therefore, the envelope of the CA is used to extract modulation information from thesignal. Its corresponding SCD is also denoted as .The PM part, b(t), comprises finite Fourier series.The CS analysis of the PM case starts with the sinusoidalwaveform .Besselformula is employed in the computation. The finalresult of this simple case can be expressed asThe geometrical expression of equation (18) is also related tolines,and is nonzero only at their intersections. The number of the lines does not depend on the number of harmonics in the modulation part, but is infinite in theory even for a single sinusoidal PM signal. In fact, Bessel coefficients limit discrete peaks in a range centring around the zero point of a–f. The amplitude of other theoretical character peaks out of the range is close to zero with the distance far away from the zero point.When the PM function comprises several sinusoidal waveforms as shown in equation (16), components of it can be expressed as bi(t), where i is Application of SSCD to gear defect detection 1387 from 0 to I. The envelope of CA can be written asWhere equals unity. According to the two-dimensionalconvolution principle, the corresponding SCD of can be represented bywhere the sign means the two-dimensional convolution on the bi-frequencyplane. The expression of is shown in equation (18) with fs replaced byifs and B by Bi and b by bi. Despite more complex expression of the SCD in the multiple sinusoidal modulation case, the result of the two-dimensional convolutionbetween has the same geometrical distribution, as it does in the single sinusoidal modulation case. The distance between the character lines ofalong the general frequency axis is the fundamental frequency fs. Therefore, convolution does not create new character peaks, but changes their amplitude. Equation (18) also represents the SCD of the signal in equation (16), although the coefficients Cln are changed by the two-dimensional convolution.4.3 CS analysis of the gear vibration signalThe second-order CS analysis of the general gear model in equation (7) is developed on the basis of the AM and PM cases. The CA of the analytic signal also has the envelope–carrier form, and the envelope of the CA is expressed as followsTwo parts in the sign { .} in equation (21) are relatedto AM and PM functions,respectively. Therefore, the corresponding SCD of has the form of two dimensional convolution of two components issued from AM and PM functionsThe expressions of and are given in equations (15) and (18).The two-dimensional convolution between and just causes thesuperposition of the character peaks in and , as it does in the PM case. Owing to the same geometrical characters, the convolution can not change the distribution, but involves change inthe number and amplitude of the effective character peaks (whose amplitude is larger than zero). Therefore,the CS characters of the gear model are also representedby lines , as it does in the AM and PM cases.4.4 SSCD analysis of the gear vibration signal and its realizationThree modulation cases have a uniform CS character, according to the aboveanalysis. Lines f = on the bi-frequency plane are their common character lines.Figure 1 shows its distribution.Only the part in the first quadrant isdisplayed because of the identical symmetry of in four quadrants. The number of these discrete points and the amplitude of the spectrum peaks reflect the modulation extent of the signal.The SCD provides redundant information for gear modulation information identification. In fact, some slices of it are sufficient for thepurpose. For the AM case, the slice of , where CF is (in the first quadrant), can be derived from equation (15)The slice contains equidistant character frequencies,and the distance between them is fs. The PM case and the combination modulation case have the similar result, which can also be expressed by equation (23), whereas the coefficientsCl have different expressions. Therefore, , where is composed ofdiscrete peaks All these character spectrum peaks correspond toodd multiples of the half shaft rotation frequency.The number and amplitude of the peaks reflect the modulation extent, thereby reflecting the severity extent of the potential defect in the gear.Similar situations will be encountered when analysing other Fig. 1 Diagram of CS character distribution slices of the SCD where CF equals the integer multiples of the shaft rotation frequency.The information redundancy of the SCD function always becomes an obstacle to its practical application in the gear defect detection. The sampling frequency must be high enough to satisfy the sampling theorem. Simultaneously, identifying modulation character relies on the fine frequency resolution.Long data series are needed because of these two factors.Therefore, huge matrix operations bring heavy burden to the computation.Moreover, sometimes it is hard to find a clear representation for the redundant information in the three-dimensional space.Therefore, the SSCD, as shown in the above analysis,is presented as a competent substitute for the SCD in detecting gear defects. In this article, the SSCD is specialized to the slice of the SCD where CF equals a certain character frequency. The SSCD can be acquired directly from the time-varying autocorrelation without computing the CA matrix and other subsequent matrix operations. Its realization is detailed as follows:(a) use the Hilbert transform to get the analytic signal ^x(t);(b) compute the time-varying autocorrelation of the analytic signal as described in equation (2);(c) select the CF a0, which equals a certain prescient character frequency, and then computethe slice of the CA (a0 equals fs for gear defect detection);(d) compute the envelope of the slice CA . It cannot be attained directlyfrom the slice CA,therefore, a technique is involved for another form ofUtilizing the equation, arrive at the squared modulus of;(e) apply the Fourier transform of with respect to the time lag t and obtain the final result of the SSCD.The SSCD can be computed according to the steps listed above. Nevertheless, the manipulation of replacing the envelope slice CA by the squared modulus of it will change the spectrumstructure. Original halfcharacter frequencies are converted into integer form (lfs) together with the appearance of some inessential high frequency components.These changes do not impact the character identification capability of the SSCD, on the contrary,it gives more obvious representation.5 SIMULATIONTwo modulated signals are used to identify the capability of the SCD and the SSCD in modulation character identification. All modulation functions of these signals are finite Fourier series. Figure 2 shows the AM case simulated according to equation(8). The AM function a(t) comprises three cosine waveforms, representing 10 Hz and its double and triple harmonics and amplitude of 1, 0.7, and 0.3 units, respectively. All initial phases in the model are randomly decided by the computer. The carrier frequency is 100 Hz, sampling frequency 2048 Hz,and the data length 16 384. Figure 3 shows the case of the combination of AM and PM simulated according to equation (7). The PM function b(t) comprises two sinusoidal waveforms with the frequency of 10 and 20 Hz and amplitude of 3 and 1 units,respectively. Other parameters are identical to the AM case.Figures 2(a) to (c) show the time waveform, the contour of its SCD analysis, and the SSCD where CF is equal to 10 Hz, respectively. Only the results of the SCD in the first quadrant are given because of its symmetry. All character points in the contour of the SCD are at the intersections of thelines f =. Their distribution is regular in the AM case. TheFig. 2 One simulated AM signal: (a) the time waveform, (b) the contour of its SCD, and (c)the SSCD at 10 HzSSCD in Fig. 2(c) comprises Fig. 2 One simulated AM signal:(a) the time waveform, (b) the contour of its SCD, and (c)the SSCD at 10 Hzand its integer multiples and reflects themodulation condition in this signal as the SCD.Fig. 3 Another simulated modulated signal with modulation phenomena in amplitude and phase: (a) the time waveform, (b) the contour of its SCD, and (c) the SSCD at 10 HzFigure 3 shows the case of the combination of AM and PM.All character points in the contour of the SCD are also at the intersections of the character lines10 Hz. In addition, the SSCD also comprises 10 Hz and its several integer multiples.When PM is involved, the results from the PM part interact with those from the AM part by the two dimensional convolution. The number of the character peaks manifestly increases when compared with the original AM case in thecontour of the SCD. The number of character peaks in the SSCD also augments.Therefore, according to the SCD or the SSCD, the same conclusion can be drawn: the second simulated signal is strongly modulated when compared with the first.Simulation results indicate that either the SCD or the SSCD has the capability of identifying the present and the extent of the modulation, disregarding its existence in amplitude or phase. The SSCD possesses the virtues of less computation and clear representation.These two factors seem to be indifferent for simulated signals, but are valuable when encountering very long data series in practice.6 EXPERIMENTAL RESULTSThree experimental vibration signals employed in this section came from 37/41 helical gears. They represented healthy, slight wear (wear on addendum of one tooth of 41 teeth gear), and moderate wear status (wear on addendum of one tooth profile of 41 teeth gear and two successive tooth profiles of 37 teeth gear), respectively. The shaft rotation frequency of the 37 teeth gear minutely fluctuates 16.6 Hz. Signals were sampled at 15 400 Hz under the same load. The data length was 37 888. Before the SSCD analysis, all experimental signals were band-pass filtered around four-fold harmonics of the tooth meshin frequency in order to identify the change in themodulation sidebands in different defect status.These filtered signals are analysed by a conventional envelope technique and the SSCD. The comparison between their results dedicates the effect of theSSCD.Figure 4 shows the case of the healthy status.Figures 4(a) to (c) are the time waveform of the experimental signal, its envelope spectrum, and its SSCD analysis at the shaft rotation frequency of the 37 teeth gear, respectively. The envelope spectrum and the SSCD have the similar spectrum structure Fig. 3 Another simulated modulated signal with modulation phenomena in amplitude and phase: (a) the time waveform, (b) the contourof its SCD, and (c) the SSCD at 10 HFig. 4 First experimental gear signal: (a) the time waveform, (b) the envelope spectrum, and(c)the SSCDcomprising the rotation frequency and several negligible harmonics. Demodulated sidebands in these two spectra are few and low because there are some modulation phenomena during the gear’s normal operation. The fluctuation in the load, the minute rotational variation, and the circular pitch error in the machining process are the possible sources of the slight modulation. There is no comparability between numeric values of the envelope spectrum and the SSCD because of different computing procedures.The slight wear case is shown in Fig. 5. Wear on one tooth profile of one of the helical meshing gears does not result in significant deviation from its normal running. Therefore, there is a little increment in amplitude in the time waveform plot. In the envelope spectrum, compared with the normal case, the amplitude of these demodulated sidebands augments a little, and the extent seems to enlarge. The increment in number and amplitude of the sidebands is attributed to the modulation condition of the signal. However, the alteration is too slight to provide enough proof for the existence of some defect in the gear. In fact, a slight defect evidently always modulates the phase of the gear vibration signal and produces little change in the amplitude.Therefore, the envelope spectrum is not sensitiveto a slight gear defect due to its fail to the PMphenomena.Figure 5(c) shows the SSCD analysis of the slightlywearing gear. More sidebands are demodulated by the SSCD when compared with the normal case in Fig. 4(c). Moreover, the amplitude isapproximately tenFig. 5 Second experimental gear signal: (a) the time waveform, (b) the envelope spectrum,and (c)the SSCDtimes that of the normal case. Changes between the status of these two operations in the SSCD are so remarkable that a conclusion of the existence of a certain gear defect can be affirmed. Different from the neglect of envelope spectrum to PM, the SSCD treats AM and PM equally. It picks up AM and PM characters simultaneously, that is to say,the SSCD is a whole embodiment of all modulation phenomena in the system. Therefore, this is an effective and reliable method for slight gear defects.The moderate wear case is shown in Fig. 6. Wear on one tooth profile of one of the meshing gears and two neighbouring tooth profiles of the other impact the running of the meshing gears. According to the time waveform, the vibration is more violent than the two cases mentioned eaerlier. In the Fig. 5 Second experimental gear signal: (a) the time waveform, (b) the envelope spectrum, and (c)the SSCDFig. 6 Third experimental gear signal: (a) the time waveform, (b) the envelope spectrum, and(c)the SSCDApplication of SSCD to gear defect detection 1391 envelope spectrum, the amplitude and the number of the sidebands continue to increase. The obvious changes, compared with the normal case, indicate the abnormality of the system. The sidebands demodulated by the SSCD also increase in amplitude and number. The SSCD is indicative of more serious defects, whereas AM phenomena are the major reflection of the moderate wear. Therefore, the envelope spectrum and the SSCD both reflect the severity extent of the modulation in the signal. Both fit to the detection of moderate gear defects.7 CONCLUSIONGear vibration signal is a typical modulated signal.The changes of themodulation condition indicate the existence and the development of defects. The SSCD is introduced in this article as a valuable method to detect gear defects. It is verified to be a whole reflection of the modulation phenomena in gear vibration and is able to pick up AM and PM information simultaneously. Experimental results show the defect detection capability of the method not only for moderate gear defects, but also for slight defects. Therefore, the SSCD method has a bright future in identifying the presence of gear defects and monitoring their evolution.ACKNOWLEDGEMENTSThis research was supported by the National Natural Science Foundation of China (no. 50175068) and the Key Project of the National Natural Science Foundation of China (no. 50335030). Experimental data came from the Department of Applied Mechanics of University Libre de Bruxelles.REFERENCES1 Dalpiaz,G. and Rivola, A. Effectiveness and sensitivity of vibration processing techniques for local fault detection in gears. Mech. Syst. Signal Process., 2000, 14(3), 387–412.2 Capdessus, C. and Sidahmed, M. Cyclostationary processes:application in gear faults early diagnosis. Mech.Syst. Signal Process., 2000, 14(3), 371–385.3 Antoni, J. and Daniere, J. Cyclostationary modeling of rotating machine vibration signals. Mech. Syst. Signal Process., 2004, 11(18), 1285–1314.4 Gardner, W. A. Exploitation of spectral redundancy in cyclostationary signals. IEEE Signal Process. Mag., 1991,8, 14–26.5 Gardner, W. A. Introduction to random processing with applications to signals and systems, 1990 (McGraw-Hill, New York).6 McFadden, P. D. and Smith, J. D. A signal processing technique for detecting local defects in a gear from the signal average of the vibration. Proc. Instn Mech. Engrs,Part C: J. Mechanical Engineering Science, 1985, 199(C4), 287–292.7 Randall, R. B. A new method of modeling gear faults. J. Mech. Des., 1982, 104, 259–267.附录二英文文献翻译部分频谱与齿轮缺陷发现相互关系的实际应用G Bi, J Chen、F C Zhou 和J He中华人民共和国,上海,上海交通大学,国家震动、声音和噪音重点实验室原稿于2005年10月16日完成,经修改后于2006年5月3日发表DOI:10.1243|0954406 JMES206摘要:振幅和振动调制相位的变化能最直接的反映出齿轮的缺陷。
七氟醚下调TRPV4
前期研究发现,机械通气可上调花生四烯酸(AA )代谢途径关键限速酶胞质型磷脂酶A2(C-PLA2)活性使肺内AA 及其致炎性代谢产物生成增加继而引起VILI ,而七氟醚可通过阻断上述病理过程发挥其抗VILI 保护作用[1,2],但机械通气及七氟醚调控C-PLA2的具体机制尚未完全阐明。
由于细胞内钙离子浓度的增加是C-PLA2活化必不可少的条件[3],而TRPV4作为一种位于细胞膜上的钙离子通道,可被机械力直接激活[4],活化的TRPV4可上调C-PLA2表达继而引起高血压小鼠动脉内皮细胞收缩[5]。
体外实验研究发现,机械通气可激活TRPV4造成肺屏障功能破坏[6],而七氟醚可通过阻断瞬时受体电位钙离子通道发挥其心肌保护作用[7]。
据此我们推测机械通气所产生的机械力激活C-PLA2的具体机制与TRPV4有关,而七氟醚可通过阻断TRPV4/C-PLA2信号通路发挥其抗VILI 保护作用。
Sevoflurane alleviates ventilator-induced lung injury in rats by down-regulating the TRPV4/C-PLA2signaling pathwayWANG Wenfa 1,YANG Yong 2,WANG LI 3,GUO Xin 3,TIAN Lingfang 1,WANG He 1,HU Yuzhen 1,LIU Rui 31Department of Anesthesiology,Chuxiong Yi Autonomous Prefecture People's Hospital,Chuxiong 675000,China;2Experimental Center of Medical Function,Kunming Medical University,Kunming 650500,China;3Department of Anesthesiology,First People's Hospital of Yunnan Province/Affiliated Hospital of Kunming University of Science and Technology,Kunming 650032,China摘要:目的探讨七氟醚抗呼吸机诱导的肺损伤(VILI )的保护作用机制。
振动感觉阈值(VPT)在糖尿病周围神经病变(DPN)中的诊断价值
振动感觉阈值(VPT)在糖尿病周围神经病变(DPN)中的诊断价值沈娟;曾辉;李连喜;包玉倩;刘芳【摘要】目的探讨以振动感觉阈值(vibrating perception threshold,VPT)检查为主联合糖尿病神经病变症状评分(diabetic neuropathy symptom,DNS)、足外观、温度觉、痛觉及触觉5种简易检查方法在糖尿病周围神经病变(diabetic peripheral neuropathy,DPN)中的诊断价值.方法 217例2型糖尿病患者记录DNS,同时行足外观检查、VPT、温度觉、痛觉、半定量音叉、10g尼龙丝检查和肌电图神经传导速度(nerve conducting velocity,NCV)测定.按神经电生理检查结果,分为不合并周围神经病变组(n=130),合并周围神经病变组(n=87),比较两组的基本情况和代谢指标.计算5种联合检查方法的敏感度、特异度、阳性预测值、阴性预测值、准确度、Youden指数以及Kappa值(κ值),与NCV检查进行相关性和一致性分析.结果两组间年龄、糖尿病病程、VPT值有显著差异,DPN组明显高于无DPN组(P<0.05).VPT与正中运动神经传导速度(motor conductingvelocity,MCV)、尺神经MCV、腓总神经MCV、腓浅神经感觉性传导速度(sensory conducting velocity,SCV)、胫神经MCV之间均呈负相关(P<0.05).5种联合检查方法与NCV检查的秩相关分析均呈显著正相关(P<0.01),VPT联合DNS检查与NCV的相关性最好(r=0.799).VPT联合DNS检查的敏感度、特异度、准确度分别为74.4%、100%、89.9%,与NCV检查高度一致(κ值为0.780).结论VPT联合DNS是准确筛查和诊断DPN的适用方法.%Objective To investigate the diagnostic values of different evaluating methods on the diabetic peripheral neuropathy (DPN). These methods include the vibrating perception threshold (VPT) combined diabetic neuropathy symptom (DNS),foot appearance inspection, temperature sensation,pain sensation and touch sensation in the patients. Methods Totally 217 patients with type 2 diabetes were recruited. They were divided into two groups including one group without peripheral neuropathy (non-PN group, n =130) and the other group complicated with peripheral neuropathy (PN group,n= 87) according to the results of electromyography. DNS, foot appearance,nerve conducting velocity (NCV),VPT, temperature sensation, pain sensation, 128Hz tuning fork andlOg monofilament examination were performed in all the patients, and the clinical characteristics, biochemical parameters and VPT were compared between the two groups. Sensitivity, specificity, positive predictive value, negative predictive value, accuracy, Youden index and the Kappa value (k value) ,and the correlation of the above assessment means were evaluated compared with the "gold standard" NCV. Results There was significant difference of age, duration of diabetes and VPT between the non-PN group and PN group. The values in the PN group were significantly higher than those in the non-PN group (P <0. 05). There were negative correlations between VPT and median nerve motor conducting velocity (MCV), ulnar nerve MCV, peroneal nerve MCV, the superficial peroneal nerve sensory conducting velocity (SCV) and tibial nerve MCV (P<0. 05). The Spearman correlation analysis showed the five methods were positively associated with NCV (All P<0. 01). There was the best association (r= 0. 799,P<00. 01) between NCV and the combination with VPT and DNS. The sensitivity, specificity and accuracy of the combined evaluation with VPT and DNS were 74. 4% , 100% , 89. 9%respectively, and was highly consistent with NCV examination (k value was 0. 780). Conclusions The combined evaluation of VPT and DNS of lower extremity was a practical and accurate method for diagnosing and screening DPN in type 2 diabetic populations.【期刊名称】《复旦学报(医学版)》【年(卷),期】2013(040)001【总页数】7页(P31-37)【关键词】糖尿病周围神经病变(DPN);神经传导速度(NCV);振动感觉阈值(VPT)【作者】沈娟;曾辉;李连喜;包玉倩;刘芳【作者单位】上海交通大学医学院附属第三人民医院内分泌科上海201900;上海交通大学附属第六人民医院内分泌代谢科上海市糖尿病临床医学中心上海市糖尿病研究所-上海市糖尿病重点实验室上海200233;上海交通大学附属第六人民医院内分泌代谢科上海市糖尿病临床医学中心上海市糖尿病研究所-上海市糖尿病重点实验室上海200233;上海交通大学附属第六人民医院内分泌代谢科上海市糖尿病临床医学中心上海市糖尿病研究所-上海市糖尿病重点实验室上海200233;上海交通大学附属第六人民医院内分泌代谢科上海市糖尿病临床医学中心上海市糖尿病研究所-上海市糖尿病重点实验室上海200233【正文语种】中文【中图分类】R587.1糖尿病周围神经病变(diabetic peripheral neuropathy,DPN)患者起病多为隐袭,发病初期往往无自觉症状,待临床症状出现时周围神经多已出现不可逆的轴索变性和节段性脱髓鞘等病理改变,严重影响患者的治疗效果和生活质量。
基于固有时间尺度分解与多尺度形态滤波的滚动轴承故障特征提取方法
基于固有时间尺度分解与多尺度形态滤波的滚动轴承故障特征提取方法关焦月;田晶;赵金明;富华丰【摘要】为了准确提取出滚动轴承的故障特征并对轴承状态进行评估,提出了一种固有时间尺度分解(intrinsic time-scale de-composition,ITD)与多尺度形态滤波相结合的滚动轴承故障特征提取方法.首先,采用ITD方法将滚动轴承故障信号分解成多个固有旋转分量(proper rotation,PR);然后,对比各个PR分量与原始信号的相关性;最后,采用多尺度形态滤波算法对相关性较大PR分量进行滤波降噪,并提取滚动轴承故障特征频率.采用所建立方法对轴承外圈故障和内圈故障实验数据进行分析.结果表明,所提出的故障特征提取方法能够有效抑制噪声,清晰准确地提取出滚动轴承故障特征频率.【期刊名称】《科学技术与工程》【年(卷),期】2019(019)014【总页数】5页(P178-182)【关键词】固有时间尺度分解;形态滤波;滚动轴承;相关系数;故障诊断【作者】关焦月;田晶;赵金明;富华丰【作者单位】沈阳航空航天大学辽宁省航空推进系统先进测试技术重点实验室,沈阳 110136;沈阳航空航天大学辽宁省航空推进系统先进测试技术重点实验室,沈阳110136;中国南方航空股份有限公司沈阳维修基地,沈阳110169;中国南方航空股份有限公司沈阳维修基地,沈阳110169【正文语种】中文【中图分类】TH165.3;TP206滚动轴承是航空发动机和燃气轮机等旋转机械的关键零件,其工作状态直接影响到设备的运行状态。
滚动轴承发生故障甚至会对旋转机械造成灾难性事故,会造成重大经济损失。
因此,对滚动轴承故障特征进行准确的提取,实现对滚动轴承故障的有效诊断具有十分重要的意义[1]。
近年来,国内外越来越多的专家学致力于轴承故障特征提取和故障识别技术的研究,取得了大量的研究成果。
针对滚动轴承故障信号非平稳、非线性且冲击特征明显的特点,小波分析[2]、经验模态分解(empirical mode decomposition, EMD)方法[3]和结合局部均值分解(local mean decomposition, LMD)方法[4]等时频分析方法被广泛的应用到故障轴承诊断中。
基于格拉姆角场与迁移学习-AlexNet_的变压器绕组松动故障诊断方法
第51卷第24期电力系统保护与控制Vol.51 No.24 2023年12月16日Power System Protection and Control Dec. 16, 2023 DOI: 10.19783/ki.pspc.230659基于格拉姆角场与迁移学习-AlexNet的变压器绕组松动故障诊断方法薛健侗,马宏忠,杨洪苏,倪一铭,万可力,迮恒鹏(河海大学能源与电气学院,江苏 南京 211100)摘要:绕组松动故障是变压器最主要的机械故障之一,尚缺乏有效的智能化诊断方法。
为此提出基于格拉姆角场与迁移学习-AlexNet的变压器绕组松动故障诊断方法。
变压器稳态运行时的振动信号存在周期性的特点,导致其构建足量具有时间相关性的图像集十分困难,提出了一种样本构建方法用于生成变压器振动信号的格拉姆角场图像集。
将生成的图像集送入AlexNet进行迁移学习,获得微调后的神经网络模型。
实验结果表明:利用该样本构建方法生成的图像集作为训练集和验证集,建立的卷积神经网络模型训练准确率与验证准确率均达到99%以上;利用变压器周期性振动信号生成的图像集作为测试集,测试准确率达到99%以上,实现了变压器绕组松动故障的准确诊断,并为周期性信号运用具有时间相关性的图像变换方法构建足量样本集提供了一种新思路。
关键词:变压器;绕组松动;振动信号;格拉姆角场;AlexNet;迁移学习;样本构建;故障诊断A fault diagnosis method for transformer winding looseness based on Gramianangular field and transfer learning-AlexNetXUE Jiantong, MA Hongzhong, YANG Hongsu, NI Yiming, WAN Keli, ZE Hengpeng(College of Energy and Electrical Engineering, Hohai University, Nanjing 211100, China)Abstract: The winding looseness fault is one of the main mechanical faults in transformers, and there is still a lack of effective intelligent diagnosis methods. Therefore, a diagnosis method for such a fault based on Gramian angular field and transfer learning-AlexNet is proposed. The periodic characteristics of the vibration signals during steady-state operation of transformers make it difficult to construct a sufficient set of images with time correlation. Therefore, a sample construction method is proposed to generate the Gramian angular field image set of transformer vibration signals. The generated image set is sent to AlexNet for transfer learning to obtain the fine-tuned neural network model. The image set generated by the sample construction method is used as the training and validation set, and the experimental results are that training and validation accuracy of the convolutional neural network model established are both above 99%. The image set generated by the periodic vibration signal of the transformer is used as the test set, with a testing accuracy of over 99%, achieving accurate diagnosis of transformer winding looseness faults. It also provides a way for constructing a sufficient sample set using time-related image transformation methods for periodic signals.This work is supported by the National Natural Science Foundation of China (No. 51577050).Key words: transformer; winding looseness; vibration signals; Gramian angular field; AlexNet; transfer learning; sample construction; fault diagnosis0 引言电力变压器作为各级变电站的核心设备,一直基金项目:国家自然科学基金项目资助(51577050);国网江苏省电力有限公司重点科技项目资助(J2021053) 承担着提高线路远距离输送能力、确保用户正常用电的关键任务[1-4]。
干涉型光纤振动传感器定位精度及解调算法研究
太原理工大学博士研究生学位论文干涉型光纤振动传感器定位精度及解调算法研究摘要分布式光纤传感具有本征安全、抗电磁干扰、耐腐蚀、可大范围连续监测等优势,近年来得到了国内外的广泛关注。
振动传感作为分布式光纤传感领域中主要的研究方向之一,在民用设施周界安防、油气管道安全监测、桥梁结构健康监测、军事基地入侵预警等领域具有广阔的应用前景。
干涉型光纤振动传感技术包括前向传输光干涉型和后向散射光干涉型两类。
基于前向传输光干涉型光纤振动传感器,如萨格纳克(Sagnac)干涉仪和马赫泽德(Mach-Zehnder)干涉仪,是将被测的振动信号转换为光纤中前向传输光的相位变化,再通过干涉将相位变化转换成光强变化。
它结构相对简单、响应速度快,但振动定位精度较低。
而后向散射光干涉型光纤振动传感器,如相位敏感光时域反射仪(phase-sensitive optical time domain reflectometer,Φ-OTDR),是利用高相干光脉冲在光纤中传输时产生的后向瑞利散射光的干涉效应,通过建立后向散射光信号与时间的关系获得振动位置信息,其定位精度高,但存在振动信号解调复杂以及实时性不高等问题。
本文围绕干涉型光纤振动传感器的定位精度及解调算法开展研究,主要内容包括:(1)研究了基于混沌光源的Sagnac高精度振动定位系统,利用外腔反馈半导体混沌激光器作为系统光源,再结合振动频谱中的高阶零频点进行定位。
实验了在12.101 km长的传感光纤上22 m的振动定位误差。
太原理工大学博士研究生学位论文(2)研究了基于计数脉冲方法的Mach-Zehnder高精度振动定位系统,将调制后的周期性脉冲序列后注入到干涉结构中,通过分析干涉脉冲序列包络特征定位振动发生的位置。
实验结果表明,当脉冲宽度为20 ns时,在总长940 m的传感光纤长度上,振动定位误差为9 m。
(3)研究了基于包络正交解调算法的Φ-OTDR振动相对振幅表征方法。
土木工程混凝土强度中英文对照外文翻译文献
<文献翻译一:原文>Strength of Concrete in Slabs, Investigates along Direction of Concreting ABSTRACTIn theory of concrete it is assumed that concrete composites are isotropic on a macro scale. For example, it is assumed that a floor slab’s or a beam’s streng th is identical in all directions and its nonhomogeneity is random. Hence neither calculations of the load-bearing capacity of structural components nor the techniques of investigating concrete in structure in situ take into account to a sufficient degree the fact that the assumption about concrete isotropy is overly optimistic. The present research shows that variation in concrete strength along the direction of concreting has not only a qualitative effect (as is commonly believed), but also a significant quantitative effect. This indicates that concrete is a composite which has not been fully understood yet. The paper presents evaluations of ordinary concrete (OC) homogeneity along component thickness along the direction of concreting. The ultrasonic method and modified exponential heads with a point contact with concrete were used in the investigations [1-3].Keywords: Concrete; Compressive Strength of Concrete; Non-Destructive1. IntroductionIn a building structure there are components which are expected to have special properties but not necessarily in the whole cross section. Components under bending, such as beams and floor slabs are generally compressed in their upper zone and the concrete’s compressive strength is vital mainly in this zone. The components are usually moulded in the same position in which they later remain in service, i.e. with their upper zone under compression. Concrete in the upper zone is expected to be slightly weaker than in the lower zone, but it is unclear how much weaker [4,5]. Also flooring slabs in production halls are most exposed to abrasion and impact loads in their upper zone which is not their strongest part. It is known from practice that industrial floors belong to the most often damaged building components.When reinforced concrete beams or floor slabs are to be tested they can be accessed only from their undersides and so only the bottom parts are tested and on this basis conclusions are drawn about the strength of the concrete in the whole cross section, including in the compressed upper zone. Thus a question arises: how large are the errors committed in this kind of investigations?In order to answer the above and other questions, tests of the strength of concrete in various structural components, especially in horizontally concreted slabs, were carried out. The variation of strength along the thickness of the components was analyzed.2. Research SignificanceThe research results presented in the paper show that the compressive strength of concrete in horizontally formed structural elements varies along their thickness. In the top zone the strength is by 25% - 30% lower than the strength in the middle zone, and it can be by as much as 100% lower than the strength in the bottom zone. The observations are based on the results of nondestructive tests carried out on drill cores taken from the structure, and verified by a destructive method. It is interesting to note that despite the great advances in concrete technology, the variation in compressive strength along the thickness of structural elements is characteristic of both old (over 60 years old) concretes and contemporary ordinary concretes.3. Test MethodologyBefore Concrete strength was tested by the ultrasonic method using exponential heads with a point contact with concrete. The detailed specifications of the heads can be found in [2,3]. The heads’ frequency was 40 and 100 kHz and the diameter of their concentrators amounted to 1 mm.In order to determine the real strength distributions in the existing structures, cylindrical cores 80 mm or 114 mm diameter (Figure 2) were drilled from them in the direction of concreting. Then specimens with their height equal to their diameter were cut out of the cores.Ultrasonic measurements were performed on the cores according to the scheme shown in Figure3. Ultrasonic pulses (pings) were passed through in two perpendicular directions I and II in planes spaced every 10 mm. In this way one could determine how ping velocity varied along the core’s height, i.e. along the thickness of the tested component.In both test directions ping pass times were determined and velocities CL were calculated. The velocities from the two directions in a tested measurement plane were averaged.Subsequently, specimens with their height equal to their diameter of 80 mm were cut out of the cores. Aver-age ultrasonic pulse velocity CL for the specimen’s central zone was correlated with fatigue strength fc determined by destructive tests carried out in a strength tester.For the different concretes different correlation curves with a linear, exponential or power equation were obtained. Exemplary correlation curve equations are given below:Lc c L c C f L f C f 38.1exp 0951.01.003.56705.232621.4=⋅=-⨯=where:fc —the compressive strength of concrete MPa,CL —ping velocity km/s.The determined correlation curve was used to calculate the strength of concrete in each tested core cross section and the results are presented in the form of graphs illustrating concrete strength distribution along the thickness of the tested component. 4. Investigation of Concrete in Industrial FloorsAfter Floor in sugar factory’s raw materials storage hall Concrete in an industrial floor must have particularly good characteristics in the top layer. Since it was to be loaded with warehouse trucks and stored sugar beets and frequently washed the investigated concrete floor (built in 1944) was designed as consisting of a 150 mm thick underlay and a 50 mm thick surface layer and made of concrete with a strength of 20 MPa (concrete A).As part of the investigations eight cores, each 80 mm in diameter, were drilled from the floor. The investigations showed significant departures from the design. The concrete subfloor’s thickness varied from 40 to 150 mm. The surface layer was not made of concrete, but of cement mortar with sand used as the aggregate. Also the thickness of this layer was uneven, varying from 40 to 122mm. After the ultrasonic tests specimens with their height equal to their diameter of 80 mm were cut out of the cores. Two scaling curves: one for the surface layer and the other for the bottom concrete layer were determined.A characteristic concrete compressive strength distribution along the floor’s thickness is shown in Figure 4.Strength in the upper zone is much lower than in thelower zone: ranging from 4.7 to 9.8 MPa for the mortar and from 13.9 to 29.0 MPa for the concrete layer. The very low strength of the upper layer of mortar is the result of strong porosity caused by air bubbles escaping upwards during the vibration of concrete. Figure 5 shows t he specimen’s porous top surface.Floor in warehouse hall with forklift truck transport The floor was built in 1998. Cellular concrete was used as for the underlay and the 150 mm thick surface layer was made of ordinary concrete with fibre (steel wires) reinforcement (concrete B). Cores 80 mm high and 80 mm in diameter were drilled from the surface layer. Ultrasonic measurements and destructive tests were performed as described above. Also the test results were handled in a similar way. An exemplary strength distribution along the floor’s thickness is shown in Figure 6.5. ConclusionsTests of ordinary concretes show unexpectedly greatly reduced strength in the upper zone of horizontally moulded structural components. This is to a large degree due to the vibration of concrete as a result of which coarse aggregate displaces downwards making the lower layers more compact while air moves upwards aerating the upper layers and thereby increasing their porosity. The increase in the concrete’s porosity results in a large drop in its compressive strength. Thanks to the use of the ultrasonic method and probes with exponential concentrators it could be demonstrated how the compressive strength of ordinary concrete is distributed along the thickness of structural components in building structures. It became apparent that the reduction in compressive strength in the compressed zone of structural components under bending and in industrial concrete floors can be very large (amounting to as much as 50% of the strength of t he slab’s lower zone). Therefore this phenomenon should be taken into account at the stage of calculating slabs, reinforced concrete beams and industrial floors [6].The results of the presented investigations apply to ordinary concretes (OC) which are increasingly supplanted by self-compacting concretes (SCC) and high-performance concretes (HPC). Since no intensive vibration is required to mould structures from such concretes one can expect that they are much more homogenous along their thickness [7]. This will be known once the ongoing experimental research is completed.Bohdan StawiskiStrength of Concrete in Slabs, Investigates along Direction of Concreting[D]Institute of Building Engineering, Wroclaw University of Technology Wybrzeze Wyspianskiego, Wroclaw, Poland Received October 15, 2011; revised November 21, 2011; accepted November 30, 2011<文献翻译一:译文>混凝土强度与混凝土浇筑方向关系的研究摘要从理论上看,假设混凝土复合材料是各项同性的从宏观尺度上讲。
滚动轴承性能退化表征与剩余寿命预测方法研究
摘要滚动轴承是机械设备传动系统中的关键部件,由于其处于重载、高速及高温等极端恶劣的运行环境中,极易发生失效,继而引发系统级故障,因此,掌握滚动轴承的性能退化状态以及剩余寿命是保障机械设备安全可靠运行的关键所在。
本文以滚动轴承的性能退化表征和剩余寿命预测为研究主题,开展轴承全寿命周期试验,在此基础上,基于轴承的振动信号,进行了特征提取、性能退化表征以及剩余寿命预测研究,主要内容如下:(1)以6207深沟球轴承(材料为:GCr15)为试验对象,利用滚动轴承加速寿命试验台,进行全寿命周期性能退化试验,监测、记录并分析全程中的状态监测量(温度、振动)的特征参数及变化规律,为后续性能退化行为表征参数的选取提供参考依据。
(2)针对振动信号的特征提取问题,构建反映轴承退化的特征集。
从时域、频域以及时频域提取了与轴承性能退化征兆相关的71个特征参量,构成原始特征集。
结果表明,在轴承的全寿命周期中,原始特征表现出不同形式的变化趋势,代表各自特征有关退化过程的独特信息,能够全面有效反映轴承的退化信息。
(3)构建健康指数,表征滚动轴承性能退化状态。
以相关性、单调性以及鲁棒性作为特征评价指标,筛选出反映轴承性能退化的敏感特征,并基于PCA方法,对多个敏感特征进行融合,构建出表征轴承性能退化的健康指数。
通过试验验证,所构建的健康指数能有效表征轴承正常运行、初始退化以及急剧退化三个阶段的退化状态。
(4)构建EMD-Kriging模型,实现滚动轴承剩余寿命预测。
首先,采用EMD 方法对健康指数进行主趋势提取;其次,基于Kriging模型对轴承剩余寿命进行预测;最后,通过试验以及与典型预测方法进行比较分析,验证了所提模型的可行性和有效性。
本文研究为滚动轴承的性能退化表征与剩余寿命预测提供了方法借鉴,对于提高滚动轴承乃至机械设备传动系统的可靠性和保障性水平具有重要的工程意义。
关键词:滚动轴承;特征提取;特征选择;性能退化表征;剩余寿命预测分类号:TH133.33; TH17AbstractRolling bearing is the key component in the mechanical equipment transmission system. Because it is in the extremely severe operating environment such as heavy load, high speed and high temperature, it is easy to fail, and then cause system level failure. Therefore, it is the key to ensure the safe and reliable operation of mechanical equipment to master the performance degradation state and remaining useful life of rolling bearing. This paper takes the performance degradation characterization and remaining useful life prediction of rolling bearing as the research subject, and carries out the bearing life cycle test. On this basis, based on the vibration signal of the bearing, the research on feature extraction, performance degradation characterization and remaining useful life prediction is carried out. The main contents are as follows:(1) Taking 6207 deep groove ball bearing (material: GCr15) as the test object, the rolling bearing accelerated life test bench was used to conduct a full life cycle performance degradation test to monitor, record and analyze the characteristic parameters of the state monitoring quantity (temperature, vibration) throughout And the change rule provides a reference basis for the selection of subsequent performance degradation behavior characterization parameters.(2) Aiming at the problem of feature extraction of vibration signals, a feature set reflecting bearing degradation is constructed. 71 feature parameters related to the signs of bearing performance degradation were extracted from the time domain, frequency domain and time-frequency domain to form the original feature set. The results show that in the life cycle of the bearing, the original features show different types of change trends, representing the distinct information about the degradation process, which can fully and effectively reflect the degradation information of the bearing.(3) Construct a health index to characterize the degradation state of rolling bearing performance. Using correlation, monotonicity and robustness as feature evaluation indexes, the sensitive features reflecting the degradation of bearing performance are selected, and based on the PCA method, multiple sensitive features are fused to construct a health index that characterizes the degradation of bearing performance. It is verified through experiments that the constructed health index can effectively characterize the degradation state of the bearing in three stages of normal operation, slight degradation and severely degradation.(4) Construct an EMD-Kriging model to predict the remaining useful life of rollingbearings. First, the EMD method is used to extract the main trend of the health index; secondly, the remaining useful life of the bearing is predicted based on the Kriging model; finally, the feasibility and effectiveness of the proposed model are verified by comparison and analysis with typical prediction methods where the same dataset is used.The research in this paper provides a method for the characterization of rolling bearing performance degradation and remaining useful life prediction, which has important engineering significance for improving the reliability and security of rolling bearing and even the transmission system of mechanical equipment.Keywords:rolling bearing; feature extraction; feature selection; performance degradation characterization; remaining useful life predictionClassification Number: TH133.33; TH17目录摘要 (I)Abstract (II)目录 .................................................................................................................... I V 1 绪论 .. (1)1.1 研究背景及意义 (1)1.2 国内外研究现状 (2)1.2.1 特征提取 (3)1.2.2 性能退化表征 (4)1.2.3 剩余寿命预测 (4)1.3 现状分析总结 (6)1.4 本文的研究思路和主要内容 (6)2 滚动轴承全寿命周期试验 (8)2.1 滚动轴承结构及失效模式 (8)2.1.1 滚动轴承结构 (8)2.1.2 滚动轴承常见失效模式 (9)2.2 滚动轴承加速寿命试验 (10)2.2.1 滚动轴承加速寿命试验台 (10)2.2.2 试验方案及流程 (11)2.2.3 试验结果分析 (14)2.3 本章小结 (18)3 滚动轴承振动信号的特征提取 (19)3.1 时域特征提取 (19)3.2 频域特征提取 (23)3.3 相似相关特征提取 (26)3.4 时频域特征提取 (28)3.4.1 小波包分解特征 (28)3.4.2 经验模态分解特征 (33)3.5 本章小结 (37)4 滚动轴承性能退化表征方法研究 (39)4.1 敏感特征选择 (39)4.2 基于主成分分析的健康指数构建方法 (41)4.2.1 主成分分析的基本原理 (41)4.2.2 健康指数的构建 (43)4.3 试验验证和结果分析 (44)4.3.1 PRONOSTIA试验介绍 (44)4.3.2 方法验证及结果分析 (46)4.4 本章小结 (51)5 滚动轴承剩余寿命预测方法研究 (53)5.1 Kriging模型 (53)5.2 基于EMD-Kriging的轴承剩余寿命预测模型 (56)5.2.1 基于EMD-Kriging的预测模型 (56)5.2.2 轴承剩余寿命预测流程 (57)5.3 试验验证 (58)5.4 本章小结 (63)6 总结与展望 (64)6.1 全文工作总结 (64)6.2 研究展望 (64)参考文献 (66)作者简历 (71)1 绪论1.1 研究背景及意义随着工业制造水平的进步和物联网技术的发展,复杂化和智能化已经成为机械设备(例如航空发动机、风力发电设备、高端机床等)的主要发展趋势。
基于RLMD和Kmeans++的轴承故障诊断方法
基于RLMD和Kmeans++的轴承故障诊断方法颜少廷1周玉国1任艳波1刘师良1颜世铛2(1青岛理工大学信息与控制工程学院,山东青岛266500)(2郑州机械研究所有限公司,河南郑州450001)摘要为了提升轴承故障诊断性能,提出了一种基于鲁棒局部均值分解(RLMD)和Kmeans++的轴承故障诊断方法。
利用RLMD方法对轴承振动信号进行分解,得到乘积函数(PF),根据PF分量与原始振动信号的相关程度选择敏感PF分量,叠加敏感PF分量构成重构信号;通过计算原始振动信号和重构信号的时域、频域统计特征形成轴承故障特征集;利用线性判别分析(LDA)提取轴承故障的Fisher特征;通过Kmeans++聚类的方法对故障特征进行聚类,得到各工况轴承的聚类中心;通过计算测试样本与聚类中心之间的汉明贴近度来实现轴承故障诊断。
利用含有不同信噪比的仿真轴承故障数据和Paderborn大学轴承数据中心的轴承故障数据评价所提出方法的有效性。
结果表明,该方法即使在样本数较少的情况下也能够准确地识别出不同类别和级别的轴承故障。
关键词轴承故障诊断鲁棒局部均值分解线性判别分析Kmeans++汉明贴近度Bearing Fault Diagnosis Method based on RLMD and Kmeans++Yan Shaoting1Zhou Yuguo1Ren Yanbo1Liu Shiliang1Yan Shidang2(1School of Information and Control Engineering,Qingdao University of Technology,Qingdao266500,China)(2Zhengzhou Research Institute of Mechanical Engineering Co.,Ltd.,Zhengzhou450001,China)Abstract To improve the performance of bearing fault diagnosis,a bearing fault diagnosis method based on Robust Local Mean Decomposition(RLMD)and Kmeans++is proposed.The product functions(PF)are ob‐tained by decomposing the bearing vibration signal using the RLMD technique.The sensitive PF components are sifted by calculating the correlation coefficients between the PF components and the original vibration signal,and the sensitive PF components are superimposed to form the reconstructed signal.The bearing fault feature set is formed by calculating the time and frequency domain statistical features of the original vibration signal and the reconstructed signal.The Fisher features of bearing failure feature are extracted by linear discriminant analy‐sis(LDA).The fault feature is clustered by the Kmeans++clustering method and the cluster center of each bearing working condition is got.The bearing fault identification is realized by calculating the Hamming ap‐proach degree between the test sample and the cluster center.The simulated bearing data with different signal-to-noise ratios and bearing data from the Paderborn university test bench are used to evaluate the effectiveness of the proposed method.Results show that the proposed method can accurately identify bearing faults with differ‐ent categories and levels even though the number of training sample is small.Key words Bearing Fault diagnosis Robust local mean decomposition(RLMD)Linear discriminant analysis(LDA)Kmeans++Hamming approach degree0引言滚动轴承是大型旋转机械传动系统重要的组成部分之一[1],由于机械传动系统工作环境复杂且长期高负荷运行,难免会对轴承造成损伤。
journal of sound and vibration格式 -回复
journal of sound and vibration格式-回复Title: Applying Advanced Signal Processing Techniques for Noise Reduction in Railway Passenger CompartmentsAbstract:Noise pollution in railway passenger compartments is a significant concern affecting passenger comfort and well-being. This study aims to explore the application of advanced signal processing techniques for noise reduction in railway interiors. Specifically, this article delves into the effects of different signal processing algorithms in mitigating noise levels and enhancing passenger experience. The techniques investigated include spectral subtraction, adaptive filtering, and blind source separation. By examining the merits and limitations of each approach, this article provides valuable insights into noise reduction strategies for railway operators and manufacturers.1. Introduction:1.1 BackgroundRailway transport has gained considerable popularity due to its efficiency and environmental advantages. However, excessive noise levels in passenger compartments present a significant challengeto railway operators seeking to improve passenger comfort. This article explores the potential of advanced signal processing techniques in combating noise pollution in this environment.1.2 ObjectiveThe objective of this study is to evaluate the effectiveness of various signal processing algorithms in reducing noise levels in railway passenger compartments. By examining the performance of spectral subtraction, adaptive filtering, and blind source separation techniques, this research aims to determine the most suitable approach for noise reduction.2. Spectral Subtraction:2.1 TheorySpectral subtraction is a common technique for noise reduction that estimates the noise spectrum in the frequency domain. This method subtracts the estimated noise spectrum from the observed noisy signal to enhance the desired signal.2.2 ImplementationTo apply spectral subtraction, the noisy signal is transformed into the frequency domain using techniques such as the fast Fouriertransform (FFT). The noise spectrum estimate is obtained by exploiting the relationship between signal and noise power over time. The estimated noise spectrum is subtracted from the observed spectrum, yielding a denoised signal.2.3 Results and DiscussionSpectral subtraction shows promising results in reducing broadband noise in railway compartments. However, performance deterioration occurs when the desired signal and noise have similar spectral characteristics. This calls for additional techniques to achieve better noise reduction.3. Adaptive Filtering:3.1 TheoryAdaptive filtering is a method that adapts the noise reduction filter to varying acoustic environments. This technique estimates the transfer function between a reference microphone and the desired microphone in the presence of noise.3.2 ImplementationAdaptive filtering involves the use of adaptive algorithms such as the least mean squares (LMS) or normalized least mean squares(NLMS) algorithms. By updating the filter weights in real-time, the adaptive filter continuously adapts to match the changing noise characteristics.3.3 Results and DiscussionAdaptive filtering demonstrates superior performance in attenuating noise in railway compartments, particularly fornon-stationary noise sources. However, the convergence time and computational requirements pose challenges, limiting real-time implementation feasibility.4. Blind Source Separation:4.1 TheoryBlind source separation is a technique that separates mixed sources in an observation space without any prior knowledge about the sources or mixing process. This method seeks to separate noise and desired signals.4.2 ImplementationBlind source separation algorithms, such as independent component analysis (ICA) and sparse component analysis (SCA), are applied to identify and separate the noise sources from thedesired signal component.4.3 Results and DiscussionBlind source separation shows promise in separating noise from desired signals in railway environments. However, accurate source separation may be challenging in complex acoustic scenarios due to the limited number of sensors available in passenger compartments.5. Conclusion:This article has discussed the application of advanced signal processing techniques for noise reduction in railway passenger compartments. The evaluation of spectral subtraction, adaptive filtering, and blind source separation methods has provided valuable insights into their effectiveness and limitations. Combining these approaches or using them selectively can result in significant noise reduction, ultimately enhancing passenger comfort and satisfaction during railway journeys. Future research could focus on developing hybrid approaches that leverage the strengths of multiple techniques to overcome their individuallimitations.。
信源与天线的相对方向英语
信源与天线的相对方向英语Relative Orientation of Source and Antenna.In the field of wireless communication, the relative orientation between the transmitting antenna and the receiving antenna plays a crucial role in determining the signal strength and quality. Understanding the impact of relative orientation is essential for optimizing communication systems and achieving reliable data transmission.Polarization.Polarization refers to the orientation of the electric field vector of an electromagnetic wave. Linear polarization occurs when the electric field vector oscillates in a straight line, while circular polarization occurs when the electric field vector rotates in a circle.The relative orientation of the transmitting andreceiving antennas with respect to polarization is critical. If the antennas are not aligned in terms of polarization, the signal strength will be significantly reduced or even completely canceled out. Therefore, it is important to use antennas with matching polarization to ensure optimalsignal transmission and reception.Horizontal and Vertical Polarization.In many communication systems, horizontal and vertical polarization are commonly used. Horizontal polarization occurs when the electric field vector is parallel to the ground, while vertical polarization occurs when theelectric field vector is perpendicular to the ground.The choice of polarization depends on various factors, such as the environment, terrain, and intended application. For example, horizontal polarization is often preferred for long-distance communication over land, while vertical polarization is suitable for communication in urban areas with tall buildings and reflective surfaces.Beamwidth and Directivity.The beamwidth of an antenna describes the angular range over which it can effectively transmit or receive signals. The directivity of an antenna is a measure of how concentrated the transmitted or received signal is in a particular direction.The relative orientation of the source and antenna with respect to beamwidth and directivity is crucial for achieving focused signal transmission and reception. If the source is located outside the beamwidth of the antenna, the signal strength will be weak or non-existent. Similarly, if the antenna is not pointed towards the source, the directivity of the antenna will be reduced, resulting in lower signal strength.Line-of-Sight Communication.Line-of-sight (LOS) communication refers to a scenario where there is a clear and unobstructed path between the transmitting and receiving antennas. In LOS communication,the relative orientation of the antennas is less critical, as the signal can travel directly from the source to the destination.However, in non-line-of-sight (NLOS) communication, where obstacles or reflections interfere with the signal path, the relative orientation of the antennas becomes more important. Proper antenna alignment can help minimize signal loss and improve communication reliability in NLOS environments.Antenna Gain and Path Loss.Antenna gain is a measure of the ability of an antenna to amplify or focus the transmitted or received signal in a particular direction. Path loss refers to the attenuation of the signal as it travels through the medium.The relative orientation of the source and antenna impacts both antenna gain and path loss. When the antennas are aligned optimally, the antenna gain is maximized, and path loss is minimized. This results in a stronger and morereliable signal. Conversely, misalignment between the antennas can lead to reduced antenna gain and increased path loss, degrading the signal quality.Conclusion.The relative orientation of the source and antenna is a fundamental factor that influences the performance of wireless communication systems. Understanding theprinciples of polarization, beamwidth, directivity, and their impact on signal strength and quality is crucial for designing and deploying effective communication networks. By carefully considering the relative orientation of the antennas, engineers can optimize signal transmission and reception, ensuring reliable and efficient data transfer in a wide range of scenarios.。
垂直振动成型CTB-50_水泥稳定碎石抗压强度增长规律及预测模型
第42卷第8期2023年8月硅㊀酸㊀盐㊀通㊀报BULLETIN OF THE CHINESE CERAMIC SOCIETY Vol.42㊀No.8August,2023垂直振动成型CTB-50水泥稳定碎石抗压强度增长规律及预测模型蒋应军1,王煜鑫1,周传荣1,李明杰2,杨㊀明2,蒋学猛3(1.长安大学特殊地区公路工程教育部重点实验室,西安㊀710064;2.河南省交通基本建设质量检测站,郑州㊀450016;3.陕西省交通工程咨询有限公司,西安㊀710003)摘要:为表征最大粒径为53mm 水泥稳定碎石(CTB-50)的抗压强度,评价了垂直振动试验方法(VVTM)的可靠性,研究了水泥稳定碎石抗压强度随水泥掺量㊁龄期的增长规律,建立了抗压强度增长方程及预测模型,并分析了级配类型对抗压强度的影响㊂结果表明:VVTM 试件抗压强度与试验段芯样相关性较高,可达91%左右;抗压强度随水泥掺量增加呈线性增大,在养护初期强度增长较快,60d 后强度趋于稳定;建立的抗压强度增长方程㊁预测模型与试验结果相关系数分别不小于0.982㊁0.976,预测值误差绝对值分别小于3%㊁6%;CTB-50的初始㊁极限抗压强度分别约为传统水泥稳定碎石(CTB-30)的1.25倍㊁1.09倍,相同的强度控制指标下,CTB-50可减少水泥用量,有利于降低工程造价,减少基层裂缝㊂关键词:路基工程;CTB-50水泥稳定碎石;垂直振动试验方法(VVTM);抗压强度;增长方程;预测模型中图分类号:U414㊀㊀文献标志码:A ㊀㊀文章编号:1001-1625(2023)08-3045-10收稿日期:2023-04-23;修订日期:2023-06-12基金项目:陕西省创新能力支撑计划(2022TD-06);交通运输行业重点科技项目(2021-MS1-011);长安大学中央高校基本科研业务费专项资金资助(300102213401)作者简介:蒋应军(1975 ),男,博士,教授㊂主要从事道路与铁道工程研究㊂E-mail:jyj@通信作者:王煜鑫,硕士研究生㊂E-mail:2021121195@Compressive Strength Growth Law and Prediction Model for CTB-50Cement-Stabilized Macadam Based on Vertical Vibration CompressionJIANG Yingjun 1,WANG Yuxin 1,ZHOU Chuanrong 1,LI Mingjie 2,YANG Ming 2,JIANG Xuemeng 3(1.Key Laboratory of Highway Engineering in Special Region of Ministry of Education,Chang an University,Xi an 710064,China;2.Henan Province Traffic Infrastructure Quality Inspection Station,Zhengzhou 450016,China;3.Shaanxi Traffic Engineering Consulting Co.,Ltd.,Xi an 710003,China)Abstract :In order to characterize the compressive strength of cement-stabilized macadam with a maximum particle size of 53mm (CTB-50),the reliability of vertical vibration compression testing method (VVTM)was evaluated,and the growth law of cement-stabilized macadam compressive strength with cement dosage and age was studied.The growth equation and prediction model of compressive strength were established,and the influence of gradation type on compressive strength was analyzed.The results show that the compressive strength of VVTM specimens is highly correlated with the core samples of test section,up to about 91%.The compressive strength increases linearly with the increase of cement dosage.The strength increases rapidly at the initial curing stage and tends to be stable after 60d.The correlation coefficients of established compressive strength growth equation and prediction model with test results are not less than 0.982and 0.976,respectively,and the absolute values of predicted value errors are less than 3%and 6%,respectively.The initial and ultimate compressive strength of CTB-50are about 1.25times and 1.09times that of conventional cement-stabilized macadam (CTB-30),respectively.With the same strength control index,CTB-50can reduce the amount of cement,which is conducive to reducing the project cost and cracks of semi-rigid subgrade.3046㊀道路材料硅酸盐通报㊀㊀㊀㊀㊀㊀第42卷Key words:subgrade engineering;CTB-50cement-stabilized macadam;vertical vibration testing method(VVTM);compressive strength;growth equation;prediction model0㊀引㊀言水泥稳定碎石凭借在技术及经济上的优势,被广泛应用于我国各等级公路基层㊂目前我国常用的水泥稳定碎石最大粒径为37.5mm(CTB-30),但其存在收缩开裂问题且尚未得到很好的解决[1-2]㊂理论上,骨料粒径越大,一则颗粒的比表面积越小,裹附㊁黏结骨料所需的水化产物越少,混合料水泥掺量越低,抗裂性㊁经济性㊁环保性更好;二则骨料间更易形成嵌挤骨架结构,触发颗粒移动所需外力更大,稳定性更强,力学性能及耐久性更好[3-4]㊂国计凯[4]㊁关笑楠[5]经研究认为增大骨料粒径可以提高水泥稳定碎石抗裂性能,课题组部分研究[6-9]也表明最大粒径为53mm的CTB-50比传统的CTB-30有更好的路用性能,有望缓解半刚性基层的开裂问题㊂力学性能是水泥稳定碎石主要路用性能之一,抗压强度作为水泥稳定碎石的重要力学性能指标,受到了研究人员的广泛关注㊂马士宾等[10]对微裂后水泥粉煤灰稳定碎石的力学性能变化规律进行了研究,结果表明:试件的力学强度随龄期增长而增大,且增长速率呈早期快㊁后期慢的规律;随粉煤灰掺量增加,试件的抗压㊁劈裂强度先增大后减小,抗压回弹模量有所降低㊂Deng等[11]研究了水泥掺量㊁养护龄期和级配类型对水泥稳定碎石力学强度的影响,结果表明:水泥稳定碎石力学强度随水泥掺量㊁养护龄期的增加而增大,相比于悬浮密实级配,骨架密实级配水泥稳定碎石的强度更高㊂朱挺等[12]通过设计正交试验分析了水泥掺量㊁压实度和级配对水泥稳定再生碎石抗压强度的影响,发现混合料抗压强度受水泥掺量和压实度影响较为显著,受级配(上限㊁中值㊁下限)影响较小㊂Xu等[13]研究了养护温度对水泥稳定碎石抗压强度的影响,结果表明,低温(10ħ)养护下试件的抗压强度增长速率小于标准温度(20ħ)养护的试件㊂Zhao等[14]㊁王洪国等[15]㊁董武等[16]对比分析了不同搅拌工艺对水泥稳定碎石抗压强度的影响,发现与常规搅拌混合料相比,振动搅拌混合料的强度更大,变异系数更低,微观结构更致密,孔隙分布更均匀且闭合程度更高㊂吕松涛等[17]㊁Sun等[18]研究了橡胶对水泥稳定碎石力学性能和抗裂性能的影响,结果表明:橡胶的掺入会降低水泥稳定碎石的7d抗压强度,但会增强其抗裂性能㊂吴启一等[19]研究了玄武岩纤维对水泥稳定多孔玄武岩碎石力学性能的影响,结果表明:混合料力学性能随纤维掺量增加先增强后减弱,当掺入纤维长度为18mm㊁掺量为集料总质量的0.1%时混合料力学性能增强效果最好㊂但以上有关抗压强度的研究多针对最大粒径Dɤ37.5mm的水泥稳定碎石展开,对最大粒径为53mm 的CTB-50抗压强度研究未见报道㊂此外,已有研究多基于静压法(static pressure method,SPM)展开,但SPM试件无法准确反映现场施工机械振动碾压成型的路面材料实际力学性能[20],而垂直振动试验方法(vertical vibration compression testing method,VVTM)试件与路面芯样相关程度较高[21-23]㊂抗压强度是水泥稳定碎石设计时的重要控制指标之一,研究并表征CTB-50的抗压强度具有实际意义㊂鉴于此,本研究以传统水泥稳定碎石(CTB-30)与超大粒径水泥稳定碎石(CTB-50)为研究对象,评价了不同成型方法(SPM㊁VVTM)试件与试验段芯样抗压强度的相关性,研究了水泥稳定碎石抗压强度增长规律,建立了抗压强度增长方程及预测模型,并分析了级配类型对抗压强度的影响,成果可供工程实践参考㊂1㊀实㊀验1.1㊀原材料与级配1.1.1㊀原材料试验用粗集料技术指标见表1,细集料技术指标见表2,水泥技术指标见表3㊂其中粗㊁细集料为陕西宝鸡顺通达矿业有限公司生产的石灰岩,粗集料按粒径大小分为五档,细集料规格为0~5mm,水泥采用陕西尧柏特种水泥有限公司生产的普通硅酸盐水泥P㊃O42.5㊂第8期蒋应军等:垂直振动成型CTB-50水泥稳定碎石抗压强度增长规律及预测模型3047㊀表1㊀粗集料技术指标Table 1㊀Technical index of coarse aggregateTechnical index Size /mm37.5~5331.5~37.519~31.59.5~19 4.75~9.5Apparent relative density 2.786 2.769 2.7612.731 2.729Flakiness content /% 2.17.57.112.9Water absorption rate /%0.410.590.91 1.690.79Crushing value /% 17.9 表2㊀细集料技术指标Table 2㊀Technical index of fine aggregateTechnical indexApparent relative density Lump content /%MB value /(g㊃kg -1)Test value 2.72800.8Canonical value ȡ2.5ɤ1.0ɤ1.0表3㊀水泥技术指标Table 3㊀Technical index of cementTechnical indexFineness%Stability /mm Setting time /min Compressive strength /MPa Flexural tensile strength /MPa InitialFinal 3d28d3d28dTest value 2.68 2.521942622.3048.20 5.808.06Canonical value ɤ10.0ɤ5.0ȡ45ɤ600ȡ21.0ȡ42.5ȡ4.0ȡ7.01.1.2㊀级配CTB-50和CTB-30级配见表4㊂其中CTB-30级配取自‘垂直振动法水泥稳定碎石设计施工技术规范“(DB 61/T 529 2011)中强嵌挤骨架密实级配范围中值,CTB-50级配由课题组经前期研究得到㊂表4㊀CTB-30和CTB-50的级配Table 4㊀Gradation of CTB-30and CTB-50Material Passing percentage /%53mm 37.5mm 31.5mm19mm 9.5mm 4.75mm 2.36mm 0.6mm 0.075mm CTB-50100.070.0 60.042.034.026.014.0 4.5CTB-30100.0100.094.064.042.032.024.012.0 4.51.2㊀试验方法1.2.1㊀试件成型方法图1㊀VVTE 构造Fig.1㊀Construction of VVTE垂直振动试验仪(vertical vibration compaction testing equipment,VVTE)构造见图1㊂经前期研究得到VVTE 的工作参数为:振动频率30Hz,名义振幅1.2mm,上车系统质量122kg,下车系统质量180kg,击实试验振动时间165s(确定最佳含水率和最大干密度),成型试件振动时间120s㊂CTB-50最大公称粒径为53mm,常规尺寸水泥稳定碎石试件(ϕ150mm ˑh 150mm)可能不再适合㊂根据初步试验,较大的试件尺寸(ϕ200mm ˑh 200mm)可消除尺寸效应的影响㊂因此,本研究CTB-50与CTB-30试件尺寸均为ϕ200mm ˑh 200mm㊂试件成型后,按‘公路工程无机结合料稳定材料试验规程“(JTG E51 2009)中T 0845 2009方法进行标准养护㊂3048㊀道路材料硅酸盐通报㊀㊀㊀㊀㊀㊀第42卷1.2.2㊀无侧限抗压强度试验方法无侧限抗压强度试验按‘公路工程无机结合料稳定材料试验规程“(JTG E51 2009)中T 0805 1994进行,加载速率为1mm /min㊂试件无侧限抗压强度按式(1)计算㊂R c =F S (1)式中:R c 为试件无侧限抗压强度,MPa;F 为试件破坏时最大压力,N;S 为试件底面积,mm 2,按式(2)计算㊂S =14πD 2(2)式中:D 为试件直径,mm㊂1.3㊀VVTM可靠性评价图2㊀CTB-50芯样Fig.2㊀Core sample of CTB-50通过对比分析相同条件下室内成型试件与路面芯样7d 抗压强度R c7的相关性,评价VVTM 的可靠性㊂试验段位于郑西高速栾双段LSZCB-1项目段太平互通D 匝道,现场取回水泥稳定碎石湿混合料进行室内成型,将成型完毕的试件转移至现场,确保与现场养护条件尽可能接近㊂图2为试验段现场CTB-50芯样,其水泥掺量为3%(质量分数,下同),密度为2.381g /cm 3,振动击实试验确定的CTB-50最大干密度为2.421g /cm 3,可知芯样压实度为98%㊂不同试件和芯样的 R c7见表5㊂其中, R c7代表试件或芯样的7d 抗压强度平均值,C v 代表变异系数,R c0.95代表95%保证率的抗压强度代表值㊂‘公路工程无机结合料稳定材料试验规程“(JTG E51 2009)规定大尺寸试件抗压强度试验结果C v ɤ15%,表5中C v 均满足此要求㊂根据表5数据可知,与SPM 试件(相关性约69%)相比,VVTM 试件与现场芯样R c 相关性更高,可达91%左右,这表明VVTM 试件可较好地模拟现场施工工艺和碾压效果,更具代表性㊂此外,由表5还可以看出,CTB-50的抗压强度大于CTB-30,这可能是因为CTB-50的粒径较大,骨料间嵌挤力更强[5]㊂表5㊀不同试件和芯样的 R c7㊁C v 和R c0.95Table 5㊀ R c7,C v and R c0.95of different specimens and core samplesMaterial Molding sampleR c7/MPa C v /%R c0.95/MPa SPM sample 5.9 4.9 5.4CTB-50VVTM sample 7.8 4.87.2Core sample8.6 6.07.8SPM sample 4.4 5.6 4.0CTB-30VVTM sample 5.8 4.5 5.3Core sample 6.4 5.3 5.92㊀结果与讨论2.1㊀抗压强度增长规律水泥稳定碎石无侧限抗压强度R c 室内试验结果见表6,P s 代表水泥掺量㊂2.1.1㊀随水泥掺量增长规律根据表6绘制不同P s 下两种级配(CTB-50㊁CTB-30)水泥稳定碎石7㊁28d 龄期R c 增长曲线,见图3㊂由图3可知,CTB-50㊁CTB-30的R c 随P s 增加呈线性增大,此外,CTB-30和CTB-50强度拟合曲线斜率近似,截距差与强度差大致相同,CTB-50的R c 高于CTB-30,且随P s 增加,R c 差值几乎不变㊂这表明,两种水泥稳定碎石R c 差异与P s 相关性较低,级配类型主导了这种差异㊂这可能是因为,在CTB-50试件中,骨料压实形第8期蒋应军等:垂直振动成型CTB-50水泥稳定碎石抗压强度增长规律及预测模型3049㊀成的嵌挤结构强度比CTB-30更高㊂表6㊀水泥稳定碎石R c 试验结果Table 6㊀R c test results of cement stabilized macadamMaterial P s /%R c /MPa 0d 3d 7d 14d 28d 60d 90d 120d 1.5 3.4 5.57.68.79.510.410.911.32.03.5 6.19.210.511.612.613.213.8CTB-50 2.5 3.5 6.910.111.813.214.715.515.83.0 3.67.410.912.914.216.016.817.53.5 3.77.711.714.115.617.318.118.84.0 3.78.212.214.916.518.219.519.91.5 2.7 4.0 6.37.38.29.29.610.32.02.8 4.47.28.79.911.011.612.2CTB-30 2.5 2.8 4.88.19.610.912.413.214.03.0 2.85.08.910.712.214.014.815.33.5 3.0 5.69.511.713.615.616.217.04.0 3.0 6.210.112.615.117.118.118.6图3㊀不同P s 时R c 增长曲线Fig.3㊀R c growth curves at different P s 2.1.2㊀随龄期增长规律根据表6绘制不同龄期T 时CTB-50㊁CTB-30的R c 增长曲线,见图4㊂图4㊀不同龄期时R c 增长曲线Fig.4㊀R c growth curves at different ages3050㊀道路材料硅酸盐通报㊀㊀㊀㊀㊀㊀第42卷由图4可知,随T 的增加,不同级配㊁不同P s 的水泥稳定碎石R c 增长规律相似,在养护初期(T <14d)增长较快,此阶段水泥水化反应最为剧烈,Ca(OH)2等水化产物较多,14d 后增长速度逐渐减缓,60d 后强度趋于稳定㊂此外,表6还列出了水泥稳定碎石初始强度(T =0d)R c0的室内试验结果,由表6㊁图4可知,水泥稳定碎石具有一定的初始强度,0d 时CTB-50㊁CTB-30的R c 差距最小,且随P s 增加,R c0的增长并不明显,这可能是因为,水泥水化反应还未完全开始,水化产物尚不多,骨料压实形成的骨架强度是试件强度的主要来源㊂2.2㊀抗压强度增长方程及预测模型2.2.1㊀强度形成机理水泥稳定碎石的强度是由水泥㊁骨料和水之间的多种相互作用所形成,包括物理作用㊁物理化学作用和化学作用等㊂物理作用包括混合料拌和㊁压实后骨料间的嵌挤作用等,物理化学作用包括骨料和水泥水化产物之间的黏附㊁水化产物的凝结硬化作用等,化学作用包括水泥水化与凝结硬化㊁离子交换反应和火山灰反应等㊂在水泥稳定碎石养护初期,初始强度R c0主要由骨料间的嵌挤力及少量水化产物的黏聚力构成,随T 的增加,水泥水化㊁凝结硬化等化学作用持续进行,水化产物不断形成,强度不断增大,直至水泥熟料用尽时,强度不再增加,即达到极限强度R c ɕ㊂2.2.2㊀强度增长方程基于以上分析,假设水泥稳定碎石存在抗压强度增长方程,并满足三个边界条件(见式(3)),由此建立水泥稳定碎石抗压强度增长方程,见式(4)[11]㊂R c T =R c0,T =0R c T =R c ɕ,T =ɕR c0<R c ɕìîíïïï(3)R c T =R c ɕ-R c ɕ-R c0λc ㊃T +1(4)式中:R c T 为龄期为T 时的抗压强度,MPa;λc 为强度增长方程回归系数㊂采用式(4)方程对表6中数据进行拟合,得到水泥稳定碎石极限抗压强度R c ɕ及强度增长方程回归系数λc ,结果列于表7,其中R 2为相关系数㊂由表7可知,拟合得到的水泥稳定碎石R c 随T 的增长方程相关系数均不小于0.982,表明式(4)可较好地描述水泥稳定碎石R c 增长规律㊂表7㊀水泥稳定碎石R c 增长方程参数Table 7㊀R c growth equation parameters of cement-stabilized macadam Material P s /%R c ɕ/MPa λc R 21.511.50.1320.9912.014.00.1400.988CTB-50 2.516.30.1310.9953.017.90.1300.9923.519.30.1350.9944.020.60.1330.9941.510.60.0980.9822.012.70.1000.988CTB-30 2.514.50.0970.9853.016.10.1010.9873.517.90.0980.9934.019.80.0950.9972.2.3㊀强度预测模型根据表6㊁表7计算不同T 时水泥稳定碎石R c T 与R c ɕ比值,见表8㊂考虑不同T 时R c T /R c ɕ的均值,绘制R c T /R c ɕ与ln(T +1)的曲线,见图5㊂第8期蒋应军等:垂直振动成型CTB-50水泥稳定碎石抗压强度增长规律及预测模型3051㊀表8㊀不同龄期时水泥稳定碎石R c T /R c ɕ结果Table 8㊀R c T /R c ɕresults of cement-stabilized macadam at different ages Material P s /%R c T /R c ɕ0d 3d 7d 14d 28d 60d 90d 120d 1.50.300.480.660.760.830.900.950.982.00.250.440.660.750.830.900.940.99CTB-50 2.50.210.420.620.720.810.900.950.973.00.200.410.610.720.790.890.940.983.50.190.400.610.730.810.900.940.974.00.180.400.590.720.800.880.950.971.50.250.380.590.690.770.870.910.972.00.220.350.570.690.780.870.910.96CTB-30 2.50.190.330.560.660.750.860.910.973.00.170.310.550.660.760.870.920.953.50.170.310.530.650.760.870.910.954.00.150.310.510.640.760.860.910.94由图5可知,R c T /R c ɕ与ln(T +1)曲线近似服从幂函数㊂因此,可假设水泥稳定碎石R c T /R c ɕ-T 存在式(5)所示函数关系㊂R c T R c ɕ=A [ln B (T +1)+C ],T ɤ120d (5)式中:A ㊁B ㊁C 为回归系数㊂采用式(5)对表8中数据进行拟合,结果见表9,回归曲线见图6,其中,R 2为相关系数㊂图5㊀R c T /R c ɕ-ln(T +1)关系Fig.5㊀Relationship between R c T /R c ɕand ln(T +1)图6㊀R c T /R c ɕ-T 拟合关系Fig.6㊀R c T /R c ɕand T fitting relationship ㊀㊀由表9㊁图6可知,采用式(5)对水泥稳定碎石R c T /R c ɕ-T 进行拟合,相关系数R 2均不小于0.976,表明所建立的R c 预测模型式(6)可较好地预测任意龄期时水泥稳定碎石的抗压强度㊂表9㊀R c T /R c ɕ-T 拟合回归系数Table 9㊀R c T /R c ɕ-T fitting regression coefficientMaterial Regression parameter A B C R 2CTB-500.2100.837 1.0070.978CTB-300.1690.992 1.0410.976CTB-50:R c T R c ɕ=0.210[ln 0.837(T +1)+1.007],T ɤ120d CTB-30:R c T R c ɕ=0.169[ln 0.992(T +1)+1.041],T ɤ120d ìîíïïïï(6)3052㊀道路材料硅酸盐通报㊀㊀㊀㊀㊀㊀第42卷为便于研究成果的应用,根据R c7测试结果对式(6)进行转化㊂由表8可知,CTB-50㊁CTB-30的R c7与R c ɕ之比的均值分别为0.62㊁0.55,则预测模型式(6)可转换为式(7)㊂CTB-50:R c T R c ɕ=0.339R c7[ln 0.837(T +1)+1.007],T ɤ120d CTB-30:R c T R c ɕ=0.307R c7[ln 0.992(T +1)+1.041],T ɤ120d ìîíïïïï(7)同理,也可根据表8中3d 龄期抗压强度试验结果R c3对式(6)进行转化,限于篇幅,此处不再赘述㊂2.3㊀方程及模型可靠性分析2.3.1㊀强度增长方程可靠性分析为评价R c 强度增长方程的可靠性,选取P s 为3%,T 分别为14㊁60㊁120d 的水泥稳定碎石的R c 实测值,并计算预测值及误差,结果见表10㊂由表10可知,R c 增长方程的预测值误差绝对值小于3%,说明式(4)方程较为准确㊂表10㊀不同龄期时R c 增长方程预测值及误差Table 10㊀Predicted values and errors of R c growth equation at different ages Material 14d 60d120d R c /MPa Measured value Predicted value Error /%R c /MPa Measured value Predicted value Error /%R c /MPa Measured value Predicted value Error /%CTB-5012.912.83-0.5416.016.28 1.7517.517.04-2.63CTB-3010.710.59-1.0314.014.22 1.5715.315.09-1.372.3.2㊀强度预测模型可靠性分析为评价R c 预测模型的可靠性,选取P s 为3%,T 分别为14㊁60和120d 的水泥稳定碎石的R c 实测值,并计算预测值及误差,结果见表11㊂由表11可知,R c 预测模型的预测值误差绝对值小于6%,表明当级配类型㊁P s 及R c7已知时,式(7)可较为准确地预测水泥稳定碎石任意龄期时的R c ㊂因此,R c 预测模型可有效缩短试验时间,减少测试量,在一定程度上避免了长期R c 的测试,具有广泛的适用性㊂表11㊀不同龄期时R c 预测模型预测值及误差Table 11㊀Predicted values and errors of R c prediction model at different ages Material 14d 60d120d R c /MPa Measured value Predicted value Error /%R c /MPa Measured value Predicted value Error /%R c /MPa Measured value Predicted value Error /%CTB-5012.912.23-5.1916.015.78-1.3817.517.45-0.29CTB-3010.710.18-4.8614.013.95-0.3615.315.78 3.142.4㊀级配类型影响研究根据表6㊁表7数据计算相同条件下CTB-50与CTB-30的R c 比值r c ,见表12㊂表12㊀CTB-50与CTB-30的R c 比值Table 12㊀R c ratio of CTB-50to CTB-30P s /%r c 0d 3d 7d 14d 28d 60d 90d 120d ɕ1.5 1.26 1.38 1.21 1.19 1.16 1.13 1.14 1.10 1.082.0 1.25 1.39 1.28 1.21 1.17 1.15 1.14 1.13 1.102.5 1.25 1.44 1.25 1.23 1.21 1.19 1.17 1.13 1.123.0 1.29 1.48 1.22 1.21 1.16 1.14 1.14 1.14 1.113.5 1.23 1.38 1.23 1.21 1.15 1.11 1.12 1.11 1.084.0 1.23 1.32 1.21 1.18 1.09 1.06 1.08 1.07 1.04Average value1.25 1.40 1.23 1.20 1.16 1.13 1.13 1.11 1.09第8期蒋应军等:垂直振动成型CTB-50水泥稳定碎石抗压强度增长规律及预测模型3053㊀图7㊀R c7-P s 关系Fig.7㊀Relationship between R c7and P s ㊀㊀由表12可知,CTB-50的抗压强度大于CTB-30,表5中数据也证明了这一点㊂CTB-50的R c0㊁R c ɕ分别约为CTB-30的1.25倍㊁1.09倍,随T 的增长,r c 平均值先增大后减小,在养护初期CTB-50的强度优势较为明显㊂这可能是因为:养护初期试件强度主要由骨架强度构成,CTB-50较CTB-30骨料粒径更大,压实后骨料间嵌挤情况更好,形成的骨架结构强度更大,表现为CTB-50的初期强度更高;但随T 的增长,水泥水化反应逐渐深入,对强度形成的贡献主要由水化产物的黏聚力提供,水化产物总量一定,由级配因素带给CTB-50的强度优势逐渐减弱[5,7]㊂根据表6绘制CTB-50㊁CTB-30的R c7与P s 关系见图7㊂由图7可知,在相同的强度控制指标下,即CTB-50㊁CTB-30要达到相同的R c7,CTB-50对应的P s 小于CTB-30㊂如水泥稳定碎石R c7要求不小于8MPa,则CTB-50㊁CTB-30的最小水泥掺量分别为1.6%㊁2.4%,前者可减少33%的水泥消耗㊂较小的水泥用量,不仅能降低工程造价,还有利于降低温缩㊁干缩系数,减少基层裂缝[24-26]㊂3㊀结㊀论1)VVTM 试件与现场芯样抗压强度相关性可达91%左右,而SPM 试件与现场芯样抗压强度相关性约为69%,VVTM 可较好地模拟现场施工工艺和碾压效果,更具代表性㊂2)水泥稳定碎石抗压强度随水泥掺量增加呈线性增大,在养护初期(T <14d)强度增长较快,14d 后增长速度逐渐减缓,60d 后强度趋于稳定㊂3)建立的抗压强度增长方程㊁预测模型与试验结果相关系数分别不小于0.982㊁0.976,预测值误差绝对值分别小于3%㊁6%,在确定水泥掺量㊁级配类型及短期强度后,可较为准确地预测水泥稳定碎石各龄期时的抗压强度㊂4)CTB-50的初始㊁极限抗压强度分别约为CTB-30的1.25倍㊁1.09倍;在相同的强度控制指标下,CTB-50水泥用量较少,有利于降低工程造价,减少基层裂缝㊂参考文献[1]㊀JIANG Y J,WANG H T,YUAN K J,et 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红外震动类型表示与英文名称
红外振动类型的英文表示方法及其全称(remove the research barrier)1、红外光谱的产生和表示在分子的振动过程中,只有那些能引起分子偶极矩改变的振动,才能吸收红外辐射,从而在红外光谱中出现吸收谱带。
多原子分子的振动是由许多简单的、独立的振动组合而成的。
在每个独立的振动中,所有原子都是以相同相位运动,可以近似地看作谐振子振动。
这种振动称为简正振动。
每个简正振动具有一定的能量,故应在特有的波数位置产生吸收。
由n个原子组成的多原子分子存在有3n—6个简正振动,而线型分子则为3n—5个简正振动。
在简单分子中,对这些基本振动进行理论解析是可能的,但在实际的复杂有机化合物中,简正振动数目很多,而且由于倍频振动和组合频振动也会出现吸收,所以使红外光谱变得很复杂。
对于所有的红外吸收谱带在理论上进行解析将是非常困难的。
因此,当红外光谱用于定性分析时,通常是利用各种特征频率吸收图表,选出与官能团和骨架构有关的吸收谱带,而且还要与待定化合物的标准光谱相比较才能得出结论。
红外光谱图的横坐标一般用波数v(单位cm-1),纵坐标常用百分透过率(T%)表示。
2、多原子分子的振动方式基团的各种振动类型用如下符号来表示:ν伸缩振动γ面外弯曲振动δ变形振动β面内弯曲振动 t扭绞振动τ扭转振动ω面外摇摆振动 s对称振动 as不对称振动r面内摇摆振动3、吸收带强度吸收带的强弱主要取决于分子振动时偶极矩变化的大小。
分子的对称性越高,偶极矩的变化越小,吸收带越弱。
一般,仅含碳和氢的化合物的吸收是较弱的。
但是由电负性差别显著的原子所组成的键,如c—N、c—o、c=o、c=N等,其吸收带一般都是很强的。
吸收带的强度用表观摩尔吸光系数来表示,也用如下符号来表示:VS(very strong,极强),S(strong,强),M(medium,中),w(weak,弱),Vw(very weak,极弱)。
红外线:infrared ray,IR中红外吸收光谱:mid-infrared absorption spectrum,Mid-IR远红外光谱:Far-IR微波谱:microwave spectrum,MV红外吸收光谱法:infrared spectroscopy红外分光光度法:infrared spectrophotometry振动形式:mode of vibration伸缩振动:stretching vibration对称伸缩振动:symmetrical stretching vibration不对称伸缩振动:asymmetrical stretching vibration弯曲振动:bending vibration变形振动:formation vibration面内弯曲振动:in-plane bending vibration,β剪式振动:scissoring vibration,δ面内摇摆振动:rocking vibration,ρ面外弯曲振动:out-of-plane bending vibration,γ面外摇摆振动:wagging vibration,ω蜷曲振动:twisting vibration ,τ对称变形振动:symmetrical deformation vibration ,δs不对称变形振动:asym metrical deformation vibration, δas 特征吸收峰:charateristic avsorption band特征频率:characteristic frequency相关吸收峰:correlation absorption band杂化影响:hybridization affect环大小效应:ring size effect吸收峰的强度:intensity of absorption band环折叠振动:ring prckering vibration。
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Int J Adv Manuf Technol(2002)19:705–713 Ownership and Copyright2002Springer-Verlag LondonLimitedThe Correlation of Vibration Signal Features to Cutting Tool Wear in a Metal Turning OperationD.E.Dimla,Snr.School of Engineering and Technology,De Montfort University,Leicester,UKThis paper describes a tool-wear monitoring procedure in a metal turning operation using vibration features.Machining of EN24was carried out using coated grooved inserts,and on-line vibration signals were obtained.The measured tool-wear forms were correlated to features in the vibration signals in the time and frequency domains.Analysis of the results sug-gested that the vibration signals’features were effective for use in cutting tool-wear monitoring and wear qualification. Keywords:Metal turning;Tool condition monitoring; Vibration signals;Wear measurements1.IntroductionDuring metal turning operations,a complex and dynamically varying system develops between the workpiece and the cutting tool.Close supervision of tool wear levels must be maintained as excessive tool wear could lead to severe deterioration of the workpiece surfacefinish,possibly incurring additional costs in material and work.In the worst-case scenario,catastrophic tool failure might lead to machine tool damage,and high replacement costs[1–3].Direct methods for determining tool wear such as those associated with measuring and correlating the volumetric loss of the cutting tool material are time consuming.A number of mechanical and physical based sensors such as touch trigger probes,and optical,radioactive,and electrical resistance measurement techniques and proximity sensors have been developed towards this purpose[3].These sensors often require the interruption of the cutting process in order to take measure-ments(post-wear monitoring),thereby increasing the lead-and downtime.Indirect methods of tool wear monitoring on the other hand, can be applied on-line(real-time),as they rely on process changes resulting from the tool wear,cutting conditions,and Correspondence and offprint requests to:Dr D. E.Dimla,Rapid Prototyping&Manufacturing Group School of Engineering and Tech-nology,De Montfort University,The Gateway,Leicester,LE19BH, UK.E-mail:ddimlaȰ variability in the workpiece material,etc.Suitable sensors have been developed for particular applications,such as static and dynamic force measurement,acoustic emission and vibration. Several methods have also been pursued in the quest to develop tool-wear monitoring systems to identify and separate tool-wear effects on the sensor signals from those emanating from cutting conditions.These methods include mathematical and adaptive models,time and frequency domain analysis,pattern recognition,artificial intelligence,and knowledge-based systems [4–6].When a cutting tool pushes through the workpiece material, the workpiece undergoes plastic deformation(dislocation movements)releasing strain energy referred to as acoustic emission(AE)as the bonds between the metal atoms are disturbed.Other sources of AE include phase transformations, friction mechanisms(tool–workpiece contact)and crack forma-tion[1,7,8].Dimla[5]has presented a brief review of AE application sensing techniques in tool-wear detection and moni-toring in metal cutting operations.There are many types of AE sensor,but only a few of these can cope with the rugged conditions that prevail in the machining environment.Most AE sensors have been designed for non-destructive testing and inspection and are therefore unsuitable for tool-wear monitoring applications as they cannot withstand the extreme conditions at the cutting point such as high temperatures,large coolant volumes,and the impact from chips[9].Many new concepts on AE sensing have been proposed for use in the metal cutting environment,e.g.Dolinsek and Kopac[9]use the coolant jet as an AE signal transmission medium between the cutting zone and a PZT transducer element.Kim et al.[10]developed an on-line cutting tool life monitoring system using an integral pre-amp AE sensor for gear shaping applications.With the AE sensor attached directly to the workpiece material,r.m.s.values of the AE signal were recorded that reportedly correlated with the pinion cutter tool wear through a series of experimental investigations.Carolan et al.[11]with the aid of a non-contact fibre optic AE sensor,carried out face milling of steels and aluminium,recording the AE signals for tool-wear monitoring. From the ensuing analysis,a model detailing the relationship between measured tool wear and the energy in the r.m.s.value of the AE signal,was developed and validated for various workpiece materials.By using a non-contact AE sensor,uncer-706 D.E.Dimla,Snrtainties from frequency response and variation that characterise the AE signal were eliminated,thus boosting confidence in the results and the reliability of the application.The most important limiting factor in the application of AE in a tool condition monitoring system(TCMS)does not lie in the sensing technology,but on the ensuing analysis[3].This is primarily due to the lack of a suitable knowledge base on AE.Consequently,the user has to experiment and establish the necessary trigger responses to a variety of machining conditions,which involves considerable work.When compared with the concept of lowering and increasing the force limits which can be understood by an operator,spectral analysis is not so easily comprehended.Hence,instead of the system being an aid to the operator,it rather presents a real-time quandary. Choosing a suitable position in which to place the AE sensors so as to sense sufficient AE signals is contentious,as an understanding of the AE path has to be established.AE propagates and proliferates over the entire machining area.A further drawback to the application of AE as an indicator of tool wear is the fact that it is more sensitive to variations in the cutting conditions and noise than to the tool condition itself.As such,using AE on its own to monitor the state of a cutting tool is a difficult task[12].AE,it could be argued, is suitable only as an additional sensing method for increased reliability.Substantially little AE is generated during the tool-wear process compared to the large amount which accompanies tool breakage and fracture[13],with as much depending on the cutting material(workpiece)structure as on the cutting tool.As the emphasis on any tool condition monitoring system would generally be on tool wear rather than tool fracture,AE is not a suitable tool-wear indicator in monitoring applications, but could be used to good effect in detecting tool-tip breakage on machining centres.The development of chatter and its subsequent progression to vibration leads to a change in the work surface relative to the instantaneous cutting direction.Excessive vibration can cause damage to the machine tool,interfering with the feedrate, cutting speed,and depth of cut.Monitoring the relative rate at which the system is disturbed in all three planes can furnish the TCMS with adequate information about the tendency of direction of movement,and hence,can give an indication of that quantity.Vibration is produced by cyclic variations in the dynamic components of the cutting forces,resulting from periodic wave motions.The nature of vibration signals arising from the metal cutting process incorporates free,forced,periodic,and random types of vibration.Direct measurement of vibration is difficult to achieve because the vibration mode is frequency dependent. Hence,related parameters are measured such as the rate at which dynamic forces change per unit time(acceleration)and the characteristics of the vibration are derived from the patterns obtained.Several investigations have been carried out to corre-late vibration signals to tool wear[5,6].El-Wardany et al.[14]investigated the use of vibration signature characteristics in on-line drill-wear monitoring and breakage.Vibration signature features sensitive to the tool wear were identified in the time(ratio of absolute mean value and kurtosis)and frequency(power spectra and cepstra ratio) domains.Experimental results showed that the kurtosis values increased drastically with drill breakage,whereas frequency analysis revealed sharp peaks indicating drill breakage.By combining both techniques,it was possible to devise an effec-tive drill monitoring system.Yao et al.[15]investigated the detection and estimation of groove wear at the minor cutting edge of a cutting tool,by monitoring vibration signatures.A multivariate time series analysis was carried out on the recorded vibration signals using an autoregressive moving averages method.The dispersion of the signals’autocovariance was obtained,which showed that the vibration signal was sensitive to the length of groove wear on the cutting tool.Dan and Mathew[16]employed a discrete modelling method known as a data dependent system to correlate vibration signals to cutting-tool wear.Results showed a consistent variation in the vibration energy within specific frequency bands,regardless of the ensuing cutting conditions.The application of spectral analysis to the acceleration signals showed sensitivity to the cutting-tool wear.Tool wear monitoring ought to involve the complex and diverse nature of the metal cutting process,in the development of a TCMS,which should provide an indication as to when the cutting tool should be changed,without compromising the workpiece surfacefinish,the machine integrity,and the manufactured component tolerances.Sensor signals for TCMS have to be robust,reliable,and applicable.The vibration signatures satisfy these conditions reasonably well,in addition to the fact that vibration signatures require fewer peripheral instruments than AE for instance.Furthermore,vibration signals have the quick response time needed to indicate changes for on-line monitoring[1].An analytical on-line system for TCM based on vibration signature features,is reported in this paper.The main objective of the study was to develop a TCM system based on a turning operation for determining characteristic vibration signal features which are sensitive to tool wear.Analytical modelling of the experimentally acquired on-line acceleration data in the three principal axes was carried out,and their suitability for tool wear monitoring by time and frequency analyses was deter-mined.The effect of tool wear on the sensitivity and repeat-ability of the vibration signals was investigated.A reasonable correlation was observed between the spectral energy at certain frequencies and the condition of the measured cutting tool. 2.Experimental procedureThe machine tool used was a centre lathe onto which was attached a Kistler triaxial(x-,y-,and z-planes)accelerometer (type8730A).A power supply/coupler(Kistler type5134)was used to amplify and decouple the acceleration(vibration) signals which were sampled at over30kHZ using an Amplicon PC-30data acquisition card.A schematic diagram of the instrumentation set-up is presented in Fig.1,and details of the workpiece and tooling material shown in Table1.The tool inserts were coated by chemical vapour deposition with P15having a thick wear resistant coating on a hard resistant substrate.Its inner coating was8m thick comprising of6m of aluminium oxide(Al2O3)and a thinner outer layerThe Correlation of Vibration Signal Features707Fig.1.Schematic diagram of the experimental test rig.Table1.Test material type and tool details.Workpiece Work material EN24BS970material Hardness Brinell255Composition0.4%C,0.28%Si,0.27%Mo,1.18%Cr,0.5%Mn,1.4%Ni Tooling materialTool holder Sandvik SSBCR2020K12Tool type SCMT120408UMTool material Sandvik Coromant P254025andP154015Overhang/mm45Cuttingfluid Noneusedof titanium nitride.P25had a thick(Ϸ10m)layer of Al2O3 over a medium size layer of titanium carbon nitride[17]. The cutting conditions were selected based on the toughness of the workpiece within the tool manufacturer’s recommended range for the workpiece–tooling geometry configuration.The tests were conducted at the following cutting conditions: Cutting speeds:275,300,and350m min−1.Feedrates:0.1,0.2,and0.3mm rev−1.Fixed depth of cut:2mmInterrupted machining was conducted using a fresh tool until the tool failed or the cutting edges were severely worn,when continued cutting risked catastrophic failure.The duration of each test allowed complete stabilisation of the cutting process to be attained while allowing for significant tool wear.Measure-ments offlank,nose,and notch wear lengths were made after the vibration signals had been recorded using a toolmaker’s microscope and the observations had been supplemented by scanning electron microscope profiling.The chip type,the presence of a built-up edge,and tool chipping or fracture were noted.3.P25Insert ResultsInspection of the results showed significant changes in the acceleration signals as the wear length on the cuttingfaceFig.2.Wear vs.time(V=300m min−1,f=0.1mm rev−1).Fig.3.Wear vs.time(V=300m min−1,f=0.3mm rev−1). increased.The results also showed that increasing the feedrate at constant speed decreased tool life,by increasing the burnout activity.The same was true for cutting speed changes at a constant feedrate,though this was more significant in terms of active tool life.3.1Time Domain AnalysisThe wear-time diagrams(Figs2–5)show that it is possible to detect the three phases of tool wear(primary,secondary,and Fig.4.Wear vs.time(V=275m min−1,f=0.1mm rev−1).708 D.E.Dimla,SnrFig.5.Wear vs.time (V =275m min −1,f =0.3mm rev −1).tertiary)but only at low feedrates,regardless of cutting speed.The tool lasted longer at low cutting speeds and the wear phases were more visibly pronounced on the Figures.The most noticeable indicator of imminent tool failure was the sudden escalation of nose wear to failure.Typically,when nose wear approached 0.2mm,there was a risk of catastrophic failure.This level of wear was also found to be an applicable safety threshold for flank wear length.Notch wear,on the other hand,increased steadily,and then remained practically the same for the remainder of tool life.Wear monitoring through the application of the sum total power (STP)or energy contained in the vibration spectra (Figs 6and 7)showed that increases in flank wear length led to an increase in the STP value.As the wear increased,the STP increased gradually,peaking at a flank wear length of 0.2mm before falling.This trend was most noticeable when cutting at high speeds and feedrates.3.2Frequency Domain AnalysisThe noisy nature of the sensor signals required an active selection or mapping of useful features from the sampled sensor signals,to yield features that might be sensitive to tool wear but not sensitive to other parameters.MATLAB codes were developed and used for all the signal processing.TheFig. 6.STP vibration spectra vs.flank wear (V =300m min −1,f =0.2mm rev −1).Fig.7.STP vibration spectra vs.flank wear (V =275m min −1,f =0.3mm rev −1).signal-processing paradigm involved obtaining the fast Fourier transform of the acceleration,passed through a Hanning win-dow for repeatability of the record length throughout.The FFT data obtained was then smoothed using a seventh-order factor to enhance the quality of any visual plots (spectra and contour plots).With the spectra plots,it was possible to visualise the amplitude variations and their corresponding frequencies,whereas the overall frequency bands were more visible on contour diagrams.3.2.1Spectra AnalysisThe vibration spectra (Figs 8–10)had two main peak frequency bands at 2–4kHz (the fundamental resonant frequency of the tool holder)and at 9–11kHz (chip lamination frequency).Detailed inspection of the spectra plots showed that the z -direction was the most sensitive to tool wear.The 2–4kHz band increased steadily,peaking before falling,just before tool failure.The 9–11kHz peak increased as the cutting tool wore,and showed the largest increase.Increasing the feedrate led to a proportional increase in the magnitude of both peaks.How-ever,at high feedrates,the spectra were noisier over wider frequencybands.Fig.8.Z -vibration spectra vs.flank wear (V =300m min −1,f =0.1mm rev −1).The Correlation of Vibration Signal Features709Fig.9.Z -vibration spectra vs.flank wear (V =275m min −1,f =0.1mm rev −1).Fig.10.X -vibration spectra vs.flank wear (V =275m min −1,f =0.3mm rev −1).3.2.2.Contour AnalysisContour diagrams (Figs 11and 12)clari fied observations made from the spectra plots (i.e.the exact location and variation in the principal frequency peaks).The contour diagrams showed a low energy concentration band at 2–4kHz and a larger band at 9–11kHz.No effects of tool wear werevisible.Fig.11.Z -vibration contour (V =300m min −1,f =0.2mm rev −1).Fig.12.Z -Vibration contour (V =275m min −1,f =0.3mm rev −1).3.3Summary of ObservationThe sensitivity of the vibration components to tool wear was obtained by building a sensitivity index table.The table was constructed using the following indices:3,most sensitive;2,moderately sensitive;1,least sensitive;0,not sensitive at all.The sensitivity matrix shown in Table 2was obtained.Table 2shows that nose and flank wear gave a coherent indication of tool wear.All the components of the vibration signal were sensitive to nose and flank wear forms.The y -and z -direction components were the most sensitive,regardless of the cutting conditions.4.P15Insert Results4.1Time Domain AnalysisInspection of the wear diagrams (Figs 13–15)reveals that the low feedrate wear –time plot gave a better indication of the tool life.After 100s of active tool cutting,a very sharp rise in wear was followed by two further rises.Flank and nose wear,as observed with the P25insert,are better indicators of tool wear/life than the notch wear.The STP vibration diagrams (Figs 16and 17)show the z -direction to be the most sensitive to both wear forms.The x -and y -curves remain constant when feedrate was increased from 0.1mm rev −1to 0.3mm rev −1,but rose slightly when the wear length exceeded 0.3mm.At this stage,the z -value was almost 300%higher compared to the x -and y -values,and hadTable 2.Sensitivity matrix for P25tool insert.Vibration componentsCriteriax -direction y -direction z -direction Sensitivity to flank wear 223Sensitivity to nose wear 233Total response456710 D.E.Dimla,SnrFig.13.Wear vs.time (V =300m min −1,f =0.1mm rev −1).Fig.14.Wear vs.time (V =300m min −1,f =0.3mm rev −1).Fig.15.Wear vs.time (V =275m min −1,f =0.3mm rev −1).a downward trend.At low cutting speeds,the STP vibration decreased (in the z -and y -directions)until the wear reached 0.1mm,and then remained constant.The x -axis did not change until a flank wear length of 0.25mm,after which,the value fellsuddenly.Fig.16.STP vibration spectra vs.flank wear (V =300m min −1,f =0.1mm rev −1).Fig.17.STP vibration spectra vs.flank wear (V =300m min −1,f =0.3mm rev −1).4.2Frequency Domain AnalysisThe vibration spectra (Figs 18–20)generally were noisier than those from machining with the P25insert.Three main peaks were identi fied in all three axes at the 1–2,3–5,and 10kHz bands,though with signi ficant variations.In the x -direction,the 1–2kHz peak had a large bandwidth that decreased as the wear length increased.No signi ficant changes occurred ontheFig.18.X -vibration spectra vs.flank wear (V =300m min −1,f =0.1mm rev −1).The Correlation of Vibration Signal Features711Fig.19.Y -vibration spectra vs.flank wear (V =300m min −1,f =0.3mm rev −1).Fig.20.Z -vibration spectra vs.flank wear (V =275m min −1,f =0.3mm rev −1).y -axis spectra.On the z -axis,the most signi ficant change was at the 10kHz peak.This increased considerably as the wear length increased and fell as the tool entered its tertiary wear phase.Increases in the feedrate led to a widening of the bandwidth,which became wider as the wear length increased.Cutting speed changes did not appear to have any signi ficant effect on the spectra plots.The contour diagram shows that except for the z -axis plot (Fig.23),the x -and y -plots (Figs 21and 22)were scattered at low and high feedrates,covering a wide bandwidth.The z -axis had its clearest and sharpest concentration at 10kHz.No other signi ficant features were immediately apparent.4.3Summary of ObservationA sensitivity matrix was constructed as before with numbers allocated (3,most sensitive;2,good indicator;1,least sensitive)and is shown in Table 3.The STP vibration components were more sensitive to tool wear than the spectra displays (considering the total response).In terms of the individual axes,the z -axis cutting direction was the most sensitive for both the STP and spectra displays.5.Discussion of ResultsAs the vibration signals consist mainly of a combination of stochastic,periodic,and superimposed harmonic signals,aFig.21.X -vibration contour (V =300m min −1,f =0.3mm rev −1).Fig.22.Y -vibration contour (V =300m min −1,f =0.1mm rev −1).method of observation that combines both aspects of signal and process behaviour is required.The computation of the sum total power contained in each spectrum ensured that the most signi ficant properties affected by cutting tool wear on the tool edges were included in the analysed signal.A possible shortcoming in these investigations was the rela-tive dif ficulty of accurately measuring the flank,nose,and notch wear lengths,especially when they were irregular.Quoted wear values would be expected to deviate from the true or ideal values because of the element of subjectivity.The maximum flank wear length (V BMax )was used as the standard measure of flank wear length.In almost all the tests,the end of tool life was indicated by the sudden escalation of both the flank and nose wear land lengths.Increased wear levels led to an increase in the contact area owing to crumbled cutting edges.The transition of friction from static to sliding owing to an increase in the contact area generates high signal pulses,resulting in an increase in the magnitude of the fundamental resonant peak.Beyond a certain flank wear value,the fundamental frequency peak begins to reduce as the contact area increases monotonically,partly712 D.E.Dimla,SnrFig.23.Z -vibration contour (V =300m min −1,f =0.3mm rev −1).Table 3.Sensitivity matrix for P15tool insert.Vibration componentsx -direction y -direction z -direction Total signalresponseSTP vibration signal 2237Vibration spectra 1135Component total 336responsebecause of plastic deformation and the acceleration of nose wear.The chips formed indicate that the high burst was due to an increase in the delamination frequency,arising from the change in deformation behaviour of the material in the shear zone.A noticeable difference in the two insert types was the occurrence of built-up edges (BUE).Although considerable BUE occurred in the P25insert,little or no BUE occurred when machining with the P15insert.Nose wear was found to rise at a faster rate than flank wear land length for both insert types.This seems to suggest that catastrophic tool failure occurred largely at the tool nose,and that nose wear was perhaps a better indicator of the end of tool life.Under such circumstances,it would be possible to use nose wear to signal the end of tool life and its imminent replacement.A practical approach would be to track both flank and nose wear levels to establish exactly which wear regime the tool was in (i.e.its wear phase).Therefore,a rise in nose wear would signal the approach of the catastrophic failure region and would,therefore,be an ideal time to replace the tool insert.6.ConclusionsThe analysis and correlation of vibration signal features to cutting tool wear have been carried out.Time domain features were deemed to be more sensitive to cutting condition than tool wear,whereas frequency based features correlated well with the tool wear.Based on the measurements of cutting tool wear form and the analysis of the vibration signatures,it has been possible to identify the trend of the sensor signals as the insert wear length increased.The characteristics showed that the measured wear values correlated well with certain resonant peak frequencies.The sensor signals were also affected by the different wear modes.It has been possible to establish distinct differences in signal characteristics when cutting was performed with a new insert from that occurring with a detrimental level of wear.AcknowledgementsThe author sincerely thanks The University of Wolverhampton Research Support Unit for its financial assistance.The valuable advice and guidance of Dr P.Lister and Dr N.Leighton is gratefully acknowledged.Special thanks to Maria Giovanna Lo Porto for painstakingly producing the figures.The Correlation of Vibration Signal Features713References1.D.E.Dimla Sr,“Multivariate tool condition monitoring in a metalcutting 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