机械工程测试英文

1、fundamentals of mechanical measurement technologybefore class self-introduction bilingualchapter 1: introduction whats measurement? applications a template of a general measurement system course contents gradingbasic concepts of measurement methods measurement: examples: scale, race, thermometeran a

2、ct of assigning a specific value to a physical variableq the extensiveness, essence and scientific significance of measurement technology:“whatever exists, exists in some amount.” “i often say that when you can measure what you are speaking about and express it in numbers, you know something about i

3、t, and when you cannot measure it, when you cannot express it in numbers, your knowledge is of meager and unsatisfactory kind. it may be the beginning of knowledge, but you have scarcely, in your thought, advanced to the stage, whatever the matter be.” - lord kelvin (william thompson) some questions

4、 to ask: whats the relationship between the measured value and the real value of a variable? how to devise a measurement or test plan? how to interpret the measured data? early measurements:length (distance), time, area and weight, etc. the rapid development of science and technology has invigorated

5、 measurement technology, and the development of modern electronics, especially the information technology has pushed forward further its development.applications of mechanical measurements machine part, vibration measurement flight of an aircraft: measurements of its course, speed, acceleration, mil

6、eage, etc. on a robot: force sensor, pressure sensor, touch sensor, vision sensor, distance sensor, etc.components of a general measurement systemsensor - transducer stagesignal conditioning stage output stage data display and recording measured object observercontroller a general measurement system

7、: sensor:a device that receives and responds to a signal or stimulus transducer:it converts this sensed information into a detectable signal, which might be electrical, mechanical, optical or otherwise. the goal is to quantify the sensed informationbulbstemdisplay scalesensorsensor-transducer stage

8、output stage:it indicates or records the value measured. this might be a simple readout display, a marked scale, or even a recording device. signal conditioning:signal conditioning equipment takes the transducer signal and modifies it to a desired magnitude. e.g. amplification, filtering, conversion

9、 etc. classification of physical quantities (in terms of time-dependent properties): static quantities and dynamic quantities static quantity: does not vary or varies slowly with time. dynamic quantity: varies rapidly with time. static measurement:the measurement of a static quantity. dynamic measur

10、ement:the measurement of a dynamic quantity.course contents chapter 2: signal analysis and processing signal classification signal representations in time and frequency domains signal convolution and correlation digital signal processingcourse contents (cont.) chapter 3: measurement system behavior

11、general model for a measurement system special cases: zero-order, first-order, second-order systems step function input and sine function input responses chapter 4: analog electrical devices and measurements current, voltage and resistance measurements analog signal conditioning amplifiers filters s

12、pecial purpose circuitscourse contents (cont.) chapter 5: sampling, digital devices and data acquisition sampling d/a converter, a/d converter data-acquisition system components chapter 6: sensors and measurements sensors strain measurement temperature measurement flow measurementtextbooks 机械工程测试原理与

13、技术，秦树人， 重庆大学出版社 工程测试技术，清华大学出版社 华中科技大学机械专业精品课程工程测试技术基础 http:/ theory and design for mechanical measurements, 4th edition, r.s. figliola / d.e.beasley, wiley grading homework: 10% attendance: 5% final: 85%chapter 2: signal analysis and processingdefinition: all the physical quantities or variables of

14、systems, such as: force, displacement, acceleration, voltage, current, light intensity, etc.input signal: the excitation to the system,output signal: the response to the system.experimental constraints of a signalan experimental signal is the image of a physical process and must be physically achiev

15、able. constraints for a signal:its energy must be finite.its amplitude is necessarily bounded. this amplitude is a continuous function because the source system inertia prohibits any discontinuity. the signal spectrum is also necessarily bounded and must tend towards zero when the frequency tends to

16、wards infinity. noise definition: an unwanted perturbation to a wanted signal. signal-to-noise ratio (s/n or snr): a measure of the extent of signal contamination by noise, expressed as ornspp /10log10db signal classifications analog signal, discrete time signal and digital signal deterministic sign

17、als and nondeterministic signals time domain signal vs. frequency domain signalclassification of waveforms analog signal: continuous time and valuestimesignalclassification of waveforms (cont.) discrete time signal (discrete time, continuous values) samplingclassification of waveforms (cont.)digital

18、 signal: both the magnitude and time are discretequantization: assigns a single number to represent a range of magnitudes of a continuous signal useful when data acquisition and processing are performed by using a digital computer.15classification of waveforms (cont.) a/d convertertypically, an adc

19、is an electronic device that converts an input analog voltage (or current) to a digital number proportional to the magnitude of the voltage or current. d/a converter example of musicsignal classification (cont.)dynamic signals deterministic signals nondeterministic signals random signalperiodic sign

20、alsaperiodic signalssimple periodic signal:0( )sin()y tactcomplex periodic signal:01( )sin()nnny tacn tstep waveform: 00( )()y tau ttramp waveform: ( )y tkt00tt forpulse waveform: 0102( )()()y tau ttau tt0t1t2ttime domain signal vs. frequency domain signaltimeamplitudefrequencyfrequency domain the t

21、ransmission device of an air compressor malfunction diagnosis: vibration analysis natural frequency, angular velocityfourier series fourier series: decomposes a periodic function or periodic signal into a sum of a series of sines and cosines01( )(cossin)nnny taan tbn t(2.1)fourier series (cont.) dir

22、ichlet conditions f(x) must have a finite number of extrema in any given interval f(x) must have a finite number of discontinuities in any given interval f(x) must be absolutely integrable over a period general periodic functions meet these conditionsdtty )(fourier series and coefficientst01( )(coss

23、in)nnny taan tbn t/20/21( )ttay t dtt/2/22( )costntay tn tdtt/2/22( )sintntby tn tdttwhere: the period of y(t)t2: angular frequency or fundamental frequencyfourier series and coefficients (cont.)may be written as01( )(cossin)nnny taan tbn t01( )cos()nnny tacn t22nnncabwherennnbarctga: amplitude of t

24、he signals frequency component: phase-shift qa0 is the constant-value or the d.c. component of a periodic signal. qthe term for n=1 is referred to as the fundamental (component), or as the first harmonic component. qthe component for n=n is referred to as the nth harmonic component. qcn: amplitude o

25、f the nth harmonic component n: phase shift of the nth harmonic componentfourier series and coefficients (cont.)fourier cosine seriesif y(t) is an even function, y(-t)=y(t), its fourier series will contain only cosine terms:fourier sine seriesif y(t) is an odd function, y(-t)=-y(t), its fourier seri

26、es will contain only sine terms:1( )sinnny tbn t0( )cosnny tan texample1find the fourier coefficients of the periodic functionand . find its fourier series.solution: ( )5y t when0t ( )5y t when0t (2 )( )y ty t0011( )sin( 5)sin5sinnby tn tdtntdtntdt001coscos55ntntnn10(1cos)nn2011( )(sinsin3sin5.)35y

27、ttttexample1 (cont.)2011( )(sinsin3sin5.)35y ttttexample1 (cont.)frequency (hz)1232527220amplitude2011( )(sinsin3sin5.)35y tttt2011cos(90 )cos(390 )cos(590 ).35tttfrequency (hz)12325272phase90amplitude-frequency spectrum phase-frequency spectrum v the spectrum of a periodic signal has the following

28、features: 1. the spectrum is a discrete spectrum; 2. the spectral lines appear only at the fundamental frequency and the harmonic frequencies; fourier series in complex formeulers formula:substitute eq. (2.2) into eq. (2.1), let)(2sin)(21costjtjtjtjeejteet(2.2)10)(21)(21)(ntjnnntjnnnejbaejbaaty3 , 2

29、 , 1)(21)(2100nacjbacjbacnnnnnn(2.3)or3 , 2 , 1)(110nececctyntjnnntjnn(2.4), 2, 1, 0)(nectyntjnn(2.5), 2, 1, 0()(1)sin)(cos(1sin)(cos)(12/2/2/2/2/2/2/2/ndtetytdttnjtntyttdtntyjtdtntytctttjnttttttn(2.6)(21nnnjbacwritewhere |cn| and are the amplitude and phase of the complex coefficient respectively.

30、nnjnncjceccnimre(2.7)(2.8)nnnccarctgreim(2.9)nnnnccc22imrefig. 2.15 two graphic representations of spectra of periodic signals example 2. find the frequency spectrum of the periodic sequence of rectangular pulses (also called periodic gate function) shown in fig. 2.16. 2.2.4 frequency representation

31、 of periodic signals fig. 2.16 periodic sequence of rectangular pulses solution: from eq. (2.6), we have 2.2.4 frequency representation of periodic signals ,2, 1,022sin2sin211)(100002/2/02/2/2/2/000nnntnntjnetdtetdtetxtctjntjntttjnnsubstituting 0=2/t into the above equation, we have definingthen eq.

32、(2.10) changes to so2.2.4 frequency representation of periodic signals , 2, 1, 0,sinntntntcn(2.10)xxxcdefsin)(sin(2.11), 2, 1, 0,2sinsin0nncttnctcn(2.12)ntjnntjnnetnctectx00sin)(2.13)fig. 2.17 frequency spectrum of periodic sequence of rectangular pulses (t=4) 2.2.4 frequency representation of perio

33、dic signals , 2, 1, 0)(0nectyntjnn2/2/0)(1tttjnndtetytc)(21nnnjbac)(21nnnjbac00ac ncjnneccncjnneccwhere2221nnnnbaccnnnnabarctgcnnnnabarctgcreim0n0n1000)sincos()(nnntnbtnaaty2nbj2nbjncnc2.2.4 frequency representation of periodic signals fig. 2.19 frequency spectra for signals of different periods whe

34、n the period becomes larger, the spectral line spacing decreases. if the period increases infinitely, i.e. if t, the original periodic signal will now become a nonperiodic signal. then the spectral lines will become denser and denser, and the line spacing tends to zero, making the whole spectral lin

35、es form a continuous spectrum. 2.2.4 frequency representation of periodic signals assuming that x(t) is a periodic function on the interval (-t/2,t/2), substituting eq. (2.15) into eq. (2.14), we get when t, the interval (-t/2,t/2) (- , ), =0=2/t 0. and n0 becomes a continuous one, .ntjnnectx0)(2.14

36、)2/2/0)(1tttjnndtetxtc(2.15)ntjntttjnedtetxttx002/2/)(1)(2.16)fourier transformwrite then eq. (2.17) becomes fourier transform and continuous frequency spectra dedtetxedtetxdtxtjtjtjtj)(21)(2)(2.17)dtetxxtj)()(2.18)dextxtj)(21)(2.19) x() is called the fourier transform of x(t), and x(t) is c

37、alled the inverse fourier transform of x().)()(xtx(2.20) fourier transform pair:the sufficient condition for the existence of a fourier transform for a nonperiodic function x(t) is that x(t) is absolutely integrable on the interval (-,+): fourier transform and continuous frequency spectra dtt

38、x )(since =2f, eqs. (2.18) and (2.19) becomeand the fourier transform pair is correspondingly written as x(f) or x() is called the continuous frequency spectrum of x(t). fourier transform and continuous frequency spectra dtetxfxftj2)()(2.21)dfefxtxftj2)()(2.22)()(fxtx(2.23)()()(fjefxfx(2.24)

39、example 3. fig. 2.23 shows a rectangular pulse gt(t) (also called gate function or window function). find its frequency spectrum. fourier transform and continuous frequency spectra otherwisetttgt, 02, 1)(fig. 2.23 rectangular pulse vthe rectangular pulse and the sinc function are a pair of f

40、ourier transform, which we write as fourier transform and continuous frequency spectra )(sin)(ctrect(2.28)properties of the fourier transform1. linearity ifthena and b are constants. )()(11xtx)()(22xtx)()()()(2121bxaxtbxtax(2.29)2. scaling property if then for a real constant a, prop

41、erties of the fourier transform )()(xtxaxaatx1)(2.30)evenisxevenistxoddisxoddistx)()()()( properties of the fourier transform fig. 2.29 scaling of the gate function gt(t) (a=3) 3. odevity assuming x(t) is a real function of t, from eq. (2.18), then properties of the fourier transform

42、)()(im)(resin)(cos)()()(jtjexxjxtdttxjtdttxdtetxxtdttxxtdttxxsin)()(imcos)()(re(2.31)the real part and the imaginary part of x()arethe modulus and the phase of the frequency spectrum are calculated as qeq. (2.31) shows that: rex()= rex(-) and imx()= -imx(-).qfrom eq. (2.32), we obtain: |x()|= |x(-)|

43、 and ()=-(-). properties of the fourier transform )(re)(im)()(im)(re)(22xxarctgxxx(2.32)if x(t) is a real and even function of time, i.e., x(t)= x(-t), then x() is an real and even function of .if x(t) is a real and odd function of time, i.e., x(t)= -x(-t),then x() is now an imaginary and odd

44、 function of . properties of the fourier transform 0cos)(2cos)()(re)(tdttxtdttxxx0sin)(2sin)()(im)(tdttxjtdttxjxjxft(real even) = real even)()(tetft222)(f0)( f(t)(f0t0ft(real odd)= imaginary odd )0()0()(tetetfatat222)(jf)0(2)0(2)( f(t)0222)(f22)(f)(fjtcalculate the fourier transform of x(-t)

45、 let =-t, then since rex() is an even function of , then properties of the fourier transform dtetxtxftj)()()()()()()()()(xdexdextxfjj)()(im)(re)(im)(re)(*xxjxxjxxfinally, we getcalled the reversal of fourier transform. note: all the above conclusions hold for the condition when x(t) is a rea

46、l function of time t. if x(t) is an imaginary function of t, then properties of the fourier transform )()()(*xxtx(2.72)()(, )()()(im)(im),(re)(rexxxxxx(2.73)()()(*xxtx(2.74)special function: unit impulse function fig. 2.36 rectangular pulse function and delta function (t) assuming a rectangular pulse p(t) of a width and an amplitude 1/ its area is equal to 1as 0, the limit of p(t) is called the unit impulse function or delta func