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Strain-Based Measurement Introduction:k 0k 2---- and z=k 1-----------------2 k 0 k 2(EQ 1-16)where: w 0 is the natural frequency and z is the damping factor.Equation 1-15 becomes:1 dk----- 0 2z+ -------------- + k2 20 = KF inw 0 d t dk 0w 0dt(EQ 1-17)Where: K = The static sensitivity of the sensor.The second order transfer function in the frequency domain can be shown toequal:H( w)=K--------------------------------------------------------æ w1 Ð æ-----ö 2 + 2 jzæ-----w ööè èw 0ø èw 0øø(EQ 1-18)Where the magnitude of this function will equal:H( w)=K-----------------------------------------------------------w1 -----èæ Ð èæ øö2øö 2 + 2zw ----------èæ øö2w 0w 0(EQ 1-19)and where the phase response is given by:zjw ( ) = atan2------------------------æ w w----- Ð ----- 0 öè w øw 0(EQ 1-20)Examples of the second-order response, Figure 1-26, are abundant. Allspring-member-based sensors will show a second-order response, up tothe first resonance frequency, with varying degrees of damping. NoteCHAPTER 1-48 The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999
Applications Note 1-8:that the phase variation with frequency will equal -90 degrees at the naturalfrequency (w n ) and will approach -180 degrees as the frequencyapproaches infinity. The second-order response is sometimes also referredto as the Ò2-poleÓ response or the simple Òspring/mass/damperÓ systemresponse.FIGURE 1-26. The Second-Order System Step-Input Response:Input/OutputAmplitudeInputOutputw n decreasingDamping Factor ( z ) = .7TimeThe Second-Order Response to a Step-Input(The effect of Natural Frequency)Input/ OutputMagnitude21.5z = .1z = .3z = .5Damping Factor IncreasingOutput1Input.50 secondsTimeThe Second-Order Response to a Step-Input(The effect of Increasing Damping Factor)The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999 CHAPTER 1-49
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The Art of Practical andPrecise Str
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Special Credits:Mrs. Helen Pierson,
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Table of ContentsBy James G. Pierso
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ContentsApplications Note 4-10:Lead
Page 10: ContentsCHAPTER 8Electrical Conside
Page 13 and 14: CHAPTER 1Strain-BasedMeasurementInt
Page 15 and 16: Applications Note 1-1: Introduction
Page 17 and 18: Applications Note 1-1: Introduction
Page 19 and 20: Applications Note 1-2:The Art of Ap
Page 21 and 22: Applications Note 1-31. The presenc
Page 23 and 24: Applications Note 1-3result in a pe
Page 25 and 26: Applications Note 1-4:The measureme
Page 27 and 28: Applications Note 1-4:uncertainty i
Page 29 and 30: Applications Note 1-5:All strain-ba
Page 31 and 32: Applications Note 1-6:Applications
Page 33 and 34: Applications Note 1-6:ical size of
Page 35 and 36: Applications Note 1-6:and where:j i
Page 37 and 38: Applications Note 1-6:5. millivolts
Page 39: Applications Note 1-6:.Electrodynam
Page 44 and 45: Strain-Based Measurement Introducti
Page 104: Strain-Based Measurement Introducti
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