The Art of Practical and Precise Strain Based ... - Webprofile.info

More documents

Recommendations

Info

Strain-Based Measurement Introduction:FIGURE 1-27. The Second-Order System Mechanical Model:q i InputMassq o OutputSpringK Lbf/InRDamper Lbf/ft/secR proportional to velocityFoundationThe electrical output of the strain-based sensor is a direct and proportionalfunction of the spring member displacement. For this reason, thefunction q o (t) is taken as being proportional to the output that wouldresult from the second-order sensor structure. The velocity of the massis defined as dq o (t)/dt and the acceleration of the mass is defined asd 2 q o (t)/dt 2 . The force that the spring will exert upon on the mass will beopposite to the forcing input and will equal -K q o (t), where K is thespring constant having units of force-per-unit-displacement. Themechanical damper will also provide a force that is opposite to the forcinginput as a function of the mass velocity and will equal -Rdq o (t)/dt,where, R is in units of force-per-unit of mass velocity.Since Force = mass X acceleration or F = MA, then:MA = S of all forces acting upon the massMA = Input force - Spring force - Damping forcedMA = q i () t Ð Kq 0 () t Ð R q0 () t dt(EQ 1-21)CHAPTER 1-52 The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999
Applications Note 1-9:Where:dMA = M q0 () t = F2d t2(EQ 1-22)Substituting (1-22) for MA in (1-21) and solving for q i (t) yields:2d dq i () t = M q0 () t + R q0 () t + Kq2d t dt0 () t(EQ 1-23)Converting from the time domain into the frequency domain using the relationshipq i (t) = e jwt as representative of a sinusoidal input, and knowingthat the output will equal:q 0 () t = H( w)q i () t(EQ 1-24)(where H(w) is the system transfer function)Then, the output must be of the form:q 0 () t = H( w)e jwt(EQ 1-25)H(w) also represents phase as well as magnitude of response. Havingestablished this equality, differentiation of equation (1-25) yields the furtherequalities:d q0 () t = H( w)jwe jwtdt(EQ 1-26)and2d q0 () t = ÐH( w)w 2 e jwtdt 2(EQ 1-27)Substitution of equations (1-24), (1-25), (1-26), and (1-27) into equation(1-23) and solving for H(w) yields:The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999 CHAPTER 1-53
Page 1 and 2:
The Art of Practical andPrecise Str
Page 3 and 4:
Special Credits:Mrs. Helen Pierson,
Page 5 and 6:
Table of ContentsBy James G. Pierso
Page 8 and 9:
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
show all

The Art of Practical and Precise Strain Based ... - Webprofile.info

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?