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Strain-Based Measurement Introduction:can be determined by finding the frequency, at which the value of thetransfer function H(w) is equal to unity plus 5%, or numerically equalto 1.05 as follows:If z = 0 (theoretically), then equation (1-28) simplifies to:1.05 = 1/[1-w 2 /w 0 2 )yielding:w = .218 w oInstrument designers and salespersons alike have, for many years,stated that the undamped second-order sensor has a flat frequencyresponse range of up to 20% of the primary resonance frequency of thesensor without really knowing why this is so. The above relationshipshows that the undamped second-order system will provide a theoreticaloutput that is within 5% of the low-frequency sensitivity of the sensorat up to 21.8% of the resonance frequency. Although all sensorstructures will possess intrinsic structural damping to some extent, renderingthe 21.8% figure as a theoretical maximum, the industryacceptedflat response range of 20% of resonance is a reasonable usefulflat bandwidth.CHAPTER 1-56 The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999
Applications Note 1-10:Applications Note 1-10:Fluidic-, Gas-, and Structural-Damping of Second-OrderSensor StructuresThis discussion relates to the damping mechanisms used in accelerometer structuresto absorb energy that would otherwise result in over-response or ringing ofthe accelerometer at its natural frequency.Damping of an accelerometer structure is the provision of an energyabsorptionsystem. Just as the shock absorbers of the family automobilewill become warm when driving over a rough road surface, the mediumused to absorb energy from the accelerometerÕs seismic system will alsoheat. With reference to the discussion of the second-order mechanical system,the resistance to motion that the damping medium exerts upon theseismic system is a function of the velocity of the seismic mass and, in general,relatively large displacements of the seismic system are required toachieve significant damping factors. The piezoelectric accelerometers arenot normally damped due to the extreme stiffness of the seismic systemresulting in low total deflections relative to the cantilevered-beam accelerometerstructures. Three basic damping mechanisms are discussed as follows:Fluidic Viscous Damping:Fluidic damping is generally achieved by filling the internal cavity of theaccelerometer with a silicone oil fill fluid. The silicone oil absorbs energyfrom the seismic system by one of two mechanisms. The first mechanismof energy absorption involves the bulk displacement of the silicone oil fillfluid from side to side as the seismic system moves. This bulk displacementof oil results in a damping factor contribution that is related to thebulk viscosity of the oil. The second mechanism relates to the film viscosityof the oil. Seismic systems are generally provided with overrange-limitingstops to impede the motion of the seismic assembly. The presence ofThe Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999 CHAPTER 1-57
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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
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ContentsCHAPTER 8Electrical Conside
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CHAPTER 1Strain-BasedMeasurementInt
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Applications Note 1-1: Introduction
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Page 19 and 20: Applications Note 1-2:The Art of Ap
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Page 25 and 26: Applications Note 1-4:The measureme
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Page 35 and 36: Applications Note 1-6:and where:j i
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