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Strain-Based Measurement Introduction:Similarly, setting equation (1-39) equal to zero, the equation may be solved tofind the value of r at which the tangential stress is equal to zero with the resultbeing:r = 0.827aWhen PoissonÔs Ratio = .3(EQ 1-45)The radial and tangential stresses are shown graphically as Figure 1-54.FIGURE 1-56.Compression0r/ as rs t3wa 24t 23wa 2 n4t 2-3W(m+1)8p mt 2Tension1.001.0In the calculation of the first-order resonance frequency for the flat, circular,uniform section, plate 1 of thickness t, under uniformly-distributed loading conditions:¥ w = load per unit area including the intrinsic mass of the diaphragm.1. Roarke P716 case 10, 6th edition, Warren C. YoungCHAPTER 1-90 The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999
Applications Note 1-13:¥ g = gravitational constant.¥ K 1 = Constant of 10.2 for the Þrst-order resonance (Higher-order resonances are given by constantsK 2 = 21.3, K 3 = 34.9 and K 4 = 39.8)¥ g = Plate density (Plate mass = pr 2 tg)K 1 Dgf n = ----- æ--------ö2pèwr 4 øWhere D =Et 3-------------------------12( 1 Ð u 2 )(EQ 1-46)Simplifies to:0.469t Egf n = -------------- æ----------------------ör 2 èg ( 1 Ð u 2 )ø(EQ 1-47)Other Considerations:1. As the diaphragm deflections become much larger than 30% of the diaphragm thickness, themedian-plane tensile stresses become dominant and diaphragm stretching will act to stiffen thediaphragm significantly. If nonlinearity performance of ±.2% is to be expected, the diaphragmmust not be deflected by more than 12% of the diaphragm thickness. If a nonlinearity performancelevel of 2% is acceptable, the diaphragm may deflect by as much as 30% of the diaphragmthickness. Additionally, with increasing diaphragm deflection and tensile loading, theinflection points on the diaphragm, for zero-radial and zero-tangential stress, will move outwardstoward the clamp, further deteriorating the nonlinearity performance of the sensor. Sincethe strain-gage class of sensors integrates the applied strain over a distance of the active diaphragm,the modification of the inflection points acts to distort the strain field that the straingages are positioned to measure.2. The ratio of the thickness-to-radius ratio of the diaphragm is an excellent indicator of diaphragmperformance. When this ratio is less than .15, the symmetrical bending theory,described, holds well. For values greater than .15, the loads normal to the plane of the diaphragm,and shear loads, must be taken into account. In the analysis of the performance of adiaphragm, both the deflection/diaphragm thickness ratio and the diaphragm thickness/radiusratio must be assessed for superior performance to result.The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999 CHAPTER 1-91
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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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Applications Note 1-1: Introduction
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Applications Note 1-2:The Art of Ap
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Applications Note 1-31. The presenc
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Applications Note 1-3result in a pe
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Applications Note 1-4:The measureme
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Applications Note 1-4:uncertainty i
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Applications Note 1-5:All strain-ba
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Applications Note 1-6:Applications
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Applications Note 1-6:ical size of
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Applications Note 1-6:and where:j i
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Applications Note 1-6:5. millivolts
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Applications Note 1-6:.Electrodynam
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Strain-Based Measurement Introducti
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