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

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