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

Strain-Based Measurement Introduction:The Linear-Variable-Differential Transformer (LVDT)-based sensorclosely approximates the zeroth-order sensor at low-to-moderate frequenciesThe First-Order Sensor:A first-order system response is the solution to the first-order differential equationas follows:dF outk 1dT+ k 0 F out = b 0 F in(EQ 1-9)ordF outtæ ö + FèdTø out = KF in(EQ 1-10)Where: t = k 1 /k 0 , The sensor time constantK = b 0 /k 0 , The static sensitivity.If d /dT is replaced by the differential operator ÒDÓ, equation 1-10 becomes:KF in = ( 1 + tD)F outSince F out /F in is defined as the Transfer Function (H):HK= -------------------- =( 1 + tD)F--------- outF in(EQ 1-11)Implies:H( w)( jw)K= --------------------- = -----------------------( jw)( 1 + jwt)F outF in(EQ 1-12)Where the magnitude of this transfer function will equal:CHAPTER 1-46 The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999