Transcript Slide 1
STRAIN MEASUREMENT CONTENTS INTRODUCTION ELECTRICAL RESISTANCE STRAIN GAGES TYPES OF STRAIN GAGES STRAIN GAGE SIGNAL CONDITIONING CALIBRATION WHAT IS STRAIN? lateral axial Strain is the amount of deformation of a body to an applied force For axial direction from the figure above a L Usually in m (x10-6) L Because of Poisson strain phenomena, D will be contracted in lateral direction, with magnitude depends on Poisson ratio (n) L n a n is the property of material, for example, steel has 0.25≤n≤0.3 CONTENTS INTRODUCTION ELECTRICAL RESISTANCE STRAIN GAGES TYPES OF STRAIN GAGES STRAIN GAGE SIGNAL CONDITIONING CALIBRATION MEASURING STRAIN The most common method for measuring strain is using strain gauge Strain gage is a device whose electrical resistance varies in the proportion of the amount of strain A in the device. The most widely used strain gages is the bonded metallic strain gage The resistance of the conductor of the strain gage R L A If differentiated this equation become: A D dA A where r = resistivity of conductor material L =conductor length A = cross-sectional area of conductor dR 2 2 R dD D Lateral strain Then the equation : dR R d d dL L a 1 2n dA A GAGE FACTOR Strain gage factor, S is defined dR R d a 1 2n d S 1 2n dR S R a usually around 2 for metallic strain gage a If the surface of a structure is in the biaxial stress condition there will be a transverse strain that will affect the strain gage output dR can be described with transverse gage factor, St St R t and Transverse sensitivity Usually small (less than 0.01) Kt St Sa CONTENTS INTRODUCTION ELECTRICAL RESISTANCE STRAIN GAGES TYPES OF STRAIN GAGES STRAIN GAGE SIGNAL CONDITIONING CALIBRATION TYPICAL METALLIC FOIL STRAIN GAGE single element strain gage two element rossete three-element rossete used in pressured diaphragms CONTENTS INTRODUCTION ELECTRICAL RESISTANCE STRAIN GAGES TYPES OF STRAIN GAGES STRAIN GAGE SIGNAL CONDITIONING CALIBRATION STRAIN GAGE SENSITIVITY Strain measurement involves a very small quantity (a few me) Therefore to measure strain, requires accurate measurement of a very small change of resistance Example: To measure a strain of 500 m, with strain gage factor= 2 Than R=Sx = 2x500 m or 0.1% If the strain gage has R=120 W (typical for a strain gage to measure strain) R=0.12 W (it’s a very small resistance change) To measure such a small change in resistance, a bridge circuit is needed to convert this change in resistance to the change in voltage STRAIN GAGE BRIDGE CIRCUIT WHEATSTONE BRIDGE For the Wheatstone bridge arrangement R3 R4 V o R 2 R 3 R1 R 4 V s For example strain gage is in R3 The initial resistance of strain gage is R3i Then to balance the bridge R3iR1-R4R2=0, then if the strain is strained R3=R3i+R3 Vo Vs R1 R 3 ( R 2 R 3 i R 3 )( R1 R 4 ) R3 small compared to R3i and can be neglected Vo become linier function of R3 then R 2 R 3 i 2 a Vo V s SR 2 R 3 i EXAMPLE A single strain gage has a nominal resistance of 120 W and a gage factor of 2.06. For a quarter bridge with 120 W fixed resistor, what will be the voltage output with a strain of 1000 mstrain for a supply voltage of 3 V? Solution: Using equation a Vo 1000 x10 6 R 2 R 3 i 2 V s SR 2 R 3 i V out (120 120 ) 2 3 x 2 . 06 x120 x120 V out 1 . 544 mV SEVERAL BRIDGE ARRANGEMENT quarter bridge circuit half bridge circuit full bridge circuit Temperature compensation Any change in resistance of RG caused by change in temperature will be compensated by the dummy gage resulting in only strain imposed in active RG will be detected CONTENTS INTRODUCTION ELECTRICAL RESISTANCE STRAIN GAGES TYPES OF STRAIN GAGES STRAIN GAGE SIGNAL CONDITIONING CALIBRATION CALIBRATION METHOD •Introducing small resistance change at the gage and calculating equivalent strain in the gage using shunt resistor in parallel with gage •Mounting a strain gage on a cantilever beam into one arm of Wheatstone bridge and observing deflection as known strain is applied to the gage, then using deflection formula for cantilever beam deflected a distance d etc THANK YOU FOR YOUR ATTENTION