MECH 373 Instrumentation and Measurements Lecture 18 Measurement

MECH 373 Instrumentation and Measurements Lecture 18 Measurement of Solid-Mechanical Quantities (Chapter 8) Strain Gauge Signal Conditioning Lecture 18 Lecture Notes on MECH 373 – Instrumentation and Measurements 1

Strain measurements • Measuring gauge resistance before and after loading – Not practical - Significant error– Resistance change in the order of measuring device resolution. • Better approach – Device to measure the resistance change rather than resistance, i. e. , Wheatstone bridge. Lecture 18 Lecture Notes on MECH 373 – Instrumentation and Measurements 2

Wheatstone Bridge • Four identical resistors. • Voltages at points B and D – same – V 0 = 0. 0, bridge = balance. • Active strain gauge R 3 , Load R 3 – bridge is unbalanced and V 0 ≠ 0. 0. • Adjust R 2 – equal to R 3, then V 0 = 0. 0 – bridge is balanced – Amount of adjustment = change of resistance in R 3. DAS. Lecture 18 Lecture Notes on MECH 373 – Instrumentation and Measurements 3

Strain measurements • Modern computer DAS – – Balance the bridge initially. – No need to re-balance it when the active gauge under-strained. – Output voltage proportional to change in gauge resistance. (later slides) Lecture 18 Lecture Notes on MECH 373 – Instrumentation and Measurements 4

Wheatstone bridge Lecture 18 Lecture Notes on MECH 373 – Instrumentation and Measurements 5

Strain measurements Lecture 18 Lecture Notes on MECH 373 – Instrumentation and Measurements 6

Strain measurements Lecture 18 Lecture Notes on MECH 373 – Instrumentation and Measurements 7

Strain measurements Lecture 18 Lecture Notes on MECH 373 – Instrumentation and Measurements 8

Strain measurements • In practice, gauges used are not truly identical. • Uncertainty in an order of 0. 1%. • Vo – nonzero even before the strain applied – Offset – Symmetric error. • Adjust the resistor to bring the bridge into initial balance. • If not – subtract it from the actual readings. Lecture 18 Lecture Notes on MECH 373 – Instrumentation and Measurements 9

Strain measurements • To improve the sensitivity of circuit for a given small strain. • Application – Symmetrical loading situations – Same strain but opposite sign – tension and compression – e. g. sensor – load cells. • R 1 and R 3 – Tensile gauges. • R 2 and R 4 – Compressive gauges. • Full bridge = 4 times the quarter bridge. Lecture 18 Lecture Notes on MECH 373 – Instrumentation and Measurements 10

Temperature compensation Lecture 18 Lecture Notes on MECH 373 – Instrumentation and Measurements 11

Temperature compensation • Temperature: – Affect resistivity, hence gauge factor S = d. R/R/εa. – Cause differential thermal expansion = structure and gauge, hence strain without mech. load. • Minimize the temp effects: – Connect R 2 and R 3 in structure with the same temperature. , R 3 = Active gauge, R 2 = dummy (compensating) gauge – Temp change on both R 2 and R 3 in same direction, hence no strain. – (Note, R 2 can be active gauge if strain is equal and opposite to R 3. ) Lecture 18 Lecture Notes on MECH 373 – Instrumentation and Measurements 12

Strain gauge in practical set-up Lecture 18 Lecture Notes on MECH 373 – Instrumentation and Measurements 13

Strain gauge in practical set-up • Required many gauges to measure structure strain/stress. • Separate bridge for each gauge. • Connect output terminals of each bridge to input channels of DAS. • Use common power supply. • R 1 and R 4 = Dummy gauges. • Each active gauge paired with a fixed gauge R 2 (compensating or active). • Bridge always complete. – Continuous recording or switch to screen for monitoring (critical gauges) Lecture 18 Lecture Notes on MECH 373 – Instrumentation and Measurements 14

Example – Quarter bridge Lecture 18 Lecture Notes on MECH 373 – Instrumentation and Measurements 15

Example Full bridge Lecture 18 Lecture Notes on MECH 373 – Instrumentation and Measurements 16