1. Instrumentation (AMME2700) 1 Instrumentation Dr. Xiaofeng Wu

2. Instrumentation (AMME2700) Unit of Study Survey 2 http://sydney.edu.au/itl/surveys/complete/

3. Instrumentation (AMME2700) Wheatstone Bridge 3

4. Instrumentation (AMME2700) Wheatstone Bridge Sensitivity  For a single active arm (e.g. R 2 ): 4

5. Instrumentation (AMME2700) Strain Gage  A strain gauge (also strain gage) is a device used to measure the strain of an object. Invented by Edward E. Simmons and Arthur C. Ruge in 1938, the most common type of strain gauge consists of an insulating flexible backing which supports a metallic foil pattern. The gauge is attached to the object by a suitable adhesive. As the object is deformed, the foil is deformed, causing its electrical resistance to change. 5

6. Instrumentation (AMME2700) Applications of Strain Gage  Stress and Strain Measurement The basic function of a strain gauge is to measure strain, and in turn stress. Strain is simply the change in length of a component divided by the original length of the component while experiencing an applied load. Stress is calculated by multiplying the strain by the modulus of elasticity for the specific material being measured.  Load Measurement Strain gauges are integral elements of load cell transducers, which measure the magnitude of an applied tensile or compressive force. The strain gauges are installed on precisely machined steel components where the exact cross section is known, and therefore the strain measurement can be converted to a load measurement output.  Pressure Measurement A pressure sensor uses the same strain gauge configuration and installation as a load cell, except that the sensor measures the applied load over a discrete area, or pressure.

7. Instrumentation (AMME2700) Gage Factor  The resistance change of the strain gage is usually measured using a Wheatstone bridge, which is related to the strain by the quantity known as the gage factor (GF). 7 ΔR is the change in resistance caused by strain R is the resistance of the undeformed gauge = ΔL/L is strain Stress: σ=ε×E m =F/A (N/m 2 ), where F is the force, A is the area, E m is the modulus of elasticity

8. Instrumentation (AMME2700) Stress 8 Stress: σ=ε×E m =F/A (N/m 2 ) where F is the force, A is the area, E m is the modulus of elasticity vivi vovo

9. Instrumentation (AMME2700) Link-Type Load Cell F

10. Instrumentation (AMME2700) Link-Type Load Cell 10 where γ is the Poisson’s ratio of the link material

11. Instrumentation (AMME2700) Beam-Type Load Cell F

12. Instrumentation (AMME2700) Beam-Type Load Cell 12

13. Instrumentation (AMME2700) Example  A strain gauge is mounted on a cantilever beam (Em =200×10 4 kN/m 2 ) of rectangular cross section. The gauge is connected in a Wheatstone bridge; initially R gauge =R2=R3=R4=120 Ω. A gauge resistance change of 0.2 Ω is measured for the loading condition and gauge orientation shown in the following figure. The input voltage is 5V. If the gauge factor is 2±0.02 (95%) estimate the strain, the voltage out and the Force F if x=0.2m, b=0.05m and h=0.001m; Also determine the sensitivity of the instrumentation. x h b R2R2 R3R3 R4R4 +- + -