1. ABE425 Engineering Measurement Systems Strain Gages, Bridges and Load Cells Dr. Tony E. Grift Dept. of Agricultural & Biological Engineering University of Illinois

2. This presentation covers measuring force (1-3), displacement (4), velocity (5) and acceleration (6) 1. Strain gage (Force) 2. Wheatstone bridge 3. S-type load cell 4. Linear Variable Differential Transformer 6. Accelerometer 5. Pro-laser Doppler velocity sensor

3. Force measurement

4. The elongation of a thin wire due to strain changes its electrical resistance which can be measured

5. Strain and stress in metals are linearly related in the elastic range (Hooke’s law) Videos (notice ‘necking’) Steel tensile test HDPE tensile test Elastic range

6. Strain gages are composed of thin wires that change their resistance by being stretched

7. The resistance of a thin wire is a function of resistivity, length and cross sectional area Resistance is proportional to Resistivity  Length L And inversely proportional to Cross sectional area A A L

8. Manipulate equation to get a resistance change expression Original equation Change in resistance is a function of partial derivatives Stick in the partial derivatives Divide by original resistance equation

9. Express the change in area in a change in diameter A AA DD D

10. Use Poisson ratio (material property) to simplify the strain gage equation Transverse strainAxial strain Poisson ratio

11. When you stretch a metal it becomes thinner. The negative ratio between transverse and axial strain is the Poisson ratio L L+  L D+  D D Transverse strainAxial strain Poisson ratio

12. Change in resistance is a function of the Poisson ratio and the change in resistivity (temperature) Strain gage factor f(temperature)

13. To measure strain in different directions, strain gages come in rosettes RectangularEquiangular

14. Here is an example of a rectangular strain gage rosette

15. Strain measurement using Wheatstone bridge

16. In a quarter bridge circuit the strain gage takes up one branch, there is no temperature compensation

17. Having four gages in the bridge gives inherent temperature compensation and increased output +e -e F

18. Switching within the bridge is a bad idea since the contact resistances are part of the bridge and the strain gages need to maintain a constant temperature

19. It is better to switch outside the bridge since 1) there is no current where the contacts are and hence no voltage drops and 2) the temperature of the strain gages is constant

20. Load cells

21. Load cells are structures fitted with strain gage sets, and built-in temperature compensation Cantilever typeHollow cylinder type. When the cylinder is compressed it becomes shorter which is measured by compressive gages and the diameter increases which is measured by the tensile gages

22. Proving rings are simple devices to calibrate load cells for larger load (up to 250kN)

23. Dynamometers are power measurement devices based on measuring torque and RPM

24. Eddy current dynamometers dissipate energy by generating magnetic fields through eddy currents. The dissipated energy is carried away using a water flow

25. Torque can be measured using a shaft torque meter that can be read with a stroboscope

26. Torque can be measured using angled strain gages and slip rings (watch out for their resistance)

27. To avoid slip rings, an microcontroller chip can be used with built-in wireless data communication RFpic 12c509 Dual Inline Package (DIP) RFpic 12c509 Surface Mounted Device (SMD)

28. Displacement measurement

29. The slider of a potentiometer can be used as a relatively inaccurate displacement sensor

30. Rotary potentiometers can be used for inaccurate angle measurement

31. A Linear Variable Differential Transformer (LVDT) is an accurate sensor for small displacements

32. LVDT’s are linear in the rated range, outside the range edge effects render them non-linear

33. In an LVDT the electrical coupling between magnets is provided by a movable core

34. LVDT’s also come in a rotary version, which allows angle measurements. Notice the complicated core shape

35. Measuring the phase difference between primary and secondary voltages yields direction

36. Signal conditioning is used to create a DC signal proportional to displacement with the correct sign for direction

37. The capacitance of a capacitor is a function of the overlap between its plates. These devices are used to measure extremely small displacements Non-linearLinear

38. The change in capacitance can be measured accurately using an AC Wheatstone bridge

39. Angular encoders can measure a shaft position. They suffer from simultaneous state changes 00000 0001 1 0010 2 0011 3 0100 4 0101 5 0110 6 0111 7 1000 8 1001 9 1010 10 1011 11 1100 12 1101 13 1110 14 1111 15

40. Gray code is a much more reliable encoding since no simultaneous state changes occur 00000 0001 1 0011 3 0010 2 0110 6 0111 7 0101 5 0100 4 1100 12 1101 13 1111 15 1110 14 1010 10 1011 11 1001 9 1000 8

41. Velocity measurement

42. The voltage output of a winding is proportional to the velocity of a magnetic core passing it Winding Permanent magnet Voltage is function of speed AND position

43. The voltage output of a winding is proportional to a magnetic core passing it Voltage is function of speed NOT position

44. Doppler shift is the simplest way to measure the speed of an object non-intrusively and linearly

45. Magnetic pickups (proximity sensors) give pulses from which the shaft RPM can be derived

46. A stroboscopic tachometer can be used to measure shaft RPM: This method is primitive and obsolete

47. Contactless tachometers can count the number of times a reflective strip passes per second and give RPM

48. Accelerometers

49. Piezoelectric sensors can be used to measure either force or (very small) displacement

50. A charge amplifier is needed to obtain signals from the Piezoelectric sensor as an accelerometer

51. Piezoelectric accelerometers have a seismic mass and can measure vibrations up to 25 kHz

52. Semiconductor type strain gage accelerometers can measure vibrations up to 100 Hz

53. A servo accelerometer is an accurate automatic compensation method that can measure 50 g

54. A vibrometer has a relatively large and measures earth quakes vibrations

55. This is what we covered today. Questions? 1. Strain gage (Force) 2. Wheatstone bridge 3. S-type load cell 4. Linear Variable Differential Transformer 6. Accelerometer 5. Pro-laser Doppler velocity sensor