NORTHERN ILLINOIS UNIVERSITY - Department of Mechanical Engineering
MEE 390 EXPERIMENTAL METHODS IN MECHANICAL ENGINEERING
©1990-1997 M. Kostic
Lab:
Calibration of and Measurement with Strain Gages
Objective: Calibration and use of Strain gages.
Apparatus: Strain gage Specimen bar Bar holder Weight hanger Standard weights (in Newtons) Strain Indicator model P-3500 Multimeter Strain Gage (SG) Links: | Specification of Strain Indicator used in this experiment Make : Measurements Group - Instruments division Model : P 3500 Gage factor range: 0.5 to 9.99 Type of strain gages: 120 W and 350 W strain gages Operation: Battery Operated Readings: Displays strain as micro strain The instrument supports the strain gages to be connected as Quarter, Half and Full bridge circuits. The display can be set normal display (absolute value) or with a magnification factor of 10. Verify data given in NOTES 1 & 2 |
Theory:
Electrical resistance of a piece of wire is directly proportional to the length and inversely to the area of the cross section. Resistance strain gage is based on that phenomenon (see Sec.11.3 Resistance Strain Gauges, Text p.488-494 or similar reference). If a resistance strain gage is properly attached onto the surface of a structure which strain is to be measured, the strain gage wire/film will also elongate or contract with the structure, and as mentioned above, due to change in length and/or cross section, the resistance of the strain gage changes accordingly. This change of resistance is measured using a strain indicator (with the Wheatstone bridge circuitry), and the strain is displayed by properly converting the change in resistance to strain. Every strain gage, by design, has a sensitivity factor called the gage factor which correlates strain and resistance as follows:
Gage factor (F) = (D R / R)/ e
where: R = Resistance of un-deformed strain gage
D R = Change in resistance of strain gage due to strain
e = Strain
As specified by the manufacturer of strain indicator, we set the initial gage factor (as 2.005 for example) and take the measurements. In our experiment, we will also assume that we do not know the gage factor of the strain gage in order to calibrate it. We may do so by calculating the theoretical strain using the appropriate formula and adjust the gage factor setting so that we get the theoretical strain value on the display of the indicator. The set gage factor for which the display coincides with the theoretical strain is the calibrated gage factor of our strain gage as applied on a particular structure (a beam in our case).
Procedure:
1. Attach the strain gage to the bar (beam) surface using five basic steps: i.e. degreasing, surface abrading, burnishing, conditioning and neutralizing.
2. Set the specimen bar (beam) to the bar holder so that the bar acts as a cantilever beam. Measure the span (L), breadth (b) and thickness (t, see NOTE 1) of the bar.
3. Measure the resistance of the strain gage using the multimeter and note it down. Connect the two ends of the strain gage as a QUARTER bridge as shown on the inner side of the strain indicator’s lid.
4. Depress the GAGE FACTOR button and set the (initial) gage factor to 2.005. This value is supplied by the strain indicator manufacturer to calibrate strain gages.
5. Depress the AMP ZERO button and rotate the knob so that the display is set to zero.
6. Depress the RUN button and see what the display shows. Using the BALANCE knob, set the display to a convenient value (zero or any other value). Since the readings are going to be relative with respect to a point, it does not make any difference if the initial setting is zero or not as long as it is taken into account. If the initial setting is not zero, the initial value should be subtracted from the reading value.
Please NOTE:
Strain displayed by the strain indicator is in micro-strain (m e), ie. the strain equals display reading times 10^{-6 }.
7. Measure the weight of the hanger (W_{H}, see NOTE 2) and convert it into Newtons (SI unit). Add the standard weights (W) to the hanger and hang it from the free end of the beam. Note down the strain indicated (e). Repeat the measurements for at least several (8) times and note down the weights and strain. Make sure the weight of the hanger is included. Weight of the beam itself does contribute to the strain and may also be considered. However, since we zeroed instrument under the load of the beam weight it is irrelevant for our measurements.
FIRST SET OF OBSERVATIONS :
Observations: (SET I)
Serial | Weight | Strain |
1 | ||
2 | ||
3 | ||
4 | ||
5 | ||
6 | ||
7 | ||
8 |
NOTE 1: W_{H }= m_{H} g = 0.166kg*9.81m/s^{2}; P = W + W_{H}; thickness t=1/8 inch, to be verified.
SECOND PART OF THE EXPERIMENT:
1. To calculate theoretical strain, we use the following formula.
s = E × e
NOTE 2: Young’s Modulus E = 200 × 10^{9} N/m^{2} for steel, or E = 70 × 10^{9} N/m^{2} for aluminum.
For a cantilever beam with a point load at its end,
M \I = s / y
Where,
M | is the moment applied, (P*x) where ‘x’ is the distance between the point of loading and the mid-section at which strain gage is fixed. |
I | is the moment of inertia about the neutral axis of bending, |
s | is the value of stress at a point which is at a distance of |
y | from the neutral axis and y = t / 2 because the strain gage is fixed to the surface of the beam. |
Finally, the formula for strain is:
e = (6 * P * x) /( E * b* t^{2} )
2. Calculate the theoretical strain values for at least 5 known values of "P". Convert it into micro strain by multiplying it with 10^{6}.
3. Measure the distance "x" between the loading point and the strain gage (see figure).
4. Note down the initial value (without load) of display on the strain indicator and zero it. Load the beam with hanger and the first value of known standard weight for which theoretical strain is calculated.
5. Keeping the indicator in RUN mode, rotate the GAGE FACTOR knob so that the display shows a strain value equal to calculated (theoretical) strain. Depress the GAGE FACTOR button and note down the gage factor value.
6. Repeat steps 4 and 5 for rest of the "P" values and tabulate the readings below.
SECOND SET OF OBSERVATIONS :
Serial Number | Weight (W) (N) | Theoretical Strain (m e ) | Gage Factor F = F(e ) |
1 | |||
2 | |||
3 | |||
4 | |||
5 |
NOTE: W_{H }= m_{H} g; P = W + W_{H}
You should expect that the gage factor for all the steps in the second part of the experiment be the same irrespective of different values of loads. This implies that gage factor is a constant for a strain gage and is dependant upon its design. However, due to different sources of errors, the above gage factors will differ somewhat and the average value may be used.
EXAMPLE: FIRST SET OF OBSERVATIONS :
Observations: (SET I)
Serial Number | Weight W [N] | Strain e [m e ] |
1 | 2 | 154 |
2 | 4 | 240 |
3 | 5 | 282 |
4 | 7 | 369 |
5 | 9 | 446 |
6 | 10 | 508 |
7 | 12 | 590 |
8 | 14 | 689 |
NOTE: W_{H }= m_{H} g; P = W + W_{H}
SECOND SET OF OBSERVATIONS :
Serial Number | Weight W [N] | Theoretical Strain (m e ) | Gage Factor F = F(e ) |
1 | 2 | 134.81 | 2.381 |
2 | 4 | 209.15 | 2.274 |
3 | 5 | 246.32 | 2.268 |
4 | 7 | 320.67 | 2.280 |
5 | 9 | 395.01 | 2.282 |
Average | 2.297 |
Average of all the 5 gage factors is 2.297