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Experiment# 1
Strain Indicator Calibration
Abstract:
The objective of this experiment is to calibrate strain indicator by relating indicated strain of indicator with actual strain. For this purpose strain gauge simulator is employed to simulate actual strain.
Introduction:
Strain :
When a bar is pulled, it causes change in its length by ∆L, making its new length = L (original length) + ∆L (change inlength). The ratio of this change in length ∆L, to the original length, L, is called strain.
ε = ∆L / L
ElectricalStrain Gauges :
The electrical strain gauges are mostly thin, rectangular-shaped strips of foil with maze-like wiringpatterns on them. When the material is strained maze-like wires are either stretched slightly thinner or pushed together and become slightly thicker. Changing the width of a metal wire changes itselectrical resistance. This change in resistance is proportional to the stress applied. A strain gauge takes advantage of this property. The change in the resistance is due to variation in the length and cross sectional area of the gauge wire.
Gauge Factor:
Gauge factor characterizes the strain gauges in terms of its sensitivity.
“Gauge factor is defined as unit change in resistance for per unit change in length of strain gauge wire.” given as
G.F. = (∆R/RG) / ε (1)
Where, Δ R - the change in resistance caused by strain,
RG - is the resistance of the undeformed gauge, and
ε – is strain.
Strain Gauge Simulator:
This simulator is a compact five-dial resistance decade box (0.01, 0.1, 1.0, 10 and 100 ohms/step), , especially for making measurements with strain gage circuitry and for calibrating strain indicators. The special feature of this simulator is very high accuracy, ±0.02% of reading at any combination of dial settings and ±0.15% for incremental changes in the 0.01 and 0.1 ohm/step decades.
There are 3 binding posts available on the V/E-40 strain gage simulator. One of these posts is marked as ground (GND). The unmarked binding posts in the following procedure will be marked as No.1 and No.2 (central post referred as post No.2).
As a precision strain gauge simulator, the v/e 40 can be used to measure non linearity of the instrumentation in quarter-bridge operation, or to verify instrument calibration over the anticipated measurement range.
V/E-20A strain indicator:
This indicator is a direct readout type indicator using constant current for bridge excitation. Its range is ±1999(X1) with 1 count resolution and 19990 (X10) with 10 count resolution.
In these experiments we will be using 2 types of lead wires, short lead wires about 2 feet length (Ls), and long lead wires about 50 feet length (Ll).
Quarter bridge circuit :
Sr no.
R ΔR (^) ε(indicated) ε(actual)
1 120 12 500 499 2 120 24 1000 998 3 120 36 1500 1497 4 120 48 2000 1998
Compression:
Sr no.
R ΔR (^) ε(indicated) ε(actual)
1 120 - 12 - 500 - 505 2 120 - 24 - 1000 - 1005 3 120 - 36 - 1500 - 1505 4 120 - 48 - 2000 - 2005
GraphicalRepresentataion:
0
500
1000
1500
2000
2500
0 500 1000 1500 2000 2500
actual strain
indicated strain
Actual strain vs. Indicated strain
actual strain vs. indicated strain
Exp. No. 2:
“Lead Wire Desensitization of Strain Indicator”
Introduction:
Gauge factor defined as F = (∆Rg/Rg)/ ε will give acceptable results only when resistance of lead wires are negligible. When resistance of leads is not negligible then actual resistance of the bridge arm containing the gage is
Ra = Rg + Rl
and effective gauge factor (Fe) is
Fe = (∆Rg/Ra)/ ε
= [∆Rg/(Rg+ Rl)]/ ε
Fe = DF (2)
Where D = (Rg/(Rg+ Rl) (3)
0 -2500 -2000 -1500 -1000 -500 0
actual strain
indicated strain
Actual strain vs. Indicated strain
actual strain vs. indicated strain
Observations and calculations:
Replacing white wire at S+
Value of R’g(s) with Ll (long wire) =115.40 Ω
Value of R’g(s) + RLs = 120Ω
Value of RLs= 120-115.4 = 4.6Ω
Part B:
Procedure of Determination of Lead Wire Desensitization
Repeat first 6 steps of the part a.
Now apply ∆R = 0.48 ohms (corresponding to a simulated strain of 2000 με with F=2) and note indicated strain.
Repeat steps (i), (ii) but this time three Ls wires are replaced by three Ll wires.
Corresponding to a simulated strain of 2000 με with F=2 again apply ∆R = 0. ohms and note indicated strain.
Indicated strain in this step will be surely less than that in step (ii).
Formulas used :
D = Rg/(Rg+RLl) = 120/(120+RLl)
Where RLl is the resistance of “active” long wire.
D =
Observations and calculations:
Value of simulated strain with short wires = 2000 με
Value of indicatedstrain with short wires and ΔR (0.48 Ω)= 1998 με
Replacing red wire at S+
Value of R’g(s) with Ll (long wire) =115.40 Ω Value of R’g(s) + RLs = 120Ω
Value of RLs= 120-115.4 = 4.6Ω
D = Rg/(Rg+RLl)= 120/124.6=0.
Replacing black wire at S+
Value of R’g(s) with Ll (long wire) =115.42 Ω
Value of R’g(s) + RLs = 120Ω
Value of RLs= 120-115.42 = 4.58Ω D = Rg/(Rg+RLl)= 120/124.58=0.
Replacing white wire at S+
Value of R’g(s) with Ll (long wire) =115.42 Ω
Value of R’g(s) + RLs = 120Ω
Value of RLs= 120-115.42 = 4.58Ω
D = Rg/(Rg+RLl)= 120/124.58=0. Average value of ‘D’= 0.
Value of simulated strain with long wires = 2000 με
Value of indicatedstrain with long wires and ΔR (0.48 Ω)= 1923 με
Part C:
Procedure for Compensation for Lead-Wire Desensitization
Next placing “Function” switch on “read” get zero display with “Balance Coarse and Balance Fine”. Next function switch on “int. Cal” set the desired calibration No. corresponding to gage factor1000 for F=2, using “Span Coarse” and “Span Fine”.
After attaining required balances disconnect the previous connections, and gauge factor setting of which installed resistance is to be determined.
Now connect the simulator and given gauge in half bridge arrangement with indicator.
Connections should be made such that binding post no.1 on simulator should be connected through short wire to S- post on indicator. Gauge ‘active’ wire connection should be made to S+ post on on the indicator. P- is common binding post for ‘common’ wire of gage and wire coming from binding post No.2 on simulator.
A strain will be displayed upon completion of half bridge arrangement. It would be positive if Rg > 120 ohm and vice versa.
In half bridge arrangement two arms of the bridge are “active”. So the strain displayed by the indicator is algebraic difference of the strain experienced by the two active arms of the bridge.
Put suitable ∆R from simulator to get both arms balanced.
Now Rg = 120 + ∆R. It includes lead wire resistance as well.
Observation and calculation:
Indicated value of strain= 4346 με
∆R=2.21 Ω
Rg = 120 + ∆R =120+2.21 = 122.21 Ω Fe = (∆Rg/Ra)/ ε = 2.
Experiment #
Large Strain Measurement with V/E-
Introduction:
Strain gage indicators have a range within which strain can be displayed by the indicator. Using this simulator we can not only measure large strains (beyond the range of indicator) but also with greater accuracy than obtainable with strain indicators.
Procedure:
Make quarter bridge arrngement of simulator with indicator. At R= 120ohms on simulator make active wire connection by connecting binding post No.1 on simulator to binding post S+ on indicator using short leads. Now connect binding post No. 2 on simulator to P- and D120 posts on indicator by using two common wires. With “Function” switch on “zero” attain zero on display by using “Instrument Zero” knob. Next placing “Function” switch on “read” get zero display with “Balance Coarse and Balance Fine”. Next function switch on “int. Cal” set the desired calibration No. corresponding to gage factor1000 for F=2, using “Span Coarse” and “Span Fine”. Set gage factor according to the gage factor of the gage through which large strain will be sensed. Make half bridge arrangement of indicator with simulator R= 120 ohms and gage in the unstrained state. There will be a displayed strain which would be basically due to mismatch of the resistance between two active arms of the bridge. Apply ∆Ri from simulator to minimize this displayed strain. Resistance of the arm containing gauge = 120 + ∆Ri Now apply large strain to the structure at which the gage is attached such that the active strain exceeds the range of the indicator.
At R= 120ohms on simulator make active wire connection by connecting binding post No.1 on simulator to binding post S+ on indicator using short leads. Now connect binding post No. 2 on simulator to P- and D120 posts on indicator by using two common wires. With “Function” switch on “zero” attain zero on display by using “Instrument Zero” knob. Next placing “Function” switch on “read” get zero display with “Balance Coarse and Balance Fine”. Next function switch on “int. Cal” set the desired calibration No. corresponding to gage factor1000 for F=2, using “Span Coarse” and “Span Fine”.
Apply ∆R = 1.2 ohm, observe indicated strain and calculate simulated strain using eq. (1).
Repeat above step with ∆R = 2.4 and 3.6 ohm.
Do the same steps with corresponding negative ∆R values.
Observations and calculations:
Applied ∆R ohms Observed strain με Calculated strain με 1.2 4980 5000 2.4 9950 10000 3.6 14910 15000
Part B:
The effect of initial resistive unbalance
If the installed gage resistance is different from the nominal resistance then the bridge will be unbalanced initially due to mismatch between the resistances of installed gage and bridge completion resistors.
Procedure:
Make quarter bridge arrngement of simulator with indicator. At R= 120ohms on simulator make active wire connection by connecting binding post No.1 on simulator to binding post S+ on indicator using short leads. Now connect binding post No. 2 on simulator to P- and D120 posts on indicator by using two common wires. With “Function” switch on “zero” attain zero on display by using “Instrument Zero” knob. Next placing “Function” switch on “read” get zero display with “Balance Coarse and Balance Fine”. Next function switch on “int. Cal” set the desired calibration No. corresponding to gage factor1000 for F=2, using “Span Coarse” and “Span Fine”.
To simulate initial resistive balance , set ∆Ri say equal to 0.6 ohm, corresponding to simulated strain of 2500 με. Observe indicated strain.
To add further 15000 με (corresponding to further ∆R = 3.6 ohm) we are to add ∆R = 3.6 ohm.
Theoretically ε = εin+ εadd = 17500 με. Observe the indicated strain. Difference is due to non-linearity.
Applied ∆R ohms
Observed strain με Calculated strain με ∆ε
0.6 2470 2500 30 2.4 9950 10000 80 3.6 14910 15000 90 4.2 17380 17500 120
Exp.6 Shunt Calibration of Strain Indicators
Introduction:
To simulate εs = -1000 με, εs = -2000 με Rc values are 59,880 ohm and 29,880 respectively. Applying these resistors across binding posts No. 1 & 2 of the simulator one by one, note the values of indicated strains.
For producing positive simulated strain the shunt calibrated resistor may be placed across S- and D120 binding posts of the strain indicator.
RC shunt calibration resistance parallel with R (k Ω)
Observed strain με Calculated strain με
Conclusion:
