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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 in length). The ratio of this change in length ∆L, to the original length, L, is called strain.
ε = ∆L / L
Electrical Strain Gauges
The electrical strain gauges are mostly thin, rectangular-shaped strips of foil with maze-like wiring patterns 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 its electrical 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
Where, Δ R - the change in resistance caused by strain,
RG - is the resistance of the unreformed 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:
Graphical Representation:
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
0 -2500 -2000 -1500 -1000 -500 0
actual strain
indicated strain
Actual strain vs. Indicated strain
actual strain vs. indicate d strain
Experiment # 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 (1) and effective gauge factor (Fe) is Fe = (∆Rg/Ra)/ ε = [∆Rg/(Rg+ Rl)]/ ε Fe = DF (2) Where D = (Rg/(Rg+ Rl) (3) It is obvious that in the situation when Fe is to be used use of F instead of Fe will result in lower indicated strain values conveying the sense that gauge seems to be desensitized (sensing less strain). To account for this desensetization effect we are to evaluate Fe which indirectly necessitates the determination of lead wire resistance.
Part A: Procedure for Determination of Lead Wire resistance
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.
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
Procedure:
Calculate Fe = DF with D = Rg/(Rg+RLl)
Repeat steps (i), (ii) of part a but this time three Ls wires are replaced by three Ll wires with F replaced by Fe.
Corresponding to a simulated strain of 2000 με with F=2 again apply ∆R = 0. ohms and note indicated strain.
Observations and calculations: Fe = DF = (0.9632)(2) = 1.
Experiment # 3
Measurement of Installed Strain Gauge
Resistance
Nominal gauge resistance is always different from installed gauge resistance. This difference can may be due to a number of reasons. To get accurate results we are to measure the actual resistance of the installed strain gauge instead of blindly using the nominal value of uninstalled gauge in calculation.
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”. docsity.com
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.
Keep on increasing ∆R through simulator, in increments, until strain
indicated on indicator is minimum. docsity.com
Corresponding to this situation reading of resistance on simulator is Rf
ohms.
Rf = 120 + ∆Rf and actual strain ε = [∆Rf - ∆Ri]/[F(120+∆Ri)]
Practically this part cannot be perfromed in lab as there are no means to
produce an appreciably large strain.
Experiment # 5
Non-Linearity of Quarter Bridge Circuit
Introduction:
Output of a Wheatstone bridge is not always linear with applied strain.
Non-linearity error increases with applied strain. Quarter bridges are
always non-linear while half bridges may be linear as well as non-linear.
Non-linearity error is more with constant voltage excited bridges than for
constant current excited bridges.
In a handbook supplied by the manufacturer of the simulator procedure
for correction of non-linearity of bridge for constant voltage quarter bridge
is described. In this case
Actual strain = Indicated strain + Non. Linearity error + Inst. Error
But unfortunately no procedure for correction of non-linearity of constant
current bridges is available in this handbook. Hence we will be observing
(and not correcting) non-linearity error.
Part A:
Bridge Initially Balanced Resistively
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.
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
Experiment # 6
Shunt Calibration of Strain Indicators
Introduction: As stated earlier calibration of the indicator means having a curve between indicated and actual (simulated) strain. We can introduce resistance change (and hence cause strain simulated) by series addition/subtraction of resistance in the form of ∆R to R (nominal value). R can also be changed by shunting R with Rc (shunt calibrated resistor). When R is shunted through Rc effective resistance of the arm becomes Reff = (RRc)/ (R+Rc) (5) Clearly Reff < R thus ∆R = [(RRc)/ (R+Rc)]- R is always negative. Therefore if shunting is done across active gage then negative strains are simulated and if shunting is done across bridge completion resistor then positive strains will be simulated. To calculate value of Rc required to simulate εs (negative strain) in the resistor R with gage factor Fi we use following relation
Rc =[ -R/(Fi εs)] – R (6)
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 εs = -1000 με, εs = -2000 με Rc values are 59,880 ohm and 29, 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
Discussion:
The experiments give an insight about the important points noted while
measuring the strain from the strain indicator. E.g., when using long leasds
instead of short leads the desentisization of gauge is also incorporated in
calculating strain from indicator for actual results. Temperature
compensation is also an important factor in measuring the strain and
calibrating the indicator. Someone can measure the strain greater than the
range of the indicator used in experiment as in experiment 4.
