LAB #4: Strain – gage based Load Cells - Manish...
Transcript of LAB #4: Strain – gage based Load Cells - Manish...
UNIVERSITY AT BUFFALO
CIE616: Experimental Methods in Civil Engineering LAB #4: Strain – gage based Load Cells
Aikaterini Stefanaki, Lisa Shrestha, Manish Kumar 7/12/2011
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Contents SECTION 1 ................................................................................................................................5
1.1 General .........................................................................................................................5
SECTION 2 ................................................................................................................................7
2.1 Introduction – General information ...............................................................................7
2.2 Purpose, Objective and scope of testing.........................................................................9
2.2.1 Axial Calibration....................................................................................................9
2.2.2 Shear Calibration ................................................................................................. 11
2.2.3 Moment Calibration ............................................................................................. 13
2.3 Prototype design information ...................................................................................... 14
2.4 Scaling and model development .................................................................................. 14
2.5 Materials and constraints ............................................................................................. 14
SECTION 3 .............................................................................................................................. 15
3.1 Specimen description .................................................................................................. 15
3.2 Loading system ........................................................................................................... 16
3.3 Instrumentation set-up, measurement system, and calibration process ......................... 18
3.4 Data acquisition .......................................................................................................... 22
SECTION 4 .............................................................................................................................. 23
4.1 General ....................................................................................................................... 23
4.2 Data monitoring and checking during the testing ......................................................... 24
4.3 Test implementation-Notes and metadata .................................................................... 24
SECTION 5 .............................................................................................................................. 25
5.1 Data recording and repository inventory ...................................................................... 25
5.2 Data verification and repository transfer ...................................................................... 25
5.3 Initial test results ......................................................................................................... 25
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SECTION 6 .............................................................................................................................. 27
6.1 Data checking, verification, and recovery .................................................................... 27
6.2 Determination and elimination of errors ...................................................................... 27
6.3 Calibration of the Load cell ......................................................................................... 27
SECTION 7 .............................................................................................................................. 32
7.1 Calculated model parameters....................................................................................... 32
7.2 Calculate response using simplified model .................................................................. 32
7.3 Calculated response using identified parameters .......................................................... 32
7.4 Comparison or response of experiment analysis with estimated parameters ................. 32
SECTION 8 .............................................................................................................................. 33
8.1 Conclusions ................................................................................................................ 33
SECTION 9 .............................................................................................................................. 35
9.1 Question 1 ................................................................................................................... 35
9.2 Question 2 ................................................................................................................... 35
References ................................................................................................................................ 36
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LIST OF FIGURES
Figure 2-1: Wheatstone Bridge (four arm bridge)[2] .....................................................................8
Figure 2-2: Axial strain measurement ........................................................................................ 10
Figure 2-3: Circuit used for axial calibration ............................................................................. 11
Figure 2-4: Strain rosettes for shear measurement ..................................................................... 12
Figure 2-5: Circuit used for shear calibration ............................................................................. 13
Figure 2-6: Circuit used for Bending calibration ........................................................................ 14
Figure 3-1: Steel blade load cell: top view, bottom view and side view ..................................... 15
Figure 3-2: Three element rosettes ............................................................................................ 16
Figure 3-3: (a) Shear force calibration and (b) Bending moment calibration .............................. 17
Figure 3-4: Shear force calibration ............................................................................................ 17
Figure 3-5: (a) Reference load cell (b) Weights ......................................................................... 19
Figure 3-6: Wheatstone bridge circuits ...................................................................................... 20
Figure 3-7: Conditioner ............................................................................................................. 21
Figure 3-8: Display monitor of data acquisition system ............................................................. 22
Figure 6-1: (a) Calibration curve for axial force, (b) Voltage signal Vs load observed in steel
blade load cell for axial force calibration ................................................................................... 28
Figure 6-2: (a) Calibration curve for shear force, (b) Voltage signal Vs load observed in steel
blade load cell for axial force calibration ................................................................................... 29
Figure 6-3: (a) Calibration curve for bending moment, (b) Voltage signal Vs load observed in
steel blade load cell for bending moment calibration ................................................................. 30
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LIST OF TABLES
Table 2-1: Analogy between Force-Deformation and Ohm’s Law ...............................................9
Table 5-1: Axial Calibration test results .................................................................................... 25
Table 5-2: Shear Calibration test results .................................................................................... 26
Table 5-3: Bending Calibration test results ................................................................................ 26
Table 5-4: Gains used in Calibration ......................................................................................... 26
Table 6-1: Error observed in axial load calibration .................................................................... 31
Table 6-2: Error observed in bending moment calibration ......................................................... 31
Table 6-3: Error observed in shear load calibration .................................................................... 31
Table 6-4: Minimum force the steel blade load cell can measure ............................................... 31
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SECTION 1 Introduction
1.1 General
This report has been prepared as a part of coursework of CIE 616 - Experimental Methods taught
by Professor A.M. Reinhorn at the University at Buffalo. This report presents the Homework on
Lab 4 done by Group 2 that includes the graduate students Aikaterini Stefanaki, Lisa Shrestha
and Manish Kumar, at CSEE, UB. The experiment was conducted in Structural Engineering and
Earthquake Simulation Laboratory (SEESL) at the university on November 14th, 2011 and
November 15th, 2011.
Experiment was done to build a load cell that could measure loads in arbitrary direction. Strain
gages were arranged in “axial load” sensitive, “shear force” sensitive and “bending moment”
sensitive bridges. Strain gages/resistors were placed on a steel plate at different locations and
orientation. Resistors were arranged with excitation and signal voltage nodes to obtain the
required circuit for each case. Loads were applied using different weight combinations. A
reference load cell was used to measure the applied load. Circuits were balanced using the
conditioner. Loads were applied to steel plate for the three cases, and calibrated with respect to a
specific voltage using multiplier gain. Calibration factor was obtained by dividing the reference
load by the voltage. Results were checked for repeatability. Steel plate was unloaded in steps and
plot of reference load vs. voltage was obtained. A straight line fit of graph produced the
corrected calibration factor.
The report has been organized in eight chapters. Chapter 1 presents a brief introduction of the
authors, subject of the assignment, lab work and the report organization. In Chapter 2 the
objectives and scope of the experiment are discussed and some general information about the
tuning of hydraulic actuators is presented. In Chapter 3, the set-up of the test is shown, along
with the loading system, the instruments used and the data acquisition system. Chapter 4 presents
the test schedules and the test procedures followed during the lab work. The raw data obtained
from the testing are given in Chapter 5 and are further processed in Chapter 6. Due to insufficient
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data, no analytical model could be presented in Chapter 7. Finally, in the last Chapter, the
findings of the experiment are summarized and some important conclusions are presented.
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SECTION 2 Scope and General Presentation
2.1 Introduction – General information
The load cell is a transducer that is used to convert force to electrical output (voltage). There are
many types of load cells, however, the most commonly used are the strain gage based load cells.
In such load cells, the gauges are bonded onto a structural member that deforms when weight is
applied. Wheatstone bridge circuit is a four strain gages circuit which results to maximum
sensitivity and temperature compensation. Other bridges can be used such as the quarter bridge
or half bridge, which consists of one and two strain gages respectively. In Wheatstone bridge,
two of the gauges are usually in tension and two in compression and are wired with
compensation adjustments. When the weight is applied to the structural member, the strain
changes the electrical resistance of the gauges in proportion to the load. Generally, the strain
gage based load cells can provide high accuracy, from 0.03% to 0.25% full scale, while the unit
cost is low and they are suitable for most of the industrial applications. [1]
The Wheatstone bridge circuit is ideal for measuring the resistance changes that occur in strain
gages. When the strain gauge is stretched its resistance increases. The basic behavior of the
resistive gauges is given by the equation:
R = ρLA
Where: R is the resistance of the gauge in Ω, ρ is the resistivity of gauge material taking into
account the temperature effects, A is the cross sectional area of the gauge and L is the length of
the gauge.
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From the previous equation, using differential form we can get:
dRR = 휀 (1 + 2휈) +
dρρ
The gauge factor GF can be defined as: GF = = (1 + 2휈) +
. The gauge factor is specified
by the manufacturer and
is considered to be zero for a wide range of strains. Hence,
휀 = ∙ .
The configuration of a Wheatstone bridge is shown in Figure 2-1.
Figure 2-1: Wheatstone Bridge (four arm bridge)[2]
The external voltage supply is V0 and is usually equal to 10 volts, while the change in voltage
across the bridge is ΔV, where ΔV = VA – VC.
For a small change in resistance of the four resistors of the Wheatstone bridge, the differential
change in voltage is given by the expression:
Δ푉V =
GF(1 + 훼) (휀 − 휀 + 휀 − 휀 )
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2.2 Purpose, Objective and scope of testing
The purpose of the experiment is to build and calibrate a strain gage based load cell, in order to
measure loads acting in arbitrary directions. The obtained results from the calibration need to be
compared with a reference load cell. More specifically, three circuits were developed to measure
the three components of a force, hence one axial sensitive, one shear sensitive and one bending
sensitive bridge were used.
At this point, it is useful to mention that Ohm’s law, V = R I can be correlated to the Force -
Deformation relationship F = K δ. Hence, the voltage V is equivalent to the force F, the stiffness
K is correlated to the resistance R and the displacement δ is correlated to the current I of a
circuit, as shown in Table 2-1.
Table 2-1: Analogy between Force-Deformation and Ohm’s Law
Force-deformation relationship Ohm’s Law
Force, F Voltage, V
Stiffness, K Resistance, R
Deformation, δ Current, I
2.2.1 Axial Calibration For axial load measurement, in addition to the axial gauge, a transverse (“dummy”) gauge was
used in order to account for temperature compensation. It should be mentioned that only the axial
gauge can be used for quick measurements, however in this case both axial and transverse
gauges will be used to increase the accuracy of the results.
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Figure 2-2: Axial strain measurement
The differential change in voltage is given by the expression:
Δ푉V =
GF4
(ε − ε + ε − ε )
Where:
ε = ε = =
, and ε = ε = −휈 ε = −
Hence,
Δ푉V =
GF4 2
PA E +
휈 PA E =
GF(1 + 휈)2 A E P
The calibration constant K0 is given by:
K =GF(1 + 휈)
2 A E
It should be mentioned that, while a half bridge could be used, a Wheatstone (full) bridge was
preferred for double sensitivity.
As shown in Section 3, gauges T1 through T5 are located on the top side of the steel blade, while
the gauges B1 to B5 are placed on the bottom side.
In order to develop a circuit sensitive to Axial Load, the gauges T1, T2, B1 and B2 were used. It
has been assumed that the top side of the steel blade is the positive side, while the bottom side of
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the blade is the negative side. Hence, gages T1 and T2 were connected to the E+(positive
excitation), and B1 and B2 to the E-(negative excitation).
In addition to this, T1- T2 and B1 - B2 should be arranged in parallel, since they share the same
force. Finally, T2 – B1 and T1 – B2 should be arranged in series since they should have the same
deformation.
The circuit that was used for the axial calibration is shown in Figure 2-3.
Figure 2-3: Circuit used for axial calibration
2.2.2 Shear Calibration For shear load measurement, a rosette with gauges at 90o apart, as shown in Figure 2-4 were
used. In that case, 휏 = , where Ax is the corresponding shear area, and σx = σy = 0. For pure
shear behavior εxy = εΑ = εC.
T2 T1
B1 B2
E-
S+
E+
S+
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Figure 2-4: Strain rosettes for shear measurement
The differential change in voltage is given by the expression:
Δ푉V =
GF4
(ε − ε + ε − ε )
휀 =P
A E
휀 = −휀 = −P
A E
Δ푉V =
GF4 4
PA E =
GF A E P
The calibration constant K0 is given by:
K =GF
A E
Once again, a full bridge was used for double sensitivity, instead of a half bridge. It should also
be mentioned that a thin steel plate was used so that the shear strains are uniform throughout the
cross section and accurate results can be obtained.
In this case, the gages T4, T5 and B4, B5 are used, since they are arranged at 90o apart. Since top
side is the assumed to be positive side, T4 –T5 were connected to E+ and B4 –B5 were connected
to E-.
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In addition to this, T4- T5 and B4 – B5 should be arranged in parallel, since they share the same
force. Finally, T4 – B5 and T5 – B4 should be arranged in series since they should have the same
deformation.
The circuit used for shear calibration is shown in Figure 2-5.
Figure 2-5: Circuit used for shear calibration
2.2.3 Moment Calibration For moment calibration, a half bridge was used since the given orientation of the gauges did not
allow the use of a full bridge for the specific calibration.
The differential change in voltage is given by the expression:
Δ푉V =
GF4
(ε − ε )
Where:
ε = =
=
= −ε , where S is the section modulus, S =
Hence, Δ푉V =
GF4 2
P LS E =
GFLV2 S E P
T4 T5
B5 B4
E-
S+
E+
S+
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The calibration constant K0 is given by:
K =GFLV2 S E
The circuit that was used for the axial calibration is shown in Figure 2-6.
In this case, the gages T3 and B3 were used. Since top side is the assumed to be positive side, T3
was connected to E+ and B3 was connected to E-.
Figure 2-6: Circuit used for Bending calibration
2.3 Prototype design information
N/A
2.4 Scaling and model development
N/A
2.5 Materials and constraints
N/A
E+
E-
S+
S+
T3
B3
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SECTION 3 Test-set-up Overview
3.1 Specimen description
The test specimen consists of a flat steel blade mounted as a cantilever beam as shown in
Figure 3-1. The flat steel blade is instrumented with strain gage at two sections A and B. Three
element rosettes are attached at both the top and bottom surface at the two section. The rosettes
in the opposite sides at each section lie on top and bottom of each other. The strain gages are
connected to appropriate Wheatstone bridge circuits that are capable of detecting axial force,
shear force and bending moments developed upon loading.
Figure 3-1: Steel blade load cell: top view, bottom view and side view
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Figure 3-2: Three element rosettes
3.2 Loading system
The loading configuration for the calibration process has been shown in Figure 3-3 through
Figure 3-4. System loading is done by applying weights in the hanger. Load is transferred to the
cantilever beam with the use of string and pulley system. For axial force and bending moment
calibration, the flat steel blade is oriented with its width, the larger dimension of the cross-
section, parallel to the horizontal (Figure 3-4 and Figure 3-3 b respectively); and for shear the
width is oriented perpendicular to the horizontal (Figure 3-3 a). For shear force and bending
moment, point load is applied at the end of the span by putting the weights in the hanger. Axial
force is induced by applying weights to the hanger and then transferring it to the end of the
cantilever beam, through the string and the pulley system.
Three element
rosette
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(a) (b)
Figure 3-3: (a) Shear force calibration and (b) Bending moment calibration
Figure 3-4: Shear force calibration
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3.3 Instrumentation set-up, measurement system, and calibration process
The steel blade load cell was setup to act as a cantilever beam with fixed support at one and point
load at the other end. As mentioned before the steel blade had three element rosettes that are
connected to Wheatstone bridge circuits. Wheatstone bridge circuit developed for the calibration
has been explained in section 2. Each strain gage has two wire connections. One end is
connected to the input excitation signal (denoted by E+ and E-) and the other is connected to the
output voltage signal (denoted by S+ and S-). The connection between the excitation and output
voltage signals to strain gages is done with the use of supplemental wires. When external
Voltage is supplied through the conditioner, the voltmeter displays the change in voltage across
the bridge caused by the change in the resistance of the gages which in turn is the results of the
strains developed in the strain gages due to the forces generated. A reference load cell (Figure
3-5), that has been pre-calibrated, was provided at the upper end of the hanger to measure force
applied in the cantilever beam.
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(a) (b)
Figure 3-5: (a) Reference load cell (b) Weights
Reference
Load Cell
Hanger
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Figure 3-6: Wheatstone bridge circuits
Supplemental
wires
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Figure 3-7: Conditioner
Calibration of the steel blade load cell involved first positioning the blade in the desired
orientation depending on the force being calibrated, as was explained in previous sections.
Imbalance in the circuit is indicated by a red light in the conditioner. Circuit balance is ensured
by turning the trimming knob in the direction opposite to the light (to negative or positive
values), until it goes off. Maximum load (50N, 40N and 20N in case of shear, bending and axial
respectively) was applied in the hanger. Gain in the conditioner was adjusted until the desired
max voltage (5 volts in case of shear and bending and 0.5 volts in case of axial) was generated
across the bridge. Calibration factor was calculated so that the force readings in the reference
Trim
Reference
load cell
conditioner
Axial force
conditioner
Shear force
conditioner
Bending
moment
conditioner
Indicator for
circuit balance
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load cell and the steel blade load cell gives the same value. After unloading, the balance in the
circuit was checked. Calibration factor was checked for incremental load steps of 10N.
Connection of the circuit is checked by applying small forces in the beam. If imbalance in the
circuit is created due to application of the load then it indicates that the circuit connection is
correct.
3.4 Data acquisition
Data acquisition for this system was done using Labview software. The voltage generated across
the Wheatstone bridge was converted to force generated. The forces in the beam measured by the
reference load cell and the steel blade load cell were displayed in the monitor. To enable the
calibration procedure the Volt signal generated in the Wheatstone bridge circuit was also
displayed. A screenshot of the display monitor of the data acquisition system has been shown in
Figure 3-8.
Figure 3-8: Display monitor of data acquisition system
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SECTION 4 Test Procedures
4.1 General
Experiment was done for three cases, in which strain gages were arranged to produce “axial
load” sensitive, “shear force” sensitive, and “bending moment” sensitive Wheatstone bridges.
Moment and shear calibration was done on the first day but due to unexpected problem with
axial calibration, axial calibration was done on the next day. As axial deformations are usually
very less compared to bending and shear deformations, it was calibrated to a voltage of 0.5V,
whereas shear and moment calibration was done using 5V.
Test schedule and repetitions have been presented in following section.
Test No. Force Sensitivity Test Description Test Date Comments
1 Shear 40 lb. calibration 11-14-2011 Calibrated to 5V
2 Shear 40 lb. unloading 11-14-2011
3 Shear 30 lb. unloading 11-14-2011
4 Shear 20 lb. unloading 11-14-2011
5 Shear 10 lb. unloading 11-14-2011
6 Shear 0 lb unloading 11-14-2011
7 Bending 20 lb. calibration 11-14-2011 Calibrated to 5V
8 Bending 20 lb. unloading 11-14-2011
9 Bending 10 lb. unloading 11-14-2011
10 Bending 0 lb. unloading 11-14-2011
11 Axial 50 lb. calibration 11-15-2011 Calibrated to 0.5V
12 Axial 50 lb. unloading 11-15-2011
13 Axial 40 lb. unloading 11-15-2011
13 Axial 30 lb. unloading 11-15-2011
14 Axial 20 lb. unloading 11-15-2011
15 Axial 10 lb. unloading 11-15-2011
16 Axial 0 lb. unloading 11-15-2011
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4.2 Data monitoring and checking during the testing
Data was monitored using the data acquisition system, which consisted of conditioner and the
computer. Screenshots of each loading and unloading steps were taken from the computer. For
balancing the circuit, data was monitored through the conditioner first and confirmed using the
values showed by the computer. Gains were directly recorded from the conditioner.
4.3 Test implementation-Notes and metadata
N/A
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SECTION 5 Test Results
5.1 Data recording and repository inventory
Data recording was done by the data acquisition system discussed in Section 3.
5.2 Data verification and repository transfer
N/A
5.3 Initial test results
The data obtained from the experiment are shown in the following tables. More specifically, the
reference load, the voltage output, the calibration factor as well as the obtained load were
recorded for increasing applied load. Additionally, the gain used for each calibration are shown
in Table 5-4.
Table 5-1: Axial Calibration test results
AXIAL CALIBRATION
Load (lb) Reference Load (N) Voltage (V) Calibration
Factor Obtained Load (N)
0 -0.488 -0.002 -444 1.22 10 44.2 -0.114 -444 50.7 20 88.7 -0.219 -444 97.0 30 133.0 -0.319 -444 141.0 40 178.0 -0.413 -444 183.0 50 222.0 -0.502 -444 223.0
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Table 5-2: Shear Calibration test results
SHEAR CALIBRATION
Load (lb) Reference Load (N) Voltage (V) Calibration
Factor Obtained Load (N)
0 1.59 0.0079 35.586 0.282 10 46.0 1.27 35.586 45.2 20 90.4 2.52 35.586 89.8 30 135.0 3.78 35.586 134.0 40 179.0 5.03 35.586 179.0
Table 5-3: Bending Calibration test results
BENDING CALIBRATION
Load (lb) Reference Load (N) Voltage (V)
Calibration Factor Obtained Load (N)
0 1.22 0.0012 18.06 0.022 10 45.7 2.51 18.06 45.3 20 90.5 5.01 18.06 90.6
Table 5-4: Gains used in Calibration
Gain
Axial Calibration 3120
Shear Calibration 10420
Bending Calibration 690
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SECTION 6 Data Processing
6.1 Data checking, verification, and recovery
N/A
6.2 Determination and elimination of errors
N/A
6.3 Calibration of the Load cell
The steel blade load cell was calibrated for axial force, shear force and bending moment.
Calibration curves, which are the plot of Reference load cell reading versus Load cell reading,
were plotted for the three cases. Straight line fit was obtained as shown in the Figure 6-1a, Figure
6-2a and Figure 6-3a . The equation for the best fit and the regression coefficient value obtained
has also been shown in the figures. It can be seen that there was good correlation between the
readings in reference load cell and the flat steel blade. Perfect positive correlation was obtained
for the case of shear and bending. The plot of the voltage signal versus load observed has also
been shown Figure 6-1b, Figure 6-2b and Figure 6-3b. The equation for the curve and regression
coefficient has been obtained. The correlation coefficient obtained between the readings in two
load cells is smaller in case of calibration for axial load. Errors between the readings of reference
load cell and the steel blade load cell for the three cases have been shown in Table 6-1 through
Table 6-3. The error between these two values is observed to be higher in case of axial load
calibration as compared to bending and shear load calibration. These two observations suggest
that the axial load calibration is the most sensitive as compared to moment and shear calibration.
The minimum volt signal that can be detected by the Wheatstone bridge circuit used to connect
the strain gages is 0.001 volts. Thus, the minimum force that the load cell can detect is this
voltage multiplied by the respective calibration factor for the three load cases as shown in Table
6-4.
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(a)
(b)
Figure 6-1: (a) Calibration curve for axial force, (b) Voltage signal Vs load observed in steel blade load cell for axial force calibration
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(a)
(b)
Figure 6-2: (a) Calibration curve for shear force, (b) Voltage signal Vs load observed in steel blade load cell for axial force calibration
30
(a)
(b)
Figure 6-3: (a) Calibration curve for bending moment, (b) Voltage signal Vs load observed in steel blade load cell for bending moment calibration
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Table 6-1: Error observed in axial load calibration
AXIAL CALIBRATION
Load Applied (lb) Reference Load Cell Reading (N)
Steel blade Load Cell Reading (N) Error (%)
0 -0.488 1.22 - 10 44.2 50.7 -14.706 20 88.7 97 -9.357 30 133 141 -6.015 40 178 183 -2.809 50 222 223 -0.450
Table 6-2: Error observed in bending moment calibration
BENDING CALIBRATION
Load Applied (lb) Reference Load Cell Reading (N)
Steel blade Load Cell Reading (N) Error (%)
0 1.22 0.022 - 10 45.7 45.3 0.875 20 90.5 90.6 -0.110
Table 6-3: Error observed in shear load calibration
SHEAR CALIBRATION
Load Applied (lb) Reference Load Cell Reading (N)
Steel blade Load Cell Reading (N) Error (%)
0 1.59 0.282 - 10 46 45.2 1.739 20 90.4 89.8 0.664 30 135 134 0.741 40 179 179 0.000
Table 6-4: Minimum force the steel blade load cell can measure
Min. voltage signal Calibration factor Min. load reading Axial -0.001 -444 0.444
Bending 0.001 18.06 0.018 Shear 0.001 35.586 0.036
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SECTION 7 Analytical Predictions
7.1 Calculated model parameters
N/A
7.2 Calculate response using simplified model
N/A
7.3 Calculated response using identified parameters
N/A
7.4 Comparison or response of experiment analysis with estimated parameters
N/A
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SECTION 8 Conclusions and Recommendations
8.1 Conclusions
Experiment was done to build a load cell that could measure loads in arbitrary direction. Strain
gages were arranged in “axial load” sensitive, “shear force” sensitive, and “bending moment”
sensitive bridges. Calibration factor was obtained for each case important conclusions have been
summarized below:
1) Moment calibration was most accurate as relatively large values of deflection were
obtained along strain gages, and axial calibration was least accurate as it produced very
low deformation along strain gages.
2) Coupling of axial, bending, and shear deformations can be avoided by applying the loads
gently.
3) Load cell should be loaded and unloaded to check if after unloading it is coming back to
zero value of voltage. Calibration factor should be checked for repeatability.
4) One should be cautious while using the resistor in the bridges, not to over expand the
opening of female end of resistor. Problem in axial calibration was encountered due to
overexpansion of one of the resistors.
5) Incremental voltage readings should be taken for different weights to obtain a more
accurate estimate of calibration factor.
6) Calibration factor in lab should be obtained using maximum values of reference load and
voltage to minimize the error.
7) Sensitivity of balanced bridge should be checked by manually pulling and pushing the
specimen.
8) Balancing of Wheatstone bridge should be done by the conditioner using TRIM and then
crosschecked using the values from data-acquisition system.
Recommendations that can be taken into consideration for future experiments are as follows:
1) As axial calibration was least sensitive, more weights can be used to experience larger
deformation along strain gages and produce accurate results.
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2) Accuracy of full bridge with four resistors can be compared with to bridge with two
resistors.
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SECTION 9
9.1 Question 1
Is it possible to modify the test set-up such that you will have same sensitivity for all three
circuits? Please document your answer (positive or negative)
It is possible to modify the test set up to get the same sensitivity for all the circuits. Sensitivity of
circuit depends on deformation through the strain gage and value of voltage to which it is
calibrated. Moment circuit was the most sensitive and axial circuit was the least sensitive. If
loads can be applied so that it produces equal deformation through strain gauges of all circuit and
they are calibrated to same voltage, we can get an “equally sensitive” moment, shear and axial
circuits.
9.2 Question 2
If we measure the direct force (or moment) and we get nonzero measurements during
calibrations in the other channels, can we still find the correct arbitrary load that produce
components which excite all circuits?
Although it’s preferred that application of load for bending sensitive circuit doesn’t produce any
deformation in other direction, it’s not a requirement. In case of non-zero deformation in other
direction, we will have a “cross-coupled” form of calibration equation, in which off-diagonal
terms are non-zero. So the arbitrary load can still be found which might excite all circuits.
3
1 11 1
2 22 2
3 33
0 0 10 0 20 0 3
Force CalibrationMatrix InitialOffsetVoltage
F a V CF a V CF a V C
: For uncoupled calibration, zero off-diagonal values
3
1 11 12 13 1
2 21 22 23 2
3 31 32 33
123
Force CalibrationMatrix InitialOffsetVoltage
F a a a V CF a a a V CF a a a V C
: For coupled calibration, non-zero off-diagonal values
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References [1] http://www.omega.com/prodinfo/loadcells.html
[2] A.M. Reinhorn, CIE616 Lecture 7, part 1