LAB #4: Strain – gage based Load Cells - Manish Kumarmanishkumar.org/research/Coursework/CIE616/HW/HW4/Lab4_Group2.… · LAB #4: Strain – gage based Load Cells ... Wheatstone

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

1

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

3

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

5

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

6

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.

7

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.

8

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+

12

Figure 2-4: Strain rosettes for shear measurement


Δ푉V =

GF4

(ε − ε + ε − ε )

휀 =P

A E

휀 = −휀 = −P

A E

Δ푉V =

GF4 4

PA E =

GF A E P


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.


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+

14


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

17

(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

20

Figure 3-6: Wheatstone bridge circuits

Supplemental

wires

21

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

22

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




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



11 Axial 50 lb. calibration 11-15-2011 Calibrated to 0.5V

12 Axial 50 lb. unloading 11-15-2011






24

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

25

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

26

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

27

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.

28

(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

29

(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

31

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



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



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

32

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

33

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.

34

2) Accuracy of full bridge with four resistors can be compared with to bridge with two

resistors.

35

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

36

References [1] http://www.omega.com/prodinfo/loadcells.html

[2] A.M. Reinhorn, CIE616 Lecture 7, part 1

Documents

LAB #4: Strain – gage based Load Cells - Manish Kumarmanishkumar.org/research/Coursework/CIE616/HW/HW4/Lab4_Group2.… · LAB #4: Strain – gage based Load Cells ... Wheatstone