Lab - Strain Measurement System

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ME56 — Instrumentation & Control Eng. The 2nd Semester S.Y.2011-2012

Lab : Strain Measurement SystemThursday, Dec.1

Objectives

In this lab, you will

1. know the technique and application of strain measurement using electrical resistance gauges.2. understand how the strain gauge output is processed.3. calibrate the electric resistance strain gauge by comparing the mechanical strain

Background reading Practical Strain gauge Measurement section (Pages E-45 ~ E-72)on the book “The pressure

strain and force Handbook” published by Omega Engineering company

A. Strain Gauge

Strain gauges are used in structural(or mechanical) engineering to evaluate stresses in elements of a structure. This involves several considerations which must always be questioned whenever thetechnique is applied. They are:

1. That the relationship between gauge strain and change of resistance is known.

It is by definition the gauge factor GF , where, G F= (dR/R) / εHowever in high class work where the direction of the principal strain is not known, it may benecessary to make allowance for the cross-sensitivity of the gauge; that is, there is a second order change of resistance duet to strain perpendicular to the long axis of the gauge. Also it is normal tomeasure the gauge factor of a few gauge from each manufactured batch, and assume this factor applies to the batch.

2. That the relationship between surface strain and stress of the structural element is known.

It is termed the modulus of elasticity E in the linear elastic stress range of the material, which permits a simple calculation of stress from σ =E ε = (E/GF) (dR/R)If the structural element is made from a non-linear elastic material, for example concrete under immediate loading, then a mathematical stress-strain law or a graph may be used to derive stressfrom strain. In more difficult situations where plasticity is involved, a stress strain graph to at leastthe recorded strain would be needed for the first loading.

3. That the gauge follows surface strain perfectly.

A successful gluing technique is needed to satisfy this condition. Through degreasing, a thin

uniform film of adhesive, and compatibility of all the materials in contact are essential. There is no

substitute for experience.

4. That there are no indeterminate reasons for change of resistance in the gauge circuit.

It does not include change of temperature as this is a factor normally taken into account by using adummy or reverse active gauge in the balancing arm of the bridge circuit. It is more likely to arise

from the variable resistance of joints or plugs and sockets in the gauge circuit, or by moisture

reducing the earth leakage resistance of parts of the circuit so that the zero balance drifts.

5. That the strain gauge meter is accurate.

Lab : Strain Measurement System /8




Having gone through the check list, it can be claimed that the use of electrical resistance strain

gauges (ERSG) presents a powerful tool for the designer in the many situations where mathematical

models are highly complex or loadings arc not known. The present range of experiments provides a

survey of the uses and possibilities.

This experiment introduces the technique and application of strain measurement using electrical

resistance gauges. Firstly there is a simple calibration beam which will permit the gauge factor to be

checked

B. Wheatstone BridgeThe HAC20 Unit accepts inputs from quarter, half or full bridge strain gauge circuits like shownthe below. These connection would be found in the most of strain measurement system dependingon the applications.

ε= - 4Vr/GF(1+2Vr) ▪(1+ Rl/Rg)

FF

FF

Rg(ε)

Rg(dummy)

Vout

- +

R1

R2

Quarter-Bridge Configuration

Rl

Rl

Rl

ε= - 2Vr/GF ▪(1+ Rl/Rg)

FF

FF

Rg(+ε)

Rg(-ε)

Vout

- +

R1

R2

Half-Bridge Configuration for Bending

Rl

Rl

Rl





ε= - Vr/GF

FF

FF

Rg(+ε)

Rg(-ε)

Vout

- +

Full-Bridge Configuration for Bending

FF

FF

Rg(-ε)

Rg(+ε)

Where, Vr = [(Vout/Vin)strained – (Vout/Vin)unstrained]

1

Dummy or

compression

4

3 2

Tension

Yellow

+ve

excitation

0V

Signal

C

T

1 Red

C

T

4

32

Blue

Yellow

Green

+ve

excitation

0V

Positive

signal

Negativesignal

For

balancing(tare)

(a) Quarter and half bridge connector (b) Full bridge connector

HAC20 Unit connector

Materials required

1set HST2/10 Strain Measurement System Bench and Accessory




ME56 — Instrumentation & Control Eng. The 2nd Semester S.Y.2011-2012 1 HAC20 Digital Strain Meter Unit1 DMM1 Calipers1 HST.14A specimen

1 HST.14B specimen1 HST.14C specimen1 HST.14D specimen

Procedure

As a general rule the color code for the gauge leads is blue and yellow for a tension gauge and red andyellow for a compression gauge but there are exception to this rule.

Part 1. Preliminary Measurement and familiarizing the HAC20 Unit1. Measure Rl, Measure Rg, the length of lead wire.2. What is accuracy of dial gauge and Calipers?

3. Check the Excitation voltage for sensor provided by HAC20 Unit.4. Practice how to operate the HAC20 Unit

Part 2. Gauge Factor and Bridge factor.1. Set up the simply supported beam HST14a as shown in the figure below on knife edges at 200

mm span with a load hanger on each overhanging end and a dial gauge at mid span to measure the upward

deflection or the beam.

2. Measure the beam section. (b, h)

3. Connect the single gauge (c) (Red and Yellow leads on the socket 4 and 3)

4. One of the gauges (Red -Yellow or Blue – Yellow leads on the socket 1 and 2) on the

cantilever HSTl4b as a "dummy" temperature compensation gauge in the form of a quarter bridge circuit to

the interface of a lead A to the meter. Keep strictly to the color coding when connecting the gauge (c) to

ensure that the red lead is connected to the correct outer socket numbered 4 and the yellow lead to socket

number 3. This will produce a +ve reading for tension. The dummy gauge leads are to be connected to the

sockets numbered 1 and 2.


200mm

300mm



h

b

Beam cross

section

400

100 100 100 100

Gauge c Gauge a

Gauge b4530


5. Power On the HAC20 meter and connect the sockets into the each channel.

6. Set the gauge factor on the meter to the value marked on beam HST14a. the gauge factor is

provided by manufacturer of the strain gauge. The strain gauge factor for the strain gauge used in this

experiment is 2.12.

7. Set the number of active gauges to one

8. Set zero the "tare" reading on the meter.

9. Add equal increments or 5 N load to each hanger simultaneously up to a maximum not

exceeding 40 N, and record the strain readings(ERSG), Analog Output and dial gauge reading for each

increment following Table 1. Carry on recording readings as the load is decreased by equal increments of 10N.

Table 1Calibration Beam

Load at ERSG Analog Mechanical Strain

Each End Strain Output Dial Gauge Deflection Strain

Reading

(N) (µε) (V) (0.01 mm) (mm) (µε)

0 0 0 0

5

10

1520

25

30

35

40

30


δ

P P

P P




20

10

0

10. Now change the single gauge (c) for gauge (a) but keeping the "dummy" gauge of HST14b.11. Set zero the meter 12. And record the gauge readings following the table 2




Reading

(N) (µε) (V) (0.01 mm) (mm) (µε)

0 0 0 0

20

40

13. Next change the single gauge to gauge (b) which is on the underside of the beam.14. connect the blue lead to socket 4.15. Set zero the meter 16. And record the gauge readings following the table3

17. Finally rearrange the whole set up to use gauges (a) and (b) to form the half bridge circuittaking care to follow the color coding at the interface (blue lead to socket 1 and red lead tosocket 4 and the yellow leads to 2 and 3).

18. Change the meter setting to two active "gauges, which will introduce a divide by two function.19. Set zero the tare reading.

20. Take readings for a set of load increments of 10 N up to 40 N following the table4.




Reading

(N) (µε) (V) (0.01 mm) (mm) (µε)

0 0 0 0

20

40




Reading

(N) (µε) (V) (0.01 mm) (mm) (µε)





0 0 0 0

10

20

3040

Results and Discussion

1. Draw the strain gauge measurement block diagram including sensor, signal conditioning andsignal presentation.

2. Plot the strain readings against load for the simply supported beam using MS EXCEL programand draw the best fit straight line through the points.

3. Calculate Hysteresis error of this strain measurement system from the collected data on theTable1 and discuss it.

4. Calculate the linearity of this strain measurement system. And discuss it.5. Note whether the three gauges give similar readings when used with the inactive dummy, and

the effect or the final arrangement. Calculate the Mechanical strain from the dial gaugedeflection using the geometrical expression and fill the calculated values on the column on eachtable.

ε = 8δh / L2

where δ = deflection

h = half the depth of the beam L = span of the beam

This, being independent of material properties, gives true strain and hence can be used to verifythe quoted gauge factor. It is possible to calculate the surface stress of the beam from

σ = M / Z


10 20 30 40

-100

0

100

200

300

400

500

600

○ ERSO Strain ● Mechanical Strain Applied Load (N)

S t r ai n ( µ ε )




and this could be compared with the stress obtained using an assumed value of the modulus of

elasticity (say 205 x 103 N/mm2) in the expression σ = Eε.

7. Plot an error analysis graph of all the results in from Table 1 up to Table 4. This is done by

calculating the mechanical strain from the dial gauge deflection values to use as abscissa, and

plotting the corresponding ordinates given by mechanical strain minus electrical strain reading.

For the reversed active arrangement it may be necessary to halve the apparent electrical strain.

9. The results of Part 2 provide data for assessing the variability or readings from strain gauges,and the magnitude of errors. Calculate the likely percentage error in reading and in F.S, andcomment on the probable sources of inaccuracies.

Conclusion


400 600 800

-30

-20

-10

0

10

20

30

40

○ Table1 ● Table2

◆Table3 ◈ Table4

Mechanical strain

M e c h ani c al S t

r ai n–El e c t r i c al s t r ai n

Error Analysis

Lab - Strain Measurement System

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