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EEE220Report Liu Qinyun-1302501

March31,2016

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Experiment 11.1Table and Graph δR

δR /R 3δV 1

1/128(78.12m)17.539mV 2

2/127(157.48m)38.828mV 3

3/126(238.01m)59.931mV 4

4/125(320.00m)80.719mV 5

5/124(403.23m)101.731mV 6

6/123(487.80m)123.064mV 7

7/122(573.77m)146.599mV 88/121(661.16m)165.039mV 99/120(750.00m)183.374mV

200400600800

50

100

150

200

[Output Voltage against the Fractional Change in Resistance

1.Determine the slope of the graph,representing the sensitivity of the bridge.

Experimental Sensitivity =2.3approximately.

2.Calculate the theoretical sensitivity of the bridge(Equation 6).

Theoretical Sensitivity =V 0=x 2(2+x )?E ?V 0=E 4

Gε(where E =10V )so that the sensitivity is 2.5

https://www.wendangku.net/doc/f811209980.html,ment on the results.

The experimental sensitivity is smaller than the theoretical

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value.By the equation,the Voltage supply may be reduce on resistors.

1.2Analysis

This part of experiment is aim to be familiar with the equipment and the principle of The Wheatsone bridge,And we can get the output

put voltage from resistance change|δV|=|E|δR

1,which could be

use at later experiment.

2Experiment2

2.1Part A-Table and Question

1.Table Mass(kg)δV y

0.00.541mV0um

0.50.805mV69um

1.0 1.039mV132um

1.5 1.322mV203um

2.0 1.482mV265um

2.5 1.836mV334um

3.0 2.006mV400um

2.Why the temperature compensation strain gauge is used?

Strain gauge material,will respond to changes in changes in temperature.To minimize sensitivity to temperature,Com-pensated gauges is used.

3.Is there any variation in temperature?And why?

There may be variation in temperature.By measure resistant of stain gauge,which is larger than120?,speculation of the phenomena is the thermal in?uence.And the graph shows that the output voltage change will is direct proportion to resistance change.

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2.2Part B-Table,Graph and Question

1.Table Mass(kg)δV y

0.0-0.171mV 0um

0.50.327mV 67um

1.00.813mV 132um 1.5 1.307mV 201um

2.0 1.787mV 265um

2.5 2.266mV 333um

3.0 2.759mV 400um

2.Graph

1

23[Output Voltage against the Displacement https://www.wendangku.net/doc/f811209980.html,pare the ?ndings of bridge output against displacement for the two parts A and B.And the relative outputs with theory.By the equation (7)V 0=x E ,which is applying one gauge,and applying two gauges equation (9)V 0=X E ,we can conclude that using two gauges will double the output voltage.It is also means the sensitivity is double than only one gauges.

4.For your best set of measurements:

(a)Calculate the strain using Equation 11.

=4

hy l 2Where h =6.27mm,y was from experiment,l =20cm.

So that,base on the data form experiment,we can get [0,0.420,0.828,1.260,1.662,2.088,2.508]?10?4(b)Calculate the gauge factor (G).

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V0=EεG Where4=10V,εare concluded in last question.

So that,G could be calculate form the series of ,In calcula-tion the second data is also deviated comparing others.Finally, G=1.83(c)What is the e?ect of using multiple strain gauges on sensitivity?

The multiple strain gauges will increase the sensitivity of mea-surement.In detail,two strain gauges will double the sensi-tivity than one strain gauges,and four strain gauges will four times the sensitivity than one gauges.

2.3Analysis

This part experiment is applying the strain gauges to measure shape change and output as voltage.The?rst part use the temperature compensation to minimize the sensitivity to thermal condition.And the second experiment aims to increase the sensitivity by apply multi-gauge bridge circuits,which use two gauges is double the sen-sitivity of using one.In addition,the graph shows that the loads change is in direct proportion to the shape change,while the shape change is in direct proportion to the strain and resistance change. 3Experiment4

3.1Table,Graph and Question

1.Table Whereεcould calculate from Equation(9)andσcould

calculated from Equation(13).

Mass(kg)δVε?10?4σ?105

0.0000

0.50.4100.420 5.859

1.00.9060.84011.717

1.5 1.375 1.25417.576

2.0 1.847 1.6682

3.434

2.5 2.343 2.07529.293

3.0 2.744 2.48935.151

2.Calculate the strain for the corresponding loads and show sam-

ple calculation.

According to Equation(9)V0=EGε

2,now we know the G=

105.61?103and V0from experiment,so the when the output

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voltage is 0.906mV =2V 0EG =1.716?10?4

https://www.wendangku.net/doc/f811209980.html,pute stress by using Equation (13)from the known loading conditions.Show a sample calculation.

σ=3W

(L ?l h 2b Which could also present as W =σh 2b 3(L ?l )Where h =6.27mm,b =25.4mm,L =59cm,l =20cm.

4.graph of stress versus strain.050100150200

0.5

1

1.5

2

2.5

[graph of stress versus strain

5.Determine the value of Young’s modulus for the beam material and compare your result with the Y =1.05?1011Nm ?2Accord-

ing to Equation (12)σ=Y εand Equation (13)σ=3W

(L ?l )h 2b ,we can get Y =3W (L ?l )h 2bεbring in W =30,(L-l)=39,h =6.27,b =25.4,and ε=2.489,we can get Y =1.412?1011

6.How does the strain measured near the pivots compare with that found for the same loading near the center in experiment 2-B?The output voltage for the pivots is bit smaller than the results at the center.It could be that the strain at the center is bigger.

3.2Analysis

To calculate the εandσ,several equations are used.In that case,using di?erence equation can verify di?erent variable from the lab

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and the constant number.So that,we can get the strains,and other variable,only from the output voltage and the constant.number previous,

4Experiment5

4.1Table and Question

1.table

Beam with hole

δV maxεmax?10?4σmax?107

A 1.405mV 3.071 3.225

B 2.139mV 4.675 4.909

https://www.wendangku.net/doc/f811209980.html,pare between:(a)the two strains at those two positions

and explain the reason.

The strains at position B is much bigger than A.The force of bending is focused on the position B,and position A is near center-line,which could not be bending so much.(b)The strain under these conditions with that at the uniform beam at the same loading.

The strains at the beam with is hole is larger than complete beam.The hole in the middle of beam could cause unstable, which results larger strain.

3.?nd the stress concentration factor k at the center of the

beam(show calculations),de?ned as

K=σmax(beamwithhole)

σmax(beamwithouthole)

Which equals https://www.wendangku.net/doc/f811209980.html,ing theσof position B to present the structure change in?uence the strain obviously.

4.Does the presence of the hole a?ect stresses and strains at

points remote from the hole?And why?

It will a?ect the stresses and strains.According to the data, theεandσis larger than complete beam.

4.2Analysis

Comparing the beam with and without hole,we can?gure the strength of same material with di?erent structure.However,the beam with a hole could also increase the sensitivity.

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5Conclusion

In this experiment,there are some problems that we met.Firstly, after connecting the circuit,the bridge box could not balance at the0mV or nearly.Based on the elements and the measurement, the balance potentiometer could be the reason,where it increase or decrease direction could not meet satisfy.Second,in measurement, the output voltage?uctuated at a range at1.5mV approximately.

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