EXP 2 MOM
Transcript of EXP 2 MOM
MECHANICS AND MATERIALS LABMEMB221
EXPERIMENT 2 - TORSION TESTSEM 1 2015/16
NAME ID1) AHMAD ARIF BIN ZAKARIA ME0932332) KAVIRAJ A/L THIAGARAJAN ME0889723) UDHAYA SHARWIN ME088983 4) MUHAMMAD AZWAN MOHAMED MANSOOR ME094005
SECTION : 4 GROUP : 5
LAB INSTRUCTOR: Pn. SITI ZUBAIDAH BTE OTHMAN
DATE OF EXPERIMENT : 03/07/2015
DUE DATE : 10/07/2015
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TABLE OF CONTENT
NO. CONTENT PAGE1. TITLE PAGE 12. TABLE OF CONTENT 23. SUMMARY 34. OBJECTIVES 35. THEORY 46. EQUIPMENTS 57. PROCEDURES 78. DATA AND OBSERVATIONS 9-109. ANALYSIS AND RESULTS 12-1310. DISCUSSIONS 1411. CONCLUSIONS 1412. REFERENCES 15
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Summary
This experiment is to find the Shear Modulus, G of the given specimens through the
measurement of the applied torque and angle of twist. It also to understand the principle of
torsion test.
During this experiment, aluminium and brass were uses as a samples to demonstrate how
materials behave during testing conditions. The torque measuring unit should be calibrated first
before the torsion test was performed, and a graph of calibration was plotted. The torsion test
was conducted and the results was taken based on given formulas, certain calculations were
calculated. From the experiment done, it is known that the shear modulus for Aluminum and
Brass to be 26.11 Gpa and 39.6 Gpa respectively. The results has a little bit different with the
theoretical value, this may happen due to certain errors.
So throughout the experiment, the objectives have been achieved. We able to identify the
modulus of shear and also understand the principle of torsion test.
Objectives
To understand the principles of torsion test.
To determine the modulus of shear, G through measurement of the applied torque and
angle of twist.
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Theory
Torsion is a variation of pure shear where in a structural member is twisted, torsional forces
produce a rotating motion about the longitudinal axis of one end of the member relative to the
other end.
Normally in each test, the torque and twisting angle are measured mainly to determine the shear
modulus, G where the shear modulus G is calculated based on this formula:-
Where
T = Torque
J = Polar moment of inertia
G = Shear modulus
Φ = Angle after application of torque
L = Length of the specimen
d = Diameter of the specimen
r = Radius of the specimen
Specimen with various type of materials, different diameters and lengths are investigated. The
effective torque is recorded with the aid of a reference rod equipped with strain gauges. The
measured torque is displayed on the measurement amplifier. This also incorporates important
principles of electronic measurement of mechanical values into the experimental program. The
unit is primarily intended for practical laboratory experiments.
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EQUIPMENT/DESCRIPTION OF EXPERIMENTAL APPARATUS
The apparatus used consists mainly of :
1. Loading device with scale and revolution counter for twisting angle measurement
2. Torque measurement unit
3. Calibration device
4. Specimen (Aluminium and Brass)
5. Track base
6. Digital torque meter
Loading Device
The torsional loading is transmitted to the specimen
by a worm gear (1) and a hand wheel (4). The
twisting angle at the output and the input is read off
by the two 360° scales (2,3). At the input side of the
gear there is in addition a 5-digit revolution counter
(5) which shows the input revolutions 1:1. The
worm gear has a reduction ratio of 62. The
specimen’s hexagon ends are set into an axial
moveable socket (6) at the worm gear output end.
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Torque Measurement Unit
In this experiment the toque will be measured by a
reference torsion rod and strain gauges. The specimen is
mounted on one side to the loading device and on the
other side to the torque measurement device.
The load torque applied to the specimen produce shear
stresses in the measurement torsion rod. These shear
stresses are proportional to the load torque. Strain gauges
are used for detecting the shear stresses.
Specimen
Figure 2.2 : Sample Specimen
Technical Data
General data
Main dimension : 1400 x 350 x 300 (mm)
Weight : 25kg
Loading device
Worm gear reduction ratio : 62
Revolution counter : 5 digit with reset
Output scale : 360˚
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Input scale : 360˚
Indicator : Adjustable
Torque measurement unit
Range : 0 – 30 Nm
Display : 6 digit, LED 14 mm
Temperature operating range : 0 – 50 ˚C
Power supply : 230V, 50/60 V
Calibration device
Maximum load : 30 Nm
Load increment : 2.5 Nm
Procedure
a) Calibration
I. The read out of the amplifier was set to zero
II. The torque measurement unit was connected to the measurement amplifier
III. The measurement amplifier was switched on at the back of plane
IV. Press and hold V button and P button to set the read outs to zero. There should no
be load torque
V. The load torque was increased by 5 Nm and the read out was noticed
VI. Check the offset after reload and set it to zero if necessary
b) Performing the test
Mounting the specimen
I. Short specimen is used in this experiment
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II. The specimen was mounted between the loading device and torque-measuring
unit
III. 19mm hexagon socket was used
IV. Make sure that the shifting holder of the load device is in the mid-position
V. Make sure that there is no preload on the specimen. If necessary turn the hand
wheel at the input of the worm gear until the read out of the amplifier is zero
VI. Both indicators at the input and output shaft of the worm gear was set to zero
VII. The dial gauge of the compensation unit was set to zero. Hence turn the turnable
scale
VIII. Revolution counter was reset
Loading the specimen
I. The hand wheel at the input gear was turned clockwise to load the specimen. Turn
it only for a defined angle increment
II. Choose an increment of a quarter rotation (90°) for the first rotation, for the
second and third rotation of a half-quarter (180°) and the 4th to 10th rotation of one
rotation (360°)
III. Divide the rotation at the input by reduction ratio of 62 to calculate the twist angle
at the specimen
IV. Fracture will occur at 100-200 rotations.
V. After each angle increment, the deformation of the measuring torsion was
compensated.
VI. The torque value was read from the display of the amplifier and note is together
with the indicated twist angle.
VII. The results was tabulated
VIII. The experiment was repeated with other specimen
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DATA AND OBSERVATIONS:
a) Calibration Test
The length of lever bar, Ɩ = 500mm = 0.5m.The applied load torque is calculated using the equation of moment which is Moment = Force x Distance
Load (N) Applied Load Torque (Nm) Amplifier Torque (Nm)
5 2.5 2.25
10 5.0 4.85
15 7.5 7.20
20 10.0 9.60
25 12.5 12.00
30 15.0 14.60
35 17.5 17.15
40 20.0 19.65
45 22.5 22.35
50 25.0 24.65
55 27.5 27.65
60 30.0 29.70
Table 1: Calibration results table
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b) Testing on Samples (Aluminium and Brass)
(Both of length, L =115mm = 0.115m):
i. Aluminium (diameter, d1 = 6.2mm = 0.0062m)ii. Brass = (diameter, d2 = 6.2mm = 0.0062m)
Rotation Angle of Gear Input
(° )
Torque, T (Nm) Angle of twist, θ (°)
Angle of twist
(Radian)Aluminium Brass
1 90 1.20 1.80 1.45 0.0253
180 2.25 3.25 2.90 0.0506
270 3.25 3.35 4.35 0.0760
360 3.70 3.50 5.80 0.1012
2 540 3.85 3.65 8.70 0.1518
720 3.85 3.90 11.61 0.2026
3 900 3.90 4.64 14.52 0.2534
1080 4.50 5.35 17.42 0.3040
4 1440 7.75 10.0 23.23 0.4054
5 1800 11.60 12.60 29.03 0.5067
6 2160 13.55 13.40 34.84 0.6081
7 2520 14.25 13.80 40.65 0.7095
8 2880 14.25 13.85 46.45 0.8107
9 3240 14.70 14.25 52.26 0.9121
10 3600 14.95 14.40 58.06 1.0133
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Table 2: Samples Testing Results
Graph 1
Graph 2
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Graph 3
Analysis and Results
Calibration Curve calculation:
Gradient of the curve = (24.65-4.85)/ (25-5)
= 0.99
Theoretically the gradient should be = 1.000
Percentage error = (1.000 - 0.99 / 1.000 ) x100 = 1%
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Calculation of G for Aluminium:
Gradient = (3.7-1.2)/(0.1012-0.0253) = 32.94
Polar moment of inertia, J = (pi x (diameter)4 ) / 32 = (pi x 0.00624) / 32 = 1.4507 x 10-10 m4
Hence the shear modulus, G = TLo / J ϕ = 32.94 X 0.115m / ( 1.4507x10-10m4)
G value for Aluminum = 26.11 GPa
Comparing with theoretical value : 27Gpa
Hence, percentage error = ((27 – 26.11) / 27) x 100 = 3.3%
Calculation of G for Brass:
Gradient of the curve is = T / ϕ = (10-5) / (0.4-0.3) = 50
Polar moment of inertia, J = (pi x (diameter)4 ) / 32 = (pi x 0.00624) / 32 = 1.4509 x 10-10 m4
Hence the shear modulus, G = TLo / J ϕ = 50 X 0.115m / (1.4509 x 10-10 m4)
G for Brass = 39.6 GPa
Comparing with theoretical value : 39 Gpa
Hence, percentage error = ((39 – 39.6) / 39) x 100 = 1.54%
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Discussion
Based on the analysis of the results, the value of G for aluminium and brass is 26.11 GPa and
39.6 GPa which is a little bit different compared to the theoretical ones. And this may due to
errors such as human error (parallax error) or this tools/equipment that used is not accurate. From
this experiment it also shown that aluminium is more ductile than brass as aluminium need less
torque to twist
The difference between specimens tested are its Modulus of Shear , G. Both materials gave us different values and this indicates that both does not behave the same when subjected to constant torsional loading. The graphs of actual torque value vs the revolution at gear output in radian also displays the trend of the curve for both materials, vividly enough for us to inspect the behaviour at various points of loading
Two common mechanical parts that are subjected to torsion are the transmission shafts in
vehicles for transmitting power from the engine and as simple as the turning of a screwdriver to
turn a screw. The torque makes the shaft twist and at the one end rotates relative to the other
inducing shear stress on any cross section. In spring, when the spring is compressed or
elongated, it created torsion due to the deflection.
Conclusion
The objective of this experiment is to determine the modulus of shear, G of both the specimen
which is aluminium and brass are achieved. This experiment was done through measurement of
applied torque and angle of twist. The calculations was done using the given formulas and from
the calculation, it was found that, there is a little bit error in finding the shear modulus for both
the specimen. The principle of torsion is clearly understood from the experiment.
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Referance
Semester 1 2015/2016. MEMB221 Mechanics and Material Laboratory Manual COE, Uniten, pp 14-19
Ferdinand P.Beer, E.Russell Johnston, Jr., John T.DeWolf. 2004. Mechanics Of Materials. 3rd Edition. McGraw Hill. pp 746.
INTERNET : http://www.engineeringtoolbox.com/modulus-rigidity-d_946.html https://en.wikipedia.org/wiki/Shear_modulus.
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