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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