1.1 Aim
Torsional Testing of Brass, Steel and Aluminum
1.2 Objective
 Learn the basics of torsion theory
 Learn and practices the principle of torsion testing,
 Find the maximum shear strain, shear stress and modulus of rigidity
 Establish the relationship degree of rotation and torque applied for the material under observation
 Understand the differences between material properties of different material
 Able to select material for different engineering components which are under torsion
2.0 Theory
2.1 Basic Torsion Theory
R.S. Khurmi & J.K. Gupta (2005) stated that Ii many engineering applications engineering components are subjected to torsion. So it is compulsory for an engineer to understand the basics of torsion theory and learn how a material of engineering component will act under torsion stresses. (pg 120121)
R.S. Khurmi & J.K. Gupta (2005) stated when an engineering component is subjected to twisting moment or torque then it is said that the engineering component is under torsion. Stress produce as a result of torsion are called torsional shear stress. Torsional shear stresses are maximum at outer surface ad minimum at the central axis. (pg 120121)
R.S. Khurmi & J.K. Gupta (2005) stated as in our case one end of a shaft is fixed and other is subjected to external torque. As said earlier that stresses produce by the torque will be zero at central axis and maximum at the outer surface. The maximum value of this torsional stress can find out by the following formula
τ/r= T/J
In above equation τ is the torsional stresses produce in the shaft, r is the radius of the shaft, T is the torque applied at the end of the shaft and J is the second polar moment of inertia of the shaft. Second polar moment of inertia of the shaft can be finding out by following formula where D is diameter of the shaft.
J= (π ×D^4)/32
This first equation can be rewritten in the form of angular displacement, modulus of rigidity and length of shaft and follow.
τ/r= Gθ/l
In above equation G is the modulus of rigidity, l is the length if the shaft and θ is the angular displacement as a result of applied torque. First and third equation can be combined to an equation through which we can find the modulus of rigidity of any material under observation. (pg 509515)
G= T/θ×l/J
2.2 Torsion Testing Machine Calibration
According to T. Udomphol (n.d) follow are the steps that should be followed to calibrate the torsion testing machine
 Take calibrating arm and put in on square end of torque shaft and by adjusting hand wheel level the shaft.
 Set SI unit on digital meter to measure torque
 Adjust the digital meter to zero turning the knob
 Put five kg on calibrating arm and make the dial gauge reading to 0 using hand wheel.
 24.5 should be reading on the digital meter
 Remove the load and reading should come back to zero
 Plot graph between torque reading and applied torque and calculate slope which have to be 1
3.0 Procedure
According to T. Udomphol (n.d) following is the procedure of operating Torsion Testing machine
 Measure the specimen initial length, initial diameter and initial gauge length and put these values on the provided table shown below.
Figure 1 specimen
Table 1Specimen Dimensions
Dimensions

Brass

Steel

Aluminum

Diameter (mm)

6

5.53

6

Length (mm)

76.5

77.09

77.15

 Mark a line along the length of specimen with the help of permanent pen. This will help us to measure the rotation during twisting.
 Calibrate the torsion testing equipment as explained above
 Use the hexagonal sockets to grip specimen on torsion testing machine
 Fix one end of specimen on input and other end on torque shaft and apply small preload
 Set torque meter to zero
 Start the process and twist the specimen with the strain increment of 0.5 degree until failure of specimen
 Record all experimental data in the provided table
 Note: before taking reading make sure that it’s not fluctuating and leveled off
 Construct relationship between degree and torque
 Establish a relation between shear strain and shear stress
 Calculate the theoretical values of second polar moment of inertia and modulus of rigidity
 While testing, following sequence (as show in table) of applying the angular displacement should be considered.
 Discuss and conclude results
Table 2angular displacement and torque
From

To

Increment

0

6

0.5

6

10

4

10

120

10

120

420

60

420

Failure

120

4.0 Results
Experiment was performed according to the steps mentions above and all the data obtain as a result of experiment is arranged in the table below.
Table 3Experimental Results
Angular Deflection

Torque Transmitted (Nm)
 
Degree

Radian

Brass

Steel

Aluminum
 
0.5

0.008727

0.81

1.2

0.06
 
1

0.017453

1.11

1.83

0.47
 
1.5

0.02618

1.47

2.46

0.76
 
2

0.034907

1.84

3.20

1.01
 
2.5

0.043633

2.72

3.93

1.32
 
3

0.05236

2.70

4.72

1.65
 
3.5

0.061087

3.11

5.54

1.99
 
4

0.069813

3.36

6.40

2.32
 
4.5

0.07854

3.98

7.27

2.66
 
5

0.087267

4.41

8.18

3.00
 
5.5

0.095993

4.84

9.15

3.33
 
6

0.10472

5.27

10.05

3.64
 
10

0.174533

7.21

14.14

5.92
 
20

0.349066

9.86

15.84

7.74
 
30

0.523599

10.76

16.32

8.07
 
40

0.698132

11.22

17

8.17
 
50

0.872665

11.48

17

7.93
 
60

1.047198

11.45

17.24

8.10
 
70

1.221731

11.88

17.06

8.2
 
80

1.396264

12.11

17.51

8.4
 
90

1.570797

12.30

17.68

8.24
 
100

1.74533

12.48

18.00

8.7
 
110

1.919863

12.60

18.22

8.7
 
120

2.094396

12.70

18.70

8.7
 
180

3.141594

13.47

19.10

9.02
 
240

4.188792

13.80

19.60

9.11
 
300

5.23599

14.47

19.60

9.48
 
360

6.283188

14.98

19.60

9.51
 
420

7.330386

15.36

20.17

9.71

very usefully thanks
ReplyDeletehow to get the value of 45960 in the equation T/0?
ReplyDeleteWheres's the calculation for steel?
ReplyDelete