- T 0 B A T B Figure 1 Figure 2 View On Section A A Figure 3 A B Rigid Base Headstock I H 1 Coarse Protractor Scale F 1 (55.24 KiB) Viewed 56 times
- T 0 B A T B Figure 1 Figure 2 View On Section A A Figure 3 A B Rigid Base Headstock I H 1 Coarse Protractor Scale F 2 (102.84 KiB) Viewed 56 times
- T 0 B A T B Figure 1 Figure 2 View On Section A A Figure 3 A B Rigid Base Headstock I H 1 Coarse Protractor Scale F 3 (21.46 KiB) Viewed 56 times
- T 0 B A T B Figure 1 Figure 2 View On Section A A Figure 3 A B Rigid Base Headstock I H 1 Coarse Protractor Scale F 4 (108.36 KiB) Viewed 56 times
- T 0 B A T B Figure 1 Figure 2 View On Section A A Figure 3 A B Rigid Base Headstock I H 1 Coarse Protractor Scale F 5 (156.46 KiB) Viewed 56 times
- T 0 B A T B Figure 1 Figure 2 View On Section A A Figure 3 A B Rigid Base Headstock I H 1 Coarse Protractor Scale F 6 (102.71 KiB) Viewed 56 times
- T 0 B A T B Figure 1 Figure 2 View On Section A A Figure 3 A B Rigid Base Headstock I H 1 Coarse Protractor Scale F 7 (45.64 KiB) Viewed 56 times
T 0 B A T B Figure 1 Figure 2 View on Section A-A Figure 3 A. B. Rigid base Headstock I: H. 1. Coarse protractor scale Fine protractor scale
C. D. E. F. G. Straining head Balanced torque arm Circular spring balance Horizontal hand wheel Spirit level J. K. L. M. N. Torsiometer Specimen Torsiometer scale Straining hand wheel Spacer From Figure 1 and Figure 2, the correlation between 0 and Y can be obtained. If the magnitudes of both angles are small: Length of arc, AB= 10 = LY (1) If the shaft material does not exceed its elastic limit, it follows Hooke's Law: Shear stress, T=GY (2) The Modulus of Rigidity (Shear Modulus), G, is one of the mechanical properties of a material that can be determined by experiment. Substituting the value of t from Equation (2) into Equation (1) and rearranging the equation: T GO L (3) The torque on the shaft is equivalent to the summation of the moments, which are due to the tangential stresses on the elements with radius r. Therefore, total torque: T= Sc(2nrdr) (4) By substituting from Equation (3) into Equation (4): GO T= co S(2order) or, GO T L where ) = constant, for the cross-sectional of area of shaft. It is calculated by: (5) J = L" (27rºhr = +R"_AD" ( 2 32 (6) where R = radius of shaft D = diameter of shaft τ Combining Equation (3) and Equation (5), gives the Universal Theory of Torsion Equation: T GO J L (7) where: G = Modulus of Rigidity (N/m? or Pa) T = torque (Nm) L = length of shaft (m) r
t = shear stress (N/ mor Pa) at radius r 0 = angle of twist (radian) J = torsional constant (m) r=radius of element (m) Then, from Equation (7), the value of G is: ΔΤ (L G A0J (8) where (AT/00) is the slope of graph of torque versus angle of twist for the elastic range.
6.0 RESULTS TABLE 1 : SPECIMEN DATA MEASUREMENT NO. 1 2 DIAMETER OF SHAFT (MM) 6.2 6.18 6.10 6.10 6.15 GAUGE LENGTH (MM) 50 50 50 50 50 3 4 AVERAGE Total Length = 154.00mm Mean Diameter = 6.15mm Parallel Length = 70.05mm TABLE 2 : RESULTS OF TORSION TEST (a) When material is still elastic Torque, T (Nm) Angle of twist (degree) 0 1 2 3 4 5 6 7 Angle of Twist (radian) from torsiometer 0 0.009 0.0165 0.025 0.033 0.0415 0.0505 0.0595 0.0685 0.078 0.088 0.098 0.108 0.118 0.128 0.137 0.139 0.1393 0.1393 0 2.1 3.8 5.5 7.1 9.0 10.6 12.1 13.4 14.6 15.5 16.2 16.9 17.5 18 18.3 18.6 19.0 19.4 8 9 10 11 12 13 14 15 16 17 18
(b) When material has yielded Torque, T (Nm) 19.5 20.3 21.0 21.0 21.5 21.5 21.0 21.0 21.0 19.4 21.4 21.4 21.4 21.4 21.4 21.4 21.4 21.4 21.4 21.4 21.4 21.4 21.5 21.6 21.6 21.6 21.6 21.6 21.6 21.6 21.6 21.6 21.6 21.6 21.6 21.6 21.6 21.6 21.6 21.6 21.6 21.6 21.6 Angle of Twist (degree) 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 620 660 680 700 720 740 760 780 800 820 840 860 21.6 21.6 21.6 880 900 920 940 960 4.2 0
6.0 RESULTS a. Plot the graph (Graph 1a) of Torque versus Angle of Twist (from torsiometer L) for the elastic region. Use the slope of this graph to determine the value of the modulus of rigidity, using Equation (8). From this graph determine the torque and then calculate the shear stress at the limit of proportionality. Plot another graph (Graph 1b), similar to Graph 1a, by using the angle of twist from the machine dial 1. Use the same procedure as above to calculate the modulus of rigidity, remembering that meter I measures over the parallel length. b. Plot the graph (Graph 2) of Torque versus Angle of Twist for the entire range, for the parallel length of the specimen. Identify and label the yield torque, ultimate torque and failure torque. C. Calculate the shear stresses, t, using Equation (7) and the corresponding values of shear strain, y, by using Equation (1), for the elastic region. Tabulate the result of these calculations in Table 3. Plot the graph (Graph 3) of t versus y. Use the slope of the graph to determine the value of G. d. Sketch the form and contour of the fractured surface of the specimen. From your observation, comment on the specimen material. e. Tabulate the summary of your results in Table 4. In your report include all data, equations, sample calculations and discussion you believe are necessary to demonstrate that you have achieved the objectives of this experiment.
7.0 DISCUSSION a. b. Discuss the results obtained from the test. Obtain from published data the shear modulus, yield shear stress and ultimate shear stress for the material being tested. Compare the published values with the experimental values. Comment the factors that affect the test accuracy. Discuss of errors involved in determining the modulus of rigidity using the angle of twist from the machine dial (t), and compare the result obtained with the value found by using the torsiometer. C. d. d.