Texas Tech University

Torsion TestExperiment

Material & Mechanics LaboratoryME 3228-001Group 509Kathryn JohnsonEric DuncanJason RobisonBibin MathewJon DaubSept/12/2015Submitted to: Pawn Maharjan

Summary

In calculating the torsion of a rod there are many different properties to consider like the length, the force applied and the angle of deflection. In the torsion experiment a rod of either steel or brass was placed with one end in a fixed chuck and the other end was placed in a rotating chuck then a force was applied to the rod. The objective of the torsion experiment was to determine the effect of applying a torsional load to a circular section [1]. In the first experiment the steel rod was placed in the chucks at a set length and a varying torque was applied to measure the angle of deflection. Experiment 1 was repeated for the brass rod. For Experiment 2 a brass rod was placed in the chucks and the applied torque was kept constant while the length of the rod was varied to measure the angle of deflection. The results for experiment 1 show how the torque applied relates to the angle of defection. The results for experiment 2 shows the effects that the length of the rod has on the angle of defection. The results of the torsion test show that the torque applied and the length of the rod are linearly proportional to the angle of defection.

Test Setup & Procedure

For the Torsion Test, the experiments were done to determine the effects of applying torsional load to a circular section. The lab consisted of a test frame with rotating chucks at the end that were used for gripping the circular rod. Two circular rods were used for the lab, both having the same cross-section geometry and the same dimensions, but one made of steel and the other made of brass. Both of the rods were 0.5 m in length. Torsion Test Lab consisted of two different experiments. In the first experiment, the length of the rod was kept constant, while the applied torque varied in each test. These tests were be done on both brass and steel rod. In the second experiment, a constant torque was applied on the rod, while the length of the rod varied in each test. Only the brass rod was used for the second experiment. Before starting the experiment, it is always important to wear any safety equipment required and follow all the safety precautions. Visually inspect all parts and check all the electrical connections before starting the experiment. In experiment 1, the length of the rod was kept constant, and the applied torque varied incrementally. The brass rod was mounted to the test frame with the rotating chucks, as shown in figure 1. The digital force display was set at 0 N using the dial, and the rod had 0 angular deflection on the angular scale. A small torque was applied to the left hand chuck until it read 1 N on the digital force display. After measuring the angular deflection, the torque applied was increased incrementally. After measuring all the angular deflections required for the brass rod, the same steps were repeated for the steel rod to find its angular deflection. Figure 1

In experiment 2, the torque was kept constant, while the length of the brass rod varied in each test. The constant force that was applied on the rod was 3 N. The brass rod was mounted to the test frame with the rotating chucks, as shown in figure 1. The digital force display was set at 3 N using the dial, and the rod had 0 angular deflection on the angular scale. The torque arm was set at 0.3 m in length at start, with 3 N constant torque applied to the rod. After measuring the angular deflection, the length of the torque arm was increased incrementally for the remaining tests.

Results

The intentions of this experiment was to determine the effects of applying a torsional load to a circular cross-section of common engineering materials. After all materials were measured, the data was collected and recorded. First experiment the length of the two rods were kept at a constant length, then the angular deflection was measured as the force was increased. Second experiment the brass rod was increased in length and the force was kept constant, then the angular deflection was then measured again. From the collected data the polar moment of inertia was calculated using equation 1, with the measured rod diameter and rod length. Some values were converted to the correct units in order to full fill the formula requirements. Equation 1

Table 1 Torque, Angular Deflection, TL, and J for the Steel RodTorque (Nm)Angular Deflection, (rad)TL (Nm)J (Nm)

00.0000

0.050.040.01553.46978E-13

0.10.070.0315.55165E-13

0.150.090.04656.93957E-13

0.20.110.0629.02144E-13

0.250.130.07751.04094E-12

Figure 1Table 2 Torque, Angular Deflection, TL, and J for the Brass RodTorque (Nm)Angular Deflection, (rad)TL (Nm)J (Nm)

00.0000

0.050.090.01556.93957E-13

0.10.130.0311.04094E-12

0.150.180.04651.45731E-12

0.20.240.0621.87368E-12

0.250.280.07752.22066E-12

These values were calculated in order to give a direct way to calculate the shear modulus using a length of 310mm. The slope of the graph in figure 2 gives the calculated shear modulus.

Figure 2

Table 3 Angular Deflection with varying lengthLength (m)Angular Deflection ()

0.309.5

0.3510.5

0.4011.5

0.4513

0.5015

Figure 3

Table 4 Published and Experimental Shear Modulus And Percentage of Error for Both RodsBeamShear Modulus (Gpa)Percentage of Difference

ExperimentalPublished

Steel74.479.66.53

Brass34.8388.42

The published shear modulus was provided in the published data given. The percent difference was calculated using equation 2 with the values recorded in lab and values published data.

Equation 2

The experimental shear modulus was calculated using the above values for TL and J by plugging in to equation 3. Equation 3

Discussion

The data from the experiment can be seen in Table 1.1, below. After the torque and angular deflection were collected, these numbers are then used to find TL and as shown in Table 1.2. Plotting the applied torque and angular deflection, as seen in Figure ____, it is evident that these two variables are linearly proportional to each other. As more torque was applied the angular deflection also increased.

Table 1.1 Torque and Angular Deflection for Steel RodForce (N)Torque (Nm)Angular Deflection ()

000

1.052.5

2.14

3.155

4.26.5

5.257.5

All calculations for the data can be found in the Appendix. From the calculations the steel rod has a shear modulus of 74.4 GPa and the brass rod has a shear modulus of 34.8 GPa. These results are fairly close to the published shear modulus of 79.6 GPa for steel and 38 GPa, for brass. These discrepancies were caused from many variables including misreading the equipment, improper calibration and inconsistencies in the rod from fatigue. The reason for the difference in shear modulus was from the different properties of the metals including the diameter, which in the steel rod was much harder and stronger allowing it to resist angular deflection more than the soft brass rod. There are different applications where both of these properties would be useful. For instance, in the oil field, when drilling deep into the earth one would want to use a metal with a high shear modulus to minimize torque. On the other hand, a lower shear modulus would be ideal for torque springs. These can be found in suspensions of a car to dampen the bumps in the road; it is also used in the sway bar of a car which adds more traction around sharp turns.Experiment 2The data in this experiment can be found in Table 1.3. When looking at the angular deflection and length plot in figure it looks very similar to the plot found in figure. These two variables are linearly proportional to each other. These properties can be used to ones advantage. Like in the examples discussed above, if the suspension torsion springs are longer that will allow the rider to experience a softer ride as more force will be translated into the torsion of the bar. However, with the oil drilling example if the drill is too long, that can cause unwanted torque which could lead up to breaking the drill. If the length cannot be changed but the application requires a more ridged bar, then either decreasing the torque, and increasing the diameter will result in less angular deflection.

Table 1.3 Length and Angular Deflection for Brass RodLength (m)AngularDeflection ()

0.309.5

0.3510.5

0.4011.5

0.4513

0.5015

Conclusion

The purpose of the torsion experiment was to study the effects of an applied torsion on a circular rod [1].The objective was to record the angular deflection to see its linear dependence on other variables and ultimately determine the objects shear modulus. The angular deflection was recorded during the first case while the torsion was increased incrementally, and then the force was kept constant and the length of the rod was lengthened incrementally. The values of the angular deflection for both rods recorded during the first experiment showed a linear dependence on the torsional force as it was increased. Both sets of values also yielded a shear modulus close to the true value given for each material. The angular deflection values recorded while the force was kept constant and the length nominally increased showed a linear dependence on length as well. The tests successfully confirmed the angular deflections dependence on force or length while producing realistic shear modulus values for the materials.

References

1.

Appendix

Table 5 Steel Rod:Dimensions:Diameter= 3mmLength= 310mmPolar Moment of Inertia (J) =Torque= Force (N) x Torque Arm Length (0.05m)Force (N)Torque (Nm)Angular Deflection ()

000

10.052.5

20.14

30.155

40.26.5

50.257.5

Table 6Brass Rod:Dimensions:Diameter= 3mmLength= 310mmPolar Moment of Inertia (J) =Torque= Force (N) x Torque Arm Length (0.05m)Force (N)Torque (Nm)Angular Deflection ()

000

10.055

20.17.5

30.1510.5

40.213.5

50.2516

Table 7Brass Rod:(Keep Force Constant) F=3NLength (m)Angular Deflection ()

0.309.5

0.3510.5

0.4011.5

0.4513

0.5015

8