Memorandum

Date:October 14, 2004

To:Professor Hamid Hashemi

From:Justin Lai

RE:Laboratory 2-Torsion, Thursday Session

Laboratory Procedures

In this laboratory experiment, we conducted torsion tests to various materials to see the stiffness and strength properties under such conditions. Looking at the geometry, material properties, and loading conditions of the shafts, we predicted and attempted to verify the behavior of the structures. Also, we used the theory to design a helical coil spring with a desired spring constant.

Answers

  1. Shear modulus G for the following materials: O1 Tool Steel: 85.8 GPa; 6061-T6 Aluminum alloy solid shaft: 36.9 GPa; polycarbonate: .959 GPa
  2. For solid aluminum shaft:

Maximum shear stress theoretical: 2 MPa

Theoretical total angle of twist: 7.9E-3 rad

Experimental total angle of twist: 5.85E-3 rad

Between the theoretical and experimental values of total angle of twist, there is about 26% error. One reason for the error is purely in the imprecision of measuring displacement. The readings were eyeballed off a ruler for the aluminum shaft. Any variation in the reading could attribute to the error. Mechanically speaking, the shaft, in the setup, is allowed to freely rotate in addition to twisting. This would alter the true value of twist.

  1. For hollow aluminum shaft:

Maximum shear stress theoretical: 3.03 MPa

Theoretical total angle of twist: 9.77E-3 rad

Experimental total angle of twist: 1.26E-2 rad

Once again, there is significant error in the total angle of twist values, about 28% error. The same causes of error in the solid shaft can apply to the case of the hollow shaft.

When the same torque is applied to both shafts of same shape (note, not same amount of material), calculations show that the hollow shaft has a higher maximum shear stress and lower angle of twist, which implies larger stiffness. Based on this, we can conclude that the hollow shaft is a better use of material for the same torsional stiffness and shear stress carrying capability as the hollow shaft can use less material but provide the same structural properties.

Also, in the experiment, the situation is such that both hollow and solid shafts have the same amount of material. The results show that the hollow shaft is stiffer and has a lower maximum shear stress.

4. The chemical composition of steel wire, music spring quality, A 228 is carbon, manganese, phosphorus, sulfur, and silicon. Through softening and tempering the steel is tempered to increase the strength and toughness of the material. The steel is placed in oil of up to 350 degrees Celsius and then after 2 hours is cooled in room temperature air.

5.Young’s modulus for spring steel, A 228: 207 GPa

Shear modulus: 79 GPa

Yield Strength: 2.1 GPa

The shear modulus and Young’s modulus make spring steel a good choice for springs to store energy. Plotting torque versus shear strain or stress versus strain, we see that the slopes are the respective moduli. The area under these curves is the energy stored in the spring, when stretched. The higher the moduli, the higher the slope and area, and therefore the more energy stored.

6.To create a spring with k = 1 N/mm, with internal radius of 6E-4 meters and coil radius of 8.5 mm, you would make it 4 turns. However, in the lab, we were unable to test this spring. Instead, we took a spring of 32 turns and calculated the theoretical stiffness according to G, r and R. The theoretical stiffness was 97 N/m while the experimental stiffness was 139 N/m. This has significant error. First, we do not know how many times the spring has been used and whether it has been stretched beyond the elastic region. Though the measurement is once again relatively crude, it should not produce that great of an error. To improve determining the stiffness experimentally, one could increase the number of data points (apply more force values) and create the spring so that there is no possibility of wear and tear on the spring.

Lai 1