Torsion Experiment
MAE 3181 Materials and Structures Laboratory
Laboratory Report #4
Helicoidal Spring – Torsion Experiment
Summary
Torsion is the action of twisting an object relative to another point; in this experiment, an electromechanical testing machine applies a controlled axial load to a steel spring. Strain and load data measurements taken from this test may be utilized to analyze various important variables such as moment, torque, and shear. Furthermore, load and strain may be plotted to analyze the relationship for each strain gauge; the relationship between applied lied and displacement is seen to be linear through plot generation within Microsoft Excel.
1. Objectives of the Laboratory Experiments
For the torsion experiment, the objective was to obtain load vs. displacement and strain data in order to analyze the results within a program such as Microsoft Excel and determine spring constant for the helical spring. The experiment is performed through the use of an electromechanical testing machine which applies a controlled axial load to a steel spring. Strain gauges attached to this spring are utilized in order to measure surface strains of the coil for the loads applied, which can be used to determine principle strains and variables such as torque, bending moment, shear force, and axial force. These variables are important towards analyzing material properties of the given specimen within the testing machine.
2. Experimental Setup
In setting up the experiment, the user must ensure spring ends are encased within concrete blocks (for safety purposes; strain energy will not be released suddenly) which are attached to an actuator and testing machine. Strain gauges are also attached to measure surface strains of the coil for the loads applied (Figure 1). The user must ensure a ball bearing is placed below the testing machine head; this acts as a spherical joint that ensures a force, and no moment, is applied (Figure 2 and 3).
The data from the testing machine is collected through a National Instruments Data Acquisition Module connected to a computer; a LabVIEW program must be setup to control the testing machine.
3. Experimental Procedure and Results
First, ensure the cement blocks and spring are correctly mounted within the testing machine; a ball bearing should be present, so no moment is generated; only a compressive load applied by the electromechanical testing machine. The LabVIEW program must be started so compression of the steel spring may occur. Once load applied has exceeded 1000 lbf, the program may be stopped. Data will be output within two .txt files which may be opened with Notepad. One data file contains Load vs. Displacement data while the second data file contains load values in the first column and strain values in the remaining six columns. Columns two to four contain strain values for the first strain gauge, while columns five to seven contain strain values for the second strain gauge. A possible source of error may be present if the ball bearing did prevent moment generation, however, in the case of our experiment the steel ball provides a point load causing moment to be negligible.
4. Data Analysis, Interpretation, and Discussion
As seen in Figure X, the load and displacement values gathered through the testing machine’s data acquisition module may be used to formulate a graph with a linear trendline (Figure 4); there is a direct linear relationship between the load applied and crosshead displacement.
Displacement vs. Load Applied
The slope of the line is the spring constant of the steel coil, 1576.7 lbf/in. The strain gauge data acquired may be utilized to generate similar graphs utilizing Microsoft Excel (Figure 5,6,7,8,9,10).
Strain vs. Load Gauge 1 1
Strain vs. Load Gauge 1 - 2
Strain vs. Load Gauge 1 3
Load (lbf)
Strain vs. Load Gauge 2 - 1
Strain vs. Load Gauge 2 2
Load (lbf)
|
Strain Gauge |
Load (lbf) |
Strain |
|
– 1 |
840 |
0.00084 |
|
– 2 |
840 |
8.4e-5 |
|
– 3 |
840 |
-0.000588 |
|
– 1 |
840 |
0.000504 |
Strain vs. Load Gauge 2 - 3
Table I – Strains at 840 lbf Applied Load
|
2 – 2 |
840 |
-0.000588 |
|
2 - 3 |
840 |
-8.4e-5 |
From the strain graphs and data, principle strains are found to be 0.000016, 0.00037, and 0.00047. Torque is found through equation 1:
T = P*d (1)
T = (840*.85) = 714 lbf*in
Moment = P*D/2 (2)
M = (840*5.75)/2 = 2415 lbf*in
σ = P/A (3)
σ = (840/ (π * .85²/4)) = 48.3 lbf/in^2
Axial force = σ * Area (4)
P = (48.3 * (π * .85²/4)) = 840 lbf
Principal strains and principal directions at locations 1 and 2 may be found assuming Young’s Modulus is 30 ksi and Poisson’s ratio is 0.3. The predicted and experimentally determined results are very similar.
5. Conclusions
In conclusion, strain values corresponding to applied load may be acquired through a testing machine applying a compressive force to a metal coil, causing displacement. These values may be analyzed through Microsoft Excel to determine the relationships between each data set. These graphs and data aid in determining values such as torque, moment, shear, and axial force which are crucial to understanding load application and torsion.
6. Recommendations
In future experiments, it would be beneficial to ensure the ball bearing is preventing a moment from forming by having it centered below the testing machine. This would eliminate any possible error presented by the formation of a moment.
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