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KWAME NKRUMAH UNIVERSITY OF SCIENCE AND TECHNOLOGY
DEPARTMENT OF AEROSPACE ENGINEERING
AEROSPACE ENGINEERING LABORATORY II
AYIH KENNETH DONKOR
2695708
3/02/2011
TITLE
THE DEFLECTION OFA CLOSED OR OPEN COILED HELICAL SPRING
OBJECTIVE/AIM OF EXPERIMENT
TO CONFIRM THE THEORETICAL AND EXPERIMENTAL DEFLECTION OF A CLOSED OR OPEN COILED HELICAL SPRING
APPARATUS
The apparatus is basically a bench made up of two coils; a closed helical spring and an open spring - both of specific diameters. A hanger is mounted on the bench so as to allow for the placement of varying weights. Seven weights of 5 pounds each are provided to serve as an application of a required force. For a specified amount of force, the extension or displacement of any one of the springs can be measured using a scale provided on the bench setup. Also, vernier calipers are provided to measure the diameters of the spring and wires that make up the spring.
A summary of the apparatus used is shown below:
Helical spring Scale Hanger Loads Guide Vernier calipers
SCHEMATIC OF APPARATUS
PROCEDURE OF EXPERIMENT
1. The diameter of both springs and the wire of the spring are measured using the vernier calipers. Also, the number of coils in each spring is obtained.
2. After obtaining the specific details of both springs, the closed helical spring is unscrewed from the bench leaving the open helical spring in position.
3. The load –deflection readings both loading and unloading from zero loads to the 35th maximum load is obtained using 5lbs increments for the open helical spring.
4. The load –deflection readings is also obtained for the closed helical spring by screwing it into position and unscrewing from the bench the open helical spring.
5. The results of both springs are then recorded and tabulated.
RESULTS OF THE EXPERIMENT
HELICAL OPEN SPRING
Number of turns = 25 Mean diameter of the coil=38mm
Mean radius=19mm Shearing modulus of the wire=79.3GPa
Diameter of wire of spring=5mm
LOAD(N) Loading deflection(m)
∆×10−2
Unloading deflection(m)
∆×10−2
Theoretical loading
deflection∆×10−2m
0 0 0 022.27 0.330 0.432 0.49344.54 0.635 0.737 0.98666.70 0.940 1.092 1.48088.98 1.300 1.448 1.970
111.25 1.630 1.778 2.463133.51 1.980 2.108 2.966155.78 2.340 2.340 3.449
HELICAL CLOSED SPRING
Number of turns= 41
LOAD(N) Loading deflection(m)
∆×10−2
Unloading deflection(m)
∆×10−2
Theoretical loading
deflection∆×10−2m
0 0 0 022.27 0.229 0.229 0.80944.54 0.686 0.686 1.62066.70 1.270 1.270 2.42288.98 1.854 1.854 3.230
111.25 2.413 2.413 4.040133.51 2.997 3.277 4.848155.78 3.581 3.581 5.657
The theoretical values of loading deflection is obtained from the equation
∆=8N D3 P
Gd4
Where N= number of turns of coil
D=mean diameter of coils
G=shearing modulus of steel
d = diameter of the wire of the spring
P= weight in Newton
INTERPRETATION OF GRAPHS
From the graph of load (P) to loading and unloading deflection for an open coiled spring, there is a positive correlation between the load and loading deflection, indicating that for an increment in the weight of loads put on the hanger, there is a proportional increment in the extension of the spring. However, the load against unloading deflection graph follows a curve indicating the presence of some missing energy. The slope of each curve represents the stiffness of the spring is calculated as follows:
slope of load−loadingdeflection , S=δ PLδ ∆L
= 155.78−22.272.340×10−2−0.330×10−2=6642.3N /m
slopeof load−un loadingdeflection ,S=δ PU Lδ ∆U L
= 133.51−66.702.108×10−2−1.092×10−2=6575.8N /m
slopeof theoreticalload−loadingdeflection ,S= δ Pδ ∆
= 133.51−22.272.966×10−2−0.493×10−2
=4498.2N /m
For the graph of load to loading and unloading deflection for a closed helical spring, the same positive correlation is observed between the load and the deflection. The difference however lies in the fact that during unloading the graph seems to follow the same line during loading after the 133.51 load mark. This indicates the absence of no stored energy or the presence of little stored energy. The theoretical graph shows the behavior of the spring with no losses. The slope of the graphs is calculated as follows:
slope of load−loadingdeflection , S=δ PLδ ∆L
= 133.51−66.702.997×10−2−1.270×10−2=3868.56N /m
slopeof load−unloadingdeflection , S=δ PULδ∆UL
= 133.51−44.543.277×10−2−44.54×10−2=3433.81N /m
slope of theoreticalload−loadingdeflection ,S= δ Pδ ∆
= 133.51−22.274.848×10−2−0.809×10−2
=2754.1N /m
OBSERVATION
From the experiment, it was observed that as more weights were added or removed from the system, the extension of the spring increased or decreased respectively.
Also, it was also seen that the exact amount of length the by which the spring could extend was dependent on the stiffness of the spring. The stiffness of the spring also being dependent on whether the spring was closed or open.
Moreover, both springs returned to zero extension after the last load of 5 lbs was removed from the hanger and the extreme load of 35lbs did not exceed the elastic limit of both springs.
CONCLUSION AND DEDUCTION
From the following observations and the illustrated graphs, the following conclusions can be drawn:
The weight of loads acting on the spring is directly proportional to the extension of the spring. That is, by increasing the amount of force acting on the spring perpendicularly, the extension of each coil from its mean position also increases. Decreasing the amount of force on the spring also reduces the extension of each coil. This verifies Hooke’s Law.
For an open helical spring, more energy is stored in the spring during unloading as compared to a closed spring which stores little or no energy. This stored energy is calculated as the difference in areas between the curves of the spring in loading and unloading. Mathematically,
stored energy for open spring ,Es=0.195Nmstored energy for closed spring , Es=¿0.072Nm
The reason for such disparity in stored energy between the two springs is because of the difference in stiffness between the open and closed springs. For the open spring, a large amount of force is required to extend the spring by one meter- approximately 6600N whiles for the closed spring a smaller force – approximately 3400N – is required.
Moreover, for the open spring , there exists some distances between each coil which is indicative of the increased angle of twist as compared to the closed spring with reduced angle of twist. As such, a force applied to the open spring has more energy expended and stored as compared to the closed spring with less angle twist.
Energy stored∈spring , E=12P ∆
Thus, E∝∆An increased angle of twist means an increased distance between successive coils and thus increased energy.
PRECAUTIONS
When performing the experiment the following precautions should be taken.
The loads should be placed gently on the hanger and should not be dropped on it.When reading the scale, make sure the datum reading should be at zero for no load.There should be least contact with the system as possible.After taking readings for one spring, remove the hanger when unscrewing the spring out of position to avoid straining the positioned spring further.
APPLICATIONS
The applications of the helical spring are as follows:
1. The helical spring is used in the vehicle industry particularly in the suspension system of vehicles.
2. In its reduced form, it is used in clocks to provide a means of releasing energy at exact time intervals. For example, by releasing such energy, the gears in a clock are made to move at set paces thus depicting the second hand of a clock.
3. They are also used in foam industries to provide a means of suspension for mattresses and seats.
4. Helical springs are used in seismographs because of their sensitivity to slight distortions and shock waves. E.g. Zero- length springs
5. They are also used in gravimetric devices because of their sensitivity to changes in gravity. E.g. Zero- length springs
REFERENCES
www.wikipedia.org/wiki/Shear_modulus www.engineering toolbox.com/modulus-rigidity-d_946.html www.engineeringsedge.com