Two Report Assignment for ( SkyEssays )
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exp6.pdf
MECHANICS LAB AM 317
EXP 6 SPRINGS IN SERIES AND PARALLEL
I. OBJECTIVES
I.1 To study the relationship of springs connected in series and parallel and determine the equivalent spring constant.
I.2 To study the unsymmetric loading of parallel springs.
II. BACKGROUND
Springs are devices that can store and release energy. Because of these properties, springs are very important in engineering. It is therefore essential that engineers understand the different types of spring combinations behave when loaded.
Springs can be combined in series, parallel and in a combination of series and parallel. Each spring or spring system can be characterized by its spring constant k. The spring constant can be determined by use of Hooke’s Law:
∆= kF 6.1
where: F = applied force ∆ = the resulting displacement
III. EQUIPMENT
III.1 Assorted springs, hooks, and aluminum bars.
III.2 Steel scales
III.3 Steel frame
IV. PROCEDURE
IV.1 Determine the spring constant for each individual spring using Eq. 6.1. When determining the spring constant, be sure the spring has an initial load sufficient to separate the coils and remove the pretension. Determine the deflection due to several loads and take the average value for the spring constant, k. You may fit a linear trendline to the force-deflection data to
R. Ehgott (Created) 2/7 04/07/01 T. Hao (Revised) 08/07/16
obtain the spring constant. k will be the slope m of the trendline ( bmxy += ) and b is the initial preload required to separate the coils of the spring.
IV.2 Set up the spring system shown in Figures 1, 2 and 3 to determine the equivalent spring constant for each system.
IV.3 Construct the spring system shown in Figure 4 and determine the equivalent spring constant. You will need to use two pairs of springs with matching spring constants to obtain good results.
k1
k2
FT
21 FFFT == 6.2
212
2
1
1 21 k
F k F
k F
k F TT
T +=+=∆+∆=∆ 6.3
2121
21 11
1
kkk F
k F
FFF k
TT
TT
T
T eq
+ =
+ =
∆+∆ =
∆ = 6.4
Figure 1 Springs in Series
k1 k2
FT
∆ 1
∆ 2
a b
L
21 ∆=∆=∆T 6.5
TTT kkkkFFF ∆+∆=∆+∆=+= 21221121 6.6
21 21 kk
kkF k
T
TT
T
T eq +=∆
∆+∆ =
∆ = 6.7
Location of when TF 21 kk ≠ :
L kk
k a
21
1
+ =
Figure 2 Springs in Parallel ( 21 ∆=∆ )
R. Ehgott (Created) 3/7 04/07/01 T. Hao (Revised) 08/07/16
k1 k2
FT
∆ 1 ∆
2
a b
L
21 FFFT += 6.8
TFL b
F =1 ; TFL a
F =2 6.9
2 2
2
1 2
2 2
2
1
1 21
k F
L a
k F
L b
k F
L a
k F
L b
L a
L b
TT
T
+=
+=∆+∆=∆
6.10
2
2
1
2
2
2 2
2
1 2
2
k a
k b
L
k F
L a
k F
L b
FF k
TT
T
T
T eq
+ =
+ =
∆ = 6.11
Figure 3 Springs in Parallel – Unsymmetric Case ( 21 ∆≠∆ )
k1 k2
FT
k3 k3
k1
33121
11 1
kkkkk
keq
+ +
++
= 6.12
Figure 4 Springs in Series and Parallel
R. Ehgott (Created) 4/7 04/07/01 T. Hao (Revised) 08/07/16
V. REPORT
V.1 Plot the force versus deflection for each individual spring and report the stiffness for each spring in a table.
V.2 Calculate the theoretical equivalent spring constants given by Eqs. 6.4, 6.7, 6.11 and 6.12 and compare them to the experimental values determined. Report the results in a table with the percent error referenced to the experimental values.
V.3 Discuss the results and draw appropriate conclusions.
VI. SELECTED REFERENCES
Thomson, W.T. and Dahleh, M.D., Theory of Vibration with Applications, 5th Edition, Pearson, 1997.
Avallone, E., Baumeister, T. and Sadegh, A., Marks’ Standard Handbook for Mechanical Engineers, 11th Edition, McGraw Hill, 2006.
Crandall, S.H., Dahl, N.C., Lardner, T.J., and Sivakumar, M.S., An Introduction to the Mechanics of Solids, 3rd Edition, McGraw Hill, 2012.
R. Ehgott (Created) 5/7 04/07/01 T. Hao (Revised) 08/07/16
Table I Spring Data
Spring # Force Reading Deflection Preload k
1
2
3
4
5
6
7
R. Ehgott (Created) 6/7 04/07/01 T. Hao (Revised) 08/07/16
Table II Measured Data
Spring System Force Reading Deflection Preload keq
Series
Parallel Balanced
Parallel Unbalanced
Series and Parallel
R. Ehgott (Created) 7/7 04/07/01 T. Hao (Revised) 08/07/16
