I.
OBJECTIVES
1.1
To study the relationship of springs connected in series and parallel
and determine the equivalent spring constant.
1.2
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:
F=K∆
6.1
Where:
F = applied force
∆ = the resulting displacement
III.
EQUIPMENT
3.1
3.2
3.3
Assorted springs, hooks, and aluminum bars.
Steel scale
Steel frame
R. Ehrgott
2/7
04/07/01
IV.
PROCEDURE
4.1
Determine the spring constant for each individual spring using
Equation 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. Excel can also be
used to obtain K by fitting a linear trendline to the force-deflection
data. K will be the slope m of the trendline (y = mx + b) and b is the
initial preload required to separate the coils of the spring.
4.2
Set up the spring system shown in Figure 6.1, 6.2 and 6.3 to
determine the equivalent spring constant for each system.
4.3
Construct the spring system shown in Figure 6.4 and determine the
equivalent spring constant. You will need to use two pairs of springs
with matching spring constants to obtain good results
FT = F1 = F2
6.2
K1
∆ T = ∆1 + ∆ 2 =
K2
Keq =
F1
F
F
F
+ 2 = T + T
K1 K 2 K1 K 2
FT
FT
FT
1
=
=
=
1
1
∆ T ∆ 1 + ∆ 2 FT FT
+
+
K1 K 2 K1 K 2
6.3
6.4
FT
Figure 6.1
SPRINGS IN SERIES
R. Ehrgott
3/7
04/07/01
∆T = ∆ 1 + ∆ 2
K1
K2
FT = F1 + F2 = K1∆1 + K2 ∆ 2 = K1∆T + K2 ∆T
6.6
FT K 1∆ T + K 2 ∆ T
=
= K1 + K2
∆T
∆T
6.7
Keq =
∆1
6.5
∆2
Location of FT when K1 ≠ K 2
FT
a=
K1
(a + b )
K1 + K 2
Figure 6.2
SPRINGS IN PARALLEL (∆
∆1 = ∆2)
FT = F1 + F2
K2
K1
∆1
F1 =
∆2
∆T =
FT
a
Keq =
F2 =
a
FT
L
6.9
b
a
b F1 a F2
∆1 + ∆ 2 =
+
L
L
L K1 L K 2
b 2 FT a 2 FT
+
L2 K 1 L2 K 2
6.10
FT
FT
L2
= 2
=
∆ T b FT a 2 FT
b2 a2
+
+
L2 K 1 L2 K 2 K 1 K 2
6.11
=
b
L
b
FT ;
L
6.8
Figure 6.3
SPRINGS IN PARALLEL, UNSYMMETRIC CASE (∆
∆1 ≠ ∆2)
R. Ehrgott
4/7
04/07/01
K1
K2
K1
Keq =
K3
1
6.12
1
1
+
K1 + K2 + K1 K3 + K 3
K3
FT
Figure 6.4
SPRINGS IN SERIES AND PARALLEL
V.
REPORT
5.1
Plot the force versus deflection for each individual spring and report
the stiffness for each spring in a table.
5.2
Calculate the theoretical equivalent spring constants given by
Equations 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.
5.3
Discuss the results and draw appropriate conclusions.
SELECTED REFERENCES
6.1
Vibration Analysis, Vierck, pp. 28-31.
6.2
Mark’s Standard Handbook for Mechanical Engineers. 8th Edition.
McGraw Hill
6.3
An Introduction to the Mechanics of Solids. Crandall and Dahl.
R. Ehrgott
5/7
04/07/01
DATA SHEET EXPERIMENT # 6
SPRINGS IN SERIES AND PARALLEL
Student Name ___________________ Group #____________________
Date Exp. Performed _____________ Instructor’s Name____________
SPRING #
FORCE
READING
DEFLECTION
PRELOAD
K
1
2
3
4
5
6
7
8
R. Ehrgott
6/7
04/07/01
DATA SHEET EXPERIMENT # 6
SPRINGS IN SERIES AND PARALLEL
Student Name _____________________ Group #____________________
Date Exp. Performed _____________ Instructor’s Name______________
SPRING
SYSTEM
FORCE
READING
DEFLECTION
PRELOAD
K
SERIES
PARALLEL
BALANCED
PARALLEL
UNBALANCED
SERIES AND
PARALLEL
R. Ehrgott
7/7
04/07/01