Formula Sheet: Springs | Design of Machine Elements - Mechanical Engineering PDF Download

 Page 1


Springs
1. Types of Springs
• Helical (Compression / Tension)
• Leaf (Laminated) Spring
• Torsion Spring
• Spiral Spring
2. Stiffness of a Spring
k =
F
d (N/m)
3. Helical Compression Spring (Circular Wire)
• Deflection:
d =
8FD
3
n
Gd
4
• Stiffness:
k =
Gd
4
8D
3
n
• Shear stress:
t =
8FDk
w
pd
3
where k
w
=
4C- 1
4C- 4
+
0.615
C
(Wahl’s factor)
• Spring index:
C =
D
d
4. Energy Stored in Spring (Strain Energy)
U =
1
2
Fd =
1
2
kd 2
1
Page 2


Springs
1. Types of Springs
• Helical (Compression / Tension)
• Leaf (Laminated) Spring
• Torsion Spring
• Spiral Spring
2. Stiffness of a Spring
k =
F
d (N/m)
3. Helical Compression Spring (Circular Wire)
• Deflection:
d =
8FD
3
n
Gd
4
• Stiffness:
k =
Gd
4
8D
3
n
• Shear stress:
t =
8FDk
w
pd
3
where k
w
=
4C- 1
4C- 4
+
0.615
C
(Wahl’s factor)
• Spring index:
C =
D
d
4. Energy Stored in Spring (Strain Energy)
U =
1
2
Fd =
1
2
kd 2
1
5. Series and Parallel Springs
• Series:
1
k
eq
=
X
1
k
i
• Parallel:
k
eq
=
X
k
i
6. Leaf Spring (Semi-elliptical)
• Maximum Bending Stress:
s =
6FL
nbt
2
• Deflection:
d =
3FL
3
8nbt
3
E
• Where:
– F = Applied load
– L = Length of spring
– n = Number of leaves
– b, t = Width and thickness of leaf
7. Torsion Spring (Circular Rod)
• Torsional moment:
t =
Mr
J
=
32M
pd
3
• Angle of twist:
? =
MT
GJ
8. Critical Frequency of Springs (Spring-Mass System)
f =
1
2p r
k
m
2