Page 410 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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k spring rate, N mm ,Nm −1 b ultimate tensile strength, MPa
k spring rate of torsion spring, [ ] allowable bending stress for torsion
b
∘
Nmm/( ) spring, MPa
L length of wire, mm e elastic limit strength, MPa
M bending moment, N mm s yield strength, MPa
m mass of spring, kg shear stress, MPa
n number of active coils i initial torsional stress, MPa
n total total number of coils s transverse shear stress, MPa
p spring pitch, mm T torsional shear stress, MPa
S shear force, N [ ] allowable shear stress of spring
S fatigue strength safety factor wire, MPa
ca
T torsional moment, N mm angular deflection, rad or ∘
U strain energy, J angular frequency, rad s −1
n
U energy loss due to friction, J
0
W section modulus, mm 3 Subscripts
w work for a deflection under a load, J
∘
pitch angle, i load or deflection at initial
coil clearance, mm installation
1 coil clearance at the maximum load, m mean value
mm max maximum value
deflection, mm min minimum value
density, kg m −3 o load or deflection at operation
bending stress, MPa s load or deflection at solid length

14.1 Introduction

14.1.1 Applications and Characteristics
Springs are resilient elements that experience appreciable deflection without permanent
deformation. They usually have predefined linear or nonlinear relationships between
applied loads and associated deflections. Therefore, springs are used to introduce con-
trollable flexibility by deflection under applied loads.
Springs can be configured to exert desired force or torque to control the motion of
machine, like valve springs in internal combustion engines. They can also be used to
absorb vibration and impact energy, such as buffer springs in suspension systems for cars
and trucks; or to store energy for subsequent release, like spiral springs used in watches.
Finally, when the relationship between the force and deflection is linear, springs can be
used for force measurement, such as helical springs in scales.

14.1.2 Types of Spring and Structures

Because of variations in spring configurations, applied loads and employed materials,
the classification of springs may have some overlap [1–4]. According to the configu-
ration, springs can be classified into helical springs, Belleville springs, spiral springs,
leaf springs and ring springs. While depending on the loads they carry, springs include
extension springs, compression springs, torsion springs and bending springs. Springs