FME461
Engineering Design II
Dr.Hussein Jama
Hussein.jama@uobi.ac.ke
Office 414
Lecture: Mon 8am -10am
Tutorial Tue 3pm - 5pm
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Spring design
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Types
Factors in spring design
Materials
Torsional
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Types of Springs
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Types of spring cont.
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Types of springs cont.
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Types of springs cont.
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Spring Design
F  ky
kF/y
1
k series
1 1 1
  
k1 k 2 k3
k parallel  k1  k 2  k3
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Factors in spring design
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High strength
High yield
Modulus may be low for energy storage
Cost
Environmental factors
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Temperature resistance (e.g. valve springs)
Corrosion resistance
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Common materials for springs
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Influence of diameter on
ultimate stress
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Influence of diameter on
ultimate stress cont.
Sut  Ad b
Sus  0.67 Sut
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Design of helical compression
springs
 Length nomenclature
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Free
Assembled
Solid or shut height
Working deflection
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Stresses in Helical Spring
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Stresses in Helical springs
cont.
At the inside of the spring
Substituting for
Gives
4<C<12
Defining the spring index
Therefore the stress is
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Equation(1)
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Effect of curvature on Stress
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Equation (1) is based on the wire being
straight
However the curvature increases the stress
on the inside of the wire
For static stress the effect of curvature can
be neglected
For fatigue the effect of curvature is important
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Effect of curvature cont.
Wahl factor
Bergstrasser
factor
The results of the two equations differ by less than 1%.
Bergstrasser factor is preferred due to simplicity
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Deflection
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The external work done on an elastic member
in deforming it is transformed into strain, or
potential, energy. If the member is deformed a
distance y, and if the force-deflection
relationship is linear, this energy is equal to
the product of the average force and the
deflection, or
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This equation is general in the sense that the
force F can also mean torque, or moment,
provided, that consistent units are used for k.
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Deflection cont..
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By substituting appropriate expressions for k,
strain-energy formulas for various simple
loadings may be obtained. For tension and
compression and for torsion,
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Deflection of a helical spring
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Using Castigliano’s theorem, strain energy is
equal to
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Substituting
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Deflection cont.
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Using the spring index
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Spring scale is
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Spring design – end treatment
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End details affect active coils
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Plain ends
Squared ends
Squared
Ground
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Number of active coils
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Stability of a column
Euler Formula
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Stability of a spring
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We know a column will buckle when the load
is too large
A compression coil spring will also buckle
ycr is the deflection corresponding to onset of
instability
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Deflection cont.
Is called the effective slenderness ratio
Alpha = end condition constant
Lo is the spring length
D is the Coil diameter
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Instability cont.
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End constraint alpha given by
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Instability cont.
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For absolute stability
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For steels it turns out
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For square and ground ends
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Static design flow chart
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Flow chart cont.
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Recommended design
conditions
Figure of merit (fom)
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Materials for springs
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Yield strength for static loading
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Depends on set
Before set removed use Wahl factor
After set removed no stress concentration used
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Properties for fatigue
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Fatigue Strength
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Torsion is relevant loading- could use von Mises
stress
Materials testing specific to helical compression
springs is available, however
Correct for temp., reliability, environment
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Properties - endurance
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Endurance Strength (steels) unlimited cycles
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For high ultimate strengths, endurance limits max
out at 45 kpsi (unpeened) and 67.5 kpsi (peened)
Small wires have high ultimate strength
Tests have been done specific to spring wire
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Temperature may require compensation
Corrosion
Reliability
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S-N and Modified Goodman
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Designing springs
Requirements
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Functionality
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Stiffness
Lengths
Diameter
Forces
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Reliable operation
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Design Choices
Static factor of safety
Fatigue factor of safety
Buckling and surge
Manufacturability
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Index C
Material
Wire and coil
diameter
Number of turns
End treatment and
constraint
Set and shot peen
Constraints (other)
• Bend radius
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Helical extension spring
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Similar in most ways to
compression springs
Usually wound to be closed
coil at zero force
Thus a preload is required
to stretch any, i.e. y=k(F-Fi )
Spring hook is a source of
failure in bending and
torsion
No set is used
One coil not considered
active
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End stresses
Bending stress:
16 DF 4 F
 A  Kb
 2
3
d
d
4C12  C1  1
2 R1
Kb 
; C1 
4C1 (C1  1)
d
Torsional stress:
8DF
 B  K w2
d 3
4C2  1
2 R2
K w2 
; C2 
4C2  4
d
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Design for fatigue
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Data available for springs with loading from
zero to some compresion value
Application often has preload… how to use?
First construct (or find) S-N curve
Next construct Mod-Goodman chart
Apply load line for given preload and design
stress
Find factor of safety to failure point
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Goodman curve
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A word about torsional springs
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The wire in a torsional spring is primarily in
bending
Spring constant is rotary M=k
Loading should act to wind up coil
Design process resembles compression
springs
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Torsional
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Homework
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Read chapter 10 of Shigley
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