Transcript AME 324B Engineering Component Design

Outline
 Spring
Functions & Types
 Helical Springs
Compression
Extension
Torsional
The Function(s) of Springs
Most fundamentally: to STORE ENERGY
Many springs can also:
push
pull
twist
Some Review
linear springs: k=F/y
F
nonlinear springs: k 
k
y
dF
dy
Parallel
Series
1
ktotal

1 1
1
 
k1 k 2 k3
ktotal=k1+k2+k3
Types of Springs
Helical:
Compression
Extension
Torsion
More Springs
Washer Springs:
Beams:
Power springs:
Helical Compression Springs
d
D
Lf
p
Nt
diameter of wire
mean coil diameter
free length
pitch
Total coils
may also need:
Do and Di
Length Terminology
minimum of 10-15%
clash allowance
Free Length
Lf
Assembled
Length
Max Working
Load
Bottomed
Out
L
L
L
a
m
s
End Conditions
Plain
Plain Ground
Na=
Active Coils
Square
Square Ground
Stresses in Helical Springs
F
Spring Index
2C  1
 max  K s
, where K s 
2C
d 3
8FD
T
F
F
T
F
C=D/d
Curvature Stress
Inner part of spring is a stress concentration
(see Chapter 4)
Kw includes both the direct shear factor and
the stress concentration factor
4C  1 0.615
 max  K w
, where K w 

4C  4
C
d 3
8FD


under static loading, local yielding eliminates stress
concentration, so use Ks
under dynamic loading, failure happens below Sy:
use Ks for mean, Kw for alternating
Spring Deflection
y
3
8FD N
4
d G
a
Spring Rate
y
3
8FD N
a
4
d G
k=F/y
k
4
d G
3
8D N
a
Helical Springs
 Compression
Nomenclature
Stress
Deflection and Spring Constant
Static Design
Fatigue Design
 Extension
 Torsion
Static Spring Design
 Inherently
iterative
Some values must be set to calculate
stresses, deflections, etc.
 Truly
Design
there is not one “correct” answer
must synthesize (a little bit) in addition to
analyze
Material Properties
 Sut
ultimate tensile strength
Figure 13-3
Table 13-4 with Sut=Adb
 Sys
torsional yield strength
Table 13-6 – a function of Sut and set
Spring/Material Treatments

Setting
 overstress material in same direction as applied
load
» increase static load capacity 45-65%
» increase energy storage by 100%
 use Ks, not Kw (stress concentration relieved)
Load Reversal with Springs
 Shot Peening

 What type of failure would this be most effective
against?
What are You Designing?
Given
Find
F, y
k, y
k
F
+
d, C, D*, Lf*, Na*, clash
allowance ()**, material**
design variables
Such that:
Safety factor is > 1
Spring will not buckle
Spring will fit in hole, over pin, within vertical space
* - often can calculate from given
** - often given/defined
Static Spring Flow Chart
if GIVEN F,y, then find k; If GIVEN k, y, then find F
N a, 
d, C
D, Ks, Kw
material strengths
material
STRESSES
DEFLECTION
Ns=Sys/
Lf, yshut, Fshut
for shut spring if possible
if not, for max working load
Three things to know:
• effect of d
• shortcut to finding d
• how to check buckling
ITERATE?
CHECK
buckling, Nshut, Di, Do
Nshut=Sys/shut
Static Design: Wire Diameter
 max  K s
8FD
d
y
3
8FD3 N a
d 4G
Based on Ns=Ssy/ and above equation for :
1 ( 2b )
8 N s C  0.5Fwork 1     Finitial  
d 

K m A


Three things to know:
• effect of d
• shortcut to finding d
• how to check buckling
use Table 13-2 to select standard d near
calculated d
Km=Sys/Sut
*maintain units (in. or mm) for A, b
**see Example 13-3A on MathCad CD
Buckling
S .R. 
Lf
D
yinit  y working
y 
Lf
Three things to know:
• effect of d
• shortcut to finding d
• how to check buckling
Helical Springs
 Compression
Nomenclature
Stress
Deflection and Spring Constant
Static Design
Fatigue Design
 Extension
 Torsion
Material Properties

Sus
ultimate shear strength
Sfw´
torsional fatigue strength
 Sus0.67 Sut

 Table 13-7
-- function of Sut, # of cycles
 repeated, room temp, 50% reliability, no corrosion

Sew´
torsional endurance limit
 for steel, d < 10mm
 see page 816 (=45 ksi if unpeened, =67.5 ksi if
peened)
 repeated, room temp., 50% reliability, no corrosion
Modified Goodman for Springs

a
Sfs
0.5 Sfw
Sfw, Sew are for torsional strengths, so von
Mises not used
C
S fs  0.5
B
S fwSus
A
0.5 Sfw
Sus

Sus  0.5 S fw
m

Fatigue Safety Factor
a
Fi=Fmin
Fa=(Fmax-Fmin)/2
Fm=(Fmax+Fmin)/2
Sfs
N fs 
Sa
a
mload
0.5 Sfw
Sa
a
mgood
0.5 Sfw
a,load = a,good at intersection
i m
N fs 
Sus
m
S fs Sus   i 
S fs  m   i   Sus a
…on page 828
What are you Designing?
Given
Find
Fmax,Fmin, y
k,  y
k
F
+
d, C, D*, Lf*, Na*, clash
allowance ()**, material**
design variables
Such that:
Fatigue Safety Factor is > 1
Shut Static Safety Factor is > 1
Spring will not buckle
Spring is well below natural frequency
Spring will fit in hole, over pin, within vertical space
* - often can calculate from Given
** - often given/defined
Fatigue Spring Design Strategy
if GIVEN F,y, then find k; If GIVEN k, y, then find F
N a, 
d, C
D, Ks, Kw
material strengths
STRESSES
S fs Sus   i 
N fs 
S fs  m   i   Sus a
DEFLECTION
Lf, yshut, Fshut
material
ITERATE?
Two things to know:
• shortcut to finding d
• how to check frequency
CHECK
buckling, frequency,
Nshut, Di, Do
Nshut=Sys/shut
Fatigue Design:Wire Diameter
as before, you can iterate to find d, or you can use an equation
derived from relationships that we already know:
1 ( 2 b )
b




N fs  1
Ad
 8CN fs 



d 
K
F

K
F

1
.
34

1
K
F
 s m
s min 
w a 

0.67A 
N fs
S fw 
 





use Table 13-2 to select standard d near
calculated d
Two things to know:
• shortcut to finding d
• how to check frequency
*maintain units (in. or mm) for A, b
**see Example 13-4A on MathCad CD
Natural Frequency: Surge
Surge == longitudinal resonance
for fixed/fixed end conditions:
1 kg
fn 
2 Wa
(Hz)
ideally, fn will be at least 13x more than fforcing…
it should definitely be multiple times bigger
Two things to know:
• shortcut to finding d
• how to check frequency
…see pages 814-815 for more
Review of Design Strategy
ITERATIVE
USING d EQUATION
Find Loading
Select C, d
Find Loading
Select C, safety factor
Find stresses
Determine material properties
Find safety factor
Solve for d, pick standard d
Find stresses
Determine material properties
Check safety factor
Strategy Review Continued
Find spring constant, Na, Nt
Find FSHUT (must find lengths and y’s to do this)
Find static shut shear stress and safety factor
Check Buckling
Check Surge
Check Di, Do if pin to fit over, hole to fit in
Consider the Following:
Helical Springs
 Compression
Nomenclature
Stress
Deflection and Spring Constant
Static Design
Fatigue Design
 Extension
 Torsion
Extension Springs
As before, 4 < C < 12
 max  K s
8FD
, use K w for  a
d 3
surge check is same as before
Lb=d(Na+1)
However, no peening, no setting,
no concern about buckling
Difference 1: Initial Force
force F
“preloading”
Fi
deflection y
F=Fi+ky
F  Fi
d 4G
k

y
8D 3 N a
Difference 1a: Deflection
3
8( F  Fi ) D N a
y
4
d G
Difference 2: Initial Stress
take initial stress as the average stress between these lines,
then find Fi
Difference 3: Ends!: Bending
 a  Kb
16DF
Kb 
C1 
d
3

4F
d
2
4C12  C1  1
4C1 (C1  1)
2 R1 2 D

C
d
2d
S e ( Sut   min )
N fb 
S e ( mean   min )  Sut  alt
Se 
S es
0.67
standard
end
Difference 3a: Ends: Torsion
4C2  1
 max  K w2
, K w2 
4C2  4
d 3
8FD
C2=2R2/d
pick a value >4
Materials
– Same
 Sys, Sfw, Sew – same for body
 Sys, Sfw, Sew – see Tables 13-10 and 1311 for ends
 Sut
Strategy
similar to compression + end stresses - buckling
Helical Springs
 Compression
Nomenclature
Stress
Deflection and Spring Constant
Static Design
Fatigue Design
 Extension
 Torsion
Torsion Springs
• close-wound, always load to close
Deflection & Spring Rate
1 MLw
 rev 
,
2 EI
Lw  length of wire  DN a
 rev,roundwire  10.8
MDN a
k
d 4E
M
 rev
Stresses
Compressive is Max – Use for Static – Inside of Coil
 imax  Kbi
M max c
32M max
 K bi
I
d 3
4C 2  C  1
K bi 
4C (C  1)
For Fatigue – Slightly lower Outside Tensile Stress – Outside of Coil
 omax  K bo
32M max
d 3
 omin  K bo
4C 2  C  1
K bo 
4C (C  1)
32M min
d 3
Materials
see Tables 13-13 and 13-14, page 850
follow book on Sewb=Sew/0.577… for now
Strategy
Select C, d

M
K
• fit over pin (if there is one)
• don’t exceed stresses
Helical Springs
 Compression
Nomenclature
Stress
Deflection and Spring Constant
Static Design
Fatigue Design
 Extension
 Torsion