Transcript AME 324B Engineering Component Design

Fastening (more complex
shapes = better function)
 Non-permanent
Bolted
 Permanent
Bolted
Welded
Bonded
Outline
 General
Thread Nomenclature & Types
 Power Screws
 Stresses in Threads
 Preloading Fasteners/Joints
 Fasteners in Shear
Threads
p
d
dp
dr
pitch
diameter (major)
pitch diameter
minor diameter
in./thread
in.
in.
in.
L
Lead
in.
Tolerance Thread Pitch
Screw Classifications
ISO (Metric)
Unified National Standard
UNC –coarse
UNF –fine
UNEF –extra fine
coarse
fine
Class 1
Class 2
Class 3
fine
d=0.25”
several levels
d=12mm
Class 2
metric
¼-20 UNF –2A
20 threads/in.
M12 x 1.75
external threads
**see Tables 14-1 and 14-2 for standard sizes**
p=1.75 mm/thread
Tensile Stress
F
F
F
t 
At
2
d
  p dr 
At  
 
4 2
2 
At also in Tables 14-1 and 14-2
Outline
General Thread Nomenclature & Types
 Power Screws

 Threads
 Loads
 Self-locking
 Efficiency
Stresses in Threads
 Preloading Fasteners/Joints
 Fasteners in Shear

Power Screw Applications
Where have you seen power screws?
 jacks
for cars
 C-clamps
 vises
 Instron material testing machines
 machine tools (for positioning of table)
Power Screw Types

Square
 strongest
 no radial load
 hard to manufacture

Acme
 29° included angle
 easier to manufacture
 common choice for
loading in both directions

Buttress (contrafuerte)
 great strength
 only unidirectional
loading
Load Analysis
What “simple machine” does a power screw utilize?
P
y
x
f
F
L
N

dp
LIFTING
L
tan  
d p




Pd p d p  L
TSu 
2 d p  L
More Completely…
LIFTING





d p  L
P
Tu  TSu  Tcollar  d p
 c dc 
2 
d p  L



LOWERING



d p  L
P
Td  d p
 c dc 
2 
d p  L

P
y
x
f
F
N

dp
L
For Acme Threads



LIFTING



d p  L cos
P
Tu  TSu  Tcollar  d p
 c dc 
2 
d p cos  L

LOWERING





d p  L cos
P
Td  d p
 c dc 
2 
d p cos  L

Friction Coefficients
oil lubricated= collar w/ bushing=0.15 ± 0.05
collar w/ bearing=0.015 ± 0.005
Self-Locking / Back Driving
self-locking – screw cannot turn from load P
back-driving – screw can be turned from load P





d p  L cos
P
Td  d p
 c dc 
2 
d p cos  L

for self-locking:
L

cos
d p
or
  tan  cos
would square or Acme of same dimensions lock first?
Wout
PL cos   tan 
e


Win
2T cos   cot 
-for lifting- higher efficiency for lowering
(also derive with frictionless torque/torque)
Efficiency
Ball Screw
Outline
General Thread Nomenclature & Types
 Power Screws
 Stresses in Threads

 Body Stresses
» Axial
» Torsion
 Thread Stresses
» Bearing
» Bending
 Buckling
Preloading Fasteners/Joints
 Fasteners in Shear

Tensile Stress
F
F
F
t 
At
2
d
  p dr 
At  
 
4 2
2 
At also in Tables 14-1 and 14-2
Torsional Stress
depends on friction at screw-nut interface
For screw and nut,
•
•
if totally locked (rusted together), the screw experiences all of torque
if frictionless, the screw experiences none of the torque
Tr 16T
 
J d 3
r
For power screw,
•
•
if low collar friction, the screw experiences nearly all of torque
if high collar friction, the nut experiences most of the torque
Thread Stresses – Bearing
F
F
2F
B 

Abearing d p nt p
Abearing=(p/2)(dpnt)
p/2
p/2
Thread Stresses – Bending
F
Mc
6F
b 

I
d r pnt
p/2
p/2
transverse shear is also present, but max stress will be at top of tooth
For both bearing and bending, F and nt are dependent on how well
load is shared among teeth, therefore
use Factual=0.38F and nt=1 (derived from experiments)
Mohr’s Circle
F
6F
x 
d r nt p
 xy 
16T
p/2
d r3
p/2
y 0
 yz  0
F
z 
At
 xz  0
z
y
x
Buckling
l
l
SR  
k
I
A
use dr
2E
S R  D  
Sy
S R  S R  D
S R  S R  D
PCR
1  S y Sr 

 S y  
A
E  2 
2
use Johnson
use Euler
PCR 
 2 EI
2
l
Outline
General Thread Nomenclature & Types
 Power Screws
 Stresses in Threads
 Preloading Fasteners/Joints

 Proof Strength
 Spring Behavior
 Loading & Deflection
 Separation of Joints

Fasteners in Shear
Preloading & Proof Strength
 stress at which bolt begins to take
a permanent set
 Sp
Preloading
• static loading: preload at roughly 90% of Sp
• dynamic loading: preload at roughly 75% of Sp
Spring Behavior
BOTH material being clamped and bolt behave as springs
(up to yield/permanent set stresses)
AE
k
l
for the bolt, threaded vs unthreaded have different spring
constants:
lt
ls
1


kb At Eb d 2
Eb
4
applied load P
Affected Area of Material
For material, basic model is as follows (shown for 2 materials being clamped)
l1
l2
1


k m Am1 E1 Am2 E2
Area is hard to define… from experiments, the following is accurate:

  d 2  d3  2
2
Am  
 d 
4 

2


When no edges nearby and same materials, even
simpler form can be used:
b(d / lm )
k m  dEAe
A and b are from Table 14-9, pg 916
Loading & Deflection
F
Pb
Fb
Fi
Pm
P
Fm

m1
b b1
m
MATERIAL
BOLT
P=Pb+Pm
Fm=Fi-Pm
Fb=Fi+Pb
Papplied relieves
compression in
material &
adds tension to bolt

Distribution of Applied Load
b= m
kb
Pb  CP, where C 
k m  kb
Pm  P  CP  P(1  C )
Applied Load to Equal Sp
How many times more would the loading on the
bolt need to be to incur permanent set?
(assuming no material separation)
F y  Fi S y At  Fi
Pby 

C
C
Pby
N load 
Pb
Yielding Safety Factor
Fm = Fi + P(C-1)
Fb = Fi + CP
Fb
b 
At
Ny=Sy/b
Separation
Separation occurs when Fm=0
Fm = Fi + P(C-1)
Fi
P0 
1 C
P0
Fi
N separation 

P 1  C P
Strategy Reviewed
See Example 14-2, p. 906
Given: joint dimensions
Find: bolt
set preload equal to 90% Sp
find lt so that you can find kb
find km
calculate C, then Pb, Pm, then Fb, Fm
find stress in bolt and separation load
Such that: factors of safety>1
Dynamic Loading of Fasteners
 Bolt
only absorbs small % of P
 Stresses
Bolt is in tension
Material is in compression
 Fatigue
is a tensile failure phenomenon
  Preloading helps tremendously in
fatigue
Outline
 General
Thread Nomenclature & Types
 Power Screws
 Stresses in Threads
 Preloading Fasteners/Joints
 Fasteners in Shear
What is Shear?
Straight Direct Shear
Direct Shear
Doweled Joints
“It is not considered good practice to use bolts or
screws in shear to locate and support precision
machine parts under shear loads”
Norton


Shear can be handled by friction caused by
bolts… but, better practice is to use dowels
Bolts need clearances… at best 2 out of a 4 bolt
pattern will bear all of load
dowels support shear, but not tensile loads
bolts support tensile loads, but not shear
Direct Shear

F
Ashear
Ashear=2x(cross sxn of dowels)
N
dowels support shear, but not tensile loads
bolts support tensile loads, but not shear
Ssy


???
0.577
S yS y

Outline Revisited
 General
 Power
Thread Nomenclature & Types
Screws
 Stresses
in Threads
 Preloading
 Fasteners
Fasteners/Joints
in Shear
Chapter
9
Welding, Brazing, Bending, and
the Design of Permanent Joints
From Shigley & Mischke, Mechanical Engineering Design
Part 3
Design of Mechanical Elements
Welding Symbols
Butt Welds
Fillet Welds
Welding Issues
 Requires
Careful Design
Skilled Welder
 Can
Cause
Weakened adherends
Thermal distortion
Removal of heat treatment
Welding References
 AWS
(American Welding Society)
 Lincoln Electric
 ASME Codes & Standards
Pressure Vessels & Piping
Nuclear Installations
Safety Codes
Performance Test Codes
Bonded Joints (thin members)
Bonded Joint Types
More Types
Peel Stresses
Good Practices
Bonding Issues
 Can
achieve
Lighter joint
Less costly joint
Better sound absorption
 Beware
Peel stresses
Environmental effects
Thermal mismatch
Bonding References
 SAMPE
(Society for the Advancement
of Material & Process Engineering)
 ASTM Committee D-14 on Adhesives