Transcript Mechanical Engineering Design Chapter 8

ME 307
Machine
Design I
ME 307
Machine
Design I
8-1
8-2
8-3
8-4
8-5
8-6
8-7
8-8
8-9
8-10
8-11
8-12
8-13
8-14
8-15
Thread Standards and Definitions
The Mechanics of Power Screws
Strength Constraints
Joints-Fasteners Stiffness
Joints-Member Stiffness
Bolt Strength
Tension Joints-The External Load
Relating Bolt Torque to Bolt Tension
Statically Loaded Tension Joint with Preload
Gasketed Joints
Fatigue Loading of Tension Joints
Shear Joints
Setscrews
Keys and Pins
Stochastic Considerations
ME 307
Machine
Design I
8-3
8-4
8-5
8-6
Strength Constraints
Joints-Fasteners Stiffness
Joints-Member Stiffness
Bolt Strength
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 3
ME 307
Machine
Design I
8-7 Tension Joints-The External Load
Static Analysis
a) External Load
Let us consider what happens when an external tensile load
connection.
P, is applied to a bolt
Assuming a clamping force, (preload Fi )is applied by tightening the nut before
external force, P is applied.
Fi = preload
P = external tensile load
Pb = portion of P taken by bolt
Pm = portion of P taken by members
Fb = Pb + Fi = resultant bolt load
Fm = Pm – Fi = resultant load on the members
C = fraction of external load P carried by bolt
1-C = fraction of external load P carried by members
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 4
ME 307
Machine
Design I
8-7 Tension Joints-The External Load
External load P is shared by bolt and members. The load P is tension, and it causes
the connection to stretch, or elongate, through some distance d
E q u ilib riu m ,
P  Pb  Pm
C o m p atib ility,
d  db  dm
R elatio n P  d ,
Pm
d 

km
Pb 
Pm 
C 
kb
km
kb  km
kb  km
Dr. A. Aziz Bazoune
kb
& Pm 
Pb k m
kb
P  CP
kb  km
kb
Pb
P  (1  C ) P
C is the stiffness constant of the joint,
For typical values of C see TABLE 8-12
Most of external Load P is taken by members
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 5
ME 307
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8-7 Tension Joints-The External Load
b) Resultant Bolt and Member Load : Fb & Fm
Fb  Pb  Fi  C P  Fi
Fm  Pm  Fi  (1  C ) P  Fi
(8-24)
Fm  0
Fi is preload; high preload is desirable in tension
connections.
Dr. A. Aziz Bazoune
(8-25)
Fi = 0.75 Fp for re-use
Fi = 0.90 Fp for permanent joint
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 6
ME 307
Machine
Design I
8-8 Relating Bolt Torque to Bolt Tension
c) Torque Required to give preload Fi
Fi f c d c
Fi d m  l  π fd m sec  
T 
 

2
2  π d m  fl sec  
tan  
l
πd m
Fi f c d c
Fi d m  tan   f s ec  
T 
 

2
2  l  f tan  sec  
d c  ( d  d w ) / 2  ( d  1 . 5 d ) / 2  1 .2 5 d
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 7
ME 307
Machine
Design I
8-8 Relating Bolt Torque to Bolt Tension
 d m  tan   f sec  

T  

  0 .6 2 5 f c  Fi d
 2 d  l  f tan  se c  

d m  tan   f sec  
K 

  0 .6 2 5 f c (8-26)
2 d  l  f t an  se c  
T  K Fi d
(8-27)
K is torque coefficient
K values are given in TABLE 815 Average Value for K = 0.2
for f = fc = 0.15 no matter
what size bolts are employed
and no matter whether the
threads are coarse or fine.
The coefficient of friction depends
upon the surface smoothness,
accuracy, and degree of lubrication.
On the average, both f and fc are
about 0.15.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 8
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Example 4 (Example 8-3 Textbook)
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 9
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Example 4 (Cont.’d)
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 10
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Example 4 (Cont.’d)
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 11
ME 307
Machine
Design I
8-9
Statically Loaded Tension Joint with Preload
d) Statically Loaded Tension Joint with Preload
Failure of joints occurs when
i) Bolt Yields
b 
Fb

CP
At
At
F ailu re starts
C (nP )
At


Fi
At
Fi
At
 b  SP
At: Tensile stress
area
 SP
L o ad facto r n 
Proof strength
S P At  Fi
CP
F o r N B o lts n 
S P At  Fi
CP / N
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 12
ME 307
Machine
Design I
8-9
Statically Loaded Tension Joint with Preload
ii) Joint separates
Let P0 be external load causing separation Fm= 0
Fm  (1  C ) P  Fi
(1  C ) P0  Fi  0
Fm  0
n0 
P0
P

Fi
P 1  C
F o r n b o lts n 

Fi
P / N 1  C

no : factor of safety against joint separation
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 13
ME 307
Machine
Design I
8-10
Gasketed Joints
g) Gasketed Joints
If a full gasket is present in joint, The gasket
pressure p is:
p  
Fm
Ag / N
With load
No. of
bolts
factor n
F m  (1  C ) nP  Fi
p  [ Fi  nP (1  C )]
Dr. A. Aziz Bazoune
N
Ag
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 14
ME 307
Machine
Design I
8-10
Gasketed Joints
IMPORTANT:
1. To maintain uniformity of pressure adjacent
bolts should not be placed more than 6
nominal diameters apart on bolt circle.
2. To maintain wrench clearance bolts should
be placed at least 3 d apart .
3. A rough rule for bolt spacing around a bolt
circle is
3
 Db
 6
Nd
where Db is the diameter of the bolt circle
and N is the number of bolts.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 15
ME 307
Machine
Design I
Example 5 (Example 8-4 Textbook)
(a) The grip is l = 1.50 in. From Table A31, the nut thickness is 35/64 in.
Adding two threads beyond the nut
of 2/11 in gives a bolt length of
 35 
 2 
L
  1.50  
  2.229 in
 64 
 11 
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 16
ME 307
Machine
Design I
(a) From Table A-17, the next fraction size bolt is 2 1/4 in.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 17
ME 307
Machine
Design I
LT  2 d  0.25 in, L  6in
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 18
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 19
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 20
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 37 Slide 21