Transcript Mechanical Engineering Design Chapter 8
ME 307 Machine Design I Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 1
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 Dr. A. Aziz Bazoune 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 Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 2
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 36 Slide 3
ME 307 Machine Design I
8-4 Joints: Fastener Stiffness
When a connection is desired that can be disassembled without destructive methods and that is strong enough to resist external tensile loads, moment loads, and shear loads, or a combination of these, then the simple bolted joint using hardened steel washers is a good solution.
Twisting the nut stretches the bolt to produce the
clamping force
. This clamping force is called the pretention or bolt preload .
This force exists in the connection after the nut has been properly tightened.
Figure 8-13
A bolted connection loaded in tension by the forces Note the use of two washers. Note how the threads extend into the body of the connection. This is usual and is desired.
L G
is the grip of the connection.
P
.
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 4
ME 307 Machine Design I
Joints: Fastener Stiffness
Figure 8-14 shows another tension-loaded connection. This joint uses cap screws threaded into one of the members.
Figure 8-14
Section of cylindrical pressure vessel.
Hexagon-head caps crews are used to fasten the cylinder head to the body.
Note the use of an O-ring seal. LG’ is the effective length of the connection (See Table 8-7) .
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 5
ME 307 Machine Design I
Joints: Fastener Stiffness
An alternative approach to this problem (of not using a nut) would be to use studs .
A stud is a rod threaded on both ends. The stud is screwed into the lower member first; then the top member is positioned and fastened down with hardened washers and nuts
Studs are regarded as permanent , and so the joint can be disassembled merely by removing the nut and washer.
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 6
ME 307 Machine Design I
Joints: Fastener Stiffness
Spring Rate : The ratio between the force applied to the member and the deflection produced by that force.
The grip thickness
L G
of a connection is the of the clamped material.
total
Total distance between the underside of the nut to the bearing face of the bolt head; includes washer, gasket thickness etc.
The grip
L G
here is the sum of the thicknesses of both members and both washers.
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 7
ME 307 Machine Design I Table 8-7 Suggested Procedure fastener Stiffness for Finding
To find different parameters use table 8-7
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 8
In joint under tension the Machine tension :
k b
unthreaded = equivalent spring constant of bolt composed of threaded
k d
members are under compression parts acting as springs in series.
and the bolt under
k t
and
1
k
b
1
k
d
1
k
t
From Chapter 5 (Springs in series) Dr. A. Aziz Bazoune
k
b
k
d
k
t
k
d
l
d
,
k
t
l
t
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
For short bolts
k b = k t
k
b
t A t
: tensile stress area (Tables 8-1, 8-2),
l t
: length of threaded portion of the grip; grip.
A d
: major diameter area of fastener;
l d
: length of unthreaded portion in
k b
: is the estimated effective stiffness of the bolt or cap screw in the clamped zone.
CH-8 LEC 36 Slide 9
ME 307 Machine Design I
8-5 Joints- Member Stiffness
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 10
ME 307 Machine Design I
8-5 Joints- Member Stiffness
There may be more than two members included in the grip of the fastener.
All together these act like compressive springs in series.
Equivalent spring constant
1 1
k m
1
k m k
1
k
2
k
1 3 ....
1
k i
If one of the members is a soft gasket, its stiffness relative to the other members is usually so small that for all practical purposes the others can be neglected and only gasket stiffness used.
With no gasket, the stiffness of the members is difficult to obtain, except by experimentation.
Compression spreads out between the bolt head and the nut and area is not uniform.
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 11
ME 307 Machine Design I
8-5 Joints Member Stiffness
Joint pressure distribution theoretical models
Ito used ultrasonic techniques to determine pressure distribution at the member interface. Results show that pressure stays high out to about 1.5 bolt radii.
Ito suggested the use of Rotscher’s pressure cone method for stiffness calculations with a variable cone angle. This method is quite complicated.
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 12
ME 307 Machine Design I
8-5 Joints Member Stiffness Figure 8-15
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 13
ME 307 Machine Design I
8-5 Joints Member Stiffness
We choose a simpler approach using a fixed cone angle.
The contraction of an element of the cone of thickness dx is subjected to a compressive force P is, from Eq. (5-3),
d
Pdx EA
The area of the element is
A
r
0 2
r i
2
x
tan
D
2 2
d
2
x
tan
D
d
2
x
tan 2
Figure 8-15b general cone geometry using a half-apex angle
.
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 14
ME 307 Machine Design I
8-5 Joints Member Stiffness
Substituting this into the previous equation and integrating the resulting equation from 0 to t gives.
k
Ed P
tan
P
ln
t t
ln
Ed
tan
D
D
d
) )
d
) )
(8-19)
For Members made of Aluminum, hardened steel and cast iron 25 o < <33 o With =30 o , this becomes
k
ln 0.574
(1.55
(1.55
E d t D d D d
) )
(8-20) Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 15
ME 307 Machine Design I
8-5 Joints Member Stiffness
k
Substituting this into the previous equation and integrating the resulting equation from 0 to t gives.
Ed P
tan
P
ln
t t
ln
Ed
tan
D
D
d
) )
d
) )
(8-19)
With =30 o , this becomes
k
ln 0.574
(1.55
(1.55
E d t D d D d
) )
(8-20) Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 16
ME 307 Machine Design I
8-5 Joints Member Stiffness
If members of the joint have the same E with symmetrical frusta (l=2t) , then they act as two identical springs in series
D = d w = 1.5 d,
this can be written as,
k m
=
k/2
. For
= 30 ° and
k m
0.5774
0.5774
0.5774
l l E d
0.5
d
2.5
d
(8-22) Finite element analysis agree with
exactly at the aspect ratio d/l = 0.4
.
= 30 o recommendation coinciding Additionally, FEM offered an exponential curve-fit of the form
k m Ed
Ae
( / )
where A and B are given in Table 8-8. (8-23) Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 17
ME 307 Machine Design I
8-5 Joints Member Stiffness
Figure 8-16
The dimensionless plot of stiffness versus aspect ratio of the members of a bolted joint, showing the relative accuracy of method of Rotsher, Michke and Motosh, compared to Finite Element Analysis (FEA) conducted by Wileman, Choudury, and Green.
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 18
ME 307 Machine Design I
8-5 Joints Member Stiffness
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 19
ME 307 Machine Design I
8-6 Bolt Strength
Bolt strength is specified by: 1. minimum proof strength S p 2. or minimum proof load F p , 3. and minimum tensile strength, S ut
The proof load is the maximum load (force) that a bolt can withstand without acquiring a permanent set.
The proof strength is the quotient of the proof load and the tensile-stress area .
The proof strength is about 90% of the 0.2% offset yield strength.
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 20
ME 307 Machine Design I
8-6 Bolt Strength
The SAE specifications are given in Table 8-9 bolt grades are numbered according to
minimum tensile strength.
The ASTM Specs for steel bolts (structural) are in Table 8-10 .
Metric Specs are in Table 8-11.
If
S p
not available use:
S p
=0.85
S y F p
=
A t S p
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 21
ME 307 Machine Design I
8-6 Bolt Strength
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 22
ME 307 Machine Design I Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 23
ME 307 Machine Design I Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 36 Slide 24