ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 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
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
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 2
ME 307
Machine
Design I
Announcements
 HW #5 Ch. 18, on WebCT
 Due Date for HW #5 is Mon. DEC. 31, 2007
 Quiz on Ch. 18, Mon. DEC. 31, 2007 ?????
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 3
ME 307
Machine
Design I
8-2
The Mechanics of Power Screws
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 4
ME 307
Machine
Design I
Example-1
A power screw is 23 mm in diameter and has a thread pitch of 7 mm.
(a) Find the thread depth, the thread width, the mean and root
diameters, and the lead, provided square threads are used.
(b) Repeat part (a) for Acme threads.
Given:
Diameter of the power screw, d = 23 mm
Thread pitch, p = 7 mm
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 5
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 6
ME 307
Machine
Design I
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 7
ME 307
Machine
Design I
The Mechanics of Power Screws
A power screw is a device used in
machinery to change the angular
motion into linear motion, and
usually,
to transmit power.
Applications:
 Lead screws of lathes
 Screws for vises, presses and
jacks
Figure 8-4
The Joyce worm-gear screw jack.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 8
ME 307
Machine
Design I
The Mechanics of Power Screws
In Figure 8-5 a square threaded power
screw with single thread having a mean
diameter dm, a pitch angle p, and a lead
angle λ, and a helix angle
ψ is loaded by
the axial compressive force
F.
We wish to find an expression for the
torque required to raise this load, and
another expression for the torque
required to lower the load.
Dr. A. Aziz Bazoune
Figure 8-5
(Square)
Portion of a power screw
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 9
ME 307
Machine
Design I
Figure 8-6
Force Diagrams (a) Lifting the load; (b)lowering the load
Imagine that a single thread of the screw is enrolled or developed (Fig. 8-6) for
exactly a single turn. Then on edge of the thread will form the hypotenuse of a
right triangle whose base is the circumference of the mean-thread- circle and
whose height is the lead. The angle λ is the lead angle of the thread . For raising the
load a force PR acts to the right and to lower the load, PL acts to the left.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 10
ME 307
Machine
Design I
For raising the load
For lowering the load
Dr. A. Aziz Bazoune
F
F
H
 PR  N sin   f N cos   0
V
 F  N cos   f N sin   0
F
F
(a)
H
  PL  N sin   f N cos   0
V
 F  N cos   f N sin   0
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
(b)
LEC 34 Slide 11
ME 307
Machine
Design I
Eliminating N from the previous equations and solving for P gives
For raising the load
For lowering the load
Dr. A. Aziz Bazoune
F  sin   f cos  
PR 
cos   f sin 
(c)
F  f cos   sin  
PR 
cos   f sin 
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
(d)
CH-8
LEC 34 Slide 12
ME 307
Machine
Design I
Next, divide the numerator and the denominator of these
equations by cos λ and use the relation tan   l  d m
For raising the load
For lowering the load
Dr. A. Aziz Bazoune
F  l  d m   f 
PR 
1   f l  dm 
PR 
F  f   l  d m  
1   f l  dm 
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
(e)
(f)
LEC 34 Slide 13
ME 307
Machine
Design I
The torque is the product of the force P and the mean radius d m 2
Torque required for raising the load
TR
to overcome thread friction and to
raise the load
Torque required for lowering the load
TL
to overcome part of the thread
friction in lowering the load
Dr. A. Aziz Bazoune
TR 
Fdm  l  f  d m 


2   dm  f l 
(8-1)
TL 
Fdm  f  d m  l 


2   dm  f l 
(8-2)
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 14
ME 307
Machine
Design I
Self Locking Condition
 If the lead is large or the friction is low, the load will lower itself
by causing the screw to spin without any external effort. In such
cases the torque TL from Eq. (8-2) will be negative or zero.
 When a positive torque is obtained from this equation, the screw
is said to be self locking
Condition for Self Locking:
 fd m  l
Dividing both sides of the above inequality by  d m and recognizing
that
l  d m  tan  , we get
f  tan 
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
(8-3)
CH-8
LEC 34 Slide 15
ME 307
Machine
Design I
Self Locking Condition
 The critical coefficient of friction for the lead concerned, f
 If f = fcr
 tan 
the nut is on the point of moving down the thread without
any torque applied.
 If f > fcr then the thread is self-locking in that the nut cannot undo
by itself, it needs to be unscrewed by a definite negative torque;
Clearly self-locking behavior is essential for threaded fasteners.
 Car lifting jacks would not be of much use if the load fell as soon as
the operating handle was released.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 16
Power Screw-Overhauling
ME 307
Machine
Design I
If f < fcr then the thread is overhauling in that the nut will unscrew by
itself under the action of the load unless prevented by a positive
tightening torque.
Some applications of power screws require overhauling behavior.
1.
The Archimedean drill
2.
Pump action screwdrivers
(Yankee screw drivers)
These devices incorporate very
large lead angles
Increasing lead (angle)
Dr. A. Aziz Bazoune
overhauling
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 17
ME 307
Machine
Design I
Power Screw-Overhauling
Sensitive linear actuators may incorporate recirculating ball screws
such as that illustrated here to reduce thread friction to levels which
go hand-in-hand with overhauling.
decreasing thread friction
Dr. A. Aziz Bazoune
overhauling
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 18
ME 307
Machine
Design I
Power Screw-Overhauling
Sensitive linear actuators may incorporate recirculating ball screws
such as that illustrated here to reduce thread friction to levels which
go hand-in-hand with overhauling.
decreasing thread friction
Dr. A. Aziz Bazoune
overhauling
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 19
ME 307
Machine
Design I
Efficiency
 If we let f  0 in Eq. (8-1), we obtain
Fl
T0 
2
(g)
which, is the torque required to raise
the load.
 The efficiency is therefore
T0
Fl
efficiency  e 

TR 2TR
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
(8-4)
CH-8
LEC 34 Slide 20
ME 307
Machine
Design I
Efficiency
f
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 21
ME 307
Machine
Design I
Power Screw- ACME Thread
F is parallel to screw axis i.e. makes angle
α= 14.5° with thread surface ignoring the
small effect of l, the resultant normal force
N is F/cos α . The frictional force = f N is
increased and thus friction terms in Eq.
(8.1) are modified accordingly:
Torque required to raise load F
d m  l  πfd m sec  
TR  F


2  πd m  fl sec  
(8-5)
ACME thread is not as efficient as square thread because of additional friction
due to wedging action but it is often preferred because it is easier to machine.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 22
ME 307
Machine
Design I
Power Screw with Collar
In most of power screw applications (load lifting) a collar is to be designed.
The presence of collar increases the friction torque. A thrust collar bearing
must be employed between the rotating and stationary members in order to
carry the axial component
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 23
ME 307
Machine
Design I
Power Screw with Collar
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 24
ME 307
Machine
Design I
Power Screw with Collar
If f c is the
coefficient of collar
friction, the torque
required is
d m  l  πfd m sec  
TR  F

  Tc
2  πd m  fl sec  
fc= collar friction coefficient
Ff c d c
dc = collar mean diameter
(8-6)
Tc 
2
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 25
ME 307
Machine
Design I
Power Screws-friction coefficients
 Friction wears thread surface for safe applications Max thread
bearing pressure is given in Table 8-4.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 26
ME 307
Machine
Design I
Power Screws-friction coefficients
Table 8-5 Coefficients of friction f for Threaded Pairs
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 27
ME 307
Machine
Design I
Power Screws-friction coefficients
Table 8-6 Thrust Collar friction coefficient, fc
 Coefficients of friction around 0.1 to 0.2 may be expected
for common materials under conditions of ordinary service
and lubrication.
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 28
ME 307
Machine
Design I
Example-2
Problem # 8.8 (modified)
Given:
• 5/8”-6ACME? i.e. d=5/8” and N=6
• f=fc= 0.15
• dc=7/16 in
• P = 6 lb
• Larm=2 3/4 in
P
Larm
F
Required:
F, efficiency, Self-Lock?
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 29
ME 307
Machine
Design I
Example-2 (Cont.’d)
Lever torque
d
TR total
p/2 =1/2N
Tc 
d
F m
2
 l  πfd m sec 

 πd m  fl sec 

  Tc

Ff c d c
2
l =1/N
R
Clamping force
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 30
ME 307
Machine
Design I
Example-2 (Cont.’d)
Efficiency
Fl
161 0.1667
Efficiency  e 

 0.26
2 TR
2   16.5
Self-lock
 fd m  l
 fd m    0.15  0.5417  0.255
l  0.1667
which is clear that it is self lock
Dr. A. Aziz Bazoune
Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8
LEC 34 Slide 31