ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and...
-
Upload
ramon-leaverton -
Category
Documents
-
view
236 -
download
2
Transcript of ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and...
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
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
8-1 8-1 Thread Standards and DefinitionsThread Standards and Definitions8-28-2 The Mechanics of Power ScrewsThe Mechanics of Power Screws8-38-3 Strength Constraints Strength Constraints 8-48-4 Joints-Fasteners StiffnessJoints-Fasteners Stiffness8-58-5 Joints-Member Stiffness Joints-Member Stiffness 8-68-6 Bolt Strength Bolt Strength 8-78-7 Tension Joints-The External LoadTension Joints-The External Load8-88-8 Relating Bolt Torque to Bolt TensionRelating Bolt Torque to Bolt Tension8-98-9 Statically Loaded Tension Joint with PreloadStatically Loaded Tension Joint with Preload8-108-10 Gasketed JointsGasketed Joints8-118-11 Fatigue Loading of Tension JointsFatigue Loading of Tension Joints8-128-12 Shear JointsShear Joints8-138-13 SetscrewsSetscrews8-148-14 Keys and PinsKeys and Pins8-158-15 Stochastic ConsiderationsStochastic Considerations
CH-8 LEC 34 Slide 2
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
AnnouncementsAnnouncements
HW #5 Ch. 18, on WebCT Due Date for HW #5 is Mon. DEC. 31, 2007 Quiz on Ch. 18, Mon. DEC. 31, 2007 ?????
CH-8 LEC 34 Slide 3
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
8-28-2 The Mechanics of Power ScrewsThe Mechanics of Power Screws
CH-8 LEC 34 Slide 4
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 34 Slide 5
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.
Example-1Example-1
Given:
Diameter of the power screw, d = 23 mm
Thread pitch, p = 7 mm
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
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
The Mechanics of Power The Mechanics of Power ScrewsScrews
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.
CH-8 LEC 34 Slide 8
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
The Mechanics of Power The Mechanics of Power ScrewsScrews
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.
Figure 8-5 Portion of a power screw (Square)
CH-8 LEC 34 Slide 9
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
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.
CH-8 LEC 34 Slide 10
Figure 8-6 Force Diagrams (a) Lifting the load; (b)lowering the load
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
For raising the load
sin cos 0
cos sin 0
H R
V
F P N f N
F F N f N
(a)
For lowering the load
sin cos 0
cos sin 0
H L
V
F P N f N
F F N f N
(b)
CH-8 LEC 34 Slide 11
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
For raising the load
sin cos
cos sinR
F fP
f
(c)
For lowering the load
(d)
CH-8 LEC 34 Slide 12
Eliminating N from the previous equations and solving for P gives
cos sin
cos sinR
F fP
f
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
For raising the load
1
mR
m
F l d fP
f l d
(e
)
For lowering the load
(f)
CH-8 LEC 34 Slide 13
Next, divide the numerator and the denominator of these equations by cos λ and use the relationtan ml d
1
mR
m
F f l dP
f l d
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
2m m
Rm
Fd l f dT
d f l
(8-1)
(8-2)
CH-8 LEC 34 Slide 14
The torque is the product of the force P and the mean radius
2md
Torque required for raising the load
to overcome thread friction and to raise the load
RT
2m m
Lm
Fd f d lT
d f l
Torque required for lowering the load
to overcome part of the thread friction in lowering the load
LT
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 34 Slide 15
Self Locking ConditionSelf 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 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
LT
Condition for Self Locking: mfd l
Dividing both sides of the above inequality by and
recognizing that , we get
mdtanml d
tanf (8-3)
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 34 Slide 16
The critical coefficient of friction for the lead concerned,
If f = fcr 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.
Self Locking ConditionSelf Locking Condition
tanf
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
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
Power Screw-Power Screw-OverhaulingOverhauling
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.
Increasing lead (angle) overhauling
CH-8 LEC 34 Slide 17
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
decreasing thread friction 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.
CH-8 LEC 34 Slide 18
Power Screw-Power Screw-OverhaulingOverhauling
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
decreasing thread friction 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.
CH-8 LEC 34 Slide 19
Power Screw-Power Screw-OverhaulingOverhauling
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 34 Slide 20
EfficiencyEfficiency
If we let in Eq. (8-1), we
obtain
0f
which, is the torque required to
raise the load.
(8-4)
0 2
FlT
(g)
The efficiency is therefore
RR T
Fl
T
Teefficiency
20
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
f
CH-8 LEC 34 Slide 21
EfficiencyEfficiency
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 34 Slide 22
Power Screw- ACME Power Screw- ACME ThreadThread
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
sec
secm m
R
m
d l πfdT F
2 πd fl
(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.
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
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
CH-8 LEC 34 Slide 23
Power Screw with CollarPower Screw with Collar
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 34 Slide 24
Power Screw with CollarPower Screw with Collar
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
fc= collar friction coefficient
dc = collar mean diameter
CH-8 LEC 34 Slide 25
Power Screw with CollarPower Screw with Collar
sec
secm m
R cm
c cc
d l πfdT F T
2 πd fl
Ff dT
2
If is the coefficient of collar friction, the torque required is
cf
(8-6)
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
Power Screws-friction Power Screws-friction coefficientscoefficients
Friction wears thread surface for safe applications Max thread bearing pressure is given in Table 8-4.
CH-8 LEC 34 Slide 26
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
Power Screws-friction Power Screws-friction coefficientscoefficients
CH-8 LEC 34 Slide 27
Table 8-5 Coefficients of friction f for Threaded Pairs
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
Power Screws-friction Power Screws-friction coefficientscoefficients
CH-8 LEC 34 Slide 28
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.
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
Example-2Example-2
Problem # 8.8 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
Required:
F, efficiency, Self-Lock?
PLarm
F
CH-8 LEC 34 Slide 29
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
Lever torque
Clamping force
R
l =1/N
2
dFfT
Tflπd
πfdl
2
dFT
ccc
cm
mmtotalR
sec
sec
p/2 =1/2Nd
CH-8 LEC 34 Slide 30
Example-2 (Cont.’d)Example-2 (Cont.’d)
ME 307 Machine Design I
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
Efficiency
161 0.16670.26
2 2 16.5R
FlEfficiency e
T
Self-lock
which is clear that it is self lock
CH-8 LEC 34 Slide 31
0.15 0.5417 0.255
0.1667
m
m
fd l
fd
l
Example-2 (Cont.’d)Example-2 (Cont.’d)