Mechanical Engineering Design Chapter 8Dr. A. Aziz Bazoune Chapter
8: Screws, Fasteners and the Design of Nonpermanent Joints
CH-8 LEC 34 Slide *
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
CH-8 LEC 34 Slide *
8-2 The Mechanics of Power Screws
8-3 Strength Constraints
8-4 Joints-Fasteners Stiffness
8-5 Joints-Member Stiffness
8-6 Bolt Strength
8-8 Relating Bolt Torque to Bolt Tension
8-9 Statically Loaded Tension Joint with Preload
8-10 Gasketed Joints
8-12 Shear Joints
8-15 Stochastic Considerations
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
Announcements
Due Date for HW #5 is Mon. DEC. 31, 2007
Quiz on Ch. 18, Mon. DEC. 31, 2007 ?????
CH-8 LEC 34 Slide *
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
CH-8 LEC 34 Slide *
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 *
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:
Thread pitch, p = 7 mm
Example-1
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
CH-8 LEC 34 Slide *
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
CH-8 LEC 34 Slide *
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
A power screw is a device used in machinery to change the angular
motion into linear motion, and usually, to transmit power.
Applications:
Figure 8-4
CH-8 LEC 34 Slide *
The Mechanics of Power Screws
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
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 *
The Mechanics of Power Screws
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 *
Figure 8-6 Force Diagrams (a) Lifting the load; (b)lowering the
load
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
For raising the load
CH-8 LEC 34 Slide *
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
For raising the load
CH-8 LEC 34 Slide *
Eliminating N from the previous equations and solving for P
gives
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
For raising the load
CH-8 LEC 34 Slide *
Next, divide the numerator and the denominator of these equations
by cos λ and use the relation
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
(8-1)
(8-2)
CH-8 LEC 34 Slide *
The torque is the product of the force P and the mean radius
Torque required for raising the load
to overcome thread friction and to raise the load
Torque required for lowering the load
to overcome part of the thread friction in lowering the load
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
CH-8 LEC 34 Slide *
(8-3)
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
Condition for Self Locking:
Dividing both sides of the above inequality by and recognizing that
, we get
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
CH-8 LEC 34 Slide *
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 Condition
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
Some applications of power screws require overhauling
behavior.
The Archimedean drill
large lead angles
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 *
Power Screw-Overhauling
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 *
Power Screw-Overhauling
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 *
Power Screw-Overhauling
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
CH-8 LEC 34 Slide *
which, is the torque required to raise the load.
(8-4)
(g)
The efficiency is therefore
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
f
Efficiency
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
CH-8 LEC 34 Slide *
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
(8-5)
*
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 *
Power Screw with Collar
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
CH-8 LEC 34 Slide *
Power Screw with Collar
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 *
Power Screw with Collar
If is the coefficient of collar friction, the torque required
is
(8-6)
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
Friction wears thread surface for safe applications Max thread
bearing pressure is given in Table 8-4.
CH-8 LEC 34 Slide *
Power Screws-friction coefficients
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
CH-8 LEC 34 Slide *
Power Screws-friction coefficients
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
CH-8 LEC 34 Slide *
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.
Power Screws-friction coefficients
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
Example-2
f=fc= 0.15
dc=7/16 in
P = 6 lb
P
Larm
F
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
Lever torque
Clamping force
Example-2 (Cont.’d)
Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of
Nonpermanent Joints
Efficiency
Self-lock
CH-8 LEC 34 Slide *