2-Lectures LEC 34

Mechanical Engineering Design Chapter 8Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
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Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints
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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
Announcements
Due Date for HW #5 is Mon. DEC. 31, 2007
Quiz on Ch. 18, Mon. DEC. 31, 2007 ?????
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8-2 The Mechanics of Power Screws
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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
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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
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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.
Figure 8-5 Portion of a power screw (Square)
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The Mechanics of Power Screws
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.
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Figure 8-6 Force Diagrams (a) Lifting the load; (b)lowering the load
For raising the load
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Eliminating N from the previous equations and solving for P gives
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Next, divide the numerator and the denominator of these equations by cos λ and use the relation
(8-1)
(8-2)
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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
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(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
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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
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
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Power Screw-Overhauling
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.
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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.
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which, is the torque required to raise the load.
(8-4)
(g)
The efficiency is therefore
f
Efficiency
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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)
*
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
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Power Screw with Collar
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fc= collar friction coefficient
dc = collar mean diameter
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If is the coefficient of collar friction, the torque required is
(8-6)
Friction wears thread surface for safe applications Max thread bearing pressure is given in Table 8-4.
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Power Screws-friction coefficients
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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.
Example-2
f=fc= 0.15
dc=7/16 in
P = 6 lb
P
Larm
F
Lever torque
Clamping force
Example-2 (Cont.’d)
Efficiency
Self-lock
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2-Lectures LEC 34

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