Files 2-Lectures LEC 34

7/31/2019 Files 2-Lectures LEC 34

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ME 307MachineDesign I

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints

CH-8 LEC 34 Slide 1


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8-1 Thread Standards and Definitions

8-2 The Mechanics of Power Screws8-3 Strength Constraints8-4 Joints-Fasteners Stiffness8-5 Joints-Member Stiffness8-6 Bolt Strength

8-7 Tension Joints-The External Load8-8 Relating Bolt Torque to Bolt Tension8-9 Statically Loaded Tension Joint with Preload8-10 Gasketed Joints8-11 Fatigue Loading of Tension Joints

8-12 Shear Joints8-13 Setscrews8-14 Keys and Pins8-15 Stochastic Considerations

CH-8 LEC 34 Slide 2


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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 ?????

CH-8 LEC 34 Slide 3


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8-2 The Mechanics of Power Screws

CH-8 LEC 34 Slide 4


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Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent JointsCH-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-1

Given:

Diameter of the power screw, d= 23 mm

Thread pitch,p = 7 mm


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Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent JointsCH-8 LEC 34 Slide 6


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CH-8 LEC 34 Slide 7


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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 andjacks

Figure 8-4

The Joyce worm-gear screw jack.

CH-8 LEC 34 Slide 8


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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 anglep, and a lead

angle , and a helix angle 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


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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 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


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For raising the loadsin cos 0

cos sin 0

H R

V

F P N f N

F F N f N

(a)

For lowering the loadsin cos 0

cos sin 0

H L

V

F P N f N

F F N f N

(b)


ME 307


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For raising the load sin coscos sin

R

F fP

f

(c)

For lowering the load (d)


EliminatingNfrom the previous equations and solving for P gives

cos sincos sin

R

F fP

f

ME 307


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For raising the load

1m

R

m

F l d f P

f l d

(e)

For lowering the load (f)


Next, divide the numerator and the denominator of these

equations by cos and use the relation tan ml d

1m

R

m

F f l d P

f l d

ME 307


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2

m mR

m

Fd l f d T

d f l

(8-1)

(8-2)


The torque is the product of the force P and the mean radius 2m

d

Torque required for raising the load

to overcome thread friction and toraise the loadR

T

2

m mL

m

Fd f d lT

d f l

Torque required for lowering the loadto overcome part of the threadfriction in lowering the loadL

T

ME 307 Self Locking Condition


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Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 15

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 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

md

tanml d

tanf (8-3)

ME 307


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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.

Iff > 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

tanf

ME 307

P S O h li


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MachineDesign I


Some applications of power screws require overhauling behavior.

1. The Archimedean drill

2. Pump action screwdrivers(Yankee screw drivers)

These devices incorporate verylarge lead angles

Power Screw-Overhauling

Iff < fcrthen the thread is overhauling in that the nut will unscrew byitself under the action of the load unless prevented by a positivetightening torque.

Increasing lead (angle) overhauling


ME 307

P S O h li


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MachineDesign I


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.



ME 307

P S O h li


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MachineDesign I


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.



ME 307h Effi i


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MachineDesign I


Efficiency

If we let in Eq. (8-1), we obtain0f

which, is the torque required to raise

the load.

(8-4)

0

2

FlT

(g)

The efficiency is therefore

RR T

Fl

T

Teefficiency2

0

ME 307M hi Effi i


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MachineDesign I


f


Efficiency

ME 307Machine P S ACME Th d


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MachineDesign I


Power Screw- ACME Thread

Fis parallel to screw axis i.e. makes angle

= 14.5with thread surface ignoring the

small effect ofl, theresultant normal force

NisF/cos. The frictional force =f Nisincreased and thus friction terms in Eq.

(8.1) are modified accordingly:

Torque required to raise load F

sec

sec

m mR

m

d l fdT F

2 d 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 307Machine

P S ith C ll


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MachineDesign I


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 tocarry the axial component


Power Screw with Collar

ME 307Machine Po er Scre ith Collar


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MachineDesign I



ME 307Machine Power Screw with Collar


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MachineDesign I


fc= collar friction coefficient

dc = collar mean diameter



sec

sec

m m

R c

m

c c

c

d l fdT F T

2 d fl

Ff dT

2

If is the

coefficient of collar

friction, the torque

required is

c

f

(8-6)

ME 307Machine Power Screws-friction coefficients


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Design I


Power Screws-friction coefficients

Friction wears thread surface for safe applications Maxthreadbearing pressureis given in Table 8-4.




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Design I




Table 8-5 Coefficients of frictionf for Threaded Pairs



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Design I




Table 8-6 Thrust Collar friction coefficient,fc

Coefficients of friction around 0.1 to 0.2 may be expectedfor common materials under conditions ofordinary service

and lubrication.

ME 307Machine Example 2


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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

Required:

F, efficiency, Self-Lock?

PLarm

F


ME 307MachineD i I Example-2 (Cont d)


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Design I


Lever torque

Clamping force

R

l=1/N

2

dFfT

Tf ld

fdl2

dFT

ccc

c

m

mm

totalR

sec

sec

p/2 =1/2Nd


Example-2 (Cont. d)

ME 307MachineDesign I Example-2 (Cont d)


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Design I


Efficiency161 0.1667

0.262 2 16.5

R

FlEfficiency e

T

Self-lock

which is clear that it is self lock


0.15 0.5417 0.255

0.1667

m

m

fd l

fd

l

Example-2 (Cont. d)

Documents

Files 2-Lectures LEC 34