ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide

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



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



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



8-28-2 The Mechanics of Power ScrewsThe Mechanics of Power Screws

CH-8 LEC 34 Slide 4



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



CH-8 LEC 34 Slide 6



CH-8 LEC 34 Slide 7



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



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



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



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)





sin cos

cos sinR

F fP

f

(c)


(d)


Eliminating N from the previous equations and solving for P gives

cos sin

cos sinR

F fP

f




1

mR

m

F l d fP

f l d

(e

)


(f)


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



2m m

Rm

Fd l f dT

d f l

(8-1)

(8-2)


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




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)




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



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




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.





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.






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



f


EfficiencyEfficiency




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.



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


Power Screw with CollarPower Screw with Collar







fc= collar friction coefficient

dc = collar mean diameter



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)



Power Screws-friction Power Screws-friction coefficientscoefficients

Friction wears thread surface for safe applications Max thread bearing pressure is given in Table 8-4.






Table 8-5 Coefficients of friction f for Threaded Pairs





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-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




Lever torque

Clamping force

R

l =1/N

2

dFfT

Tflπd

πfdl

2

dFT

ccc

cm

mmtotalR

sec

sec

p/2 =1/2Nd


Example-2 (Cont.’d)Example-2 (Cont.’d)



Efficiency

161 0.16670.26

2 2 16.5R

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)Example-2 (Cont.’d)

Documents

ME 307 Machine Design I ME 307 Machine Design I Dr. A. Aziz BazouneChapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide