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 8-1 8-2 8-3 8-4 8-5 8-6 8-7 8-8 8-9 8-10 8-11 8-12 8-13 8-14 8-15 Dr. A. Aziz Bazoune Thread Standards and Definitions The Mechanics of Power Screws Strength Constraints Joints-Fasteners Stiffness Joints-Member Stiffness Bolt Strength Tension Joints-The External Load Relating Bolt Torque to Bolt Tension Statically Loaded Tension Joint with Preload Gasketed Joints Fatigue Loading of Tension Joints Shear Joints Setscrews Keys and Pins Stochastic Considerations Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 2

ME 307 Machine Design I

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 ?????

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 3

ME 307 Machine Design I

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 4

ME 307 Machine Design I

Example-1

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: Diameter of the power screw, d = 23 mm Thread pitch, p = 7 mm

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 5

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

The Mechanics of Power Screws

A power screw is a device used in machinery to change the angular motion into linear motion, and

 

Lead screws of lathes Screws for vises, presses and jacks Figure 8-4 The Joyce worm-gear screw jack.

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

ME 307 Machine Design I

The Mechanics of Power Screws

In Figure 8-5 a square threaded power screw with single thread having a mean diameter

d m

, 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. Dr. A. Aziz Bazoune Figure 8-5 (Square) Portion of a power screw Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 9

ME 307 Machine Design I Figure 8-6 Force Diagrams (a) Lifting the load; (b)lowering the load 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

P R

acts to the right and to lower the load,

P L

acts to the left.

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 10

ME 307 Machine Design I For raising the load For lowering the load

 

F H F V



P R



N

sin  

N

cos  

f N

cos   0

f N

sin   0  

F H F V

  

L N

sin  

N

cos  

f N f N

cos  sin   0  0 (a) (b)

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 11

ME 307 Machine Design I Eliminating

N

from the previous equations and solving for

P

gives For raising the load

P R



F

 sin cos    

f f

cos sin    (c)

For lowering the load

P R

 cos cos   

f

 sin sin    (d)

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 12

ME 307 Machine Design I Next, divide the numerator and the denominator of these equations by cos

λ

and use the relation

tan  

l



d m

For raising the load

P R



F

1  

l

 

f l d m

  

d m



f

For lowering the load

P R

 1    

l f l

 

d d m m

  (e) (f)

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 13

ME 307 Machine Design I The torque is the product of the force P and the mean radius

d m

2

Torque required for raising the load

T R

to overcome thread friction and to raise the load

T R



Fd m

2  

l

 

d m



m f l

  (8-1)

Torque required for lowering the load

T L

to overcome part of the thread friction in lowering the load

T L



Fd m

2     

m d m

 

l f l

   (8-2)

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 14

ME 307 Machine Design I

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

T L

negative or zero.



When a positive torque is obtained from this equation, the screw is said to be self locking Condition for Self Locking:



fd m



l



d m l



d m

 tan 

f



tan

 (8-3)

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

ME 307 Machine Design I

Self Locking Condition

 The critical coefficient of friction for the lead concerned,

f



tan

  If

f = f cr

the nut is on the point of moving down the thread without any torque applied.

 If

f > f cr

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.

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 16

ME 307 Machine Design I

Power Screw-Overhauling

If

f < f cr

then the thread is tightening torque.

overhauling

in that the nut will unscrew by itself under the action of the load unless prevented by a positive

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

Increasing lead (angle) overhauling

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 17

ME 307 Machine Design I

Power Screw-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

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 18

ME 307 Machine Design I

Power Screw-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

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 19

ME 307 Machine Design I

Efficiency



T

0 

Fl

2

 (g)

which, is the torque required to raise the load.



The efficiency is therefore

efficiency



e



T T

R

0 

Fl

2 

T

R

(8-4)

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 20

ME 307 Machine Design I

Efficiency

f Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 21

ME 307 Machine Design I

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

increased and thus friction terms in Eq. (8.1) are modified accordingly: is Torque required to raise load F

T

R



F d 2

m

 

l



πd

m

πfd

m



fl

sec sec     (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.

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 22

ME 307 Machine Design I

Power Screw with Collar

In most of power screw applications (load lifting) a 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 collar is to be designed. Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 23

ME 307 Machine Design I

Power Screw with Collar

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 24

ME 307 Machine Design I

Power Screw with Collar

f

coefficient of collar friction, the torque required is

T R



F d m 2

 

l



πd m πfd m



fl

sec sec     

T c T c



Ff d c c 2

(8-6)

f c

= collar friction coefficient

d c

= collar mean diameter

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 25

ME 307 Machine Design I

Power Screws-friction coefficients

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

thread

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 26

ME 307 Machine Design I

Power Screws-friction coefficients

Table 8-5 Coefficients of friction

f

for Threaded Pairs

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 27

ME 307 Machine Design I

Power Screws-friction coefficients

Table 8-6 Thrust Collar friction coefficient ,

f

c

 Coefficients of friction around 0.1 to 0.2 may be expected for common materials under conditions of ordinary service and lubrication.

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 28

ME 307 Machine Design I

Example-2

Problem # 8.8 (modified) Given:

•

5/8”-6ACME? i.e. d=5/8” and N=6

•

f=f c = 0.15

•

d c =7/16 in

•

P = 6 lb

•

L arm =2 3/4 in Required: F, efficiency, Self-Lock?

P

L arm

F Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 29

ME 307 Machine Design I

Example-2 (Cont.’d)

Lever torque

d

p/2 =1/2N T R



total



F d m 2

 

l



πd m πfd m



fl

sec sec     

T c T c



Ff c d c 2

l =1/N

R Clamping force

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 30

ME 307 Machine Design I

Example-2 (Cont.’d)

Efficiency

Efficiency Fl

2 

T R

 2 16.5

 0.26

Self-lock

 

l fd m



l



fd m

 

0.1667



0.15



0.5417



0.255

which is clear that it is self lock

Dr. A. Aziz Bazoune Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints CH-8 LEC 34 Slide 31