Me Machine Design Notes 09

8/2/2019 Me Machine Design Notes 09

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ME311 Machine Design

W Dornfeld05Nov2009 Fairfield University

School of Engineering

Lecture 9: Screws

(Chapter 16)


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Thread Geometry

Hamrock

Page 707

Diameters

Major

Crest

PitchRoot

Minor

Thread Height

Thread Pitch

Thread

Angle

p

inchThreadsn1

)/( =

The Pitch Diameter

is midway between

the Major and Minor

Diameters.


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Thread Types

Hamrock

Page 708

Single-, double-, and triple-threaded screws.Also called single-, double-, and triple-start.

Lead =

3 x Pitch

AcmeThread

SquareThread

Lead =

1 x Pitch

Acme threads are used in C-Clamps, vices, and cartoons.


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Details of Thread Profiles

Hamrock

Page 708

Relationships for M (metric) and UN (unified = US) screw threads.

Example:

UN: -20, means 0.25in. Major diameter & 20 threads/inch.

M: M8x1.25, means 8mm Major diameter & pitch of 1.25mm

Thread Height

pp

ht 8660.0)30tan(

5.0=

=


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Power Screws

Looking at a squarethread screw, we unwind

one turn:

Lead2 rm

This shows an inclined

ramp with angle

mr

Lead

2tan 1=

W

rm

rc

Lead

Threadfriction

Collar

friction

Mean

thread

radius

Mean

collar radius

Load

on nut

c

The Mean Radius is midway

between the Crest and Root Radii.


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Square Thread Screw Torque

The torque required toraise the load W is

and to lower the load, we

flip two signs:

+

+= ccmraise rrWT

tan1

tan

+

+

= ccmlower rrWT

tan1

tan

W

rm

rc

Lead

c

Hamrock

Page 715


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If the thread form is not square but has an angle ,replace the thread friction with the effective friction

Power Screw Thread Angle

)2/cos(

=e

The effect:

Square: = 0, /2= 0, 1/cos(0) = 1.0

Acme: = 29, /2= 14.5, 1/cos(14.5)= 1.033

Unified: = 60, /2= 30, 1/cos(30)= 1.15

The thread angle effectively increases surface friction between 3 and 15%

Note: Instead of/2, Hamrock uses

The difference is negligible.

)1tan(costan 1 =n


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Ball Screws Have Low Friction

Recirculating balls roll between ball screw

and ball nut to minimize friction.

These almost always overhaul.


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Our Scissors Jack

End with nutHandle End with ball

thrust bearing

1522 Lb Tension

1015 Lb


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Using Dornfeld Lecture Equations

dp= 0.436 in.

N = 8 Threads/InchLead = 1/N = 0.125 in.

==== 11.1)11111.1(tan)1/111.1(1

111.1tan

1tan 111

mr

Lead

..11.110000.1

00000.1)000.1)(111(

)11111.1)(0000.1(1

11111.11111.1

1

111.1111

tan1

tan

InLb

rrWT ccmraise

==

+=

+

+=

Thread angle b = 60

= 0.15W = 500 Lb.

Because this is not a square thread, must use effective coefficient offriction = /cos(/2) = 0.15/cos(30) = 0.15/0.866 = 0.1732

0


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Using Hamrock Equations

dp= 0.436 in.

N = 8 Threads/InchLead = 1/N = 0.125 in.

==

===

===

111.11)11111.1(tan

)00000.11111.1(tan)11tan00.1(costan)

1

tan(costan

11111.1)tan(;11.11

tan

1

111

1

n

n

mr

Lead

..11.1111111.1

11111.1)111(

)00000.1)(11.1(111.1

11.1)11111.1)(111.1()111.1)(111(

11.1tan11.11.11cos

)11.111.1tan1.11)(cos1/111.1(111

tancos

)tan)(cos1/(

InLb

rd

WT ccn

np

raise

==

+=

+=

+

+=

Thread angle b = 60

= 0.15W = 500 Lb.

[Eqn.

16.10]The equations are equivalent. Pick whichever one suits you best.

How close is this to /2 = 30?

0


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Overhauling Revisited

+

+

= cc

n

np

lower rd

WT

tancos

)tancos)(2/(

Power screws can lower all by themselves if the friction

becomes less than the tangent of the lead angle, . This corresponds to the numerator in the Tlower equation going

negative, with the transition being where the numerator is Zero.

You can use either Dornfeld or Hamrock equation, but

remember that the Dornfeld equation is Effective friction, and you

must multiply by cos(/2) to get the actual friction.

The equations are equivalent. Pick whichever one suits you best.

+

+= ccmlower rrWT

tan1

tan

tancos n=

tan)2/cos()2/cos(tan==

=e

e

Transition when:Hamrock:

Dornfeld:


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Failure Modes: Tensile Overload

When the tensile stress on a bolt exceeds thematerials Proof Strength, the bolt will

permanently stretch.

t

A

P= Where At is the Tensile Stress Area for

the bolt the equivalent area of asection cut through the bolt.

Hamrock

Page 731

29743.0

)7854.0(

=

ndA ct

For UN threads,

2)9382.0)(7854.0( pdA ct =

For M threads,

dc = Crest Dia (in.)

n = threads/in.

dc = Crest Dia (mm)

p = pitch (mm)


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Failure Modes: Thread Shear

Shear of Nut Threads Shear of Bolt Threads

ldA crestshear = ldA rootshear =

l

The shear strength

of the bolt and nut

material may not

be the same.


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Failure Modes: Shank Shear

4

2

shankshear

dA

=

Bolts are not really intended to be used this way unless they are

Shoulder Bolts:

Typically the preload from tightening the bolt clamps the joint,

and the friction between the members holds the joint.

111

11

shankshankshear

ddA

==


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Bolt Preload

So the bolt is really a spring that stretches

and creates preload on the joint.

JH Bickford explains :

'When we tighten a bolt,( a) we apply torque to the nut,

( b) the nut turns,

( c) the bolt stretches,

( d) creating preload.'

PKDT crest=

We use the Power Screw equations to determine how torque results

in preload. This can be approximated simply by:

Where T is torque, Dcrest is the bolt crest diameter, P is the preload,

and K is a dimensionless constant. K = 0.20 for clean, dry threads

and K = 0.15 for lubricated threads.


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Bolt Stiffness

A bolt looks like two

springs in series: one

rod with the Crest

diameter and one with

the Root diameter.

Their lengths areincreased to reflect the

head and nut.

++

+=

22

4.04.041

r

rt

c

cs

b d

dL

d

dL

Ek

shankL

threadL

Hamrock

Page 725


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Bolt Stiffness Exercise

Calculate the stiffness of a 3/8-16 screw that is

4 in. long and clamps 3.5 of material. Use

Eqn. 16.23 to determine shank length.

shankL

threadL

Hamrock

Page 726

boltLclampL

threadL

Note: Hamrock uses Lt in Eqns. 16.21 and

16.22/23, BUT THEY ARE DIFFERENT THINGS!

In 16.21 it is the Clamped thread length;

in 16.22/23 it is Total thread length.

Lt

in

16.22/23

Lt in

16.21


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Joint Stiffness

The material clamped bythe bolt also acts like a

spring in compression.

Effectively, only the material

in the red double conical

area matters.

There are many methods to

calculate this stiffness.

Compare these calculator

stiffness results fromtribology-abc.com with

Hamrocks Example 16.6

Hamrock

Page 727


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Bolt Strength

For Metric grades, the first number x 100 = Sut in MPa. The

fraction x Sut = Sy. Ex: grade 12.9 has Sut 1200 MPa and

Sy 0.9x1200 = 1080 MPa.Hamrock

Page 731


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Bolt Loading

Generally, bolts are preloaded to:

75% of Proof Load for reused

connections

90% of Proof Load for permanent

connections

where Proof Load = Proof Strength x At.

The Proof Strength is approximately at

the elastic limit for the material.

Hamrock

Page 733

Proof

0.2%Yield

Ultimate

S


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Recommended Site:

BoltScience.com

Documents

Me Machine Design Notes 09