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
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