MEP 209: Design of Machine elements LEC 10

2
Introduction
The helical-thread screw was very
important invention for application in:
• power transmission,
• angular to linear motion change,
• generation of large forces,
• non-permanent joints.
Fastening: the major target is to reduce
number of joins. One of the most
interesting subjects in engineering:
Example:
- Boeing 747 requires as many as 2.5 million fasteners. Some are very expensive.
Designer’s aim is to select an adequate fastener (bolt, nut, cap, screw …) for an
application in question: - the shape and the arrangement
- the size and other functional parameters
- to check if selected fastener can sustain required load
MPE 209 - Dr Mohamed Elfarran

Ahmed Kovacevic, City University London3
Definitions
and standards
Pitch
distance between adjacent thread forms
measured parallel to the thread axis.
Major diameter (d, dc)
Largest diameter of a screw thread
Mean–Pitch diameter (d2, dp)
Mean diameter; teeth section is p/2 long
Minor diameter (d1, dr)
Smalest diameter of the thread
Orientation
Threads are usually right-handed (RH)
unless otherwise required
Thread angle
60o for M and UN threads
Thread height (H)
For M and UN threads
3
2
H p=
Crest of the thread
May be flat or round

Design web
4
Screw Threads
Metric Threads:
• Thread angle = 60o
• Symmetric profiles
• Identified as M and MJ
• Coarse and fine pitch
• Specification of the thread:
M12 x 1.75
The metric thread
designation
Nominal major
diameter
Pitch:
coarse or fine

(all dimensions in mm)
Metric
threads

Design web
6
Screw Threads
Metric Threads:
• Thread angle = 60o
• Identified as M and MJ
• Coarse and fine pitch
M12 x 1.75
The metric thread
designation
Unified threads:
(usually pipe threads)
Thread angle = 60o
• Serief UN and UNR
• Coarse (C) and fine (F) pitch
¼ in-20 UNRC
Nominal major
diameter
Pitch:
coarse or fine
Nominal major
diameter
Threads per inch
(coarse or fine)
Thread series:
UNC, UNF,
UNRC, UNRF

Unified Screw Threads (dimensions in “)

8
Threaded Fasteners
Hexagon head bolt
Fillet – stress concentration
Start of the thread
Thread root fillet in the
plane of the nut
Ideal bolt
length:
1-2
threads
to remain
when
fully
bolted
The purpose of a bolt is to clamp two or more parts together.
The clamping load stretches or elongates the bolt and remains as preload
When tightening, bolt head should be held stationary – nut should turn.

9
Properties of a threaded fastener
Bolt - has a nut which turns to tighten
Screw - turns itself in the threaded hole
Stud - has no head and is threaded on both sides
Clearance hole - 15-20% larger than a bolt/stud size
Taped hole - drilled smaller than the minor dia.
extends deeper than the stud
Stud depth - 1.5 times the major diameter
Thread length - only a couple of threads longer than a bolt
The shank diameter of a 'waisted' bolt is less than
the thread diameter; allows a thread run out
which reduces stress concentration.
A Washer under the nut ensures uniformity of a
contact.
A bolt's 'grip' is the combined thickness of the
fastened parts

10
Load that a bolt can sustain
b
t
F
A
σ =
r
P
A
τ =
class no. 4.6 5.8 8.8 9.8 10.9 12.9
St Tensile [Mpa] 400 500 800 900 1000 1200
Sy Yield [Mpa] 240 400 640 720 900 1080
Sp Proof [Mpa] 225 380 590 650 830 970
Elongation % 22 20 12 10 9 8
Shear stress:
Tensile stress:
Strength
table

11
Typical cap-screw heads
Fillister head Flat head Hexagonal socket head

Other types of screw heads in use
Hexagonal washer faced regular
nut
regular nut chamfered on both sides
jam nut with washer face
jam nut chamfered on both sides
Nuts

13
Setscrews
regular nut chamfered on both sides
jam nut with washer face
jam nut chamfered on both sides

Bolt Specification
Nominal diameter
¼-20 x ¾ in UNC-2 Grade 5 Hex head bolt
Threads per inch
length
Thread series
Class fit
Material grade
Head type
M12 x 1.75 ISO 4.8 Hex head bolt
Metric
Nominal diameter
Pitch
Material class

15
Multiple threaded screws
(a) Single, (b) double, (c) triple threaded screws.
l=3pl=2pl=p

Design web
14
Threads for power screws
Square and Acme threads:
• Used for power transmission
• These have preferred sizes but also can vary
• Modifications to these threads are easy
Preferred Pitches for power threads:

Mechanics of Power Screws
 Power screw
◦ Used to change angular motion into
linear motion
◦ Usually transmits power
◦ Examples include vises, presses,
jacks, lead screw on lathe
Fig. 8–4

 Find expression for torque required to
raise or lower a load
 Unroll one turn of a thread
 Treat thread as inclined plane
 Do force analysis
Fig. 8–5
Fig. 8–6 MPE 209 - Dr Mohamed Elfarran

 For raising the load
 For lowering the load
Fig. 8–6 MPE 209 - Dr Mohamed Elfarran

 Eliminate N and solve for P to raise and lower the load
 Divide numerator and denominator by cosl and use relation
tanl = l /p dm

Raising and Lowering Torque
 Noting that the torque is the product of the force and the mean
radius,

Tension Loaded Bolted Joint
 Grip length l includes
everything being compressed
by bolt preload, including
washers
 Washer under head prevents
burrs at the hole from
gouging into the fillet under
the bolt head
Fig. 8–13

Pressure Vessel Head
 Hex-head cap screw in
tapped hole used to fasten
cylinder head to cylinder
body
 Note O-ring seal, not
affecting the stiffness of the
members within the grip
 Only part of the threaded
length of the bolt contributes
to the effective grip l
Fig. 8–14

Effective Grip Length for Tapped Holes
 For screw in tapped hole,
effective grip length is

Bolted Joint Stiffnesses
 During bolt preload
◦ bolt is stretched
◦ members in grip are
compressed
 When external load P is
applied
◦ Bolt stretches further
◦ Members in grip
uncompress some
 Joint can be modeled as a
soft bolt spring in parallel
with a stiff member spring
Fig. 8–13

Bolt Stiffness
 Axially loaded rod,
partly threaded and
partly unthreaded
 Consider each portion as
a spring
 Combine as two springs
in series

Procedure to Find Bolt Stiffness

Member Stiffness
 Stress distribution spreads from face of
bolt head and nut
 Model as a cone with top cut off
 Called a frustum

Tension Loaded Bolted Joints

Tension Loaded Bolted Joints
 During bolt preload
◦ bolt is stretched
◦ members in grip are compressed
 When external load P is applied
◦ Bolt stretches an additional
amount d
◦ Members in grip uncompress same
amount d Fig. 8–13

Stiffness Constant
 Since P = Pb + Pm,
 C is defined as the stiffness constant of the joint
 C indicates the proportion of external load P that the bolt will
carry. A good design target is around 0.2.

Bolt and Member Loads
 The resultant bolt load is
 The resultant load on the members is
 These results are only valid if the load on the members remains
negative, indicating the members stay in compression.

17
Example
The cover of a pressurised cylinder is attached by a
self-energising seal and 6 identical bolts M10x1.5 of
class 8.8. The fluid pressure is essentially constant at 6
MPa. A safety factor of three is required. Check if the
given bolt can sustain the pressure!
P=6MPa 6 class 8.8 M10x1.5
ds=120 mm Nd=3
-----------------------------------------------------------------------------
St /σ=?
SOLUTION:
Force on the cover
caused by the pressure:
2 2
6 0.12
6 10 67858 67.9
4 4
s
c s c
d
F p A p F N kN
π π ⋅
= ⋅ = = ⋅ = =
Force on the individual bolt 67.9 11.3
6 6
c
b b
F
F F kN= = =
From tables: Tensile stress area Proof strength
2
58tA mm= 590pS MPa=
Stress on each bolt: 11300 194
58
b
t
F
MPa
A
σ σ= = =
Selected number of bolts can sustain the load
590
3.04
194
p
d
S
N
σ
= = ≈

MEP 209: Design of Machine elements LEC 10

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MEP 209: Design of Machine elements LEC 10