Me312 dsulec10-screws-170213050612

ME 312 – Machine Design
Dr. Bilal A. Siddiqui,
Asst. Prof (ME)
1
Spring 312 (c) Bilal Siddiqui 2016 2/13/2017

Screw, Fastners and Non-permanent
Joints
The helical thread screw is one the most important mechanical device.
It forms the basis of
Power screws: change angular motion to linear motion (presses, jacks, etc.)
threaded fasteners for non-permanent joints.
Typical methods for non-permanently joining parts:
Bolts
Nuts
Screws
Rivets
retainers, locking devices, pins, keys, adhesives etc.
2

Can something like a nut and screw be
important?
Fasteners will always be need to facilitate disassembly for maintenance etc.
One of the key targets of current design for manufacture is to reduce the number of fasteners.
Boeing’s 747 airliner requires 2.5 million fasteners, some of which cost several dollars each.
To keep costs down manufacturers constantly review new fastener designs, installation
techniques, and tooling.
Design and Manufacture of fasteners is a huge industry globally
Methods of joining parts are extremely important in the engineering of a quality design
3

Nomenclature4
Sharp vee threads shown for clarity; the crests and roots are actuallyflattened
or rounded during the forming operation.
Pitch is the distance between adjacent thread turns parallel to thread axis. The pitch in B.E.
units is the reciprocal of the number of thread turns per inch (N).
The major diameter d is the largest diameter of a screw thread.
The minor (or root) diameter dr is the smallest diameter of a screw thread.
Pitch diameter dp is a theoretical diameter between major & minor diameters.
The lead l, not shown, is the distance the nut moves parallel to screw axis when the nut is
given one turn. For a single thread, the lead is the same as the pitch.
A multiple-threaded screw is one having two or more threads cut beside each other.
Most screws, bolts, and nuts all have single threads
A double-threaded screw has a lead equal to twice the pitch
If the bolt is turned clockwise, the bolt advances toward the nut. I.e. it closes.
The thread angle is 60◦ and the crests of the thread may be either flat or rounded.

Unified classes of threads
The UN (unified common) class of screw is the most commonly used series in common applications. It is
The UNRF (unified reduced fatigue) profile has a rounded fillet at the root of the thread. Due to reduced stress
concentration, they are used where high fatigue strength is required.
Unified (UN and UNRF) threads are specified by the nominal major diameter, no of threads per inch, and thread
series, for example, 0.58 in-18 UNRF or 0.625 in-18 UNRF.
Metric threads are specified by writing the diameter and pitch in millimeters
M12 × 1.75 is a thread having a nominal major diameter of 12 mm and a pitch of 1.75 mm. [Note that the letter M
here means it is metric unit designation]
Many tensile tests of threaded rods have shown that an unthreaded rod having a diameter equal to the mean of
the pitch diameter and minor diameter will have the same tensile strength as the threaded rod. The area of this
unthreaded rod is called the tensile-stress area At of the threaded rod. See tables 8-1 and 8-2
2/13/2017Spring 312 (c) Bilal Siddiqui 2016
5

Table 8-1
Table 8-2
2/13/2017
6
Spring 312 (c) Bilal Siddiqui 2016

Thread for Power Screws
Square and Acme threads are used on screws when power is to be
transmitted.
Preferred pitches are listed. However, other pitches can be and often are
used, since the need for a standard for such threads is not great.
7

Threaded Fasteners – Bolts and Screws
Screws, nuts and bolts
Bolts are for the assembly of two unthreaded components, with the aid of a nut. Screws
in contrast are used with components, at least one of which contains its own internal
thread
The purpose of a bolt is to clamp two or more parts together.
The clamping load stretches or elongates the bolt; the load is obtained by twisting the
nut until the bolt has elongated almost to the elastic limit.
hold the bolt head stationary and twist the nut; in this way the bolt shank will not feel
the thread-friction torque.
Points of stress concentration are at the fillet, at the start of the threads (runout), and at
the thread-root fillet in the plane of the nut ( when present)
The diameter of the washer face is the same as the width W of hexagon.
8

Threaded Fasteners - Nuts9
In applications where vibration or rotation may work a nut loose, various locking mechanisms
may be employed: Adhesives, safety pins or lockwire, nylon inserts, or slightly oval-shaped
threads.
A rule of thumb is that preloads of 60 %of proof load rarely loosen.
Sometimes we use two nuts to prevent loosening. In local jargon it is called “check-nut”
A car hub, with the centralnut
hidden behind a
castellated nut cover that is
locked against rotation usinga
cotter pin. The effect is similar
to using a castellated nut.

Why Hexagonal?
The most common shape for bolt-heads and nuts is hexagonal
6 sides give a good granularity of angles for a tool to approach from (good in tight
spots)
More (and smaller) corners would be vulnerable to being rounded off.
It takes only 1/6th of a rotation to obtain the next side of the hexagon and grip is
optimal.
Polygons with more than 6 sides do not give the requisite grip and polygons with
less than 6 sides take more time to be given the next grip position.
Other specialized shapes exist for certain needs, such as wings for finger
adjustment and captive nuts for inaccessible areas
10

Threaded Fasteners - Washers
The ideal bolt length is one in which only one or two threads project from the nut after
it is tightened.
Bolt holes may have burrs or sharp edges after drilling.
These could bite into the fillet and increase stress concentration.
Therefore, washers must always be used under the bolt head to prevent this.
They should be of hardened steel and loaded onto the bolt so that the rounded edge
of the stamped hole faces the washer face of the bolt.
Sometimes it is necessary to use washers under the nut too.
11
Plain (left) and split (right)washers
Belleville or conical washer Curved disc spring washer Toothed lock washer with external teeth

Threaded Fasteners - Gaskets
A gasket is a mechanical seal which fills the space between two or more mating
surfaces, generally to prevent leakage from or into the joined objects while under
compression.
Gaskets allow "less-than-perfect" mating surfaces on machine parts where they can fill
irregularities.
Gaskets are commonly produced by cutting from sheet materials.
It is usually desirable that the gasket is able to deform and tightly fills the space it is
designed for, including any slight irregularities. A few gaskets require an application of
sealant directly to the gasket surface to function properly.
Gaskets are normally made paper, rubber, silicone, metal, cork, felt, neoprene, nitrile
rubber, fiberglass, Teflon) or a plastic polymer.
Most industrial gasket applications involve bolts exerting compression >2000 psi
The more compressive load exerted on the gasket, the longer it will last!
12
Some seals and gaskets
1. O-ring
2. fiber washer
3. paper gaskets
4. cylinder head gasket

O-rings
An O-ring is a gasket in the shape of a torus made of an elastomer
It is designed to be seated in a groove and compressed during assembly between
two or more parts, creating a seal at the interface.
O-rings are one of the most common seals used in machine design because they
are inexpensive, easy to make, reliable, and have simple mounting requirements.
They can seal tens of MPa of pressure
There are O-ring materials which can tolerate temperatures as low as -200 C or as
high as 250+ C.
13

Washers and Gaskets
14
Section of cylindrical pressure
vessel. Hexagon-head cap
screws are used to fasten the
cylinder head to the body.
Note the use of an O-ring seal.
A bolted connection loaded in
tension by the forces P. Note
the use of two washers. Note
how the threads extend into the
body of the connection.
When a connection is desired that can be disassembled without destructive methods
and that is strong enough to resist external tensile loads, moment loads, and shear
loads, or a combination of these, then the simple bolted joint using hardened-steel
washers is a good solution. Such a joint can also be dangerous unless it is properly
designed and assembled by a trained mechanic.

Cap-screws: bolting without nut15

Stud Screw – Alternate to not using nut
A stud is a rod threaded on both ends.
A stud is screwed into the lower member first
then the top member is positioned and fastened down with hardened washers and nuts.
Studs are regarded as permanent
Joint can be disassembled merely by removing the nut and washer
Threaded part of lower member not damaged by reusing threads (unlike screws)
16

Head studs
17
Sometimes, both ends are tightened with nuts.
This joint is non-permanent.
In engines, an important decision to choose b/w head bolt or head stud.
Head bolts are also twisted during torqueing, which means not all torque is
converted into clamping force.
Stud bolt is more efficient in torqueing. No torque lost in twisting.
Head bolts more convenient for disassembly though
head studs are better suited for high-performance vehicles
with greater power requirements, while head bolts are
more practical for personal, everyday automobiles.

Grip of the Fastener
𝑇𝐿 =
The thread length of inch-series bolts, where d is the nominal diameter, is
2𝑑 +0.25", 𝑓𝑜𝑟 𝐿≤6"
2𝑑 +0.50", 𝑓𝑜𝑟 𝐿>6"
𝐿 𝑇 =
For metric bolts it is
2𝑑 +6𝑚𝑚,
2𝑑 +12𝑚𝑚,
2𝑑 +25𝑚𝑚,
𝑓𝑜𝑟 𝐿≤ 125𝑚𝑚
𝑓𝑜𝑟125𝑚𝑚 < 𝐿> 200𝑚𝑚
𝑓𝑜𝑟 𝐿> 200𝑚𝑚
The ideal bolt length is one in which only one or two threads project from the nut
after it is tightened.
During tightening, the 1st thread of the nut tends to take the entire load
But yielding occurs & load is eventually divided over about 3 nut threads.
The grip l of a connection is the total thickness of the clamped material.
Due to a few threads taking the load, 𝑙≠ 𝐿 𝑇
18

Fastener and Grip Length
017Spring 312 (c) Bilal Siddiqui 2016 2/13/2
19
Find H and t from
tables A-31 andA-
32

Nut and Washer Dimensions
20

Stiffness of the Bolt
Twisting the nut stretches the bolt to produce the clamping force. This clamping
force is called the pretension or bolt preload.
Since the members are being clamped together, the clamping force that produces
tension in the bolt induces compression in the members.
deflection produced by that force. (𝐹 = 𝑘bΔ𝑙⇒ 𝑘 𝑏 =
𝐹
Δ𝑙
𝐸 𝐴 Δ𝑙
Δ𝑙
= 𝑙
=
𝐴 𝐸
𝑙
)
21
Find E from
Table 8-8
Stiffness of portion of a
bolt or screw clamped The spring rate is the ratio between the force applied to the member and the
zone consists
a) Unthreaded portion
𝑑
𝐴 𝑑
𝐸
𝑘 = 𝑙𝑑
a) Threaded portion
𝑘𝑡 =
𝐴 𝑡 𝐸
𝑙𝑡
Two springs in series
𝑘
1 1 1
=
𝑘
+
𝑘𝑏 𝑡 𝑑

Stiffness of the Joint
Since the members are being clamped together, the clamping force that produces
tension in the bolt induces compression in the members.
Clamped members also act like springs in series
The spring rate of the members being joint by the fastener is
Where E is the modulus of elasticity of the material of the members. In this formula we
assume all the members being jointed are of the same material
22
Find E from
Table 8-8
If one of the
members is a soft
gasket, its stiffness
relative to the other
members is
usually so small that
for all practical
purposes the others
can be neglected
and only
the gasket stiffness
used.

An Example
As shown above, two steel plates are clamped by washer-faced 1
in-20 UNF × 11
2 2
2
in SAE grade 5 bolts each with a standard 1
N steel plain washer.
(a) Determine the bolt spring rate kb.
(b) Determine the member spring rate km
(c) Determine the length of the bolt.
23

Answer
From Table A–32, the thickness of a standard 1/2N plain washer is
0.095 in. From Table A-31, height for 0.5” nut is H=0.4375”
𝑑 4
d=0.5”,  𝐴 = 𝜋
𝑑2 =0.196 𝑖𝑛2, For all materials 𝐸 =30 𝑀𝑝𝑠𝑖
Grip length, 𝑙=0.5+0.75+0.095= 1.345“
Length of bolt is 𝐿> 𝑙+ 𝐻 ≅1.8"
Threaded length of bolt is 𝐿 𝑇 =2𝑑 +0.25= 1.25"
Length of unthreaded portion in grip 𝑙𝑑= 𝐿− 𝐿 𝑇 =0.55"
Threaded portion in the grip 𝑙𝑡= 𝑙− 𝑙𝑑=1.345−0.55= 0.795"
From Table 8-1, 𝐴 𝑇 =0.159 𝑖 𝑛2
𝑏The bolt stiffness is 𝑘 =
0.1960.159 30×106
0.1961.25 +0.159(0.095)
=3.59×106𝑙 𝑏/𝑖 𝑛
𝑚Member stiffness is 𝑘 =
0.5774𝜋 30×106 0.5
2 ln 50.5774 1.345 +0.50.5
0.5774 1.345 +2.50.5
=14.64×106 𝑙 𝑏/𝑖 𝑛
2/13/2017
Spring 312 (c) Bilal Siddiqui 2016
24

Bolt Strength
The proof load is the maximum load (force) that a bolt can withstand without acquiring a
permanent set.
The proof strength Sp is the ratio of proof load and tensile-stress area.
In the specification standards for bolts, the strength is specified by stating SAE or ASTM
minimum quantities, the minimum proof strength, or minimum proof load, and the
minimum tensile strength.
Min proof load is load at which 1% fasteners fail. 99% fasteners exceed it
The bolt grades are numbered according to the tensile strengths.
The grade of the nut should be the grade of the bolt.
Refer to Tables 8-9, 8-10 and 8-11 for minimum strength of steel bolts
ASTM threads are shorter because ASTM deals mostly with structures; structural
connections are generally loaded in shear, and the decreased thread length provides
more unthreaded shank area (remember 𝐴 𝑑 > 𝐴𝑡).
25
Typical stress-strain diagram
for bolt materials

Bolt Head Markings
The bolt grades are numbered according to the tensile strengths.
Grades are printed (grades or some geometric code) along with
manufacturer logo on the bolt head.
Unmarked bolts should be avoided as they may be unstandardized.
26

27

28

Standard Bolt Lengths
29

External Loads
N = Number of bolts in the joint
The bolt takes only 20% of the load, the rest is borne by the members
30
𝑏𝜎 =
𝑏
𝐴 𝑡
=
𝐹 𝐶𝑃 +𝐹 𝑖
𝐴 𝑡
𝑖, 𝜎 =
𝐹
𝑖
𝐴 𝑡
The entire joint behaves like two springs in parallel, since they
deflect by the same amount. Therefore, 𝐹 = 𝐹𝑏+ 𝐹 𝑚 andhence
𝑘 = 𝑘 𝑏 +𝑘 𝑚
The clamping force, aka preload Fi , has been correctly applied by tightening the nut before external
load P is applied.
Fi = preload
Ptotal = Total external tensile load applied to the joint
P = external tensile load per bolt
Pb = portion of P taken bybolt
Pm = portion of P taken bymembers
Fb = Pb + Fi = resultant bolt load
Fm = Pm − Fi = resultant load on members
C = fraction of external load P carried by bolt
1 − C = fraction of external load P carried by members

External Loads
Load is equally shared by bolts, 𝑃 = 𝑃𝑡𝑜𝑡𝑎𝑙
𝑁
P is tension load  It causes both bolt and member to deform by Δl
This is like springs in parallel. 𝑃 𝑏 = 𝑘𝑏Δ𝑙and 𝑃 𝑚 =𝑘 𝑚Δ𝑙
Since 𝑃 = 𝑃 𝑏 +𝑃 𝑚 = kb +km Δ𝑙=
𝑘 𝑏
𝑏
k +k k +kb m b m
𝑘
𝑚
𝑃 = 𝑃𝑚
Let 𝐶 =
𝑘 𝑏
𝑘 𝑏 +𝑘 𝑚
be the “stiffness of the joint”
Hence, we can write 𝑃 𝑏 = 𝐶𝑃 and 𝑃 𝑚 = 1− 𝐶 𝑃
Resultant loads are therefore 𝐹𝑏 = 𝑃 𝑏 + 𝐹𝑖= 𝐶𝑃 + 𝐹𝑖and 𝐹 𝑚 = 1− 𝐶 𝑃 −𝐹𝑖
31

Factors of Safety in Static Loads
As a rule, a bolt will either fracture during tightening, or not at all.
For non-permanent joints, it is recommended that preload Fi is of 75 % of proof
load Fp=SPAt
For permanentjoints,Fi=0.9Fp
𝒑The yielding FoS against the static stress exceeding proof strength is 𝒏 =
𝑺 𝒑
𝝈
𝒃
Another indicator of yielding that is sometimes used is a load factor nL which is
applied only to the load P as a guard against overloading.
𝑳
𝑺 𝑷 𝑨𝒕 −𝑭𝒊 𝑺 𝑷 𝑨𝒕 −𝑭𝒊
𝒏 = =
𝑷 𝒃 𝑪
𝑷
It is essential for a safe joint that external load be smaller than that needed to
cause the joint to separate. If separation occurs, then the entire external load is
borne by the bolt (remember bolt bears only 20-40% load in a joint)!
𝟎The load factor guarding against joint separation is 𝒏 =
𝑭 𝒊
𝑷 𝟏−𝑪
32

Bolt Tension and Bolt Torque
High preload is very desirable in important bolted connections.
The preload is the “muscle” of the joint, and its magnitude is determined by the bolt
strength. If the full bolt strength is not used in developing the pretension, then
money is wasted and the joint is weaker.
In such cases the wrench torque required to develop the specified preload must be
estimated.
The torque wrench has a built-in dial that indicates the proper torque.
Defining a torque coefficient K, we can relate preload with torque required
𝑇 = 𝐾𝐹𝑖 𝑑
K depends on the type of surfaces as well as lubrication
If not mentioned, you can take K=0.2
33

Another Example
A 3/4 in-16 UNF ×2 1
in SAE grade 5 bolt is subjected to a load P of 6 kip in a
2
tension joint. The initial bolt tension is Fi = 25 kip. The bolt and joint stiffnesses are
kb = 6.50 and km = 13.8 Mlbf/in,respectively.
(a) Determine the preload and service load stresses in the bolt. Compare these to
the SAE minimum proof strength of the bolt.
(b) Specify the torque necessary to develop the preload
Calculate the factors of safety and load factors.
Answer:
Done in class.
34

Yet another example
 cross section of a grade 25 cast-iron pressure vessel. N bolts are to be used to
resist a separating force of 36 kip.
(a) Determine kb, km, and C.
(b) Find number of bolts required for a load factor of 2 where the bolts may be reused
when the joint is taken apart.
(c) With the number of bolts obtained in part (b), determine actual load factor for
overload, the yielding factor of safety, and the load factor for joint separation.
Answer:
Done in class
35

Me312 dsulec10-screws-170213050612

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Me312 dsulec10-screws-170213050612

Similar to Me312 dsulec10-screws-170213050612 (20)

Recently uploaded

Recently uploaded (20)

Me312 dsulec10-screws-170213050612