ME08-08D-T

Machine Design 1
(lec/lab)
Shafting

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Prepared
Engineeringby: Engr Triztan S. dela Cruz
 shaft
• Is a rotating machine element which either receives power, transmits power or
both.
• Are of circular cross section
• Maybe solid or hollow depending upon the application
• Maybe of two types
-Transmission shaft
-Machine shaft

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
Technological University of the Philippines - Taguig
Bachelor of Science in Mechanical Engineering
Transmission shaft

• They receive
power from one
end and delivers
power at one
end

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 Machine shaft
• Integral part
of machine
• They are the
main
member in a
machine

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
Axle
• It is a non-rotating member used for supporting rotating wheels etc.
and it does not really transmitting the torque, it is only acted upon by
bending moment mostly.

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
Spindle
• Simply a short shaft

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 Transmission shafts from
the PSME Code,
Machinery’s handbook,
Kent’s M.E. handbook,

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
Terms such as lineshaft, headshaft, transmission
shaft, machinery shaft, countershaft, and flexible
shaft are names associated with special usage.
Most machine design books generally use the term shaft to mean
all of the above term

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 Material

• Mostly steel
• Medium carbon steel

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Bachelor of Science in Mechanical Engineering
Shaft design aspects
•Strength
•Rigidity or stiffness

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
General rule for shaft design
• In stiffness the shaft dimensions is obviously are going
to be much higher compared to what you will get if
you consider the strain criteria.

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
Factors to consider in shaft design
1. Critical speed
Is the speed where it becomes dynamically unstable.
Note: the frequency of free vibration of a non-rotating shaft is the
same as critical speed

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 Standard sizes of shaft
Typical sizes for solid shaft

Standard sizes of shafts Note: this will be serve as a

guidelines for availability but maybe
Up to 25 mm 0.5 mm increments there will be some changes
depending on the manufacturer but
25 to 50 mm 1.0 mm increments its better to design our best on this
type of available sizes which will
50 to 100 mm 2.0 mm increments obviously make an economic
decision.
100 to 200 mm 5.0 mm increments

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 Materials for shaft
• Hot rolled plain carbon steel
- Is a mill process which involves rolling the steel at high temperatures over
1700 degrees Fahrenheit. This steel is then cooled, which causes it to shrink, this means
there is less control over the size and shape of the finished product. This is part of the
reason hot rolled steel is typically cheaper than cold rolled steel. Hot rolled steel is used
when precise shapes and tolerances are not required. The three ways to identify the hot
rolled steel are scaly surface finish, rounded edges on bar stock and non-oily surface.
Typical application of hot rolled steel is our railroad tracks trailer parts and other materials
in the construction and welding trades. Hot rolled has a better values of tensile strength
and yield point and machining require to have smooth surfaces

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 Materials for shaft
Cold drawn plain carbon steel
- Cold rolled steel is essentially hot rolled steel that has been processes further. While hot
rolled steel is heated and cooled, cold rolled steel is heated, cooled at room temperature followed by
annealing and temper rolling. This additional processes allow for a wider range of finishes, and closer
dimensional tolerances. The term cold rolled steel is mistakenly used on all products but the name
actually refers to the rolling of flat rolled sheet and coil products. The term cold finishing or cold drawn
is used when referring to bar products, which usually consist of cold drawn through a die to create the
shape. The three ways to identify the cold rolled steel are a very smooth surface and a very sharp
edges on a bar stock. It use for machine parts, axles, automotive components and much more.
Machining is minimum and it has wide acceptability for general purpose transmission,

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 Materials for shaft
• Alloy steels
- Are made by combining carbon steel with one or more alloying
element. Adding different combinations and proportions of elements gives
the steel different characteristics.
3 desired Attribute
1. Hardness
2. Corrosion resistance
3. Retention of hardness and strength

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 Materials for shaft
• Alloy steels
- Some common alloying elements used to achieve these characteristics like:
Chromium - which adds increased toughness and wear resistance
Cobalt – used to improve hot hardness for application like cutting tools
Manganese – which increases surface hardness and resistance to strain, hammering and
shock
Molybdenum – which is used to increase strength and resistance to shock and heat
Nickel – used to increase strength and toughness while also improving corrosion resistance
Tungsten – which adds hardness and improves grain structure while improving heat
resistance

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 Materials for shaft
• Alloy steels
- Some common alloying elements used to achieve these characteristics like:
Vanadium – increases strength, toughness and shock resistance with improved corrosion
resistance
Chromium vanadium – is used to greatly improve tensile strength while remaining easy to
bend and cut

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
• Alloy steels
Materials for shaft
Most commonly used grades of alloy steel
1. 4140 – chromium molybdenum steel with good strength to wear resistance excellent toughness and
ductility with the ability to resist stress and creep at prolonged high temperatures
2. 4340 – nickel chromium molybdenum steel, with deep hardenability, high strength and high fatigue
to tensile ratio.
3. 6150 – a chromium vanadium steel that features excellent toughness, shock and abrasion resistance
4. 8620 – nickel chromium molybdenum steel, with good toughness and ductility with increased case
hardness

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 Materials for shaft
• Alloy steels
- Some common alloying elements used to achieve these
characteristics are chromium which adds increased toughness and wear
resistance
- used for relatively severe service conditions
- however, to obtain total effect of alloying elements, parts need to be heat
treated
- lesser tendency to crack
- lesser warp and distortion
- residual stresses are less compared to carbon steel

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 What if strength is not important?

• In situation comes that not always the strength of the shaft is very important
but take note strength is a criteria for the design and the shaft required to be
very distant that means it should have less wear in that particular case, one
can has to keep his/her attention more on to make this shaft surface such
that it is were resistance in comparison maybe strength is not that important
so you know this where resistance of the shaft means that one has to harden
the surfaces.

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 Common type of surface hardening
methodologies
• Case hardening- is a process of surface hardening whereby the surface or case is substantially harder than the core or inside metal.
• Carburizing- is a process of adding carbon to the surface of steel by exposing it to hot
carbonaceous solids, liquids.
• Cyaniding - As in liquid carburizing, cyaniding is accomplished by immersing the part
in a hot ( about 1550 Fahrenheit ) liquid salt bath, sodium cyanide (NaCN) being a
common medium in both processes.
• Nitriding- In surface hardening by nitriding, the machine and heat-treated part is placed in a nitrogenous environment, commonly ammonia
gas, at temperature much lower than those used in the previously describes processes, say 1000 Fahrenheit.

- are very common in hardening the surfaces where wear resistance becomes
important one has to hardening these in such kind of situations
Technological University of the Philippines - Taguig
Bachelor of Science in Mechanical Engineering
Design consideration
• Design based on strength

• Design based in stiffness

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
Design based on strength

• Is easily understandable in this situation is that it should be able to

withstand the external load which is coming and acting on the shaft
• So we have to take care of the material properties etc. so that the
shaft do not fail.

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
Design based in stiffness

• If we consider the design based on stiffness then it comes to the

picture is that even if you are having a strength of the shaft its
deflection should be limited to a desired extension of the desired
limit.

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 Design consideration
• Example
- if we try to bend a pen, what will happen? We may observe a deflection on the pen
or may not break altogether but it will have a simpler large deflection suppose applied by
relatively smaller load. This in certain cases is not desirable or in other words, suppose you
apply a torsion in both ends, then what happens? The ball pen may not break once again
but it can twist to a desirable extent so this is also sometimes not desirable that means
while designing the shaft then what will have is the requirement that neither it should
deflect to a large extent by application of external torque. In both the cases, what should be
the tolerance level of either the deflection or the twist upon the use of the shaft?Consider
the design based on strength at the beginning and then discuss the design of the shaft
based on stiffness.

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
Maximum torsional stress formula
16T
• Ss = 3 = Ssd
πD Solid shaft

16TD
• Ss = = Ssd
π(D4 −d4 )
Hollow shaft

16T 1 𝑑 B is the ratio of inner

• Ss = 3 = Ssd ∶ 𝐵= to the outer shaft
πD 1−𝐵4 𝐷
and k for solid shaft
=0

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
Angle of twist ( torsional deformation)

TL
θ= ; radians
JG
π 4
J= D
32
π 4
J= D − d4
32
Technological University of the Philippines - Taguig
Bachelor of Science in Mechanical Engineering
SHAFTS UNDER PURE BENDING

Maximum flexural stress

𝑀𝑐 𝜋 4 32𝑀
𝑆𝑓 = 𝑆𝑏 = where I = 𝐷 𝑆𝑓 =
𝐼 64 𝜋𝐷3
𝑡𝑟𝑦 𝑡𝑜 𝑚𝑒
𝑆𝑢𝑠𝑜𝑓𝑖𝑟𝑠𝑡 =
𝑝𝑎𝑑𝑒𝑑𝑒
Technological University of the Philippines - Taguig
Bachelor of Science in Mechanical Engineering
 SHAFTS UNDER PURE BENDING

32MD
ℎ𝑜𝑙𝑙𝑜𝑤 • Sf = = Sd 𝑐𝑜𝑑𝑒? 𝑡𝑟𝑦 𝑡𝑜 𝑚𝑎𝑖𝑑
π(D4 −d4 ) 𝑆𝑢𝑠𝑜𝑓𝑖𝑟𝑠𝑡 =
𝑠ℎ𝑎𝑓𝑡 𝑃𝑎𝑑𝑜𝑑𝑜

ℎ𝑜𝑙𝑙𝑜𝑤 32M 1 d 𝑡𝑟𝑦 𝑡𝑜 𝑚𝑒 𝑜𝑛𝑐𝑒

𝑠ℎ𝑎𝑓𝑡
Sf = = Sd ∶ B= 𝑆𝑢𝑠𝑜𝑓𝑖𝑟𝑠𝑡 = ( )
πD3 1−B4 D 𝑃𝑎𝑑𝑒𝑑𝑒 𝑏𝑒𝑓𝑜𝑟𝑒 1 −

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 PL3
•y=
Shaft deflection Csc EI For special case only

Shaft acts as a cantilever Shaft is simply supported Shaft has fixed supports
with load P at free end with load P at midspan with load P at midspan

𝐶𝑠𝑐 = 3 𝐶𝑠𝑐 = 48 𝐶𝑠𝑐 = 192

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 A.S.M.E Formulas
Shaft Design Stresses (Only Sy and Su are known)

𝑆𝑠𝑑 =0.3 𝑆𝑦
• 𝑆𝑠𝑑 =0.18 𝑆𝑢
ቅ Shear Design stress whichever is smaller: If shaft has a
keyway, consider a strength
reduction factor of 0.75

𝑆𝑠𝑑 = 0.6 𝑆𝑦 whichever is smaller: If

ቋ Normal Design stress
𝑆𝑠𝑑 = 0.36 𝑆𝑢 shaft has a keyway, consider
a strength reduction factor
of 0.75

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
Allowable deformations
Angle of Twist

Transmission shaft:

𝜃𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 =1° in a length of 20 diameters

Machinery shaft:

𝜃𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 =1° in a length of 20 diameters

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
Allowable deformations

• Transmission shaft:

ˠ𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 = 0.01 inch per foot of length between spports

• Machinery shaft:

ˠ𝑎𝑙𝑙𝑜𝑤𝑎𝑏𝑙𝑒 = 0.002 inch per foot of length

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 Transmission shafts from the PSME Code, Machinery’s handbook,
Kent’s M.E. handbook,

𝑁𝐷 where:
Above formulas were based on design
stresses of:
𝑃= P = horsepower transmitted - 4 ksi for main power transmitting

𝑘 N = rpm
D = shaft diameter in inches
shafts
- 6 ksi for line shafts and,
- 8.5 ksi for small/short shafts, and
countershafts
Note:
𝑓𝑜𝑟 𝑚𝑎𝑖𝑛 𝑝𝑜𝑤𝑒𝑟 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑖𝑛𝑔 𝑠ℎ𝑎𝑓𝑡 𝑘 = 80
Code: PaNDak 𝑓𝑜𝑟 𝑙𝑖𝑛𝑒 𝑠ℎ𝑎𝑓𝑡 𝑐𝑎𝑟𝑟𝑦𝑖𝑛𝑔 𝑝𝑢𝑙𝑙𝑒𝑦𝑠 𝑘 = 53.5
𝑎𝑛𝑑 𝑓𝑜𝑟 𝑠𝑚𝑎𝑙𝑙, 𝑠ℎ𝑜𝑟𝑡𝑠ℎ𝑎𝑡𝑠 𝑎𝑛𝑑 𝑐𝑜𝑢𝑛𝑡𝑒𝑟𝑠𝑎ℎ𝑓𝑡𝑠 = 38

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 Empirical Formulas from Machinery Handbook

Required Shaft Diameter:

•for an allowable angle of •for an allowable angle of •for short, solid shaft
twist not exceeding 0.08 twist not exceeding 1 in a subjected only to
per foot of length length of 20 diameters heavy transverse shear
4 3
𝐷 = 0.29 𝑇 𝐷 = 0.1 𝑇 1.7V
where: D=
Ss
D = shaft diameter in inches
T = torque in in-lb
V = maximum transverse shear load, lb
Ss = maximum torsional shearing stress, psi
Technological University of the Philippines - Taguig
Bachelor of Science in Mechanical Engineering
 Shaft Supported length VS. Shaft Diameter
(Deflection is limited to 0.01 inch per foot of length

• Shafting subjected
to no bending Shafting subjected to bending
action except its action due to pulleys
own weight
where:
3 L = maximum distance between 3
𝐿 = 8.95 𝐷2 𝐿 = 5.2 𝐷2
bearings, feet
D = shaft diameter in inches 2 𝐿
2 𝐿 𝐷3 =
𝐷3 = 5.2
8.95
Dare to try Love, Its not fine Dare to try Love, Finds two

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
Sample Problems
𝑀𝑁.𝑚
• A shaft is transmitting 1 at 240 rpm. Determine the diameter of
𝑆
shaft if the maximum permissible torque excesses mean torque by
20%. Take maximum allowable stress as 60 Mpa.
2𝜋TN
Given: 𝑃=
60
P= 1 MW
𝑁. 𝑀 2𝜋(N. M)N Take note: Better use this
N= 240 rpm 𝑠
=
60 units for faster computation
𝑇𝑚𝑎𝑥 = 1.2 𝑇𝑚𝑒𝑎𝑛
Safe Stress = 60 Mpa

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 𝐵𝑦 𝑈𝑠𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑐𝑟𝑖𝑡𝑒𝑟𝑖𝑎
𝑟𝑒𝑣
𝑁. 𝑚 2𝜋Tmean (240 )
1𝑥106 = 𝑠 16𝑇𝑚𝑎𝑥
𝑠 60 𝑆𝑠𝑚𝑎𝑥 =
𝜋𝐷3
𝑇𝑚𝑒𝑎𝑛 = 39,788.74 𝑁. 𝑚 𝑜𝑟 39,788.74 𝑥103 𝑁. 𝑚𝑚

16 47,746,488 𝑁. 𝑚𝑚
𝑇𝑚𝑎𝑥 = 1.2 39,788.74 𝑥103 𝑁. 𝑚𝑚 60 𝑀𝑃𝑎 =
𝜋𝐷3

𝑇𝑚𝑎𝑥 = 47,746,488 𝑁. 𝑚𝑚

𝑫 = 𝟏𝟓𝟗. 𝟒𝟒 𝒎𝒎

Better use 160 mm for safe design

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 A shaft made of mild steel is required to transmit a 100 KW at 300 rpm. The
supported length of the shaft is 3 meters. It carries two pulleys each weighing 1500 N
supported at distance of one meter from the ends respectively. Assuming safe value of stress
as 60 Mpa, determine the diameter of the shaft.

Pulley 1500 N Pulley 1500 N

𝐺𝑖𝑣𝑒𝑛:
P= 100 KW Support Support
N= 300 RPM bearing bearing
L=3 meters Shaft
W=1500 N
Safe Stress= 60 MPa
1m 1m

3m

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
Solve for the Diameter of shaft based on
bending and twisting moment
• Power transmitted by shaft (twisting moment)

2𝜋𝑇𝑁
𝑃=
60
rev
𝑁. 𝑚 2𝜋T 300
100𝑥103 = min
𝑠 60

𝑇 = 3,183.099 𝑁. 𝑚 𝑜𝑟 3183.099𝑥103 𝑁. 𝑚𝑚

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
 Bending moment

• 1500 𝑁 • 1500 𝑁 Reactions at each supported end

A C D B
𝑅𝐴 = 𝑅𝐵 = 1500 𝑁 𝑏𝑒𝑐𝑎𝑢𝑠𝑒 𝑡ℎ𝑒 𝑏𝑒𝑎𝑚 𝑖𝑠 𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐𝑎𝑙
1m 1m
𝑅𝐴 𝑅𝐵 Bending moment at point C

𝑀 = 𝐹. 𝐷
𝑀 = 1500 𝑁 𝑥 1 𝑚𝑒𝑡𝑒𝑟

𝑀 = 1500 𝑁. 𝑚

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
Equivalent Torque

• 𝑇𝑒𝑞 . = 𝑀2 + 𝑇 2

𝑇𝑒𝑞 = 1500 𝑁. 𝑚 2 + 3183.099 𝑁. 𝑚 2

𝑇𝑒𝑞 = 3518.82 𝑁. 𝑚

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
Solving for the diameter of the shaft

• Strength criteria for shaft design

16 Teq
𝑆𝑠𝑚𝑎𝑥 =
𝜋𝐷3 𝐷 = 68 𝑚𝑚 𝑓𝑜𝑟 𝑎 𝑠𝑎𝑓𝑒 𝑑𝑒𝑠𝑖𝑔𝑛 𝑎𝑛𝑑
𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑡𝑦 𝑡𝑜 𝑡ℎ𝑒 𝑚𝑎𝑟𝑘𝑒𝑡
16 3518.82 𝑥103 𝑁. 𝑚𝑚
60 𝑀𝑃𝑎 =
𝜋 𝐷 3

𝐷 = 66.85 𝑚𝑚

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
The shaft of a vertical turbo-generator set in a hydroelectric power plant has an
outside diameter of 305 mm and inside diameter of 254 mm. The shaft transmits
5000 hp at 750 rpm. The total weight of the shaft and the turbine runner is 54
metric tons. Determine the maximum normal stress of the shaft.

a. 33.58 Mpa c. 32.08 Mpa

b. b. 30.75 Mpa d. 35.42 Mpa

Technological University of the Philippines - Taguig

Bachelor of Science in Mechanical Engineering
Technological University of the Philippines - Taguig
Bachelor of Science in Mechanical Engineering
Technological University of the Philippines - Taguig
Bachelor of Science in Mechanical Engineering
Technological University of the Philippines - Taguig
Bachelor of Science in Mechanical Engineering