MIDTERMS

MACHINE DESIGN

AXLE – non rotating bar which doesn’t transmit any SHAFT KEYS - are small machine member inserted
torque between a shaft and a hub to prevent angular rotation.

COUNTER SHAFT – secondary shaft which is not directly KEY - usually made from steel and is inserted or
connected to power source but driven by its through mounted between the shaft and the hub of the
belt, chain or gear drive component in an axial direction to prevent relative
movement.
CRANK SHAFT – used in multi cylinder
KEYSEAT - recess in the shaft
LINE SHAFT or MAIN SHAFT – transmission shaft driven
by prime mover KEYWAY – recess in the hub

PRESSURE VESSEL – any vessel which operates under SHIFT VARIATIONS - Shaft and hub keyways are often
pressure or the pressure is more than atmospheric cut on key seating machines

SHAFT – rotating bar generally of circular cross section SUNK KEYS - sunk into the shaft for half its thickness,
where the measurement is taken at the side of the key
- a mechanical device supported by a bearing
RECTANGULAR KEYS - wider than their height
SPINDLE – a short axle and shaft
PARALLEL SUNK KEYS - either rectangular or square
THERMAL STRESS – temperature changes cause the
sections but without the taper
body to expand or contract
GIB HEAD SUNK KEYS - added to make it easier to
TORSIONAL STRESS – shear stress produced when we
remove
apply the twisting moment to the end of a shaft about
its axis FEATHER KEYS - attached to the shaft or the hub to
permit relative axial movement
TORSION – twisting of an object due to an applied
torque WOODRUFF KEYS a semi-circular disc and fits into a
circular recess in the shaft machined by a woodruff
TRANSMISSION SHAFT – directly connected powers
keyway cutter

SADDLE KEYS - are not sunk into the shaft and hub
instead, they are only sunk into the hub

FLAT SADDLE KEYS - tapered at the top and flat at the

bottom

HOLLOW SADDLE KEYS - tapered at the top and curved

at the bottom

TANGENT KEYS - are fitted as a pair at right angles

ROUND/CIRCULAR KEYS - circular in section and fit into

holes drilled partly into the shaft and the hub
 FORMULAS: 𝑆𝑡 = 𝛿𝐸(𝑡2 − 𝑡1)

PRESSURE VESSEL Shaft Power

Thin-walled cylinder (tangential stress / hoop stress) 𝑃 = 2𝜋𝑇𝑁

transverse section
2𝜋𝑇𝑁
𝑃=
𝑃𝑖 𝐷𝑖 33000
𝑆𝑡 =
2𝑡 P = power, KN, Hp
Thick-walled cylinder (longitudinal stress / axial stress)
T= torque, KN.m, ft-lb
𝑃𝑖 𝐷𝑖
𝑆𝑙 = N = angular speed, rps, rpm
4𝑡
Thin-walled spherical
𝑃𝑖 𝐷𝑖 Strength of shaft assumed allowable stress
𝑆𝑡 = 𝑆𝑙 =
4𝑡 𝐷3 𝑁
Main shaft: (4000 psi) 𝑃=
For maximum tangential stress at the inside 80

𝑃𝑖 (𝑟𝑜2 + 𝑟𝑖2 ) − 2𝑃𝑜 𝑟𝑜2 𝐷3 𝑁

𝑆𝑡𝑖 = Line shaft: (6000 psi) 𝑃=
𝑟𝑜2 − 𝑟𝑖2 53.5

𝐷3 𝑁
For maximum tangential stress at the outside Short Shaft: (8500 psi) 𝑃= 38
2𝑃𝑖 𝑟𝑖2 − 𝑃𝑜 (𝑟𝑜2 + 𝑟𝑖2 ) Stress in shaft when subjected to pure tension
𝑆𝑡𝑖 =
𝑟𝑜2 − 𝑟𝑖2
𝑇𝑐 16𝑇
Maximum wall thickness Solid: 𝑆= = 𝜋𝐷3
𝐽
16
𝐷𝑖 𝑆𝑡 + 𝑃𝑖 (ductile) 𝑆 = 𝜋𝐷3 (√𝑚2 + 𝑡 2 )
𝑡= [√ −1
2 𝑆𝑡 − 𝑃𝑖
16
(brittle) 𝑆 = 𝜋𝐷3 (𝑚 + √𝑚2 + 𝑡 2)
Thermal Stress
𝑇𝑐 16𝑇𝐷𝑜
𝛿 =∝ 𝐿(𝑡2 − 𝑡1) Hollow: 𝑆= =
𝐽 𝜋[𝐷𝑜4 −𝐷𝑖4 ]
𝛿 = coefficient of thermal expansion, m/m.c
16𝐷𝑜
(11.6x10^-6 m/m.c)
(ductile) 𝑆= (√𝑚2 + 𝑡 2 )
𝜋𝐷3

t1 = initial temperature 16𝐷𝑜

(brittle) 𝑆= (√𝑚2 + 𝑡 2 )
𝜋(𝐷𝑜4 −𝐷𝑖4 )
t2 = final temperature
Angle of deflection
L = total length
𝑇𝐿
Deformation due to equivalent axial stress 𝜃=
𝐽𝐺
𝑃𝐿
𝛿= T = thickness
𝐴𝐸
L = length
𝐿 𝜋
𝑺𝑡 = J= (𝐷4 )
𝐸 32

𝜹thermal = 𝜹axialstress G = 11.5x10^6

Power in keys Design of 3-keys separated by 120deg
2𝜋𝑇𝑁 Torque transmitted per key
𝑃=
60
𝑻
Torque transmitted by the key 𝑻𝒌 = × 𝟏. 𝟏𝟓
𝒏𝒌
𝑻 = 𝑭(𝒓) Based on compressive stress
𝑫 𝟒𝑻(𝟏. 𝟓)
𝑻 = 𝑭( ) 𝑺𝒄 =
𝟐 𝑫𝒕𝑳𝒏𝒌
Design of keys Based on shearing stress
Based on torsional stress 𝟐𝑻(𝟏. 𝟓)
𝑺𝒔 =
𝟏𝟔𝑻 𝑫𝒃𝑳𝒏𝒌
𝑺= (pure tension of a solid shaft)
𝝅𝑫𝟑
𝑫 = shaft diameter
𝟎.𝟔 𝑺𝒚 𝟏𝟔𝑻
= 𝝅𝑫𝟑 (Sy = yield stress based on a shaft material) 𝑻 = torque transmitted
𝑵
𝒕 = thickness of the key

Based on compressive stress 𝑳 = length of the key

𝟒𝒕 𝒃 = width of the key

𝑺𝒄 =
𝑫𝒕𝑳
𝒏𝒌 = no. of the keys
Based on shearing
𝟐𝒕
𝑺𝒔 =
𝑫𝒃𝑳
Factor of Safety

N = 1.5 (for smooth loading)

N = 2.0-2.5 (for minor shock loading)

N = 4.5 (for sever shock loading)

Design of 2-keys separated by 90deg

Torque transmitted per key

𝑻
𝑻𝒌 = × 𝟏. 𝟐
𝒏𝒌
Based on compressive stress
𝟒𝑻(𝟏. 𝟐)
𝑺𝒄 =
𝑫𝒕𝑳𝒏𝒌
Based on shearing stress
𝟐𝑻(𝟏. 𝟐)
𝑺𝒔 =
𝑫𝒃𝑳𝒏𝒌