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ME‐205 : Element of machine dynamics and design
Dr. Muhammad Wasif
Assistant Professor – I.M.D.
Ph.D. (CAD/CAM – Canada), M.Engg. (Mfg. Engg. – NEDUET),
B.E. (Mech. Engg. – NED UET). Member ASME and PEC
Room : 1st on LHS of main corridor, ground floor – IM Building
Machine dynamics : Gear Trains
1
Gear Drives
• Are more efficient and durable than the flexible power drives.
• Due to different designs of gears, these can used to transmit
torque and angular velocity in a wide variety of applications.
• Due to no slippage between two gear, power loss in the gear
drives are negligible.
• Gear drives are used for precise velocity ratios and high
power transmission applications.
• These are used in compact machines with less center
distances.
2ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)

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Gear Drives ‐ Limitation
• Machining of gears are much costlier than the
manufacturing of flexible power drives.
• It requires proper method of lubrication, for longer
life and efficient operation.
• Machining error and misalignment cause the noise
and vibrations, which result in failure of the gear
drives.
3ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
Classification of Gear Drives
4ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)

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Classification of Gear Drives
5ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
Differential of
engine
Wind turbine Engine
Transmission
Opposite direction Same direction Linear direction
Gear Drives for Parallel Shafts
6ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
Spur Gears
• Lengthwise teeth direction is parallel to the gear
rotation axis (uniform cross section).
• Easy to machine,
• High quality gears can be produces.
• Available in different types of tooth design and pressure angles.
In a gear pair, gears exerts only thrust force on each other.
Applications : Watches, toys, transmission drives etc.
Spur Gears

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Gear Drives for Parallel Shafts
7ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
Helical Gears
• Teeth lengthwise direction is oblique to the
gear rotation axis (increase length of teeth)
• Carry more load due to long teeth.
• Gear pair exert axial as well as thrust fore to
each other.
• Can also be used for non‐parallel shafts.
• These gears are more expensive than the spur
gear and slightly less efficient.
• Applications : Transmission of car, motorcycle.
Helical
Gears
8ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)

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Gear Drives for Non‐Parallel Shafts
9ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
Bevel Gears
• Are used for non‐parallel, intersecting and non‐
intersecting shafts.
• Straight, zerol and spiral bevel gears are different
types of bevel gear, based on different curvatures
of teeth.
• Spiral bevel gears are more durable, produce less
vibration, due to gradual contact b/w curved
teeth.
• Hypoid gear is a special type of spiral bevel gear
with pinion at an offset.
Straight Bevel Gears
Spiral Bevel Gears
Gear Drives for Non‐Parallel Shafts
10ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
Bevel Gears
• Spiral bevel gears provide high reduction ratio.
• Have high contact ratio with less noise, than the
straight or zerol bevel gears.
• Spiral bevel gears are more expensive and
machined by complex machine tools.
• Applications : Vehicle transmission, choppers.
Miter Gears
• Special type of bevel gear used for 90 degree
shaft with 1:1 velocity ratio.
Miter Gears

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11ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
12ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)

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Gear Drives for Non‐Parallel Shafts
13ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
Worm Gears
• Worm is a shank having at least one complete
tooth (thread), which drives the wheel having teeth
in helical direction, to be driven by a worm.
• Provides high reduction ratio
• Worm pair rotates in one direction and restrict the
rotation in opposite direction. i.e. worm drives the
wheel, wheel cannot drive a worm, therefore, it
locks the mechanism in one direction.
• Noiseless operation.
• Applications : chain block, speed reducer.
Worm Gears
14ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)

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15ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
Gear Nomenclature
16ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
Pitch Point
• The basic requirement of gear‐tooth
geometry is the provide the velocity ratios
exactly constant.
• The action of a pair of gear teeth satisfying
this requirement is termed conjugate
gear‐tooth action.
• Law of gearing states;
“As the gears rotate, the common
normal to the surfaces at the point of contact
must always intersect the line of centers at
the same point P, called the pitch point.”

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Gear Nomenclature
17ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
Pitch Circles
• A Circle passing through the pitch point,
with the center at the rotation axis of the
gear is called pitch circle.
• A gear with larger pitch circle is called
member gear, whereas, other gear with
smaller pitch circle is called pinion. No
matter which one is driver or driven.
• The velocity ratio and center distance are;
. .
0.5 =
Where, p=pinion, g=gear, =angular velocity
d=pitch diameter, r=pitch radius.
Gear Nomenclature
18ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
Pressure Angle
• Circle passing through the pitch
point, with the center at the rotation
axis of the gear is called pitch circle.
• The gear with larger pitch circle is
called member gear, whereas, gear
with smaller pitch circle is called
pinion. No matter which one is driver
or driven.
• The velocity ratio between two gear
is;
. .
Where, p=pinion, g=gear, =angular
velocity
d i h di f h

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Gear Nomenclature
19ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
• For a 3D spur gear, pitch cylinder is
considered, which is formed by pitch circle
pulled about the rotation axis of the gear.
• The tooth surface above the pitch cylinder
is called “face”, whereas, tooth surface
below the cylinder is called ” flank”.
• Circular pitch (p) : Distance measured on
the circumference of the pitch circle from
a point of one tooth to the corresponding
point on the next tooth.
• Pressure angle () : It is the angle between
the common normal to two gear teeth at
the point of contact and the common
tangent at the pitch point.

Gear Nomenclature
20ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
Profile

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Gear Nomenclature
21ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
• For a 3D spur gear, pitch cylinder is
considered, which is formed by pitch circle
pulled about the rotation axis of the gear.
• The tooth surface above the pitch cylinder
is called “face”, whereas, tooth surface
below the cylinder is called ” flank”.
• Circular pitch (p) : Distance measured on
the circumference of the pitch circle from
a point of one tooth to the corresponding
point on the next tooth.
∙ ∙
• Diametral pitch (P) : No. of teeth per inch.

Gear Nomenclature
22ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
• Module (m) : Pitch diameter in mm.
1
• Addendum : It is the radial distance of a tooth
from the pitch circle to the top of the tooth.
• Dedendum : It is the radial distance of a tooth
from the pitch circle to the bottom of the
tooth.
• Addendum circle : It is the circle drawn
through the top of the teeth and is concentric
with the pitch circle.
• Dedendum circle : It is the circle drawn
through the bottom of the teeth. It is also
called root circle.
• Total depth : It is the radial distance between
the addendum and the dedendum circle of a
• gear.

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Gear Nomenclature
23ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
• Clearance : It is the radial distance from
the top of the tooth to the bottom of the
tooth, in a meshing gear.
• Working depth. It is radial distance from
the addendum circle to the clearance
circle. It is equal to the sum of the
addendum of the two meshing gears.
• Tooth thickness : It is the width of the
tooth measured along the pitch circle.
• Tooth space : It is the width of space
between the two adjacent teeth measured
along the pitch circle.
• Backlash : It is the difference between the
tooth space and the tooth thickness, as
measured on the pitch circle.
Gear Nomenclature
24ME‐205, Elements of Machine design and dynamics, conducted by Dr. Muhammad Wasif (Asst. Professor ‐ IMD, NEDUET)
• Top land : It is the surface of the top of the
tooth.
• Face width : It is the width of the gear
tooth measured parallel to the axis of
rotation.
• Profile : It is the curve formed by the face
and flank of the tooth.
• Fillet radius : It is the radius that connects
the root circle to the profile of the tooth.
• Path of contact : It is the path traced by
the point of contact of two teeth from the
beginning to the end of engagement.

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Refernces
25
• R.S. Khurmi, G.K. Gupta, 2005, A text book of machine design, New Dehli‐ India,
EURASIA PUBLISHING HOUSE.
• R. G. Budynass, J.K. Nisbett, 2005, Shigley’s Mechanical Engineering Deisgn, New
York –USA, McGraw Hill.
• R.C. Juvinall, K.M. Marshek, 2012, Fundamental of Machine Componenet Design,
NJ, John Willey and Sons.
• http://www.mae.ncsu.edu/eischen/
• http://www.khkgears.co.jp/en/gear_technology/pdf/gearabc_b.pdfB. J. Hamrock
• http://www.xtek.com/pdf/wp‐gear‐terminology.pdf
• http://www.khkgears.co.jp/en/gear_technology/pdf/gearabc_b.pdf