Transcript Slide 1

GEARS
 Classification of gears – Gear tooth terminology -
Fundamental Law of toothed gearing and involute
gearing – Length of path of contact and contact ratio Interference and undercutting - Gear trains – Simple,
compound and Epicyclic gear trains - Differentials
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Spur Gears
Gears:
Gears
are
machine elements that
transmit motion by means
of successively engaging
teeth. The gear teeth act
like small levers.
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Power transmission systems
Belt/Rope Drives -
Large center distance of the shafts
Chain Drives
- Medium center distance of the shafts
Gear Drives
-
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Small center distance of the shafts
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Friction Discs
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Spur Gears animation
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Bevel Gears animation
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Applications animation
Conveyor/Counting
Gear train
Watch gear wheels
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Gear Pump
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Industrial Applications
Printing machinery parts
Diesel engine builders
Rotary die cutting machines
Hoists and Cranes
Blow molding machinery
Boat out drives
Agricultural equipment
Automotive prototype and reproduction
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Industrial Applications
Newspaper Industry
Plastics machinery
Motorcycle Transmissions
Polymer pumps
Automotive applications
Commercial and Military operations
Special gear box builders
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Industrial Applications
Heavy earth moving vehicles
Canning and bottling machinery builders
Special machine tool builders
Book binding machines
Marine applications
Injection molding machinery
Military off-road vehicles
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Stamping presses
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Classification
Gears may be classified according to the relative
position of the axes of revolution. The axes may be
parallel, intersecting and neither parallel nor intersecting.
1. Gears for
connecting
parallel shafts
Spur Gears:
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External contact
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Internal contact
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Helical gears
Parallel Helical gears
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Heringbone gears
(Double Helical gears)
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Bevel gears
2. Gears for connecting
intersecting shafts – Bevel Gears
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Bevel gears
Straight bevel gears
Spiral bevel gears
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3. Gears for neither parallel nor
intersecting shafts.
Worm & Worm Wheel
Crossed-helical gears
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Rack and Pinion
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Worm and Worm Wheel
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Hypoid Gear
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Hypoid Gear
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Gear Box
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Terminology
Spur Gears
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Terminology
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Definitions
Addendum:
The radial distance between the Pitch
Circle and the top of the teeth.
Arc of Action: Is the arc of the Pitch Circle between
the beginning and the end of the engagement of a
given pair of teeth.
Arc of Approach: Is the arc of the Pitch Circle
between the first point of contact of the gear teeth
and the Pitch Point.
Arc of Recession: That arc of the Pitch Circle
between the Pitch Point and the last point of contact
of the gear teeth.
Backlash: Play between mating teeth.
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Definitions
Base Circle: The circle from which is generated the
involute curve upon which the tooth profile is based.
Center Distance: The distance between centers of two
gears.
Chordal Addendum: The distance between a chord,
passing through the points where the Pitch Circle
crosses the tooth profile, and the tooth top.
Chordal Thickness: The thickness of the tooth
measured along a chord passing through the points
where the Pitch Circle crosses the tooth profile.
Circular Pitch: Millimeter of Pitch Circle circumference
per tooth.
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Definitions
Circular Thickness: The thickness of the tooth
measured along an arc following the Pitch Circle
Clearance: The distance between the top of a tooth and
the bottom of the space into which it fits on the meshing
gear.
Contact Ratio: The ratio of the length of the Arc of
Action to the Circular Pitch.
Dedendum: The radial distance between the bottom of
the tooth to pitch circle.
Diametral Pitch: Teeth per mm of diameter.
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Definitions
Face: The working surface of a gear tooth, located
between the pitch diameter and the top of the tooth.
Face Width: The width of the tooth measured parallel
to the gear axis.
Flank: The working surface of a gear tooth, located
between the pitch diameter and the bottom of the teeth
Gear: The larger of two meshed gears. If both gears
are the same size, they are both called "gears".
Land: The top surface of the tooth.
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Definitions
Line of Action: That line along which the point of contact
between gear teeth travels, between the first point of
contact and the last.
Module: Millimeter of Pitch Diameter to Teeth.
Pinion: The smaller of two meshed gears.
Pitch Circle: The circle, the radius of which is equal to the
distance from the center of the gear to the pitch point.
Diametral pitch: Teeth per millimeter of pitch diameter.
Pitch Point: The point of tangency of the pitch circles of
two meshing gears, where the Line of Centers crosses the
pitch circles.
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Definitions
Pressure Angle: Angle between the Line of Action and
a line perpendicular to the Line of Centers.
Profile Shift: An increase in the Outer Diameter and
Root Diameter of a gear, introduced to lower the
practical tooth number or acheive a non-standard
Center Distance.
Ratio: Ratio of the numbers of teeth on mating gears.
Root Circle: The circle that passes through the bottom
of the tooth spaces.
Root Diameter: The diameter of the Root Circle.
Working Depth: The depth to which a tooth extends
into the space between teeth on the mating gear.
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Formulae
Circular pitch  pc 

Diam etralpitch

D
T

T

Diam etralpitch  pd 
 
Circular pitch D pc
Teeth
Pitch diam eter
Diam etralpitch

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Teeth X Circular pitch
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Formulae
 Teeth on pinion 

 Circular pitch
Center dis tance  


2
 Teeth on Gear 



Teeth on pinion Teeth on Gear

2  Diam etral pitch
Base Circle Diameter PitchDiameter Cos 
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Forumulae Specific to Gears
with Standard Teeth
Addendum
= 1 ÷ Diametral Pitch
= 0.3183 × Circular Pitch
Dedendum
= 1.157 ÷ Diametral Pitch
= 0.3683 × Circular Pitch
Working Depth
= 2 ÷ Diametral Pitch
= 0.6366 × Circular Pitch
Whole Depth
= 2.157 ÷ Diametral Pitch
= 0.6866 × Circular Pitch
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Forumulae Specific to Gears
with Standard Teeth
Clearance
= 0.157 ÷ Diametral Pitch
= 0.05 × Circular Pitch
Outside Diameter = (Teeth + 2) ÷ Diametral Pitch
= (Teeth + 2) × Circular Pitch ÷ π
Diametral Pitch
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= (Teeth + 2) ÷ Outside Diameter
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Law of Gearing
Tooth profile 1 drives tooth profile 2
by acting at the instantaneous
contact point K.
N1 N2 is the common normal of
the two profiles.

N1 is the foot of the perpendicular
from O1 to N1N2
N2 is the foot of the perpendicular
from O2 to N1N2.
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Law of Gearing
Although the two profiles have
different velocities V1 and V2 at
point K, their velocities along
N1N2 are equal in both
magnitude
and
direction.
Otherwise the two tooth
profiles would separate from
each other. Therefore, we have
O1 N1 1 O2 N2 2
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
4.1
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Law of Gearing
1 O2 N 2

2 O1 N1
4.2

We notice that the intersection
of the tangency N1N2 and the
line of center O1O2 is point P,
and from the similar triangles
O1 N1 P  O2 N2 P
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4.3
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Law of Gearing
Therefore, velocity ratio
1 O2 P

2 O1 P
4.4

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Law of Gearing
From the equations 4.2 and 4.4,
we can write,
1 O2 P O2 N 2


2 O1 P
O1 N1
4.5

-ratio of the radii of the two base
circles and also given by;
O1 N1 O1P cos
O2 N 2  O2 P cos
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and
4.6
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Law of Gearing
-centre distance between the base
circles
O1O2  O1 P  O2 P
O1 N1 O2 N 2


cos
cos
O1 N1  O2 N 2

cos

4.7 
 = pressure angle or the angle of
obliquity. It is angle between the common
normal to the base circles and the
common tangent to the pitch circles.
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Constant Velocity Ratio
A common normal (the line of action)
to the tooth profiles at their point of
contact must, in all positions of the
contacting teeth, pass through a
fixed point on the line-of-centers
called the pitch point
Any two curves or profiles engaging
each other and satisfying the law of
gearing are conjugate curves, and
the relative rotation speed of the
gears will be constant (constant
velocity ratio).
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Conjugate Profiles
To obtain the expected velocity ratio
of two tooth profiles, the normal line
of their profiles must pass through
the corresponding pitch point, which
is decided by the velocity ratio. The
two profiles which satisfy this
requirement are called conjugate
profiles.
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
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Conjugate action
It is essential for correctly
meshing gears, the size of the
teeth ( the module ) must be
the same for both the gears.
Another requirement the
shape of teeth necessary for
the speed ratio to remain
constant during an increment
of rotation; this behaviour of
the contacting surfaces (ie.
the teeth flanks) is known as
conjugate action.
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