Download GEARs Length Of Path Of Contact

Introduction & History
Classifications
Nomenclature
Types of gears
Objectives & applications
Numerical Analysis
A Gear is a rotating machine part having cut teeth, or cogs,
which mesh with another toothed part in order to transmit
torque.
Why Is a Transmission Necessary?
What Does a Transmission Do?
Why Is a Transmission Necessary?
Provide torque multiplication at low speeds
Reduce engine RPM at highway speeds
Allow the engine to operate within its most efficient RPM range
Allows the engine to be disengaged from the rear wheels while
the vehicle is not moving (torque converter & clutch)
What Does a Transmission Do?
The basic purpose of a transmission breaks down into 3 parts
Ability to alter shaft RPM
Ability to multiply torque
Ability to reverse the direction of shaft rotation
Gears are the means of
Changing the direction of motion,
Increase or decrease the speed of the applied
motion.
Magnify or
Example:
Egg Beater
reduce the force that you apply.
Friction wheels:
The motion and power transmitted by gears is kinematically
equivalent to that transmitted by friction wheels or discs.
Advantages of Gear drives:

It transmits exact velocity ratio

It may be use to transmit large power

It may be used for small centre distance of shafts

It has high efficiency

It has reliable services

It has compact layout
Disadvantages of Gear drives:
It costs expensive to manufacture
Any type of error may cause vibrations and noise
It requires suitable lubricant and reliable method of applying
it, for proper operation of gear drives
Nomenclature
Nomenclature
Nomenclature
Pitch circle. It is an imaginary circle which by pure rolling action, would give the same
motion as the actual gear.
Pitch circle diameter. It is the diameter of the pitch circle. The size of the gear is
usually specified by the pitch circle diameter. It is also known as pitch
diameter.
Pitch point. It is a common point of contact between two pitch circles.
Pitch surface. It is the surface of the rolling discs which the meshing gears have
replaced at the pitch circle.
Pressure angle or angle of obliquity. 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. It is
usually denoted by φ.
The standard pressure angles are 14 1/2 ° and 20°.
Nomenclature
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.
Circular pitch. It is the distance measured on the circumference of the pitch
circle from a point of one tooth to the corresponding point on the next tooth. It
is usually denoted by pc.
Nomenclature
Diametral pitch. It is the ratio of number of teeth to the pitch circle diameter in
millimetres. It is denoted by pd .
Module. It is the ratio of the pitch circle diameter in millimeters to the number
of teeth. It is usually denoted by m.
Clearance. It is the radial distance from the top of the tooth to the bottom of
the tooth, in a meshing gear. A circle passing through the top of the meshing
gear is known as clearance circle.
Total depth. It is the radial distance between the addendum and the dedendum
circles of a gear. It is equal to the sum of the addendum and dedendum.
Working depth. It is the 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.
Nomenclature
Tooth space . It is the width of space between the two adjacent teeth measured
along the pitchcircle.
Backlash. It is the difference between the tooth space and the tooth thickness,
as measured along the pitch circle. Theoretically, the backlash should be zero,
but in actual practice some backlash must be allowed to prevent jamming of the
teeth due to tooth errors and thermal expansion.
Face of tooth. It is the surface of the gear tooth above the pitch surface.
Flank of tooth. It is the surface of the gear tooth below the pitch surface.
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 its axis.
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.
Nomenclature
Path of contact. It is the path traced by the point of contact of two teeth from
the beginning to the end of engagement.
*Length of the path of contact. It is the length of the common normal cut-off by
the addendum circles of the wheel and pinion.
** Arc of contact. It is the path traced by a point on the pitch circle from the
beginning to the end of engagement of a given pair of teeth. The arc of contact
consists of two parts, i.e.
(a) Arc of approach. It is the portion of the path of contact from the beginning
of the engagement to the pitch point.
(b) Arc of recess. It is the portion of the path of contact from the pitch point to
the end of the engagement of a pair of teeth.
Law Of Gearing:
The common normal at the point of contact
between a pair of teeth must always pass through the
pitch point.
Mathematically,
Velocity Of Sliding Of Teeth:
The velocity of sliding is the velocity of one tooth relative to
its mating tooth along the common tangent at the point of contact..
Mathematically,
VS = (ω1 + ω2 )QP
We see from equation that the,
“velocity of sliding is proportional to the distance of the point
of contact from the pitch point.”
Length Of Path Of Contact:
path of approach.
Path of recess.
Path Of Contact
Length Of Arc Of Contact:
Arc of approach.
Arc of recess.
Arc Of Contact
Contact Ratio:
The contact ratio or the number of pairs of teeth in contact is defined
as the “ratio of the length of the arc of contact to the circular pitch”.
Mathematically,
Contact ratio or number of pairs of teeth in contact is
c
lassification
According to the position of axes of the shafts.
The axes of the two shafts between which the motion is to be
transmitted, may be
(a) Parallel,
(b) Intersecting, and
(c) Non-intersecting and non-parallel.
c
lassification
According to the position of axes of the shafts.
(a) Spur Gears (Parallel)
c
lassification
According to the position of axes of the shafts.
 Spur Gears Applications
 Spur Gear and Plastic Spur Gears used
in a film winding component.
Spur Gears used in automatic packing machine.
Spur Gears are used in the film-cutting
component.
c
lassification
According to the position of axes of the shafts.
(b) Helical Bevel Gears(Non-Parallel & Intersecting)
c
lassification
According to the position of axes of the shafts.
Double Helical Gears(Non-Parallel & Intersecting)
c
lassification
According to the position of axes of the shafts.
Screw Gear (Crossed Helical Gear):
c
lassification
According to the position of axes of the shafts.
(b) spiral gears(Non-Parallel & Non-Intersecting)
c
lassification
According to type of Gearing. The gears, according to the type of gearing may
be classified as :
(a) External gearing,
(b) Internal gearing, and
(c) Rack and pinion.
External gearing,
c
lassification
According to type of Gearing.
(b) Internal gearing.
(c) Rack and pinion.
c
lassification
According to type of Gearing.
(c) Rack and pinion.
t
ypes
Worm gear and wheel:
.
Worm and wheel
c
lassification
According to the peripheral velocity of the gears. The gears, according to the
peripheral velocity of the gears may be classified as :
(a) Low velocity,
velocity less than 3m/s
(b) Medium velocity,
velocity between 3 and 15 m/s
(c) High velocity.
velocity more than 15 m/s
.
c
lassification
According to position of teeth on the gear surface. The teeth on the gear
surface may be:
(a) straight,
(b) inclined, and
(c) curved.
bjectives
GEARS USED TO CHANGE DIRECTION
bjectives
GEARS USED TO CHANGE SPEED
bjectives
GEARS USED TO CHANGE SPEED
bjectives
GEARS USED TO INCREASE MECHANICAL ADVANTAGE
bjectives
 ANCHOR WINCH
bjectives
Gears used in Modern Vehicles
Manual transmission
Unsynchronized transmission
Synchronized transmission
Synchronized transmission
Gear variety
Applications and popularity
bjectives
Gears used in Modern Vehicles
 Automatic transmission
 Hydraulic Automatic Transmission: A hydraulic automatic transmission
consists of the following parts:
1. Torque converter
3. Clutches and bands,
History and improvements
2. Planetary gear set,
4.Hydraulic & lubricating oil:,
umerical
Gear Ratios:
•
When two gears are in mesh, a gear ratio exists
Driven Gear = Ratio
Drive Gear
• Example:
–
–
–
–
Drive gear has 14 teeth
Driven gear has 28 teeth
28  14 = 2:1 ratio (two to one ratio)
The drive gear must rotate twice to make the driven gear rotate
once
umerical
Speed Change:
The change in RPM from the input gear to the output gear is
directly proportional to the gear ratio
• Example:
3:1 gear ratio
– Input gear turns at 900 RPM
– Output gear turns at 300 RPM
umerical
Torque Multiplication:
The change in torque from the input gear to the output gear is
directly proportional to the gear ratio.
• Example:
3:1 gear ratio
– Engine turns input gear at 900 RPM with 50 lb/ft of force
– Output gear turns driveshaft at 300 RPM with 150 lb/ft of
force
umerical
Numerical Problems:
Example 12.2.
The number of teeth on each of the two equal spur gears in mesh
are 40. The teeth have 20° involute profile and the module is 6 mm. If the arc
of contact is 1.75 times the circular pitch, find the addendum.
umerical
Numerical Problems:
Example 12.3:
A pinion having 30 teeth drives a gear having 80 teeth. The profile of the
gears is involute with 20° pressure angle, 12 mm module and 10 mm
addendum. Find the length of path of contact, arc of contact and the contact
ratio.