8 – GEARS ME 418
TOPIC NO. 8
without slipping. Gears may not be so
This topic includes the following: mounted; then there may be said to be
in operating pitch circle and a standard
8.1 Spur Gear pitch circle. The pitch circle is also the
8.2 Helical Gear trace of the pitch cylinder (pitch
8.3 Bevel Gear surface) as it intersects a plane normal
8.4 Worm Gear to the axis.
The pitch point of meshing gears is the
point of tangency of the pitch circles; for
an individual gear, the pitch point will be
located where the tooth profile cuts the
standard pitch circle.
The addendum circle (also outside
circle) is the circle that bounds the outer
ends of the teeth. The addendum
A. SPUR GEARS
cylinder encloses a gear. The diameter
2Spur
of this circle is called the outside
gears are toothed wheels whose tooth
diameter. The addendum a is the radial
elements are straight and parallel to the
distance between the pitch circle and
shaft axis; they are used to transmit motion
the addendum circle.
and power between parallel shafts.
2Definitions of Terms
The pitch circle is the basis of
measurement of gears. The size of a
gear is its pitch circle diameter in inches,
called the pitch diameter. For
interchangeable gear teeth, it is
intended that the pitch circles of mating
gears be tangent in which case, these The dedendum circle or root circle is the
imaginary circles roll on one another circle that bounds the bottoms of the
MACHINE DESIGN 1 by ENGR. GERALD T. AGUILA Page 34
,8 – GEARS ME 418
teeth. The dedendum d is the radial between the teeth for lubricant, and to
distance from the pitch circle to the root allow for the expansion of the teeth with
circle, that is, to the bottom of the tooth a temperature rise.
space.
The whole depth is equal to the
addendum plus the dedendum. The
working depth is the radial distance from
the addendum circle to the working
depth circle which marks the distance
that the mating tooth projects into the
tooth space; it is the sum of the The face width is the length of teeth in
addendums of mating gears. an axial direction.
The clearance is the radial distance The face of the tooth is the surface of
between the working-depth circle and the tooth between the pitch cylinder
the root circle; it is the dedendum minus and the addendum cylinder.
the mating addendum.
The flank is the surface of the tooth
The circular thickness, also called tooth between the pitch and root cylinders.
thickness, is the width of tooth measured
along the pitch circle. The chordal The top land is the surface of the top of
thickness is the tooth width measured the tooth.
along the chord at the pitch circle. The
width of space or tooth space is the The bottom land is the surface of the
space between teeth measured along bottom of the tooth space.
the pitch circle.
When two gears are in mesh, the smaller
Backlash is the tooth space minus the is called the pinion and the larger the
circular thickness. When backlash exists gear.
between two gears, one gear can be
turned through a small angle while the The angle of action is the angle through
mating gear is held stationary. Backlash which the gear turns from the time a
is necessary to care for errors and particular pair of teeth come into
inaccuracies in the spacing and in the contact until they go out of contact. The
form of the tooth, to provide a space
MACHINE DESIGN 1 by ENGR. GERALD T. AGUILA Page 35
, 8 – GEARS ME 418
arc of action subtends the angle of The velocity ratio mw, is the angular
action. velocity of the driver divided by the
angular velocity of the driven gear. For
spur gears, this ratio varies inversely as
the pitch (or base-circle) diameters and
as the tooth numbers.
mw = ω1/ω2 = n1/n2 = D2/D1 = N2/N1
where n is angular velocity in, say
Source:
2Virgil Moring Faires, “Design of Machine Elements”, 4 th
revolutions per minute, the subscript
edition, Macmillan Company, 1962 1 refers to the driver and the
subscript 2 refers to the driven gear.
The gear ratio mg is the number of teeth
in the gear divided by the number of
teeth in the pinion. When the pinion is
the driver, mg = mw.
Base Circle and Pressure Angle
2
Source:
3Venton Levy Doughtie and Alex Vallance, “Design of
Machine Members” 4th edition, McGraw-Hill Inc.,1964 The base circle is the circle from which
The angle of approach is the angle the involute is generated.
through which the gear turns from the
time a particular pair of teeth come into The operating pressure angle is
contact until they are in contact at the determined by the center distance,
pitch point. because once the profiles are
established, involute gars may be
The angle of recess is the angle through moved away from each other, thereby
which the gear turns from the time a increasing the backlash, and still
given pair of teeth is in contact at the operate correctly with no change of
pitch point until they pass out of mesh. velocity ratio. Since the generating line
The angle of approach plus the angle of remains tangent to the base circles, the
recess is equal to the angle of action. effects of increasing the center distance
are to increase the pressure angle and
MACHINE DESIGN 1 by ENGR. GERALD T. AGUILA Page 36
TOPIC NO. 8
without slipping. Gears may not be so
This topic includes the following: mounted; then there may be said to be
in operating pitch circle and a standard
8.1 Spur Gear pitch circle. The pitch circle is also the
8.2 Helical Gear trace of the pitch cylinder (pitch
8.3 Bevel Gear surface) as it intersects a plane normal
8.4 Worm Gear to the axis.
The pitch point of meshing gears is the
point of tangency of the pitch circles; for
an individual gear, the pitch point will be
located where the tooth profile cuts the
standard pitch circle.
The addendum circle (also outside
circle) is the circle that bounds the outer
ends of the teeth. The addendum
A. SPUR GEARS
cylinder encloses a gear. The diameter
2Spur
of this circle is called the outside
gears are toothed wheels whose tooth
diameter. The addendum a is the radial
elements are straight and parallel to the
distance between the pitch circle and
shaft axis; they are used to transmit motion
the addendum circle.
and power between parallel shafts.
2Definitions of Terms
The pitch circle is the basis of
measurement of gears. The size of a
gear is its pitch circle diameter in inches,
called the pitch diameter. For
interchangeable gear teeth, it is
intended that the pitch circles of mating
gears be tangent in which case, these The dedendum circle or root circle is the
imaginary circles roll on one another circle that bounds the bottoms of the
MACHINE DESIGN 1 by ENGR. GERALD T. AGUILA Page 34
,8 – GEARS ME 418
teeth. The dedendum d is the radial between the teeth for lubricant, and to
distance from the pitch circle to the root allow for the expansion of the teeth with
circle, that is, to the bottom of the tooth a temperature rise.
space.
The whole depth is equal to the
addendum plus the dedendum. The
working depth is the radial distance from
the addendum circle to the working
depth circle which marks the distance
that the mating tooth projects into the
tooth space; it is the sum of the The face width is the length of teeth in
addendums of mating gears. an axial direction.
The clearance is the radial distance The face of the tooth is the surface of
between the working-depth circle and the tooth between the pitch cylinder
the root circle; it is the dedendum minus and the addendum cylinder.
the mating addendum.
The flank is the surface of the tooth
The circular thickness, also called tooth between the pitch and root cylinders.
thickness, is the width of tooth measured
along the pitch circle. The chordal The top land is the surface of the top of
thickness is the tooth width measured the tooth.
along the chord at the pitch circle. The
width of space or tooth space is the The bottom land is the surface of the
space between teeth measured along bottom of the tooth space.
the pitch circle.
When two gears are in mesh, the smaller
Backlash is the tooth space minus the is called the pinion and the larger the
circular thickness. When backlash exists gear.
between two gears, one gear can be
turned through a small angle while the The angle of action is the angle through
mating gear is held stationary. Backlash which the gear turns from the time a
is necessary to care for errors and particular pair of teeth come into
inaccuracies in the spacing and in the contact until they go out of contact. The
form of the tooth, to provide a space
MACHINE DESIGN 1 by ENGR. GERALD T. AGUILA Page 35
, 8 – GEARS ME 418
arc of action subtends the angle of The velocity ratio mw, is the angular
action. velocity of the driver divided by the
angular velocity of the driven gear. For
spur gears, this ratio varies inversely as
the pitch (or base-circle) diameters and
as the tooth numbers.
mw = ω1/ω2 = n1/n2 = D2/D1 = N2/N1
where n is angular velocity in, say
Source:
2Virgil Moring Faires, “Design of Machine Elements”, 4 th
revolutions per minute, the subscript
edition, Macmillan Company, 1962 1 refers to the driver and the
subscript 2 refers to the driven gear.
The gear ratio mg is the number of teeth
in the gear divided by the number of
teeth in the pinion. When the pinion is
the driver, mg = mw.
Base Circle and Pressure Angle
2
Source:
3Venton Levy Doughtie and Alex Vallance, “Design of
Machine Members” 4th edition, McGraw-Hill Inc.,1964 The base circle is the circle from which
The angle of approach is the angle the involute is generated.
through which the gear turns from the
time a particular pair of teeth come into The operating pressure angle is
contact until they are in contact at the determined by the center distance,
pitch point. because once the profiles are
established, involute gars may be
The angle of recess is the angle through moved away from each other, thereby
which the gear turns from the time a increasing the backlash, and still
given pair of teeth is in contact at the operate correctly with no change of
pitch point until they pass out of mesh. velocity ratio. Since the generating line
The angle of approach plus the angle of remains tangent to the base circles, the
recess is equal to the angle of action. effects of increasing the center distance
are to increase the pressure angle and
MACHINE DESIGN 1 by ENGR. GERALD T. AGUILA Page 36
