ME3180
ME 3180 - Mechanical Engineering Design
Gears
Lecture Notes #1
Prof. I. Charles Ume
The George W. Woodruff School of Mechanical Engineering
ME3180
Why Do We Use Gears ?
Reduce or increase speed
Reduce or increase torque
Transmit power around corners or over distances
We want (at various times)
• Efficiency
• Reliability
• Accuracy
• Smoothness
• Quiet operation
The George W. Woodruff School of Mechanical Engineering
ME3180
Types of Gears
Types of Gears:
• Spur and Helical
– Used for parallel shafts
• Helical
• Bevel
• Worm
These three can
be used for nonparallel shafts.
Spur Gears
American Gear Manufacturing
Association (AGMA)
• Defined the standard used in
the text
• There are other standards...
Study Tables 13-1 thru 13-5
Shigley
• Table has all necessary terms
for gears
Worm Gears
Helical Gears
Bevel Gears
Images From: Boston Gear and Chicago Gear Works
The George W. Woodruff School of Mechanical Engineering
ME3180
Spur Gears
Metal Spur Gears
Used to transmit torque and angular
velocity
More efficient than simple rolling
cylinders because there is no slip
Designed to work on parallel shafts
Teeth are parallel to shaft
Common Uses:
• Watches, Clocks, Printers
• Rack - Car Steering, Diving Boards
Rack and Pinion
Images From: Chicago Gear Works
and Small Parts Inc
Delrin Spur Gears
The George W. Woodruff School of Mechanical Engineering
ME3180
Helical Gears
Teeth are angled with respect to
the axis of rotation (10-45o)
Direction of angle determines
"hand" of gear
Two configurations:
Parallel - two gears with opposite
hands on parallel axes
Helical Gears
Crossed-Same hand gears
perpendicular to each other
Used to reduce noise and
vibration (parallel)
Used in distributors and
speedometers (crossed)
Images From: Norton and Chicago Gear Works
The George W. Woodruff School of Mechanical Engineering
ME3180
Bevel Gears
Cut on mating cones instead of
mating cylinders (like spur,
helical)
Axes intersect at the apices of
mating cones
Two types of bevel gears
• Straight - teeth run straight up
to apex of cone
• Spiral - teeth cut at curved
angles up around the cone
Bevel Gears
Spiral bevel gears run more
smoothly and quietly than
straight bevel gears
Images From: Norton and Boston Gear
The George W. Woodruff School of Mechanical Engineering
ME3180
Worm Gears
A worm gear and a worm
together are called a wormset
• Worm
– Helical gear with one continuous
tooth
– Analogous to screw thread
• Worm Gear
– Analogous to a nut
Connects non-parallel and nonintersecting shafts (usually at
right angles)
Advantages
• High gear ratios in small
packages because worm only
has one tooth (typically up to
100:1)
• Usually self locking
Worm Gears
Images From: Norton and Chicago Gear Works
The George W. Woodruff School of Mechanical Engineering
ME3180
ME 3180 - Mechanical Engineering Design
Spur Gears
Lecture Notes
The George W. Woodruff School of Mechanical Engineering
ME3180
Gear Tooth Theory
Simplest means of transferring
rotary motion from one shaft to
another is by two or more rolling
cylinders
When teeth are added to the
rolling cylinders, they become
gears and are called a gearset
• Pinion - Smallest gear in a
gearset
• Gear - Larger gears in a gearset
• Rack - Linear gear if gear is a
straight bar
The George W. Woodruff School of Mechanical Engineering
ME3180
Fundamental Law of Gearing
The angular velocity ratio, mV, between gears of a gearset
must remain constant thoughout the mesh
out
rin
N in
mV 


in
rout
N out
out = angular velocity of output gear
in = angular velocity of input gear
rin = pitch radius of input gear
(Eq. 11.1a)
rout= pitch radius of output gear
Nin = number of teeth on input gear
Nout = number of teeth on output gear
The + sign depends on internal or external gearset
– External gearset reverses direction of rotation between input
and output gears. External gearset requires a negative sign (-)
– Internal gearset has same direction of rotation of input and
output gears. Internal gearset requires a positive sign (+)
The George W. Woodruff School of Mechanical Engineering
ME3180
Fundamental Law of Gearing
Mechanical advantage (torque ratio), mA, is the reciprocal of mV
This means that torque is exchanged for velocity
in
rout
N out
1
mA 



mV out
rin
N in
(Eq. 11.1b)
Gear Ratio, mG, is what is commonly referred to when
specifying gear trains
• It is the magnitude of either the velocity ratio or torque ratio,
whichever is > 1.
mG  mV or mG  mA for mG  1
(Eq. 11.1c)
The George W. Woodruff School of Mechanical Engineering
ME3180
Gear Tooth Shape
Gear tooth contours must be conjugates of each other.
When tooth profiles, or cams, are designed to
produce constant angular velocity ratio during
meshing, they are said to have conjugate action. The
following tooth profiles will produce conjugates:
• Cycloid
– Used in watches and clocks
• Involute
– Most common type used in gears
– Principle Advantage: ensures that center-distance errors
do not affect velocity ratio
Generating an Involute
• String is tangent to base circle
• Center of curvature is point of tangency of string with
base circle
• Tangent to involute is normal to string
The George W. Woodruff School of Mechanical Engineering
ME3180
Examples of Conjugate Gears and Cams
The George W. Woodruff School of Mechanical Engineering
ME3180
Construction of Involute Profile
The George W. Woodruff School of Mechanical Engineering