1. ME 3180 - Mechanical Engineering Design
Gears
Lecture Notes #1
Prof. I. Charles Ume

2. 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

3. Types of Gears Types of Gears: Spur and Helical Helical Bevel Worm
Used for parallel shafts
Helical
Bevel
Worm
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
These three can be used for non-parallel shafts.
Helical Gears
Spur Gears
Bevel Gears
Worm Gears
Images From: Boston Gear and Chicago Gear Works

4. 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
Metal Spur Gears
Rack and Pinion
Images From: Chicago Gear Works and Small Parts Inc
Delrin Spur Gears

5. 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
Crossed-Same hand gears perpendicular to each other
Used to reduce noise and vibration (parallel)
Used in distributors and speedometers (crossed)
Helical Gears
Images From: Norton and Chicago Gear Works

6. 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
Spiral bevel gears run more smoothly and quietly than straight bevel gears
Bevel Gears
Images From: Norton and Boston Gear

7. Worm Gears A worm gear and a worm together are called a wormset
Helical gear with one continuous tooth
Analogous to screw thread
Worm Gear
Analogous to a nut
Connects non-parallel and non-intersecting 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

8. ME 3180 - Mechanical Engineering Design
Spur Gears
Lecture Notes

9. 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

10. Fundamental Law of Gearing
The angular velocity ratio, mV, between gears of a gearset must remain constant thoughout the mesh
(Eq. 11.1a)
out = angular velocity of output gear
in = angular velocity of input gear
rin = pitch radius of input gear
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 (+)

11. Fundamental Law of Gearing
Mechanical advantage (torque ratio), mA, is the reciprocal of mV
This means that torque is exchanged for velocity
(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.
(Eq. 11.1c)

12. 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

13. Examples of Conjugate Gears and Cams

14. Construction of Involute Profile