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

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me 3180 mechanical engineering design

ME 3180 - Mechanical Engineering Design


Lecture Notes #1

Prof. I. Charles Ume


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

Types of Gears

  • Types of Gears:
    • Spur and Helical
      • 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


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


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 gearsperpendicular 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


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 gearsrun more smoothly and quietly than straight bevel gears

Bevel Gears

Images From: Norton and Boston Gear


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 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


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

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 (+)

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)


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