Transmission Machine Components

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Transmission Machine Components
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Gears

• Gears simply change the parameters of mechanical
  power

Pitch-Line Velocity
P
r1
r2
gear
pinion
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Tooth Forces
T1
r1
F1
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Normal velocity must match. Using similar
triangles
v2 cos?2     v1 cos?1       where
  v1  ?1 . O1C         v2  ?2 . O2C 
Want constant rotation rate ratio
?2 /?1     v2 . O1C/v1 . O2C    
O1C.cos?1 /O2C.cos?2                
O1 C1 /O2 C2     O1 P / O2 P 
Point P must be fixed
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Effect of Errors
Shafts farther apart than spec.
Shafts at spec. distance
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Involute Tooth Profile

• The two curved surfaces of mating teeth, contact
  as a line

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Types of Gears

• Spur Gears
• Teeth are parallel to rotation axis
• Transmit power between shafts with parallel axes
• Helical Gears
• Teeth inclined to the axis of rotation
• Used for the same applications as spur gears, but
  have less noise due to gradual tooth engagement

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Types of Gears, cont.

• Bevel Gears
• Teeth on a conical Surface
• Used with intersecting shafts
• Worm Gears
• Similar to a screw
• Used with non-parallel and non-intersecting
  shafts typically with high speed ratios

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Rack and Pinion

• A rack is an unwound spur gear
• Turns rotary motion in to linear motion

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Anatomy of a Gear

• Pitch Circle
• Theoretical circle upon with all calculations are
  based
• Diametral Pitch
• Module
• Pressure Angle
• For gears to work together they must have the
  same pitch (or module) and pressure angle

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Multiple Gear Stages

• Gear ratios from a multi-stage gear train
  multiply together

T3
T2
T4
T1
21 reduction
21 reduction
21 reduction
Overall a 81 reduction
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Efficiency

• In reality gears are not 100 efficient
• Good quality spur gears are typically in the 90
  efficiency range
• This can be a problem with multiple (large) gear
  reductions

Each a 21 reduction with 95 efficiency
Overall a 321 reduction, but only 77 efficient
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Belts and Chains

• Belts are essentially the same as spur gears but
  they have the ability to have large offsets

P1
P2
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Slip

• Belts rely on friction and to prevent slip
  tension must be maintained
• Chains and timing belts that have teeth with
  positive engagement can help prevent slip

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Shafts
Energy used to overcome the forces resulting from
misalignment will reduce the overall efficiency
of your system
Parallel misalignment
Angular misalignment
This is the key to doing well in the transmission
contest
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Pins

• Pins hold two parts together based upon the shear
  strength of the pin
• Pins are good when the joint must take both
  thrust and shear
• Pinned joints are easy to analyze and reliable
• Pinned joints can be used as a mechanical fuse

• Pinned joints are difficult to assemble and
  disassemble because pins are typically press fit
  into place

shaft
gear
pin
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Keys

• Keys transmit torque in shear across the length
  of the key
• Keys have all the advantages of pins, but they
  are easy to install in remove
• Keys do not take any axial load

Woodruff key Used to reduce stress concentrations
in the shaft
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Clamp Fit

• Clamps depend upon friction and the bolted
  connection between two parts (or a single part
  with a flexure) to develop the clamping force
• Clamped connections can be easy and reliable for
  low torque applications

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Press (Interference) Fits

• Two parts can be pressed together if the hole is
  manufactured smaller than the shaft that is
  installed
• The load between these two parts is taken in
  friction developed by the strain of the press fit
• Manufacturing tolerances are very tight for this
  type of connection
• For a 0.25 diameter shaft with a class FN2 fit
• Shaft 0.2510 0.2514
• Hole 0.2500 0.2506
• Difficult to disassemble without damage to the
  parts

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Splines

• Splines are essentially matching internal and
  external gears used to transmit torque
• Splines are extremely reliable and efficient
• Splines are difficult to manufacture

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Retaining Rings

• Retaining rings are used to constrain things
  axially in one direction on a shaft
• Installed by machining a groove into one of the
  mating parts
• Can be made external or internal

External
E-Style External
Internal
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Shaft Connections
Coupler transmits torque and allows for
misalignment
Key or set screw transmits torque
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Couplers

• Bellows
• Spider Coupling
• Helical
• Universal Joint

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Bearing and Bushings
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Bushings

• Bushings have sliding contact and rely on low
  friction at the point or line of contact

r
F
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Rolling Element Bearings

• Replace sliding contact with rolling contact
  which is much more efficient

Outer Race
Ball
Separator (retainer)
Inner Race
Image courtesy of Barden Precision Bearing
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Rolling Contact
?1
ri
ro
rLi
rLo
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Spherical Bearings

• Allows for misalignment in all rotational degrees
  of freedom
• Constrains in all translational degrees of
  freedom
• Good for low speed / high load applications

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A Brief Into to SpecifyingElectric Motors
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Electric Motors

• Torque is proportional to current
• Speed is proportional to voltage
• An electric motor generates an Electromotive
  Force (back EMF) as it spins
• A portion of the input voltage goes to doing work
  and a portion goes to overcome the back EMF

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Kt
Ke
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Electric Motors
For a given voltage
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Electric Motor Power
Cant always operate here due to heat
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Continuous Operating Range