me321 kinematics and dynamics of machines
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ME321 Kinematics and Dynamics of Machines. Steve Lambert Mechanical Engineering, U of Waterloo. Gears. Spur Gears - Parallel shafts and ‘straight’ teeth. Gears . Example internal spur gear. Example rack and pinion. Helical Gears. - PowerPoint PPT PresentationTRANSCRIPT
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ME321 Kinematics and Dynamics of
MachinesSteve Lambert
Mechanical Engineering, U of Waterloo
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Gears
Spur Gears - Parallel shafts and ‘straight’ teeth
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Gears
Example internal spur gear
Example rack and pinion
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Helical Gears
Helical gears are smoother and quieter than spur gears, but
are more expensive, are not easily engaged, and they generate a thrust load
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Bevel Gears
Straight bevel gears
Skew bevel gears
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Hypoid and Worm Gears
Hypoid gear
Worm gear
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Fundamental Law of Gearing
We require a constant velocity ratio.
For this to be possible, the common normal of the contacting tooth flanks must always pass through the pitch point.
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Involute Action
Imagine that the gears are replaced by two cylinders connected by a string
This system will satisfy our fundamental law
The path traced by Q will represent our tooth profile
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Involute Action
These are equivalent.
Path traced by point Q is an Involute.
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Gear Tooth Nomenclature
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Gear Nomenclature
Pitch CircleCircular PitchAddendumDedendumClearance
Diametral Pitch:
DNP
Circular Pitch:
PNDCP
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Standard Gears
DNP
Diametral Pitch:
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Interacting Gears
• Centre Distance (r2 + r3)
• Contact Ratio
• Interference
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Contact Ratio
Contact ratio is the average number of teeth in contact
CR = length of line of action / base (circle) pitch
CR = l / BP
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Contact Ratio
CR = l / BP, where:
Line of action:
l = AC-AP + DB-DP
NrBP
rDP
rarDB
rAPrarAC
B
2sin
cos
sincos
3
23
233
2
22
222
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Interference
Interference occurs if point C falls outside point D
- contact beyond involute profile occurs if
O2C > O2D
where:
2222
222
sincrDO
arCO
b