1. ME321 Kinematics and Dynamics of Machines
Steve Lambert
Mechanical Engineering,
U of Waterloo
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2. Gears
Spur Gears - Parallel shafts and ‘straight’ teeth
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3. Gears
Example internal spur gear
Example rack and pinion
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4. 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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5. Bevel Gears
Straight bevel gears
Skew bevel gears
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6. Hypoid and Worm Gears
Hypoid gear
Worm gear
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7. 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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8. 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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9. Involute Action These are equivalent.
Path traced by point Q is an Involute.
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10. Gear Tooth Nomenclature
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11. Gear Nomenclature Pitch Circle Circular Pitch Addendum Dedendum
Clearance
Diametral Pitch:
Circular Pitch:
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12. Standard Gears
Diametral Pitch:
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13. Interacting Gears Centre Distance (r2 + r3) Contact Ratio Interference
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14. 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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15. Contact Ratio CR = l / BP, where: Line of action: l = AC-AP + DB-DP
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16. Interference Interference occurs if point C falls outside point D
- contact beyond involute profile occurs if
O2C > O2D
where:
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