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Gears & Gear Systems: Gear Fundamentals (Changing Centre Distance (For…
Gears & Gear Systems: Gear Fundamentals
Image - Breakdown
Gearbox
Power density [W/kg] or [W/m3] are comparative parameters of interest during concept selection
The load-path through a gearbox is quite complex and ‘inefficient’
Much of the material in a gearbox is ‘on vacation’ while a gearbox is ‘working’
Ratio
Power Rating
Efficiency
Gears
Parallel Axis
Spur Gear
Gear Trains
Gear Force Analysis
Manufacturing
Gear Structural Design
Gear Fundamentals
Gear Failure Modes
Helical Gear
Non-Parallel Axis
Bevel Gear
Worm Gear
Gear Types
#
Spur Gear Terminology
d = Pitch circle diameter
N = number of teeth
p = Circular pitch
p = π d / N
m = module
m = d / N
Addendum = module
Dedendum = 1.25 module
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Law of Gears
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Conjugate Action
The angular velocity ratio between the gears of a gear set
remains constant throughout the mesh
Fundamental law of gearing
The common normal of the tooth profiles, at all contact
points within the mesh, must always pass through a fixed
point on the line of centers, called the pitch point.
Profiles that meet this requirement
Cycloidal profile – (obsolete)
Involute profile
The involute profile cannot
exist below the base circle
Actual profile depends on
manufacturing method
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Sketching Gears
Fundamentals
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v = r1
w1 = r2
w2
Pressure Angle
Standard Types:
Φ = 20⁰ or 25⁰
Tooth Action
Angle of recess
Pitch point to final contact
Angle of Action
Angle of approach + Angle
of recess
Angle of approach
Initial contact to pitch
point
Line of Action
ab (Pressure line)
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Rack
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Sides of involute teeth on rack are parallel lines
Spur gear with infinite diameter
Pb = PcCosΦ
Contact Ratio
Contact Ratio, Mc, time averaged number of teeth in contact.
Minimum recommended ratio for smooth operation
Mc > 1.2
Minimum preferred ration
Mc > 1.4
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Changing Centre Distance
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New (larger) operating pitch circles
Base circles remain unchanged
Pressure angle increases
For involute tooth form
The velocity ratio remains unchanged
The law of gearing is still satisfied
Backlash increases
Backlash
The clearance between mating teeth measured at the pitch
circle
Backlash is provided for a variety of reasons
backlash prevents gears from jamming
A small amount of backlash is desirable to provide for lubricant space and
differential expansion
Backlash is always present due to manufacturing tolerances
Small amount of backlash not a problem for non-reversing
torque
Any increase or decrease in center distance of two gears in any mesh will cause an increase or decrease in backlash
Increase in backlash as a function of centre distance:
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Interference and Undercutting
Involute tooth profile is only defined outside base circle
Portion of tooth below base circle not involute
Tooth interference may occur
Gear teeth produced by a generation process:
Interference eliminated
Undercutting occurs
Can be prevented by avoiding gears with too few teeth
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NB Image Minimums and Maximums