Basic Geometric Calculations for Spur Gears
Input Parameters
Gear type - internal or external gear
Gear ratio and tooth numbers 
Pressure angle (the angle of tool profile) α
Helix angle β
Module m (for metric calculation)
Diametral Pitch P (for English units)
Unit addendum a *
Unit clearance c *
Unit dedendum fillet r f *
Gear widths b 1 , b 2
Unit corrections x 1 , x 2
Summary of unit correction Σ x = x 1 + x 2
Calculated parameters
Gearing number
Tangential module
Normal pitch
Axial pitch
Base pitch
Helix angle on the basic cylinder
Axial pressure angle
Rolling/working pressure angle
Axial rolling/working pressure angle
Pitch diameter
Base circle diameter
Theoretical center distance
Real center distance
Feed factor/addendum lowering
Outside diameter
d a1,2 = d 1,2 + 2m (a * + x 1,2 - Δ y ) | ||
- for internal gearing the interference check is done as well |
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for km > 0 is accomplished by addendum lowering d a2 = d a2 - 2km |
Root diameter
Work pitch diameter
Virtual Number of Teeth
Virtual Pitch Diameter
Virtual Base Circle Diameter
Virtual Outside Diameter
Tooth thickness (measured normally on the pitch diameter)
Tooth width on the chord (measured normally)
Addendum height above the chord
Unit addendum width (measured normally)
Operating width of gearings
Relative width
Factor of mesh duration
ε γ = ε α + ε β | ||
Factor of profile mesh duration | ||
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(the minus sign applies to internal gearing) | ||
Factor of step mesh duration | ||
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Minimum correction without tapering
Minimum correction without undercut
Minimum correction with the allowable undercut
Checking chordal dimension
W 1,2 = ((z w - 0.5) π + z 1,2 inv α t ) m cos α) + 2 x 1,2 m sin α where: | |||
z w | is the tooth number across which the measure is performed | ||
Checking size across rollers/balls
