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
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Auxiliary Geometric Calculations |
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Design According to the Strength Calculation |
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Design of Gearing Width |
Calculated parameters
Gearing number
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for i > 1 |
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u = i |
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for i < 1 |
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u = 1 / i |
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Tangential module
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Normal pitch
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p = π m |
Axial pitch
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p t = π m t |
Base pitch
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p tB = p t cos α t |
Helix angle on the basic cylinder
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sin β b = sin β cos α |
Axial pressure angle
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Rolling/working pressure angle
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Axial rolling/working pressure angle
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Pitch diameter
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d 1,2 = z 1,2 m t |
Base circle diameter
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d b1,2 = d 1,2 cos α t |
Theoretical center distance
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Real center distance
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Feed factor/addendum lowering
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Outside diameter
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d a1,2 = d 1,2 + 2m (a * + x 1,2 - Δ y ) |
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- 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
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d f1,2 = d 1,2 - 2m (a * + c * - x 1,2 ) |
Work pitch diameter
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Virtual Number of Teeth
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Virtual Pitch Diameter
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d n1,2 = z v1,2 m |
Virtual Base Circle Diameter
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d bn1,2 = d n1,2 cos(α) |
Virtual Outside Diameter
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d an1,2 = d n1,2 + d a1,2 – d1,2 |
Tooth thickness (measured normally on the pitch diameter)
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s 1,2 = p/2 + 2m x1,2 tg α |
Tooth width on the chord (measured normally)
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s c1,2 = s 1,2 cos 2 α |
Addendum height above the chord
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Unit addendum width (measured normally)
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where:
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Operating width of gearings
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b w = min( b 1 , b 2 ) |
Relative width
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Factor of mesh duration
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ε γ = ε α + ε β |
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Factor of profile mesh duration |
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(the minus sign applies to internal gearing) |
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Factor of step mesh duration |
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Minimum correction without tapering
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where: a 0 * = a * + c * - r f * (1 - sin α) |
Minimum correction without undercut
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Minimum correction with the allowable undercut
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Checking chordal dimension
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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: |
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z w |
is the tooth number across which the measure is performed |
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Checking size across rollers/balls
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- for even tooth number |
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M 1,2 = D s1,2 + d M |
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- for odd tooth number |
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M 1,2 = D s1,2 cos(90 / z 1,2 ) + d M where: |
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d M |
wire (ball) diameter |
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diameter of the wire center circle |
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wire (ball) contact angle |
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