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

Auxiliary Geometric Calculations

Distribution of Unit Corrections for Single Gears

Design of the Module and Tooth Number

Design of Tooth Number

Design According to the Strength Calculation

Calculation of Helix Angle

Calculation of Summary Correction

Design of Gearing Width

Calculation of Maximum Dedendum Filleting

Calculated parameters

Gearing number

	for i > 1
		u = i
	for i < 1
		u = 1 / i

Tangential module

Normal pitch

p = π m

Axial pitch

p t = π m t

Base pitch

p tB = p t cos α t

Helix angle on the basic cylinder

sin β b = sin β cos α

Axial pressure angle

Rolling/working pressure angle

Axial rolling/working pressure angle

Pitch diameter

d 1,2 = z 1,2 m t

Base circle diameter

d b1,2 = d 1,2 cos α t

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
		for km > 0 is accomplished by addendum lowering d a2 = d a2 - 2km

Root diameter

d f1,2 = d 1,2 - 2m (a * + c * - x 1,2 )

Work pitch diameter

Virtual Number of Teeth

Virtual Pitch Diameter

d n1,2 = z v1,2 m

Virtual Base Circle Diameter

d bn1,2 = d n1,2 cos(α)

Virtual Outside Diameter

d an1,2 = d n1,2 + d a1,2 – d1,2

Tooth thickness (measured normally on the pitch diameter)

s 1,2 = p/2 + 2m x1,2 tg α

Tooth width on the chord (measured normally)

s c1,2 = s 1,2 cos 2 α

Addendum height above the chord

Unit addendum width (measured normally)

where:

Operating width of gearings

b w = min( b 1 , b 2 )

Relative width

Factor of mesh duration

	ε γ = ε α + ε β
	Factor of profile mesh duration
		(the minus sign applies to internal gearing)
	Factor of step mesh duration

Minimum correction without tapering

where: a 0 * = a * + c * - r f * (1 - sin α)

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

	- for even tooth number
		M 1,2 = D s1,2 + d M
	- for odd tooth number
		M 1,2 = D s1,2 cos(90 / z 1,2 ) + d M where:
		d M	wire (ball) diameter
			diameter of the wire center circle
			wire (ball) contact angle