Worm and WormGear Design Equations and Calculator

Gears Engineering and Design

Equations for American Standard Fine Pitch Worms and Wormgears
Per. ANSI B6.9

Worm Gear

P = Circular pitch of wormgear
P = axial pitch of the worm
Px, = in the central plane
Px = Axial pitch of worm
Pn = Normal circular pitch of worm and wormgear = Px cos λ = P cos ψ
λ = Lead angle of worm
ψ = Helix angle of wormgear
n = Number of threads in worm
N =Number of teeth in wormgear
N = nmG
mG = Ratio of gearing = N / n
l = lead of a worm which is the distance any one thread advances in a single revolution.

Lead Angles: There are Fifteen standard lead angles: 0.5, 1, 1.5, 2, 3, 4, 5, 7, 9, 11, 14, 17, 21, 25, and 30 degrees.

Pitches: Eight standard axial pitches have been established to provide adequate coverageof the pitch range normally required: 0.030, 0.040, 0.050, 0.065, 0.080, 0.100, 0.130, and0.160 inch. Axial pitch is used as a basis for this design standard because:

1) Axial pitch establisheslead which is a basic dimension in the production and inspection of worms;
2) The axialpitch of the worm is equal to the circular pitch of the gear in the central plane; and
3) Only one set of change gears or one master lead cam is required for a given lead, regardless oflead angle, on commonly-used worm-producing equipment.

Worm Dimensions Equations (All dimensions are in inches unless otherwise specified).

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Preview Worm Wormgear Design Calculator

Lead
l = nPx

Pitch Diameter
d = 1 / ( π tan λ )

Outside Diameter
do = d + 2a

FW = [ Do2 - D2 ] 1/2

Wormgear Dimensions Equations

Pitch Diameter
D = NP / π = N Πε / π

Outside Diameter
D o = 2C - d / (2a)

Face Width
FGmin = 1.125 • [ ( do + 2c)2 - ( do - 4a)2 ]1/2

Dimensions Worm and Wormgear

Addendum
a = 0.3183Pn

Whole Depth
ht = 0.7003Pn + 0.002

Working Depth Clearance
c = ht - hk

Tooth Thichness
tn = 0.5Pn

Normal Pressure Angle (Approx.)
Φn = 20°

Center Distance
C = 0.5 • (d + D)

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