Related Resources: gears

Worm and WormGear Design Equations and Calculator

Gears Engineering and Design

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

P = Circular pitch of wormgear
P = axial pitch of the worm
P_x, = in the central plane
P_x = Axial pitch of worm
P_n = 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 = nm_G
m_G = 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).

ALL calculators require a Premium Membership

Preview Worm Wormgear Design Calculator

Lead
l = nP_x

Pitch Diameter
d = 1 / ( π tan λ )

Outside Diameter
d_o = d + 2a

F_W = [ D_o² - D² ] ^1/2

Wormgear Dimensions Equations

Pitch Diameter
D = NP / π = N Π_ε / π

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

Face Width
F_Gmin = 1.125 • [ ( d_o + 2c)² - ( d_o - 4a)² ]^1/2

Dimensions Worm and Wormgear

Addendum
a = 0.3183P_n

Whole Depth
h_t = 0.7003P_n + 0.002

Working Depth Clearance
c = h_t - h_k

Tooth Thichness
t_n = 0.5P_n

Normal Pressure Angle (Approx.)
Φ_n = 20°

Center Distance
C = 0.5 • (d + D)