Involute Spline ANSI B92.1 Equations and Design
American National Standard Involute Splines  These splines or multiple keys are similar in form to internal and external involute gears. In general manufacturing external splines is facilitated either by hobbing, rolling, or on a gear shaper, and internal splines either by broaching or on a gear shaper. The internal spline is held to basic dimensions and the external spline is varied to control the fit. Involute splines have maximum strength at the base, can be accurately spaced and are selfcentering, thus equalizing the bearing and stresses, and they can be measured and fitted accurately.
Equations for Involute Spline Basic Dimensions ANSI B92.11970, R1993
Term

Symbol

30 deg φ_{D}

37.5 deg φ_{D}

45 deg φ_{D}


Flat Root Side Fit

Flat Root Major Dia Fit

Fillet Root Side Fit

Fillet Root Side Fit

Fillet Root Side Fit


2.5/ 5  32/ 64 Pitch

3 /6  16 /32 Pitch

2.5/ 5  48/ 96 Pitch

2.5/ 5  48/ 96 Pitch

10/ 20  128/ 256 Pitch


Stub Pitch

P_{s}

2P

2P

2P

2P

2P


Pitch Diameter

D

N/P

N/P

N/P

N/P

N/P


Base Diameter

D_{b}

D cos φ_{D}

D cos φ_{D}

D cos φ_{D}

D cos φ_{D}

D cos φ_{D}


Circular Pitch

p

π/P

π/P

π/P

π/P

π/P


Minimum Effective Space Width

s_{v}

π/(2P)

π/(2P)

π/(2P)

(0.5π + 0.1) / P

(0.5π + 0.1) / P


Major Diameter, Internal

D_{ri}

(N + 1.35)/P

(N + 1)/P

(N + 1.8)/P

(N + 1.6)/P

(N + 1.4)/P


Major Diameter, External

D_{o}

(N + 1)/P

(N + 1)/P

(N + 1)/P

(N + 1)/P

(N + 1)/P


Minor Diameter, Internal

D_{i}

(N  1 )/ P

(N  1 )/ P

(N  1 )/ P

(N  0.8 )/ P

(N  0.8 )/ P


Minor Dia. Ext.

2.5/5 thru 12/ 24 pitch

D_{re}

(N  1.35)/ P

(N  1.8)/ P

(N  1.3)/ P

…


16/ 32 pitch and finer

(N  1.2)/ P


10/ 20 pitch and finer

…

(N  1 )/ P


Form Diameter, Internal

D_{Fi}

(N + 1) / P + 2cF

(N + 0.8) / P  0.004 + 2cF

(N + 1) / P + 2cF

(N + 1) / P + 2cF

(N + 1) / P + 2cF


Form Diameter, External

D_{Fe}

(N  1)/ P  2cF

(N  1)/ P  2cF

(N  1)/ P  2cF

(N  0.8)/ P  2cF

(N  0.6)/ P  2cF


Form Clearance (Radial)

c_{F}

0.001 D, with max of 0.010, min of 0.002


π = 3.1415927
Note: All spline specification table dimensions in the standard are derived from these basic formulas by application of tolerances.
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