Related Resources: gears

Involute Spline ANSI B92.1 Equations and Design

Gear Design and Engineering

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 self-centering, thus equalizing the bearing and stresses, and they can be measured and fitted accurately.

Equations for Involute Spline Basic Dimensions ANSI B92.1-1970, R1993

Term		Symbol	30 deg φD			37.5 deg φD	45 deg φD
			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		Ps	2P	2P	2P	2P	2P
Pitch Diameter		D	N/P	N/P	N/P	N/P	N/P
Base Diameter		Db	D cos φD	D cos φD	D cos φD	D cos φD	D cos φD
Circular Pitch		p	π/P	π/P	π/P	π/P	π/P
Minimum Effective Space Width		sv	π/(2P)	π/(2P)	π/(2P)	(0.5π + 0.1) / P	(0.5π + 0.1) / P
Major Diameter, Internal		Dri	(N + 1.35)/P	(N + 1)/P	(N + 1.8)/P	(N + 1.6)/P	(N + 1.4)/P
Major Diameter, External		Do	(N + 1)/P	(N + 1)/P	(N + 1)/P	(N + 1)/P	(N + 1)/P
Minor Diameter, Internal		Di	(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	Dre	(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		DFi	(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		DFe	(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)		cF	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.