Internal Spur Gears

Determining Dimension under Pins

TO GET	HAVING	RULE	FORMULA
N	Number of teeth	Given	12
DP	Diametral pitch		24
α	Pressure angle		14.5
s	Arc space width		0.06800
d	Pin diameter		0.06701
PD	Pitch diameter	N/DP	0.50000
BD	Base diameter	PD•COS(α)	0.48407
A		s/PD	0.13600
D		d/BD	0.13843
INVα	Involute function of α	TAN(α)-[α(π/180)]	0.00554
INVβ		A+INVα-D	0.00312
β	Pressure angle to pin center	see tables page (G14)	11.00809
CC	Twice the center distance of pin and gear	BD/COS(β)	0.49488
DE	Dimension under pins even # of teeth	CC-d	0.42787
DO	Dimension under pins odd # of teeth	CC•COS(90/N)-d	***************
Φ	Pressure angle to point of tangency	TAN(Φ)=TAN(β)+D	19.33857
RT	Radius to point of tangency	BD/[2•COS(Φ)]	0.25651

Determining Arc Space Width Given Dimensions under Pins

TO GET	HAVING	RULE	FORMULA
N	Number of teeth	Given	44
DP	Diametral pitch		24
α	Pressure angle		14.5
d	Pin diameter		0.06701
DE	Dimension under pins even # of teeth		1.76152
DO	Dimension under pins odd # of teeth		**********
PD	Pitch diameter	N/DP	1.83333
BD	Base diameter	PD•COS(α)	1.77494
CE	Twice the center distance of pin and gear even # of teeth	DE+d	1.82853
CO	Twice the center distance of pin and gear odd # of teeth	(DO+d)/COS(90/N)	**********
β	Pressure angle to pin center	COS(β)=BD/CE or CO	13.90611
INVβ	Involute function of b	TAN(β)-[β(π/180)]	0.00488
D		d/BD	0.03775
INVα	Involute function of α	TAN(α)-[α(π/180)]	0.00554
s	Arc space width	PD(INVβ+D-INVα)	0.06800