SPUR GEARS |
| To Obtain |
From Known |
Symbol and Formula
|
| Pitch diameter |
Number of teeth and pitch |
D = N = N·Pc
Pd p |
| Circular Pitch |
Diametral pitch or number of
teeth and pitch diameter |
Pc = p =
pD
Pd
N |
| Diametral pitch |
Circular pitch or number of
teeth and pitch diameter |
Pd
= p = N
Pc
D |
| Number of teeth |
Pitch and pitch diameter |
N =DPd
= D
Pc |
| Outside diameter |
Pitch and pitch diameter or
pitch and number of teeth |
Do =D + 2
= N+2
Pd
Pd |
| Root diameter |
Pitch diameter and dedendum |
DR = D - 2b |
| Base circle diameter |
Pitch diameter and pressure
angle |
Db=D cos f |
| Base pitch |
Circular pitch and pressure
angle |
Pb = Pc
cos f |
Tooth thickness at
standard pitch diameter |
Circular pitch |
Tstd = Pc
= pD
2 2N |
| Addendum |
Diametral pitch |
a =
1
Pd |
| Center distance |
Pitch diameters Or number
of teeth and pitch |
C=D1+D2=N1+N2=Pc(N1+N2)
2 2Pd
2p |
| Contact ratio |
Outside radii, base radii,
center
distance and pressure angle |
mp = (Ro²-Rb²)½+(ro²-rb²)½-C
sin f
Pc cos f |
| Backlash (linear) |
From change in center
distance |
B = 2 (DC) tan f |
| Backlash (linear) |
From change in tooth
thickness |
B = DT |
Backlash (linear)
along line of acvon |
Linear backlash along pitch
cirde |
BLA = B cos f |
| Backlash, angular |
Linear backlash |
aB = 6880 B
(arc minutes)
D |
Minimum number of
teeth for no undercutting |
Pressure angle |
N =
2
sin² f |
| Dedendum |
Pitch diameter and
root diameter ( DR ) |
b = ½(D-DR) |
| Clearance |
Addendum and dedendum |
c = b - a |
| Working depth |
Addendum |
hk = 2a |
Pressure angle
( standard ) |
Base circle diameter and
pitch
diameter |
f
=cos-1 Db/D |
Operating pressure
angle |
Actual operating pitch
diameter
and base circle diameter |
f =cos-1 Db/D' |