Gear Formula
A formula for the most common of gears that is spur gears is
given here:
| To calculate |
If Defined Already |
Formula |
| Diametral Pitch (P) |
Pitch Diameter(D), No. of teeth (N) |
P=N/PD |
| Diametral Pitch (P) |
Circular Pitch(p) |
P=3.14116/P |
| Diametral Pitch (P) |
Outside diameter (OD), Number of teeth(N) |
P=(N+2)/OD |
| Pitch diameter(D) |
No. of teeth (N), Diametral Pitch (P) |
D=N/P |
| Outside diameter (OD) |
No. of teeth (N), Diametral Pitch (P) |
OD=N+2/P |
| No. of teeth (N) |
Pitch Diameter(D), Diametral Pitch (P) |
N=P*D |
| Addendum(a) |
Diametral Pitch (P) |
a=1/P |
| Dedendum(d) |
Whole depth(hw), addendum |
d=hw-a |
| Tooth thickness(t) at Pitch diameter |
Diametral Pitch (P) |
t=1.5708/P |
| Working depth(WD) |
Addendum(a) |
WD=2a |
| Centre Distance (C) |
Normal Diametral Pitch (P)and the number of teeth(N) in both gears |
C=(N1+N2)/P |
| Centre Distance (C) |
Pitch diameter(D)of both gears |
C=(D1+D2)/P |
| Circular Pitch(p) |
Diametral Pitch (P) |
p=3.1416/P |
| Whole depth(hW)for 20 pitch or finer |
Diametral Pitch (P) |
hw=2.2/p+0.002 |
| Whole depth(hW)for coarser than 20 pitch |
Diametral Pitch (P) |
hw=2.157/P |
Formula for Helical Gears
| To calculate |
When Defined |
Formula |
| Normal Diametral pitch(Pn) |
Transverse D.P(P), Helix Angle (A) |
Pn=P/cosA |
| Pitch Diameter (D) |
Number of teeth (N), Helix Angle (A), Normal D.P.(Pn) |
D=N/(Pn)*CosA |
| Outside diameter(OD) |
Pitch Diameter(D), addendum (a) |
OD=D+(2*a) |
| Outside diameter(OD) |
Normal D.P.(Pn), Pitch Diameter (D) |
OD=D+2/Pn |
| Helix Angle(A) (for parallel shift drive) |
Pitch Diameter (D), Number of teeth (N), Diametral pitch.(Pn) |
Cos A=N/Pn*D |
| addendum (a) |
Normal Diametral pitch(Pn) |
A=1/Pn |
The following Helical gear formula would prove to be useful in calculating
various Gear nomenclatures associated with Helical Gears:
| Serial No. |
To Find |
Having |
Rule |
| 1 |
Transverse Diametral Pitch |
Pitch diameter and number of teeth |
Number of teeth/Pitch diameter |
| 2 |
Transverse Diametral Pitch |
Normal D.P. And helix angle |
Normal D.P. * cosine of the helix angle |
| 3 |
Pitch diameter |
Transverse D.P. and number of teeth |
Number of teeth/Transverse D.P |
| 4 |
Normal Diametral pitch |
Transverse D.P. and helix angle |
Transverse D.P./cosine of the helix angle |
| 5 |
Helix angle |
Normal D.P. and Transverse D.P. |
Divide Transverse D.P. by Normal D.P.- quotient is the cosine of the
helix angle |
| 6 |
Transverse pressure angle |
Helix angle and normal P.A |
Divide tangent of normal P.A by cosine of the helix angle quotient
is the tangent of Transverse P.A |
| 7 |
Normal circular tooth thickness |
Normal Diametral pitch |
1.5708/Normal Diametral pitch |
| 8 |
Whole depth |
Normal Diametral pitch |
1.0/Normal Diametral pitch |
| 9 |
Outside diameter |
Pitch diameter and Addendum |
Add two Addendums to the pitch diameter |
| 10A |
Whole depth(coarser than 20 D.P.) |
Normal Diametral pitch |
2.250/Normal Diametral pitch |
| 10B |
Whole depth(20 D.P. And finer) |
Normal Diametral pitch |
Divide 2.2 by normal D.P. and then add 0.002 |
| 11 |
Clearance |
Whole depth and Whole depth |
subtract two Addendums from the whole depth |
