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Gear Design and Selection Application
Resources:
Spur Gear design formula for geometry, pitch, tooth clearance and critical functional data.
(Inch Units Applicable for Constants)
Spur Gear Design Calculator
Calculate |
When
Defined |
Formula |
Diametral
Pitch (P) |
Pitch
Diameter (PD) and the Number of Teeth (N) |
P
= N / PD |
Diametral
Pitch (P) |
Circular
Pitch (p) |
P
= 3.1416/p |
Diametral
Pitch (P) |
Outside
Diameter (OD) and the Number of Teeth (N) |
P
= (N+2)/OD |
Pitch
Diameter (PD) . |
Number
of teeth (N) and the Diametral Pitch (P) |
PD
= N/DP |
Outside
Diameter (OD) |
Number
of teeth (N) and the Diametral Pitch (P) |
OD
= (N+2)/DP |
Number
of Teeth (N). |
Pitch
Diameter (D) and the Diametral Pitch (P) |
N
= PD * DP |
Addendum
(a) . |
Diametral
Pitch (P) |
a
= 1/DP |
Dedendum
(d) |
Whole
Depth and Addendum |
d
= hw - a |
Tooth
Thickness (t) at the Pitch Diameter |
Diametral
Pitch (P) |
t
= 1.5708/P |
Working
Depth (WD). |
Addendum |
WD
= 2(a) |
Center
Distance (C) |
Normal
Diametral Pitch (P) and the Number of Teeth in Both Gears |
C
= (N1+N2)/2P |
Center
Distance (C) |
Pitch
Diameters of both gears |
C
= (PD1+PD2)/2 |
Circular
Pitch (p) |
Diametral
Pitch (P) |
p
= 3.1416 / P |
Whole
Depth (hw) for 20 Pitch & finer . |
Diametral
Pitch (P) |
hw
= 2.2/P + .002 |
Whole
Depth (hw) for Coarser than 20 Pitch . |
Diametral
Pitch (P) |
hw
= 2.157/P |
Equations Tooth Parts, 20-and 25-degree Involute Full-depth Teeth ANSI Coarse Pitch Spur Gear Tooth Forms ANSI B6.1
Spur Gear Design Calculator
Find |
Diametral Pitch, P, Known |
Circular Pitch, p, Known |
Addendum |
a = 1.000 / P |
a = 0.3183 x p |
Dedendum (Preferred) |
b = 1.250 / P |
b = 0.3979 x p |
(Shaved or Ground Teeth)a
|
b = 1.350 / P |
b = 0.4297 x p |
Working Depth |
hk = 2.000 / P |
hk = 0.6366 x p |
Whole Depth (Preferred) |
ht = 2.250 / P |
ht = 0.7162 x p |
|
ht = 2.350 / P |
ht = 0.7480 x p |
Clearance (Preferred)b |
c = 0.250 / P |
c = 0.0796 x p |
a When gears are preshave cut on a gear shaper the dedendum will usually need to be increased to 1.40/P to allow for the higher fillet trochoid produced by the shaper cutter. This is of particular importance on gears of few teeth or if the gear blank configuration requires the use of a small diameter shaper cutter, in which case the dedendum may need to be increased to as much as 1.45/P. This should be avoided on highly loaded gears where the consequently reduced J factor will increase gear tooth stress excessively.
b A minimum clearance of 0.157/P may be used for the basic 20-degree and 25-degree pressure angle rack in the case of shallow root sections and use of existing hobs or cutters.
Helical Gear
Calculate |
When
Defined |
Formula |
Normal D.P. (Pn) |
Transverse D.P.(P) and the Helix Angle (A) |
Pn=
P / cos A |
Normal D.P. (Pn) |
Number
of teeth (N) and the Helix Angle (A) |
Pn=
N / (D X cos A) |
Pitch
Diameter (D) |
Number
of teeth (N), the Normal Diametral Pitch and the Helix Angle (A) |
D
= N / (Pn X cos A) |
Outside
Diameter (OD) |
Pitch
Diameter (D) and the Addendum (a) |
OD
= D + (2 X a) |
Outside
Diameter (OD) |
Normal
Diametral Pitch (P) and the Pitch Diameter (D) |
OD
= D + 2/Pn |
Helix
Angle (A) for Parallel Shaft Drive |
Number
of Teeth (N), Pitch Diameter (D) and the Diametral Pitch (P) |
Cos
A = N / (Pn X D) |
Addendum
(a) |
Normal
Diametral Pitch (Pn) |
a
= 1 / Pn |
Lead
(L) |
Pitch
Diameter (D) and Pitch Helix Angle |
L
= (pi*D) / Tan |
Circular Pitches and Equivalent Diametral Pitches Table
Circular Pitch |
Diametral Pitch |
Module |
Arc Thickness
of Tooth on Pitch Line |
Addendum |
Working Depth
of Tooth |
Dedendum or Depth
of Space Below Pitch Line |
Whole Depth
of Tooth |
| 4 |
0.7854 |
32.3402 |
2.0000 |
1.2732 |
2.5464 |
1.4732 |
2.7464 |
| 3 - 1/2 |
0.8976 |
28.2581 |
1.7500 |
1.1140 |
2.2281 |
1.2890 |
2.4031 |
| 3 |
1.0472 |
24.2552 |
1.5000 |
0.9549 |
1.9098 |
1.1049 |
2.0598 |
| 2 - 3/4 |
1.1424 |
22.2339 |
1.3750 |
0.8753 |
1.7506 |
1.0128 |
1.8881 |
| 2 - 1/2 |
1.2566 |
20.2117 |
1.2500 |
0.7957 |
1.5915 |
0.9207 |
1.7165 |
| 2 - 1/4 |
1.3963 |
18.1913 |
1.1250 |
0.7162 |
1.4323 |
0.8287 |
1.5448 |
| 2 |
1.5708 |
16.1701 |
1.0000 |
0.6366 |
1.2732 |
0.7366 |
1.3732 |
| 1 - 7/8 |
1.6755 |
15.1595 |
0.9375 |
0.5968 |
1.1937 |
0.6906 |
1.2874 |
| 1 - 3/4 |
1.7952 |
14.1488 |
0.8750 |
0.5570 |
1.1141 |
0.6445 |
1.2016 |
| 1 - 5/8 |
1.9333 |
13.1382 |
0.8125 |
0.5173 |
1.0345 |
0.5985 |
1.1158 |
| 1 - 1/2 |
2.0944 |
12.1276 |
0.7500 |
0.4775 |
0.9549 |
0.5525 |
1.0299 |
| 1 - 7/16 |
2.1855 |
11.6223 |
0.7187 |
0.4576 |
0.9151 |
0.5294 |
0.9870 |
| 1 - 3/8 |
2.2848 |
11.1169 |
0.6875 |
0.4377 |
0.8754 |
0.5064 |
0.9441 |
| 1 - 5/16 |
2.3936 |
10.6116 |
0.6562 |
0.4178 |
0.8356 |
0.4834 |
0.9012 |
| 1 - 1/4 |
2.5133 |
10.1062 |
0.6250 |
0.3979 |
0.7958 |
0.4604 |
0.8583 |
| 1 - 3/16 |
2.6456 |
9.6010 |
0.5937 |
0.3780 |
0.7560 |
0.4374 |
0.8154 |
| 1 - 1/8 |
2.7925 |
9.0958 |
0.5625 |
0.3581 |
0.7162 |
0.4143 |
0.7724 |
| 1 - 1/16 |
2.9568 |
8.5904 |
0.5312 |
0.3382 |
0.6764 |
0.3913 |
0.7295 |
| 1 |
3.1416 |
8.0851 |
0.5000 |
0.3183 |
0.6366 |
0.3683 |
0.6866 |
| 15/16 |
3.3510 |
7.5798 |
0.4687 |
0.2984 |
0.5968 |
0.3453 |
0.6437 |
| 7/8 |
3.5904 |
7.0744 |
0.4375 |
0.2785 |
0.5570 |
0.3223 |
0.6007 |
| 13/16 |
3.8666 |
6.5692 |
0.4062 |
0.2586 |
0.5173 |
0.2993 |
0.5579 |
| 3/4 |
4.1888 |
6.0639 |
0.3750 |
0.2387 |
0.4775 |
0.2762 |
0.5150 |
| 11/16 |
4.5696 |
5.5586 |
0.3437 |
0.2189 |
0.4377 |
0.2532 |
0.4720 |
| 2/3 |
4.7124 |
5.3903 |
0.3333 |
0.2122 |
0.4244 |
0.2455 |
0.4577 |
| 5/8 |
5.0265 |
5.0532 |
0.3125 |
0.1989 |
0.3979 |
0.2301 |
0.4291 |
| 9/16 |
5.5851 |
4.5479 |
0.2812 |
0.1790 |
0.3581 |
0.2071 |
0.3862 |
| 1/2 |
6.2832 |
4.0426 |
0.2500 |
0.1592 |
0.3183 |
0.1842 |
0.3433 |
| 7/16 |
7.1808 |
3.5373 |
0.2187 |
0.1393 |
0.2785 |
0.1611 |
0.3003 |
| 2/5 |
7.8540 |
3.2340 |
0.2000 |
0.1273 |
0.2546 |
0.1473 |
0.2746 |
| 3/8 |
8.3776 |
3.0319 |
0.1875 |
0.1194 |
0.2387 |
0.1381 |
0.2575 |
| 1/3 |
9.4248 |
2.6947 |
0.1666 |
0.1061 |
0.2122 |
0.1228 |
0.2289 |
| 5/16 |
10.0531 |
2.5266 |
0.1562 |
0.0995 |
0.1989 |
0.1151 |
0.2146 |
| 2/7 |
10.9956 |
2.3100 |
0.1429 |
0.0909 |
0.1819 |
0.1052 |
0.1962 |
| 1/4 |
12.5664 |
2.0213 |
0.1250 |
0.0796 |
0.1591 |
0.0921 |
0.1716 |
| 2/9 |
14.1372 |
1.7967 |
0.1111 |
0.0707 |
0.1415 |
0.0818 |
0.1526 |
| 1/5 |
15.7080 |
1.6170 |
0.1000 |
0.0637 |
0.1273 |
0.0737 |
0.1373 |
| 3/16 |
16.7552 |
1.5160 |
0.0937 |
0.0597 |
0.1194 |
0.0690 |
0.1287 |
| 1/6 |
18.8496 |
.5053 |
0.0833 |
0.0531 |
0.1061 |
0.0614 |
0.1144 |
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