Basic Gear Formulas (pg 2)

Spur and Helical Gears

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Any gear will mesh and run with any other gear of the same pitch. Recommend meshing stainless steel with aluminum gears for smoother running, longer life and silent operation. For best operation helical gear should run with thrust washers - see PIC standard stock thrust washers on page 6-11 and reference below.

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Table 2.2 MINIMUM NUMBER OF PINION TEETH VS. PRESSURE ANGLE AND HELIX ANGLE HAVING NO OBJECTIONABLE UNDERCUT
Helix Angle Degrees	Minimum number of teeth to avoid undercut. Normal pressure Angle, Øn, degrees
Helix Angle Degrees	14 1/2	20	25
0 (spur gears)	32	18	12
5	32	17	12
10	31	17	11
15	29	16	11
20	27	15	10
23	26	14	10
25	25	14	9
30	22	12	8
35	19	10	7
40	15	9	6
45	12	7	5

Table 2.3 20-DEGREE PRESSURE ANGLE INVOLUTE FINE-PITCH SYSTEM FOR MODIFIED 17 TEETH OR LESS SPUR PINIONS (All tabular dimensions are given in inches for 1 diametral pitch. For other pitches divide tabular values by diametral pitch.)
Pinion Dimensions			Standard Center-Distance System (Long and Short Addendum) Gear Dimensions¹				Enlarged Center - Distance System Standard Mating Gear Diameter²
Number of Teeth n	Outside Diam.	Cir. Tooth Thickness at Standard Pitch Diam.	Decrease in Standard Outside Diam.	Cir. Tooth Thickness at Standard Pitch Diam.	Recom- mended Minimum Number of Teeth (N)	Contact Ratio, n Mating with N³	Increase Over Standard Center Distance	Contact Ratio Two Equal Pinions³
10	12.8302	1.8730	0.8302	1.2686	33	1.419	0.4151	1.135
11	13.7132	1.8304	0.7132	1.3112	30	1.450	0.3566	1.186
12	14.5963	1.7878	0.5963	1.3538	27	1.473	0.2982	1.238
13	15.4793	1.7452	0.4793	1.3964	25	1.493	0.2397	1.290
14	16.3623	1.7027	0.3623	1.4389	23	1.508	0.1812	1.344
15	17.2453	1.6601	0.2453	1.4815	21	1.516	0.1227	1.398
16	18.1234	1.6175	0.1284	1.5241	19	1.519	0.0642	1.436
17	19.0114	1.5749	0.0114	1.5667	18	1.522	0.0057	1.511
The outside diameters of small pinions are enlarged to avoid undercut. Enlargements are based on addendum proportions of the basic rack, figure 2.1, of . When different proportions are used, the outside diameter must be adjusted accordingly. 1. To maintain standard center distances when using enlarged pinions, the mating gear diameters must be decreased by the amount of the pinion enlargement. 2. If mating gears are made with standard tooth proportions, the center distances must be increased as shown. 3. Nominal Values: will vary due to effects of tolerances.