Machinery's Handbook, 31st Edition
HELICAL GEARING 2285 cutter. The thickness of the tooth at the pitch line equals 1.571 divided by the normal diametral pitch. After a tooth space has been milled, the cutter should be prevented from dragging through it when being returned for another cut. This can be done by lowering the blank slightly, or by stopping the machine and turning the cutter to such a position that the teeth will not touch the work. If the gear has teeth coarser than 10 or 12 diametral pitch, it is well to take a roughing and a finishing cut. When pressing a helical gear blank on the arbor, it should be remembered that it is more likely to slip when being milled than a spur gear, because the pressure of the cut, being at an angle, tends to rotate the blank on the arbor. Angular Position of Table: When cutting a helical gear on a milling machine, the table is set to the helix angle of the gear. If the lead of the helical gear is known, but not the helix angle, the helix angle is determined by multiplying the pitch diameter of the gear by 3.1416 and dividing this product by the lead; the result is the tangent of the lead angle which may be obtained from trigonometric tables or a calculator. American National Standard Fine-Pitch Teeth for Helical Gears.— This Standard, ANSI B6.7-1977, provides a 20-degree tooth form for both spur and helical gears of 20 diametral pitch and finer. Formulas for tooth parts are given on page 2214 . Enlargement of Helical Pinions, 20-Degree Normal Pressure Angle: Formula (4) and the accompanying graph are based on the use of hobs having sharp corners at their top lands. Pinions cut by shaper cutters may not require as much modification as indicated by (4) or the graph. The number 2.1 appearing in (4) results from the use of a standard tooth thickness rack having an addendum of 1.05/ P n which will start contact at a roll angle 5 degrees above the base radius. The roll angle of 5 degrees is also reflected in Formula (4). To avoid undercutting of the teeth and to provide more favorable contact conditions near the base of the tooth, it is recommended that helical pinions with less than 24 teeth be enlarged in accordance with the following graph and formulas. As with enlarged spur pinions, when an enlarged helical pinion is used it is necessary either to reduce the diameter of the mating gear or to increase the center distance. In the formulas that follow, φ n = normal pressure angle; φ t = transverse pressure angle; ψ = helix angle of pinion; P n = normal diametral pitch; P t = transverse diametral pitch; d = pitch diameter of pinion; d o = outside diameter of enlarged pinion; K h = enlargement for full depth pinions of 1 normal diametral pitch; and n = number of teeth in pinion.
45 40 35 30 25 20 15 10
9 Teeth
11 10
13 12
14
15
17 16
19 18
5 0
21 20
22
23
1.4
0
Enlargement K h , in Inches, for 1 Diametral Pitch, 20° Pressure Angle Pinions 0.2 0.4 0.6 0.8 1.0 1.2
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