Machinery's Handbook, 31st Edition
Bevel Gearing 2267 Offset of Cutter for Milling Bevel Gears.— When milling bevel gears with a rotary formed cutter, it is necessary to take two cuts through each tooth space with the gear blank slightly off center, first on one side and then on the other, to obtain a tooth of approximately the correct form. The gear blank is also rotated proportionately to obtain the proper tooth thickness at the large and small ends. The amount that the gear blank or cutter should be offset from the central position can be determined quite accurately by the use of the table Factors for Obtaining Offset for Milling Bevel Gears in conjunction with the following rule: Find the factor in the table corresponding to the number of cutter used and to the ratio of the pitch cone radius to the face width; then divide this factor by the diametral pitch and subtract the result from half the thickness of the cutter at the pitch line. Factors for Obtaining Offset for Milling Bevel Gears
Ratio of Pitch Cone Radius to Width of Face F C a k
No. of Cutter
1 3 2 1
1 4 2 1
1 5 2 1
1 3 4 1
1 3 4 3
1 4 4 1
1 4 4 3
1 3
1 4
1 5
1 6
1 7
1 8
1 0.254 0.254 0.255 0.256 0.257 0.257 0.257 0.258 0.258 0.259 0.260 0.262 0.264 2 0.266 0.268 0.271 0.272 0.273 0.274 0.274 0.275 0.277 0.279 0.280 0.283 0.284 3 0.266 0.268 0.271 0.273 0.275 0.278 0.280 0.282 0.283 0.286 0.287 0.290 0.292 4 0.275 0.280 0.285 0.287 0.291 0.293 0.296 0.298 0.298 0.302 0.305 0.308 0.311 5 0.280 0.285 0.290 0.293 0.295 0.296 0.298 0.300 0.302 0.307 0.309 0.313 0.315 6 0.311 0.318 0.323 0.328 0.330 0.334 0.337 0.340 0.343 0.348 0.352 0.356 0.362 7 0.289 0.298 0.308 0.316 0.324 0.329 0.334 0.338 0.343 0.350 0.360 0.370 0.376 8 0.275 0.286 0.296 0.309 0.319 0.331 0.338 0.344 0.352 0.361 0.368 0.380 0.386 Note.—For obtaining offset by above table, use formula: T P 2 Offset factor from table = − P = diametral pitch of gear to be cut T = thickness of cutter used, measured at pitch line To illustrate, what would be the amount of offset for a bevel gear having 24 teeth, 6 diametral pitch, 30-degree pitch cone angle and 1 1 ∕ 4 -inch face or tooth length? In order to obtain a factor from the table, the ratio of the pitch cone radius to the face width must be determined. The pitch cone radius equals the pitch diameter divided by twice the sine of the pitch cone angle = 4 ÷ (2 × 0.5) = 4 inches. As the face width is 1.25, the ratio is 4 ÷ 1.25 or about 3 1 ∕ 4 to 1. The factor in the table for this ratio is 0.280 with a No. 4 cutter, which would be the cutter number for this particular gear. The thickness of the cutter at the pitch line is measured by using a vernier gear tooth caliper. The depth S + A (see Fig. 2; S = addendum; A = clearance) at which to take the measurement equals 1.157 divided by the diametral pitch; thus, 1.157 ÷ 6 = 0.1928 inch. The cutter thickness at this depth will vary with different cutters and even with the same cutter as it is ground away, because formed bevel gear cutters are commonly provided with side relief. Assuming that the thickness is 0.1745 inch, and substituting the values in the formula given, we have: . . . 2 01745 6 0280 00406 Offset inch = = = Adjusting the Gear Blank for Milling.— After the offset is determined, the blank is ad- justed laterally by this amount, and the tooth spaces are milled around the blank. After having milled one side of each tooth to the proper dimensions, the blank is set over in the
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