Machinery's Handbook, 31st Edition
2266 Bevel Gearing Selecting Formed Cutters for Milling Bevel Gears.— For milling 14 1 ∕ 2 -degree pressure angle bevel gears, the standard cutter series furnished by manufacturers of formed mill- ing cutters is commonly used. There are 8 cutters in the series for each diametral pitch to cover the full range from a 12-tooth pinion to a crown gear. The difference between formed cutters used for milling spur gears and those used for bevel gears is that bevel gear cutters are thinner because they must pass through the narrow tooth space at the small end of the bevel gear; otherwise the shape of the cutter and, hence, the cutter number are the same. To select the proper number of cutter to be used when a bevel gear is to be milled, it is necessary, first, to compute what is called the “Number of Teeth, N ′ for which to Select Cutter.” This number of teeth can then be used to select the proper number of bevel gear cutter from the spur gear milling cutter table on page 2229 . The value of N ′ may be com puted using the last formula in the table on page 2262 . Example 1: What numbers of cutters are required for a pair of bevel gears of 4 diametral pitch and 70 degree shaft angle if the gear has 50 teeth and the pinion 20 teeth? The pitch cone angle of the pinion is determined by using the first formula in the table on page 2262 : . ; tan cos sin cos sin 70 70 033064 18 18 P P ° ° ° ′ α α R R = + = + = = The pitch cone angle of the gear is determined from the second formula in the table on page 2262 : 70 18 18 51 42 G P ° ° ′ ° ′ α α R = − = − = The numbers of teeth N ′ for which to select the cutters for the gear and pinion may now be determined from the last formula in the table on page 2262 : . cos cos N N 18 18 20 211 21 for the pinion teeth P P ′ ° ′ . α = = = . cos cos N N 51 42 50 807 81 for the gear teeth G G ′ ° ′ . α = = = From the table on page 2229 the numbers of the cutters for pinion and gear are found to be, respectively, 5 and 2. Example 2: The cutters for a pair of bevel gears are required where the gear has 24 teeth and the pinion 12 teeth. The shaft angle is 90 degrees. As in the first example, the formulas given in the table on page 2262 will be used. . . . tan cos cos N N N N 12 24 05000 26 34 90 26 34 63 26 12 26 34 134 13 24 63 26 536 54 and for pinion teeth for gear teeth P P G P G P ' ' ' ' ° ′ ° ° ′ ° ′ ′ ° ′ ′ ° ′ . . α α α α R = = = = = − = − = = = = = And from the table on page 2229 the cutters for pinion and gear are found to be, respec tively, 8 and 3. Use of Table for Selecting Formed Cutters for Milling Bevel Gears.— The table beginning on page 2264 gives the numbers of cutters to use for milling various numbers of teeth in the gear and pinion. The table applies only to bevel gears with axes at right angles. Thus, in Example 2 given above, the numbers of the cutters could have been obtained directly by entering the table with the actual numbers of teeth in the gear, 24, and the pinion, 12. N N 20 50 P G
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