Machinery's Handbook, 31st Edition
CHECKING GEAR SIZES 2317 Table for Determining the Chordal Dimension: Table 10 gives the chordal dimensions for one diametral pitch when measuring over the number of teeth indicated in Table 11. To obtain any chordal dimension, it is simply necessary to divide chord M in the table (oppo site the given number of teeth) by the diametral pitch of the gear to be measured and then subtract from the quotient one-half the total backlash between the mating pair of gears. In cases where a small pinion is used with a large gear and all of the backlash is to be obtained by reducing the gear teeth, the total amount of backlash is subtracted from the chordal dimension of the gear and nothing from the chordal dimension of the pinion. The applica tion of the tables will be illustrated by an example. Table 11. Number of Teeth Included in Chordal Measurement Tooth Range for 14 1 ∕ 2 ° Pressure Angle Tooth Range for 20 ° Pressure Angle Number of Teeth to Gage Over Tooth Range for 14 1 ∕ 2 ° Pressure Angle Tooth Range for 20 ° Pressure Angle Number of Teeth to Gage Over
12 to 18 19 to 37 38 to 50 51 to 62
12 to 18 19 to 27 28 to 36 37 to 45
2 3 4 5
63 to 75 76 to 87 88 to 100 101 to 110
46 to 54 55 to 63 64 to 72 73 to 81
6 7 8
9 This table shows the number of teeth to be included between the jaws of the vernier caliper in measuring dimension M as explained in connection with Table 10. Example: Determine the chordal dimension for checking the size of a gear having 30 teeth of 5 diametral pitch and a pressure angle of 20 degrees. A total backlash of 0.008 inch is to be obtained by reducing equally the teeth of both mating gears. Table 10 shows that chordal distance for 30 teeth of one diametral pitch and a pressure angle of 20 degrees is 10.7526 inches; one-half of the backlash equals 0.004 inch; hence, . . . 5 10 7526 0 004 2 1465 Chordal dimension inches = − = Table 11 shows that this is the chordal dimension when the vernier caliper spans four teeth, this being the number of teeth to gage over whenever gears of 20-degree pressure angle have any number of teeth from 28 to 36, inclusive. If it is considered necessary to leave enough stock on the gear teeth for a shaving or fin ishing cut, this allowance is simply added to the chordal dimension of the finished teeth to obtain the required measurement over the teeth for the roughing operation. It may be advisable to place this chordal dimension for rough machining on the detail drawing. Formula for Chordal Dimension M.— The required measurement M over spur gear teeth may be obtained by the following formula in which R = pitch radius of gear, A = pres sure angle, T = tooth thickness along pitch circle, N = number of gear teeth, S = number of tooth spaces between caliper jaws, F = a factor depending on the pressure angle = 0.01109 for 14 1 ∕ 2 ° ; = 0.01973 for 17 1 ∕ 2 ° ; = 0.0298 for 20 ° ; = 0.04303 for 22 1 ∕ 2 ° ; = 0.05995 for 25 ° . This factor F equals twice the involute function of the pressure angle. . cos M R A R T N S F 62832 # # # = + + a k Example: A spur gear has 30 teeth of 6 diametral pitch and a pressure angle of 14 1 ∕ 2 degrees. Determine measurement M over three teeth, there being two intervening tooth spaces. The pitch radius = 2 1 ∕ 2 inches, the arc tooth thickness equivalent to 6 diametral pitch is 0.2618 inch (if no allowance is made for backlash) and factor F for 14 1 ∕ 2 degrees = 0.01109 inch.
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