Machinery's Handbook, 31st Edition
2314
CHECKING GEAR SIZES Table 9. Backlash Allowances for External and Internal Spur Gears
14 1 ∕ 2 °
17 1 ∕ 2 °
20 °
25 °
30 °
No. of Teeth
Ext.
Int.
Ext.
Int.
Ext.
Int.
Ext.
Int.
Ext.
Int.
5
.0019 .0024 .0018 .0024 .0017 .0023 .0015 .0021 .0013 .0019 .0024 .0029 .0022 .0027 .0020 .0026 .0017 .0022 .0015 .0018 .0028 .0032 .0025 .0029 .0023 .0027 .0019 .0022 .0016 .0018 .0030 .0034 .0026 .0030 .0024 .0027 .0020 .0022 .0016 .0018 .0031 .0035 .0027 .0030 .0025 .0027 .0020 .0022 .0017 .0018 .0032 .0036 .0028 .0031 .0025 .0027 .0020 .0022 .0017 .0018 .0035 .0037 .0030 .0031 .0026 .0027 .0021 .0022 .0017 .0017
10 20 30 40 50
100 200
.0036 .0038 .0031 .0031 .0027 .0027 .0021 .0022 .0017 .0017 External Gears: For each 0.001 inch reduction in pitch-line tooth thickness, reduce measurement over wires obtained from Table 1, Table 2, Table 7, or Table 8 by the amount shown below. Internal Gears: For each 0.001 inch reduction in pitch-line tooth thickness, increase measurement between wires obtained from Table 3 or Table 4 by the amounts shown below. Backlash on pitch line equals double tooth thickness reduction when teeth of both mating gears are reduced. If teeth of one gear only are reduced, backlash on pitch line equals amount of reduction. Example: For a 30-tooth, 10-diametral pitch, 20-degree pressure angle external gear, the measurement over wires from Table 1 is 32.4102 ÷ 10. For a backlash of 0.002, this measurement must be reduced by 2 × 0.0024 to 3.2362 or (3.2410 − 0.0048). Measurements for Checking Helical Gears Using Wires or Balls.— Helical gears may be checked for size by using one wire, or ball; two wires, or balls; and three wires, depending on the case at hand. Three wires may be used for measurement of either even or odd tooth numbers provided that the face width and helix angle of the gear permit the arrangement of two wires in adjacent tooth spaces on one side of the gear and a third wire on the oppo- site side. The wires should be held between flat, parallel plates. The measurement between these plates, and perpendicular to the gear axis, will be the same for both even and odd numbers of teeth because the axial displacement of the wires with the odd numbers of teeth does not affect the perpendicular measurement between the plates. The calculation of measurements over three wires is the same as described for measurements over two wires for even numbers of teeth. Measurements over One Wire or One Ball for Even or Odd Numbers of Teeth: This mea surement is calculated by the method for measurement over two wires for even numbers of teeth and the result divided by two to obtain the measurement from over the wire or ball to the center of the gear mounted on an arbor. Measurement over Two Wires or Two Balls for Even Numbers of Teeth: The measurement over two wires (or two balls kept in the same plane by holding them against a surface parallel to the face of the gear) is calculated as follows: First, calculate the pitch diameter of the helical gear from the formula D = Number of teeth divided by the product of the normal diametral pitch and the cosine of the helix angle, D = N ÷ ( P n × cos ψ ). Next, calculate the number of teeth, N e , there would be in a spur gear for it to have the same tooth curvature as the helical gear has in the normal plane: N e = N /cos 3 ψ . Next, refer to Table 7 for spur gears with even tooth numbers and find, by interpolation, the decimal value of the constant for this number of teeth under the given normal pressure angle. Finally, add 2 to this decimal value and divide the sum by the normal diametral pitch P n . The result of this calculation, added to the pitch diameter D , is the measurement over two wires or balls. Example: A helical gear has 32 teeth of 6 normal diametral pitch, 20 degree pressure angle, and 23 degree helix angle. Determine the measurement over two wires, M , without allowance for backlash. D = 32 ÷ 6 × cos 23 ° = 5.7939; N e = 32 ÷ cos 3 23 ° = 41.027; and in Table 7, fourth column, the decimal part of the measurement for 40 teeth is 0.2473 and that for 42 teeth is 0.2485.
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