


Checking Gear Size by Measurement over Wires or Pins 
The wire or pin method of checking gear sizes is accurate, easily applied, and especially useful in shops with limited inspection equipment. Two cylindrical wires or pins of predetermined diameter are placed in diametrically opposite tooth spaces. If the gears has an odd number of teeth, the wires are located as nearly opposite as possible. The overall measurement M is checked by using and sufficiently accurate method of measurement. The value of measurement M when the pitch diameter is correct can be determined easily and quickly by means of the calculated values in the accompanying tables.
Measurements for checking external Spur Gears when Wire Diameter Equals I.728 Divided by Diametral Pitch: For any other diametrical pitch, divide the measurements by whatever diametrical pitch is required. The result shows what measurement M should be when the pitch diameter is correct and there is no allowance for backlash. The procedure for obtaining a given amount of backlash will be explained later. For external spur gears the wire size equals I.728 divided by the diametral pitch.
Even Number of Teeth: To illustrate the use of the table, assume that a spur gear has 32 teeth of 4 diametral pitch and a pressure angle of 20 degrees. The measurement for 1 diametral pitch is 34.4130; Hence for 4 diametral pitch, the measurement equals 34.4130 / 4 = 8.6032 inches. This is the actual measurement over the wires when the pitch diameter is correct, provided there is no allowance for backlash.
Measurements for Checking Internal Gears When Wire Diameter Equals 1.44 Divided by Diametral Pitch: The measurements between wires for checking internal gears of 1 diametral pitch. For any other diametral pitch, divide the measurement by the diametral pitch required . These measurements are based upon the Van Keuren standard wire size, which , for internal spur gears, equals 1.44 divided by the diametral pitch.
Even Number of Teeth: For an even number of teeth, assume that the number of teeth = 3.80 and pressure angle is 14 ½ degrees; then for diametral pitch , figure at left of decimal point = given number of teeth 2 = 380 2 = 378. Figure at right of decimal point lies between values for 300 and 400 teeth and is obtained by interpolation. Thus , 380 – 300 = 80 (change to .80); hence, decimal required = .8795 + (.80 X .0008) = .88014. Total dimension = 378.88014.
Odd Number of Teeth: For internal gears having odd numbers of teeth, assume that number of teeth = 337 and pressure angle is 1486 degrees; then for 1 diametral pitch, figure at left of decimal point = given number of teeth 2 = 337 – 2 = 335. Figure at right of decimal point lies between decimal values for 301 and 401 teeth and is obtained by interpolation. Thus , 337 – 301 = 36 (change to .80); .8736  .8759 = .0017. hence, decimal required = .8759 + (.36 X .0017) = .8765 . Total dimension = 335.8765.
Measurements for Checking External Spur Gears when Wire Diameter Equal 1.68 Divided by Diametral Pitch: For checking the pitch diameters of external spur gears of 1 diametral pitch. For any other diametral pitch, divide the measurement by whatever diametral pitch is required. The result shows what measurement M should be when the pitch diameter is correct and there is no allowance for backlash. The procedure for checking for a given amount of backlash when the diameter of the measuring wires equals 1.68 divided by the diametral pitch is explained under a subsequent heading.
To find measurement M of an external spur gear using wire sizes equal to 1.68 inches divided by the diametral pitch.
Allowance for Backlash: The measurements over wires when the pitch diameters are correct and there is no allowance for backlash or play between meshing teeth. Backlash is obtained by cutting the teeth somewhat deeper than standard, thus reducing the thickness. Usually, the teeth of both mating gears are reduced in the thickness an amount equal to onehalf of the total backlash desired. However, if the pinion is small, it is common practice to reduce the gear teeth the full amount of backlash and the pinion is made to standard size.
Measurements for Checking Helical Gears using Wires or Balls: Helical gears may be checked for size by using one wire, or balls, two wires, or balls and three wires, depending on the case at hand. These wires may be used for measurement of either even or odd tooth numbers provided that the face width and helix angle of the gear. The measurements 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 measurements 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, calculated 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 ÷ (Pn X cos ψ). Next , calculate the number of teeth, Ne, there would be in a spur gear for it to have the same tooth curvature as the helical gear has in the normal plane.
Measurement over Two Wires or Two Balls for Odd Numbers of Teeth : The procedure is similar to that for two wire or two ball measurement for even tooth numbers except that a correction is made in the final M value to account for the wires or balls not being diametrically opposite by onehalf tooth interval. In addition care must be taken to ensure that the balls or wires are kept in a plane of the gear rotation as described previously.
Checking Spur Gear Size by Chordal Measurement Over Two or More Teeth : Another method of checking gear sizes, that is generally available. A vernier caliper is used to measure the distance M over two or more teeth. The measurement over two teeth, but three or more teeth might be included, depending upon the pitch. The jaws of the caliper are merely held in contact wit the sides or profiles of the teeth and perpendicular to the axis of the gear. Measurement M for involute teeth of the correct size. 




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