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Table 4-1     The Calculation of Standard Spur Gears No. Item Symbol Formula Example Pinion Gear 1 Module m   3 2 Pressure Angle a   20º 3 Number of Teeth z1, z2*   12 24 4 Center Distance a  (z1 + z2)m    *          2 54.000 5 Pitch Diameter d zm 36.000 72.000 6 Base Diameter db d cos a 33.829 67.658 7 Addendum ha 1.00m 3.000 8 dedendum hf 1.25m 3.750 9 Outside Diameter da d + 2m 42.000 78.000 10 Root Diameter df d - 2.5m 28.500 64.500 * The subscripts 1 and 2 of z1 and z2 denote pinion and gear.

All calculated values in Table 4-1 are based upon given module - in and number of teeth z1 and z2 If instead module m, center distance a and speed ratio i are given, then the number of teeth, z1 and z2, would be calculated with the formulas as shown in Table 4-2. Table 4-2   The Calculation of Teeth Number No.  Item Symbol Formula Example 1 Module m   3 2 Center Distance a   54.000 3 Speed Ratio i   0.8 4 Sum of No. of Teeth z1+z2   2a    m 36 5 Number of Teeth z1, z2 i(z1+z2)    i+1 (z1+z2)    i+1 16 20 Note that the numbers of teeth probably will not be integer values by calculation with the formulas in Table 4-2. Then it is incumbent upon the designer to choose a set of integer numbers of teeth that are as close as possible to the theoretical values. This will likely result in both slightly changed gear ratio and center distance. Should the center distance be inviolable, it will then be necessary to resort to profile shifting. This will be discussed later in this section. 4.2 The Generating Of A Spur Gear    Involute gears can be readily generated by rack type cutters. The hob is in effect a rack cutter. Gear generation is also accomplished with gear type cutters using a shaper or planer machine.

4.3 undercutting   From Figure 4-3, it can be seen that the maximum length of the line-of-contact is limited to the length of the common tangent. Any tooth addendum that extends beyond the tangent points (T and T') is not only useless, but interferes with the root fillet area of the mating tooth. This results in the typical undercut tooth, shown, in Figure 4-4. The undercut not only weakens the tooth with a wasp-like waist, but also removes some of the useful involute adjacent to the base circle.   From the geometry of the limiting length-of-contact (T-T', Figure 4-3), it is evident that interference is first encountered by the addenda of the gear teeth digging into the mating-pinion tooth flanks. Since addenda are standardized by a fixed value (ha = m), the interference condition becomes more severe as the number of teeth on the mating gear increases. The limit is reached when the gear becomes a rack. This is a realistic case since the hob is a rack-type cutter. The result

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