This month's tip addresses a question I was asked recently: "What is meant by Long and Short Addendums on gears". The following should give a better understanding of this procedure.

Whenever a gear set is required where one of the gears is considerably smaller than the other (high ratio), Its teeth may be severely undercut, thus decreasing their strength, and reducing the contact ratio of the gear set. To alleviate this problem the long and short addendum gear design method was devised. With it the pinion outside diameter is increased (long addendum) and the gear outside diameter is decreased (short addendum) by an equal amount. The numbers of teeth, the center distance of the set, the working depth and the pressure angle remain the same. When the gear teeth are generated, the tool is shifted radially outward on the pinion and radially inward on the gear by the same amount.

The amount of the necessary profile shift depends basically on the pressure and the number of teeth on the pinion. Other considerations are increased sliding velocities of the tooth flanks, minimum acceptable top land on the pinion tooth and beam strength requirements for the gear sets.

To establish the limits of profile shift it is most practical to investigate the tooth geometry of a series of gears with different pressure angles and various numbers of teeth, all having the same diametrical pitch. Profile shifts for other diametrical pitches can then be proportionally calculated.

The German industry standards express the profile shift as a function of the module by establishing a profile shift factor (X).

The same factor (X) can be used for calculations with the diameter pitch where:

The minimum values of the profile shift factors are shown in Figure 1 for pressure angles 15° and 20°. Again, values for theoretical and practical limits are indicated. The practical limits are generally acceptable.

In spur gear set of ø = 20°, where a 10 tooth pinion drives a 25 tooth gear, a minimum positive shift factor of X + 0.25 would be required to eliminate the undercut on the 10 tooth pinion. The 25 tooth gear would then have to have a -0.25 profile shift factor. This is well within acceptable limits, since a 25 tooth gear will reach the point of being undercut with a profile shift factor of -0.65 (see Figure 2).

If the gear set of 10 and 25 teeth is of 6 diametral pitch, the generating tool would be radially shifted out on the 10 tooth pinion and shifted in on the 25 tooth gear by:

The root and outside diameters of gear and pinion would also be decreased, respectively increased by this same amount.