That X Factor

Our international readers are no doubt chuckling over this silly, American “long addendum” terminology. The “civilized world” has long relied on a more precise concept of “rack offset coefficient” to account for outside diameter changes. While I agree that “rack shift” is a more accurate term, its calculation can be confusing to many designers. Some of the confusion occurs because of the insistence of some experts that backlash be factored into the mathematics. I find that to be an unnecessary complication for the designer as backlash comes from a number of other things besides tooth thickness; actual manufacturing tolerance is not always known at the design stage. When I first had to calculate rack offset coefficient -X factor in most computer programs, I was blessed to have the guidance of Bob Errichello’s GearTech AGMA218 user manual. Bob is one of the best teachers of gear design (and a longtime Gear Technology Technical Editor) and his manual lays out the calculation in very clear formulas. I won’t repeat those formulas here, but will point out a few conventions to memorize:

1. Standard gears on standard centers both have X factors of ZERO.
2. If the major diameter is bigger than standard, the X factor is POSITIVE.
3. If the major diameter is smaller than standard, the X factor is NEGATIVE.
4. On standard centers, “long and short” addendum sets will have a total X factor of ZERO.
5. A POSITIVE total X factor means the centers are larger than standard.
6. A NEGATIVE total X factor means the centers are smaller than standard.

Most commercial software packages conform to the standard rack offset formulas and you can find many excellent technical papers on the topic in the Gear Technology archives, so I will not attempt to summarize the theories here. Some of the popular objectives are strength balancing; durability balancing; scoring risk reduction; noise reduction; undercut avoidance; and specific sliding control. Our archives are keyword searchable to save you time.