February 16, 2024
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:
- Standard gears on standard centers both have X factors of ZERO.
- If the major diameter is bigger than standard, the X factor is POSITIVE.
- If the major diameter is smaller than standard, the X factor is NEGATIVE.
- On standard centers, “long and short” addendum sets will have a total X factor of ZERO.
- A POSITIVE total X factor means the centers are larger than standard.
- A NEGATIVE total X factor means the centers are smaller than standard.