Posted by Brian Dengel - The Gear Forum on July 21, 1999 at 10:20:00:

In Reply to: Long Addendum posted by Don on July 19, 1999 at 07:38:20:

When a pinion has less then 16 teeth the process of hobbing an involute profile will cause what is known as undercut. In order to prevent this degradation of the tooth strength, the gear can be produced using a process known as addendum modification. This is acomplished by increasing the working pitch diameter through the use of profile shifting. The coefficient of profile shift is the numerical value assign to this. It can range form -1.00 to +1.00. A positive shift is typically applied to a pinion which will be sujected to undercut and a negative shift is applied to the bull gear. It is not necessary to apply a negative shift to the bull gear unless you want to maintain the original center distance.

By increasing a pinion's working pitch diameter, you will increase the center distance of the gear set. You can either compensate for the change in center distance by adjusting the shafting or by applying a negative profile shift to the bull gear.

If you have a known center distance and you wish to calculate the coefficient of profile shift, you will also need to know the number of teeth on each gear, the module (pitch), and the pressure angle.

The method of calculation is as follows:

A) calculate the center distance increment factor. This is the center distance divided by the module minus one half the sum of the total number of teeth.

B) determine the working pressure angle. This is the inverse cosine of quotient of the cosine of the pressure angle and two times the C.D. increment factor divided by the total number of teeth plus one.

c) determine the sum of profile shifting. This is the quotient of the total number of teeth times the difference in the involute function values of the pressure angles divided by two times the tangent of the working pressure angle.

d) distribute the total coefficient between the two gears.

If you have any questions on this procedure, please feel free to contact us at (516) 437-6700.