To begin, we have the A group of gear hobs (for involute gears) with trapezoidal profile teeth with angles of 12.5, 20, and 25 degrees. In this A group, converting can be done between any of the angles (six variations in all.)
Also we have the B group of shaft hobs for involute splines for trapezoidal profile teeth with angles of 30, 37.5, and 45 degrees. In this B group, converting can be done between any of the angles (again, six variations in all.)
And, last, we have the C group of hobs that can be converted between any angle of trapezoidal profiles of hob’s teeth A and B groups.
In sum, there is a total of 30 variations possible for one fixed-width P. Converting the angles of teeth is done simply by grinding the outside and inside diameters of the teeth hobs and relieving on the “Matrix” grinder with an abrasive disk with corresponding angle.
Most gear shops have a lot of old and new hobs sitting on shelves, so using these for either type of hob also will have an economic benefit, as well as helping to fill a need in emergency situations. Computer programs, algorithms, and tables confirm that conversions among the A group (gear hobs) start from P4 ad continue through P5 to P48.
To convert the B group, start from P10 to P48 for any hob's teeth angles, but angles 37.5 to 30 degrees and visa versa starts from P6, P8 to P48 (spline shaft hobs). Converting in the C group (involute gear hobs and involute spline shaft hobs A and B) starts from P10 to P48 for any angle, but 37.5 to 20 and 25 degrees, and for 30 to 20 and 25 degrees, starts from P6 to P48. The same method works effectively for converting larger angles P (P12, P16 to P48.)
Further, we also developed a computer program that shows the decline for profile teeth after grinding does not pass standard’s tolerances.
Computer program can be checked graphically by inscribing two teeth of the profile hob with one angle to another hob’s teeth with another angle, and vice versa (working with the same pitch.) This involves drawing two teeth of a hob with a common profile in 20:1 scale, or more, and inscribing this drawing into another drawing of two teeth hob with another profile. Drawing can be done by measuring on an optical comparator or calculating using standard formulas. A computer with CAD software and zoom function also can be used.
In any event, by compiling two drawings and transferring the angle from the drawings to the second hob will show how much material can be removed from the source teeth to create the size of the new hob’s teeth. As a precaution, though I recommend making a test cut before actually producing the gear and spline shafts. We use the same method for converting metric modules.