This is an idea for a computer program to convert certain sizes of involute spline shaft hobs into different sizes, and vice-versa, as they have the same circular pitch or diametral pitch (P). It is based on a principle of converting. The computer program is based on six short algorithms or formulas, and will convert a 45-degree trapezoidal tooth profile hob into a 37.5-degree trapezoidal tooth profile hob, a 45-degree into a 30-degree, and a 37.5-degree into a 30-degree hob. This means grinding and relieving a larger angle on the teeth for receiving teeth with smaller angles – group A. Grinding can be done on the grinder “Matrix.”
The same process also can be done in the reverse (vice versa.) For that, I can grind and relieve a 37.5-degree trapezoidal tooth profile hob into either a 45-degree or 30-degree trapezoidal tooth profile hob, and a 30-degree to a 45-degree trapezoidal tooth profile hob.
The resulting smaller ground angles accept teeth with bigger angles – group B. For this, grinding can be done with abrasive disc with angle. By simply grinding and relieving, shops can create either type of hob in an emergency situation. At most shops that produce involute spline shafts and hobs, a lot of old and new hobs sit on shelves, so using them for either type of hob also has an economical benefit.
This program gives us essential the size M1 for grinding the inside diameter of the hob for group A, and the size M2 for grinding the outside diameter hob for group B. For both groups, the conversion starts from P10 to P48 for 45 degrees, to either angle and reverse, and from P6 to P48 for 37.5 degrees to 30 degrees and reverse.
As we see, we have a wide range for converting involute spline shaft hobs (10 number of P). All M1 and M2 sizes are calculated according to P.
We check the computer program by converting a graphical one. I draw in a scale of 20:1 or more two to three 45-degree tooth hobs on tracing or film paper, or on the computer screen (CAD, zoom.) The same step is done separately for the 37.5-degree and 30-degree hob teeth.
Then, I inscribe (for group A) the drawing of the teeth of a 37.5 degree hob into a 45-degree hob, a 30-degree hob into a 45-degree hob, and 30-degree hob into a 37.5-degree hob, making sure the tops of the teeth match up and the vertical axes are congruent.
For the inverse (vice versa) conversion (group B), I make certain that the vertical axes and big theoretical bases (which equal 3.14159:P) are congruent. Also, inscribing can be done on the computer screen or on the optical comparator.
All drawings can be done by measuring old and new hobs using an instrumental microscope or optical comparator, or calculated using standard formulas.
In any event, the composite drawing shows how much material to remove from the source teeth to create new size teeth for involute spline shaft hob. As a precaution though, I make a test cut before actually producing involute spline shafts.