11-01-2012, 06:04 PM
For cutting racks in the shaper and getting the tooth spacing right there is no substitute for using gear tooth verniers, simply grind a pointed tool with a small flat on the tip, use either 14.5 or 22 degrees depending on the pressure angle required, set a depth stop on the down feed to ensure you don't cut too deep, advance the rack to the approximate centre of the next groove, plunge to depth and then measure the tooth thickness at halfway deep and slowly back cut until the tooth is the correct thickness for the pitchline, then cut forwards until the groove is the right size. The math for gears is much easier than you think, On a rack and at the pitchline the width of the tooth and gap should be equal and exactly half of the pitch measurement.
As a Math example, for a ten tooth 10dp gear the pitch circle diameter is exactly one inch and the tooth width at the pitch line is so close to (pi x 1inch / 10)/2 and it's exactly the same calc to find the tooth thickness on the matching rack. Pi is a part of the calcs for rack teeth as a rack is effectively a spur gear of infinite diameter, and Pi is a ratio of the circumference:diameter of a circle and as dp stands for diametral pitch.
The metric module system works on a similar system but all the formulae and the measuring system is completely different
So as you can see there's no reason to be scared of the math it's all simple add, subtract, multiply and divide stuff, no calculus required. Of course I have simplified this a bit but it is fine for any hobby use and the values have no allowance for clearance, once again for hobby use no problem just make the teeth a few thou less than the exact numbers that the formulae churn out.
Oh and discaimer time, I just pulled this out of my memory so if you are going to use it check it first or let me know and I will double check / proof read your calcs.
Regard Rick
As a Math example, for a ten tooth 10dp gear the pitch circle diameter is exactly one inch and the tooth width at the pitch line is so close to (pi x 1inch / 10)/2 and it's exactly the same calc to find the tooth thickness on the matching rack. Pi is a part of the calcs for rack teeth as a rack is effectively a spur gear of infinite diameter, and Pi is a ratio of the circumference:diameter of a circle and as dp stands for diametral pitch.
The metric module system works on a similar system but all the formulae and the measuring system is completely different
So as you can see there's no reason to be scared of the math it's all simple add, subtract, multiply and divide stuff, no calculus required. Of course I have simplified this a bit but it is fine for any hobby use and the values have no allowance for clearance, once again for hobby use no problem just make the teeth a few thou less than the exact numbers that the formulae churn out.
Oh and discaimer time, I just pulled this out of my memory so if you are going to use it check it first or let me know and I will double check / proof read your calcs.
Regard Rick
Whatever it is, do it today, Tomorrow may not be an option and regret outlasts fatigue.