Posted by BillS on April 04, 2013 at 08:12:57:
In Reply to: Re: Hobbing Prime Spurs using differential posted by gearhead1 on April 02, 2013 at 11:35:54:
Hi Gearhead,
Sorry to be so late in responding -
First, pick a feed and calculate "C".
Next round "C" to nearest integer. "C" must be an integer for this method to work - This was left out in the FAQ and I'm sorry for that. I made corrections to that FAQ topic link today!
Substitute "C" into index formula as shown in the FAQ topic. Pick +/- 1 according to the hand you want for index/feed setup. Likely it doesn't matter which at this stage.
Note that you will have integers in numerator and denominator. Now, this next part may be trial and error, since you need to factor numerator and denominator into useable gear sizes. If you started with a reasonable angle (i.e. not too small, say 15 degrees) and you have a good selection of change gears (i.e. not too many missing sizes), it should not take too long to manipulate numerator/denominator (i.e. multiply, factor, or divide ) to get a working selection of change gear sizes.
Sometimes you will have to change "C" value and start manipulating numerator/denominator all over again.
If you get this far, you will see that your prime gear has disappeared from the index change gear set.
Since you had to change "C" value to an integer, the corresponding table feed changed as well. So calculate the new table feed to 5 or 6 places:
Table Feed = PI/[ NDP x C x SIN(Helix angle)]
Next calculate the Feed Gear Ratio. Use your formula however it may be stated (here is an example):
Feed gear ratio = Table Feed / Mach feed const
Use 5 or 6 decimal places for both table feed and decimal gear ratio to get a change gear match as accurate as possible.
If you experience helix angle error with this procedure it would have to be due to mismatch(es) between ideal gear ratios and corresponding gear sets.
Also, it seems to me that you can start out with workable index gears and feed gears and, calculate the actual lead (or helix angle). This would be the lead (or helix angle) you would use to find the differential ratio and gear set. Again, it is of utmost importance to match gear sets very closely to their calculated decimal ratios. Actually, approximating a decimal index ratio to a set of index gears requires recalculating feed gear decimal ratio to compensate for the error in index. But that's for another topic.
Can't say it enough - It is important to match ALL gear sets very closely to their calculated decimal ratios. Remember, you are not cutting a spur gear by synchronizing index gear set to machine's internal gearing (index constant).
Again, I am very sorry for the error in the article. I should have caught it, so it seems you are the first to catch it. For that, both visitors and I thank you.
I suspect the small angle you're seeing is due to small mismatches between actual gear sets and "ideal" gear sets. There is always an error in this method, but with a complete range of change gears, it can be made very small.
If extreme accuracy is required, use the method described to make a change gear. If the size of the prime change gear is too large for the machine, make two smaller pitch change gears that will mesh together - one being the prime gear and the other a suitable change gear to mesh with it. You would still use 4 index change gears total, but the prime and its meshing member would be smaller in size to mount on the machine. This would synchronize the index, omit the differential set altogether, would allow feed to be anything you want, and allow multiple cuts - all good reasons to cut your prime change gear.
Whew! I think that is a good place to start from. Comments anyone?