It seems that the differential is a black box that isn't understood that well. In my opinion you need to ignore the index and diff. sets of gears that are the most accurate and instead find sets of gears that almost exactly bracket the perfect ratio and allow the diff. to average them together--in other words look for near perfect additive inverses.
Setting up something today, it occurred to report back -
A
STANDARD set-up, requiring lead gears to interact with the diff, with resulting accuracy out to 7 places in inches. ( .0000007055104" ) That's a real world, every day example.
I think you have the approach needed to decide if this will work, but you need to remember that when hobbing the error will accumulate on each revolution of the gear being cut so you need to make some estimate of how many revolutions it will make in the process. And this will vary with the width of the gear being cut as the cutter is slowly fed across the width of the teeth. And be sure to allow extra revolutions for it to enter into the cut and at least partially exit the other side.
Exactly so. I tried to point this out in my earlier reply, but you did so more betterer.
But to go down another track, as I see it, the problem with hobbing a large tooth count gear is that you need all the prime numbers in it's tooth count in your gear train and sooner or later you get to a point where you lack one or more of them in your set of change gears. If I had to make a single such a gear, I would probably do it with a dividing head or rotary table, using angular settings. I would make a table of those settings using a program, like Excel and work carefully with it. If I had to make several such gears then I would use one of several techniques to make a hole circle that incorporates the needed prime number(s) and use that to make the gears. To me these seem far easier than going to a lot of math that may be error prone and a possibly undetected mistake could leave a small, undetected but significant error in the gears being made. This error may not show up until the gear is actually in use.
My point is that it is relatively easy to make a gear or hole circle with any number of teeth or divisions in any shop that has a dividing head or rotary table. And that gear or hole plate can/will be just as accurate as the dividing head or rotary table used to make it, plus or minus some small error inherent in the process. And when this shop made gear or hole circle is used to make more gears, any small errors in it will be divided down by a large factor in the process so any error from it in the final product will be completely negligible.
I would only resort to hobbing if I needed a relatively large number of gears of this high tooth count or if it was expected to be a repetitive job. Then I would make the needed prime number gear first using the above processes. There would be no worry about any cumulative error at all.
An I wrong here?
Yes and no.
Accuracy and relative ease are the primary reasons to Hob in your example. To the point though, you are correct in methods usable to
GET the Hob running.
Frankly, when I run into the proverbial immovable object, faced with the uncomfortable surrounding, I will usually WEDM the Prime I need and then use that to finish the job that is set up. After, I'll make at least one more of that Prime, by Hobbing.
I dont understand ? Please educate me ..
As I see it, gears have a limited accuracy based on
1. both tooth counts/dividing ratios/math
2. process imperfections, so that the teeth are not perfectly evenly sized, or perfectly positioned on the gear blank
From what I though I knew, precision gears are on the order of 0.01 - 0.001 degrees angular accuracy.
== 36 seconds to 3.6 seconds.
Does this seem right ? Too accurate, not accurate enough ?
It would seem to me, that using a simple, cheap optical encoder to measure and correct on angular position would or could easily achieve 10x (or 100x) better resolution, with no compounding errors, ever.
4 M count encoder == 1/111.000 counts per degree.
Its not purist, and old tech, but cheap, easy, and avoids the issue of large expensive specialist gears.
I am just asking, as maybe there is something I am not seeing..
As Forrest points out to you, there are
A LOT of factors to consider and account for/prevent while Gear Making™. And they are not limited to the Gear Blank, either. Hob run out, eccentricity, and condition are all
BIG influences. As are workholding and similar conditions for it. Any semi-trained monkey can make toothed wheels. There is quite a bit to consider and account for when making good, close tolerance Gears.
Hanermo,
I don't know about the Metric world but in USA we have 15 AGMA grades of gearing intended to fulfill requirements ranging from exposed weather gearing for draw bridge mechanism to gearing to that suited for the finest most accurate apparatus and very high power density high speed gearing for jet engines,helicopters, turbine reduction gears etc and everything in between. I'm sure the Metric community has comparable standards every bit as comprehensive and stringent.
There are several categories of error that crank into the various grades and their proportionate effect on grade and service is calculated by formulae. Among the error components are indexing error, eccentric error, profile error, and several others that escape me.
AGMA standards account for Module Pitches as well.
And thus, the fun begins... 