This is something I have just been chewing over, so I was interested
to see this thread. However, I can't get your spreasheet to reproduce
Ivan Law's numbers. This could be me being dumb - but for a 20 degree
PA, and 1 DP, and gears between 17 and 20 teeth, Ivan says the
diameter of the button cutters should be 7.8 inches, and the spacing
8.7 inches - but your spreadsheet says diameter 5.8 to 6.8 and centres
6.8 to 7.8.
I can see it is recommened that the tool holding the buttons mounts
them at an angle of about 5 degrees so as to get front clearance, and
then grinding them at about 9 degress to get 4 degrees top rake. Which
I suppose makes the cutting edge oval - so maybe the diameter is a bit
tricky to define. Maybe this is part of it.
Does it reproduce Ivan Law's number when you use it ?
On Sat, 25 Aug 2007 16:46:15 -0700, Cheshire Steve
I can see Duncan's spreadsheet but no a way to use it.
There are two ways to use buttons to produce gear cutters.
One was devised in the 19th Century by various persons, Grant was one
and the method used by Ivan.
Both are correct although they do come up with different figures.
Where they differ is the old version which was also copied by Unwin in
ME in the 60's, use a blank of a known width and touch the buttons on
the edge of the blank THEN infeed.
In Ivan's method which isn't clear from the small illustration.
Although he specifies a width, that part isn't taken into account in
the calculations as he touches the button face on to the blank, moves
sideways to centralise the buttons on the blank, THEN infeed's.
If you draw both sets of calculations onto a geometrically correct
gear they overlap almost exactly.
May I point you to an article I wrote some years ago?
I think I can see one reason why your spreadsheet doesn't match the
numbers that are in Ivan Law's book - I think Ivan has optimised
things. I see you have used the radius at the pitch point (as defined
by Ivan) as the cutter radius. I have set up a spreadsheet to vary
diameter and seperation of circular cutters and then use the Excel
solver to optimise for a best fit over the whole involute surface. You
can get a better match to the involute than using the radius at the
pitch point - and it seems to invokve slightly larger diameter
cutters. I suspect the values in Ivans tables reflect this. He has
done some optimisation he has not told us about.
Although I can see a better fit using his cutter diameters, I can't
reproduce matching figures for the centre distances for these cutters.
Could be something in my spreadsheet !
Of course none of this might matter in the great scheme of things - I
have no feel for how sensitive the smooth running of a gear is to
deviations from the involute curve - clearly the use of single cutters
to cover a range of gear sizes in commercial practice suggests near
enough is good enough.
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