I've been reading Ivan Law's book on making gear cutters and he described the design and build of a "button cutter" to generate an approimation of the involute profile.
Mr. Law sets out two tables of design information for the cutters, one
20deg pressure angle and the other is at 30deg pressure angle. The design data is normalised at one diametrical pitch.
The puzzle I have is that the two buttons are of diameter "D" and the distance between the button centres is "C".
The thing I'm struggling with is that in both tables "C" is less than "D". How can this be?
Too be honest it's a bit of an armchair question as I've had a kind offer from one of the guys on the group to cut the two gears I'm after, but can't abide leaving things I don't understand to one side!
C is less than D to make cutters to cut gears with the smaller number of teeth. In those cases, you have to grind flats on the buttons in order to get the required distance apart. It's all to do with the geometry of involute gear teeth.
Search the newsgroup for "Ivan Laws" and you will find a couple of threads on this topic and one contains a link to a spreadsheet written by Duncan Munroe. I ended up concluding that there is an error in the tables in my 2006 copy of this book, but as I was after 14.5 degree PA then I had to resort to my own calculations anyway. It is a shame that Ivan Law didn't spell out how he calculated the numbers in his tables so we could check his workings - but on the other hand it is important to realise that circular cutters are only an approximation to the involute, and even pre-made cutters cover a range of gears. So there is a fair bit of tolerance.
I have a spreadsheet that will calculate these values. You can see it here:
It calculates the button diameter, pitch and infeed for the form tool described by Ivan Law in his book "Gears and Gear Cutting". To obtain actual sizes then either divide by the DP of the actual gear to get sizes in inches or multiply by the module to get sizes in millimeters.
The table in the book is acknowledged as being in error and other tables exist on the 'net. One of these can be found here:
by John Stevenson)
An article in Engineering in Miniature (Oct 1998) by D A G Brown describes the process and gives a set of formulae for calculating the relevant dimensions. I have used those calculations in this spreadsheet. The calculations are a bit scruffy but accurate in as much as they replicate the results of DAG Brown. Where those results differ from other published tables there are a couple of reasons. One is rounding errors. Another is that the tables often give dimensions for a cutter intended to cover a range of gears. The compiler of the table may have chosen any particular number of teeth for that cutter in the range quoted.
In general it seems that close enough will do. For example, take the No4 cutter (26-34 teeth). For this, the range of button sizes is 8.89 to
11.63. Any button size you pick will be an approximation for the other tooth numbers.
A related discussion I came across had the following suggestion from Jerry Kieffer: He makes single point form tool by using an end-mill to cut the profile out of a suitable blank. He says that for any given gear, there will probably be a standard size end mill of a diameter close enough for the task in hand. So for example, to make a 48 tooth,
0.5module gear, the button diameter would be 16.42 * 0.5 = 8.21mm. An
8mm end mill would be quite close enough using Jerry's method.
Please note that I have never had to make my own cutters but expect to one day which is why have taken the trouble to keep track of these bits and pieces.