# Thread: Which gear cutter do I need?

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The rack is in better condition. The first two photos below are from the edge of the rack, where there is minimal wear. The second two photos are from the middle where there is the most wear. This is the table drive for a manual surface grinder.

Do you thing the rack is serviceable? If so, could I use the less-worn section to determine the correct cutter for the gear?

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Well you get a bit of a break. You have a helical gear mating with a spur gear rack.
That means the angle between the helical gear shaft and the travel direction of the rack cannot be 90 degrees.
The angle between them is the helix angle of the gear.

I'll bet there are a tooth or two on each end of the rack that the gear does not ride on. Wear there should be nonexistent. Measure there.

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Originally Posted by Erich
I'll bet there are a tooth or two on each end of the rack that the gear does not ride on. Wear there should be nonexistent. Measure there.
What should I measure on the rack? Distance between teeth?

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Originally Posted by pinstripe
What should I measure on the rack? Distance between teeth?
Distance from the back of the rack (the mounting face) and a drill shank (in) that fits midway in the tooth space.

Ideally, you'd re-cut the rack teeth to a common pin measurement. Index from a calculated table enter on the DRO. The linear pitch for 14 Dp is pi / 14 or 0.2244.

The best pin size would be 1.7280 / 14 or 0.1243 theoretically. Your reading on a rack will be comparative - face to pin - so anything close will do like a 1/8 drill shank.

If you don't have a DRO but can gear the dividing head to the table lead screw, drive the lead screw from the dividing head tail shaft using the hole circles through what would ordinarily be lead gearing to increment your rack indexes. Calculation will be required.

The helix angle of the pinion equals the angle of the pinion shaft to the rack motion.

The shim adjustment factor equals the trial reading / Tan Pa. You got 0.041" trial backlash and you want 0.003"? 0.038" / 0.3640 = 0.104" shim.

You probably won't care about pitch diameter on the new replacement gear. You can re-cut the one you have a little deeper if there is stock. On assembly, trial fit the rack to the new gear, determine the shim to bring the rack to the desired backlash, and make a one piece (preferably) to suit.
Last edited by Forrest Addy; 07-17-2017 at 08:53 PM.

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Pitch & OD diameter for helicals, (Number of Teeth/DP x cosine of the lead angle) + (1/DP x 2) When cutting helicals on a gear hobber you can not use the normal gearing used for that number of teeth. On a 30:1 base ratio machine for a 45 tooth gear the index gearing would be 30-Idler-45 with a single lead hob. Helicals work a little different. Its been awhile but for a 45T 20° RH Helix the formula for the index gears woulld involve the cosine of the lead angle plus a constant. The constant is also involved in the calculation for the feed gears. Both the index and feed gears must work in concert. And once you start cutting you cannot drop the feed out. This is because depending on the hand of the gear you are advancing or retarding the the index of the gear relative to the hob. As to cutting helicals on a universal. Never had to. We had a gear hobber. The big problem with cutting helicals is the factoring the index and feed ratios. The gear trains need to be accurate to .9999 to 1.0000 or better. But now thanks to the net there is an online gear train calculator. Do a search here for the thread I posted here in. Also useful for determiing the ratios for odd pitch thread forms on the lathe

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All milling machine-made spur gears have the same circular pitch measured normal to the gear form.

Machinery's Handbook has excellent details on thus matter.

For Pinstripe (the OP) as you live in OZ and have Hare and Forbes (aka "Machinery House") tool seller in Sydney, if you don't have it already, buy and read (and re-read) until you "get it"). It is a very good publication and is for people Machine Shops.

Your maths will need to be pretty good but relevant to machine shop trainees.

https://www.machineryhouse.com.au/L341

And while you are at it but these essential books:

https://www.machineryhouse.com.au/L341

https://www.machineryhouse.com.au/L343

https://www.machineryhouse.com.au/L344

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Originally Posted by Spin Doctor
Pitch & OD diameter for helicals, (Number of Teeth/DP x cosine of the lead angle) + (1/DP x 2) When cutting helicals on a gear hobber you can not use the normal gearing used for that number of teeth. On a 30:1 base ratio machine for a 45 tooth gear the index gearing would be 30-Idler-45 with a single lead hob. Helicals work a little different. Its been awhile but for a 45T 20° RH Helix the formula for the index gears woulld involve the cosine of the lead angle plus a constant. The constant is also involved in the calculation for the feed gears. Both the index and feed gears must work in concert. And once you start cutting you cannot drop the feed out. This is because depending on the hand of the gear you are advancing or retarding the the index of the gear relative to the hob. As to cutting helicals on a universal. Never had to. We had a gear hobber. The big problem with cutting helicals is the factoring the index and feed ratios. The gear trains need to be accurate to .9999 to 1.0000 or better. But now thanks to the net there is an online gear train calculator. Do a search here for the thread I posted here in. Also useful for determiing the ratios for odd pitch thread forms on the lathe
Trivial quibble: depending, of course, whether your hobber is equipped with a lead differential. Those with, index the same ratio, helical or spur. Those without, index Vs feed.

The beauty of the lead differential is the feed can be disengaged at any time without affecting the lead timing with the hob spindle making traversing back to start a new cut a simple evolution.

BTW The gear ratio calculator I use came from Conrad Hoffmann's website. Yes indeed that little application saved me a zillion hours of hand working continued fractions. I haven't found an Android phone app that works irrational four gear compound ratios for all integers 16 to 120
Last edited by Forrest Addy; 07-18-2017 at 12:47 AM.

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Trivial quibble: depending, of course, whether your hobber is equipped with a lead differential. Those with, index the same ratio, helical or spur. Those without, index Vs feed.

The beauty of the lead differential is the feed can be disengaged at any time without affecting the lead timing with the hob spindle making traversing back to start a new cut a simple evolution.

BTW The gear ratio calculator I use came from Conrad Hoffmann's website. Yes indeed that little application saved me a zillion hours of hand working continued fractions. I haven't found an Android phone app that works irrational four gear compound ratios for all integers 16 to 120
Any help?

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Originally Posted by oldtiffie
Any help?
Maybe. I'll need to find the time to read through it. Got a heap of work piled up at the moment.

I appreciate all the replies above, but I haven't had time to digest them properly. I'm surprised at how complex some of the answers are. It's all a bit over my head at the moment.

Looking at the F&D Tool catalog https://www.fdtool.com/, I should only need four pieces of information to select a gear cutter:

1. The pressure angle. Mcgyver said it's most likely 20 degrees in post #2.
2. The cutter number. With 17 teeth, it should be cutter 6 according to the table on page 36 of the catalog.
3. The hole size. That one is easy, I only have a 1" arbor for the mill.
4. The diametrical pitch. Mcgyver said 14 DP. George cast some doubt on that due to the helix angle, but Mcgyver came back saying that it would still be the same cutter if the angle is under 20 degrees. Erich's suggestion to measure the angle between the rack and shaft sounds like the most accurate way to confirm this. I haven't been able to check it because the castings are being reground at the moment, but I will check when they come back.

So does all the information above look correct, or do I need more information to determine which cutter I need?

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