This is *not* a hypothetical question, BTW.

One of my lathes I was able to pick up cheap because it had a couple of
things missing from it. One of those things was a 16 tooth helical
gearwheel that is driven by the leadscrew to provide timing information
on when to throw the half-nuts into mesh when screw-cutting. Anyway, the
manufacturers (Harrisons) tell me this part is no longer available so I
shall have to cut one for myself, basically.
What I'd like to know is, can one back-calculate the required dimensions
of this gearwheel from the leadscrew it meshes with? I'd have thought so,
but welcome informed opinion on the matter. Say for example the leadscrew
(Acme thread form if it matters) is 6TPI and the missing gear is known,
from old user manuals, to have 16 teeth. The helix angle can be taken
from the leadscrew (or could be worked out simply from the pitch of it)
and 16 teeth at 6TPI should enable one to work backwards to find the
pitch circle diameter - or the base circle diameter at least.
If I do this, are other parameters like the pressure angle and MOD values
automatically taken care of, or is there still some additional data
required to cut the new gear that simply cannot be inferred from the
existing machinery?

thanks,

CD.

On 20/04/2016 21:23, Cursitor Doom wrote:
This is *not* a hypothetical question, BTW.

One of my lathes I was able to pick up cheap because it had a couple of
things missing from it. One of those things was a 16 tooth helical
gearwheel that is driven by the leadscrew to provide timing information
on when to throw the half-nuts into mesh when screw-cutting. Anyway, the
manufacturers (Harrisons) tell me this part is no longer available so I
shall have to cut one for myself, basically.
What I'd like to know is, can one back-calculate the required dimensions
of this gearwheel from the leadscrew it meshes with? I'd have thought so,
but welcome informed opinion on the matter. Say for example the leadscrew
(Acme thread form if it matters) is 6TPI and the missing gear is known,
from old user manuals, to have 16 teeth. The helix angle can be taken
from the leadscrew (or could be worked out simply from the pitch of it)
and 16 teeth at 6TPI should enable one to work backwards to find the
pitch circle diameter - or the base circle diameter at least.
If I do this, are other parameters like the pressure angle and MOD values
automatically taken care of, or is there still some additional data
required to cut the new gear that simply cannot be inferred from the
existing machinery?

Have you asked the manufacturer whether they still have the drawings?
Depending on just how long it has been out of production, they could
still have those on file, even if they no longer supply the part.


--
Colin Bignell

On Thu, 21 Apr 2016 09:29:06 +0100, Nightjar cpb wrote:

Have you asked the manufacturer whether they still have the drawings?
Depending on just how long it has been out of production, they could
still have those on file, even if they no longer supply the part.

Ha! Fat chance of that. The gear itself is no longer available, but they
just happen to have *one* left as part of a complete new indexing head
for 240 quid. They won't sell the gear separately. They kindly offered to
cut me a new gear, though, for 160! Bear in mind the equivalent Myford
part is just 12 quid. So yes, they have the drawings but there's a
negative cash incentive to part with them. Anyway, it's more fun to to
work things out; more of a challenge I reckon.

I've given it some more thought; I'm almost there...I think.

The key dimension of this gear and the one that really matters is its
diameter. Everything else - I think - is known and follows from that. Its
diameter will be it's circumference divided by pi. So what will its
circumference be? The answer is the same as the length that 16 teeth
occupy along the leadscrew it meshes with. But I suspect this is only an
approximation.
Don't mind me talking to myself here. It often helps to clarify my
thinking. But feel free to chip in if you've spotted something I may have
missed.

On Wednesday, 20 April 2016 21:26:40 UTC+1, Cursitor Doom wrote:
This is *not* a hypothetical question, BTW.

One of my lathes I was able to pick up cheap because it had a couple of
things missing from it. One of those things was a 16 tooth helical
gearwheel that is driven by the leadscrew to provide timing information
on when to throw the half-nuts into mesh when screw-cutting. Anyway, the
manufacturers (Harrisons) tell me this part is no longer available so I
shall have to cut one for myself, basically.
What I'd like to know is, can one back-calculate the required dimensions
of this gearwheel from the leadscrew it meshes with? I'd have thought so,
but welcome informed opinion on the matter. Say for example the leadscrew
(Acme thread form if it matters) is 6TPI and the missing gear is known,
from old user manuals, to have 16 teeth. The helix angle can be taken
from the leadscrew (or could be worked out simply from the pitch of it)
and 16 teeth at 6TPI should enable one to work backwards to find the
pitch circle diameter - or the base circle diameter at least.
If I do this, are other parameters like the pressure angle and MOD values
automatically taken care of, or is there still some additional data
required to cut the new gear that simply cannot be inferred from the
existing machinery?

thanks,

CD.

Could you make a cutter that matches the leadscrew, and then use it to cut another gear?

On 21/04/2016 21:54, wrote:
On Wednesday, 20 April 2016 21:26:40 UTC+1, Cursitor Doom wrote:
This is *not* a hypothetical question, BTW.

One of my lathes I was able to pick up cheap because it had a couple of
things missing from it. One of those things was a 16 tooth helical
gearwheel that is driven by the leadscrew to provide timing information
on when to throw the half-nuts into mesh when screw-cutting. Anyway, the
manufacturers (Harrisons) tell me this part is no longer available so I
shall have to cut one for myself, basically.
What I'd like to know is, can one back-calculate the required dimensions
of this gearwheel from the leadscrew it meshes with? I'd have thought so,
but welcome informed opinion on the matter. Say for example the leadscrew
(Acme thread form if it matters) is 6TPI and the missing gear is known,
from old user manuals, to have 16 teeth. The helix angle can be taken
from the leadscrew (or could be worked out simply from the pitch of it)
and 16 teeth at 6TPI should enable one to work backwards to find the
pitch circle diameter - or the base circle diameter at least.
If I do this, are other parameters like the pressure angle and MOD values
automatically taken care of, or is there still some additional data
required to cut the new gear that simply cannot be inferred from the
existing machinery?

thanks,

CD.

Could you make a cutter that matches the leadscrew, and then use it to cut another gear?

That could work, but you would need to rotate the gear in sympathy with
the cutter.

On Thu, 21 Apr 2016 22:26:41 +0100, Fredxxx wrote:

Could you make a cutter that matches the leadscrew, and then use it to
cut another gear?

Already done it. That was the easy bit.

That could work, but you would need to rotate the gear in sympathy with
the cutter.

That's called "hobbing" but there are other methods. I prefer to cut mine
on a milling machine with an indexing attachment.
In any case, I just need to know the diameter of the blank to use for the
gear. That's the only thing that's holding me back - at the moment....

On Thu, 21 Apr 2016 23:10:02 +0000, Cursitor Doom wrote:

On Thu, 21 Apr 2016 22:26:41 +0100, Fredxxx wrote:

Could you make a cutter that matches the leadscrew, and then use it to
cut another gear?

Already done it. That was the easy bit.

That could work, but you would need to rotate the gear in sympathy with
the cutter.

That's called "hobbing" but there are other methods. I prefer to cut
mine on a milling machine with an indexing attachment.
In any case, I just need to know the diameter of the blank to use for
the gear. That's the only thing that's holding me back - at the
moment....


I made a pair for the M250 out of acetal using a fly cutter but I had the
original gears to work from. I did not worry about helix as the gear is
only say 4 mm thick.

Anyway this is the answer - I think

Leadscrew is 4 TPI = 6.35 mm per tooth

mm per tooth / Pi = MOD = 6.35/3.1418 = 2.021268 MOD

DP = 2.54/MOD = 2.54/2.021268 = 12.56637 DP

OD of gear = N+2/DP = 16 (desired tooth count)+2 /12.56637 = 1.432"

Yes I could have stuck with MOD but as your lathe is imperial perhaps you
work in imperial. I'm sure the more mathematically able would do it
differently. The tooth profile etc only has to be there or thereabouts
and it will work fine.

On Fri, 22 Apr 2016 09:22:44 +0000, Julian Barnes wrote:

I made a pair for the M250 out of acetal using a fly cutter but I had
the original gears to work from. I did not worry about helix as the gear
is only say 4 mm thick.

Anyway this is the answer - I think

Leadscrew is 4 TPI = 6.35 mm per tooth

mm per tooth / Pi = MOD = 6.35/3.1418 = 2.021268 MOD

DP = 2.54/MOD = 2.54/2.021268 = 12.56637 DP

OD of gear = N+2/DP = 16 (desired tooth count)+2 /12.56637 = 1.432"

Yes I could have stuck with MOD but as your lathe is imperial perhaps
you work in imperial. I'm sure the more mathematically able would do it
differently. The tooth profile etc only has to be there or thereabouts
and it will work fine.

A helpful contribution, I'm sure. Just can't help thinking that your end
result of just under 1.5" seems rather small. I'll check your working
later as I'm a bit tied up right now, but I suspect you've made an error
somewhere.

On Fri, 22 Apr 2016 09:22:44 +0000, Julian Barnes wrote:

Anyway this is the answer - I think

Leadscrew is 4 TPI = 6.35 mm per tooth

mm per tooth / Pi = MOD = 6.35/3.1418 = 2.021268 MOD

DP = 2.54/MOD = 2.54/2.021268 = 12.56637 DP

OD of gear = N+2/DP = 16 (desired tooth count)+2 /12.56637 = 1.432"

No, this can't be right, surely. Whoever heard of a DP of 12.56637??
Doesn't make sense. The whole depth of cut on the leadscrew is about
0.134" which would suggest a DP of 16 (they're always round numbers on
stock gears). Tables tell us that the Addendum for a 16DP gear is 0.0625"
and the OD will be the PD + 2*A. Getting there.....