Chainring/Cog Tooth Profiles

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walawalaoxenfree

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Mar 22, 2011, 11:39:40 AM3/22/11
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I spoke with two veteran machinists about my chainring project.
They both said that the tooth profile changes with the number of teeth
on a cog.
So the tooth profile of a 20 tooth cog is different than the profile
of a 50 tooth cog that takes the same chain.

Anybody out there have chainring/cog drawings that take this into
consideration.

I ask because I'd like to send some mill cutters to be ground and I
need to add a drawing.

Amir

Arthur Marks

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Mar 22, 2011, 1:04:53 PM3/22/11
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There is no short answer here. You need Machinery's Handbook. If you
have the 28th Ed. in the larger hardback, it is on page 2459.
Categorically, it is the following section: Machine
Elements>Transmission Roller Chain>Table 6: American National
Standard Roller Chain Sprocket Flange Thickness and Tooth Section
Profile Dimension ANSI/ASME B29.1M-1993 (R1999). -Arthur.

Jim Merz

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Mar 22, 2011, 6:14:13 PM3/22/11
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If you have an optical comparator it is easy to reverse engineer the
tooth profile. A CAD system would be very helpful to do the reverse
engineering job. The important thing to get is the radius of the part
the chain roller mates with and the diameter of the circle tangent
with all these radii. This is very important and needs to be done with
some accuracy. It's best if you can copy a new (or not worn anyway)
ring of the same size as you are making. Does not need to be the same
brand, copy a Campy ring if you can as they are nicely made. I think
if you try to make the profile using an end mill it will be very
difficult to control these critical dimensions, even if you have a
good dividing head. CNC mill is much better and less time consuming.
Good luck.

Jim Merz
Big Sur CA

On Mar 22, 10:04 am, Arthur Marks <arthur.ma...@gmail.com> wrote:
> There is no short answer here.  You need Machinery's Handbook.  If you
> have the 28th Ed. in the larger hardback, it is on page 2459.
> Categorically, it is the following section:  Machine
> Elements>Transmission Roller Chain>Table 6:  American National
> Standard Roller Chain Sprocket Flange Thickness and Tooth Section
> Profile Dimension ANSI/ASME B29.1M-1993 (R1999).  -Arthur.
>
> On Tue, Mar 22, 2011 at 10:39 AM, walawalaoxenfree
>

James Kenney

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Mar 22, 2011, 8:31:13 PM3/22/11
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You guys are making this way too complicated.
Yes, the proper tooth form is an involute, & it does vary with # of teeth.
If it were 2 gears meshing it would be very important, or if the chain
didn't have so much play in the rollers, it would be a concern.

However, bicycle chains, even the best have an enormous amount of play in
the rollers, relative to the degree of precision we are using here.
A 5/16", or 8mm end mill matches the roller diameter almost exactly, giving
just a small amount of clearance.
I have made many rings/cogs in all sizes, & they mesh nicely, yet don't skip
or jump.
All that is needed is a small chamfer with a file on the sharp edges of the
teeth after cutting the profile with the end mill.
Of course this is only a method you would use for 1 or 2 pieces, not
production.
What is important is the spacing, that's why I told Amir to use a bolt
circle program, it is more accurate than a dividing head, but requires a
digital readout, or CNC.
James Kenney

Ken Cline

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Mar 22, 2011, 10:34:42 PM3/22/11
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On 22 Mar 2011, at 6:31 PM, James Kenney wrote:

> Yes, the proper tooth form is an involute, & it does vary with # of teeth.

Involute profiles are for spur gears, not roller chain sprockets.

As you suggest, one can make a reasonable sprocket by cutting a pattern of circles on the blank and relieving the tops to allow for clearance as the chain unwinds. A working familiarity with geometry may be necessary, but it is not rocket science (though the Machinery's Handbook explanation is confusing enough to make it seem so).

Jim Adney

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Mar 22, 2011, 11:37:54 PM3/22/11
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On 22 Mar 2011 at 20:34, Ken Cline wrote:

> On 22 Mar 2011, at 6:31 PM, James Kenney wrote:
>
> > Yes, the proper tooth form is an involute, & it does vary with # of teeth.
>
> Involute profiles are for spur gears, not roller chain sprockets.

Right, the problem is similar, but different. The tooth profiles
shown in the Machinery's Handbook are also standard tooth profiles as
used in roller chain drives like those in coaster brake and 3-speed
cogs. Derailleur gear teeth have different profiles that I've never
quite understood, and I think it's more than simply truncated tooth
tops.

If you compare tooth profiles from the 2 different kinds of cogs the
difference will be instantly obvious. My impression is that if you
try to use the standard profile with a derailleur bike, the chain
will climb right up the side of the tooth and slip.

Or maybe it is simply a matter of truncated tooth tops....

Has anyone looked at this closer than I have?


--
*******************************
Jim Adney, jad...@vwtype3.org
Madison, Wisconsin, USA
*******************************

Nick Foley

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Mar 24, 2011, 11:40:24 AM3/24/11
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I've never machined cogs... but I have looked at a lot of old freewheels... and nearly all old 5-speed freewheel clusters used simple, squared off teeth and (visually) identical tooth profiles for all cog sizes.  I'm sure they aren't going set any records for the smoothest shifting, but they certainly work fine, and don't slip. 

Arthur Marks

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Mar 24, 2011, 12:13:46 PM3/24/11
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My understanding is that there is an ANSI standard for straight-line
(bicycle terminology: "single speed") motion transmissions. All of
the ramps, pins and curvilinear tooth profiles are proprietary
creations from individual companies testing and designing for specific
shifting applications. Surely they are have become intertwined as
they learn from each other's designs over the years. You will not
find a standard definition, for example, of the Shimano, Campagnolo or
SRAM tooth profiles. I believe the tooth form for all of the above is
essentially identical---meaning looking at the tooth perpendicular to
its rotation on the sprocket. I've never given them comparative
scrutiny, but it would be informative. Perhaps an article for Bicycle
Quarterly is suggested here? :) It would be interesting to include
some of the independent companies such as White Industries, etc. in
the comparison. Without the large dollar engineering support of the
primary component manufacturers, I would expect them to use a
comparatively simpler design. It may also be one reason that most
niche component manufacturers stick with offering single-speed
freewheels and cranks. Maybe not, though; it is just a thought.
-Arthur

On Tue, Mar 22, 2011 at 10:37 PM, Jim Adney <jad...@vwtype3.org> wrote:
> Derailleur gear teeth have different profiles that I've never
> quite understood, and I think it's more than simply truncated tooth tops.

Jim Adney

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Mar 24, 2011, 3:18:17 PM3/24/11
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On 24 Mar 2011 at 11:40, Nick Foley wrote:

> I've never machined cogs... but I have looked at a lot of old freewheels...
> and nearly all old 5-speed freewheel clusters used simple, squared off teeth
> and (visually) identical tooth profiles for all cog sizes. I'm sure they
> aren't going set any records for the smoothest shifting, but they certainly
> work fine, and don't slip.

That was my point. Our cogs and chainwheels use different tooth forms from
those standard forms shown in the Machinery's Handbook.

--
Jim Adney
jad...@vwtype3.org
Madison, WI USA

jkhhead

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Mar 24, 2011, 9:35:10 PM3/24/11
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The simple design cogs I have made have been mostly used on fixed gear
bikes.
However, I have made a couple for my geared bikes
also...........without the ramps/pins, they don't shift as well, but
once in gear, they run fine.
James

Andrew R Stewart

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Mar 24, 2011, 9:53:35 PM3/24/11
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Jim- I can say that the tooth profiles that Sturmey Archer used on their AW
hubs back in the made in England days sucked for derailleur shifting. I
converted a FW hub into an eight speed rig with cogs set back to back and a
derailleur. The derailleur shift was almost worthless. Andy.

Andrew R Stewart
Rochester, NY

Jim Adney

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Mar 24, 2011, 11:38:56 PM3/24/11
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On 24 Mar 2011 at 21:53, Andrew R Stewart wrote:

> Jim- I can say that the tooth profiles that Sturmey Archer used on their AW
> hubs back in the made in England days sucked for derailleur shifting. I
> converted a FW hub into an eight speed rig with cogs set back to back and a
> derailleur. The derailleur shift was almost worthless. Andy.

That's what I expected, but glad to have confirmation from someone
who actually tried it. I doubt that SA was different from any other
non-derailleur system. Coaster brake and 3-speed hubs all tended to
have tooth profiles that resemble those in the Machinery's Handbook.

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