Exact ratio of SRAM 3-speed hub



D

Doug Goncz

Guest
By disassembling an SRAM 3x7 hub I have determined the gearing is 17-15-47.
That is, the sun gear was counted as 17 teeth, the ring as 47, and the planet
gears computed to be 15. It is not necessary to know the gear module or even
whether the module is metric or inch based to make this calculation reliably.
Pitchs circles add and subtract as integers. The center to center distance
remains unknown but is not relevant.

Now, what are the ratios of a 17-15-47 epcicyclic gear train?

SRAM says they are 0.73, 1, and 1.36.

I need more accurate figures. Rational numbers are to be preferred in my
calculation.

Can any of you here help?


Yours,
Doug Goncz ( ftp://users.aol.com/DGoncz/incoming )
Student member SAE for one year.
I love: Dona, Jeff, Kim, Mom, Neelix, Tasha, and Teri, alphabetically.
I drive: A double-step Thunderbolt with 657% range.
 
S

Sheldon Brown

Guest
Doug Goncz wrote:

> By disassembling an SRAM 3x7 hub I have determined the gearing is 17-15-47.
> That is, the sun gear was counted as 17 teeth, the ring as 47, and the planet
> gears computed to be 15. It is not necessary to know the gear module or even
> whether the module is metric or inch based to make this calculation reliably.
> Pitchs circles add and subtract as integers. The center to center distance
> remains unknown but is not relevant.
>
> Now, what are the ratios of a 17-15-47 epcicyclic gear train?
>
> SRAM says they are 0.73, 1, and 1.36.
>
> I need more accurate figures.


"Need?"

> Rational numbers are to be preferred in my calculation.
>
> Can any of you here help?


Yep. A tinkerer like you really oughta spring for a copy of
_Machinery's Handbook_ one of the most wonderful books in existence.

A quick look for "epicyclic gearing" in the index led me to:

D = 1 + C/A where C is the size of the sun pinion, and A is the size of
the gear ring.

Thus, your example yields:

D = 1 + 17/47

which is rational but not round.

1.3617021276596...

1.000000000

0.734375

Sheldon "Numbers" Brown
+--------------------------------------------------------+
| As far as the laws of mathematics refer to reality, |
| they are not certain; and as far as they are certain, |
| they do not refer to reality. --Albert Einstein |
+--------------------------------------------------------+
Harris Cyclery, West Newton, Massachusetts
Phone 617-244-9772 FAX 617-244-1041
http://harriscyclery.com
Hard-to-find parts shipped Worldwide
http://captainbike.com http://sheldonbrown.com
 
Doug Goncz writes:

> By disassembling an SRAM 3x7 hub I have determined the gearing is
> 17-15-47. That is, the sun gear was counted as 17 teeth, the ring
> as 47, and the planet gears computed to be 15. It is not necessary
> to know the gear module or even whether the module is metric or inch
> based to make this calculation reliably. Pitch circles add and
> subtract as integers. The center to center distance remains unknown
> but is not relevant.


> Now, what are the ratios of a 17-15-47 epicyclic gear train?


The planets must bridge the gap between sun and ring gear, where:

47t-17t = 30t and 30t/2 = 15t

The planets have, by themselves, no bearing on the ratio other than to
fit into the annular space. The ratio is that in one revolution of
the planets the ring gear moves ahead 47t+17t = 64t and that 64t/47t =
the step up ratio and the step down ratio is the reciprocal.

> SRAM says they are 0.73, 1, and 1.36.


> I need more accurate figures. Rational numbers are to be preferred
> in my calculation.


The SRAM numbers are as usual, reciprocals of each other as they must
be with a simple planetary.

(1/0.73) = 1.36 and the converse.

the more exact numbers are: 0.734375 and 1.361702

However, you should be able to come up with this on your own if you are
really in engineering school.

Jobst Brandt
[email protected]
 
On Mon, 04 Oct 2004 19:51:43 GMT,
[email protected] wrote:

>Doug Goncz writes:
>
>> By disassembling an SRAM 3x7 hub I have determined the gearing is
>> 17-15-47. That is, the sun gear was counted as 17 teeth, the ring
>> as 47, and the planet gears computed to be 15. It is not necessary
>> to know the gear module or even whether the module is metric or inch
>> based to make this calculation reliably. Pitch circles add and
>> subtract as integers. The center to center distance remains unknown
>> but is not relevant.

>
>> Now, what are the ratios of a 17-15-47 epicyclic gear train?

>
>The planets must bridge the gap between sun and ring gear, where:
>
>47t-17t = 30t and 30t/2 = 15t
>
>The planets have, by themselves, no bearing on the ratio other than to
>fit into the annular space. The ratio is that in one revolution of
>the planets the ring gear moves ahead 47t+17t = 64t and that 64t/47t =
>the step up ratio and the step down ratio is the reciprocal.
>
>> SRAM says they are 0.73, 1, and 1.36.

>
>> I need more accurate figures. Rational numbers are to be preferred
>> in my calculation.

>
>The SRAM numbers are as usual, reciprocals of each other as they must
>be with a simple planetary.
>
>(1/0.73) = 1.36 and the converse.
>
>the more exact numbers are: 0.734375 and 1.361702
>
>However, you should be able to come up with this on your own if you are
>really in engineering school.
>
>Jobst Brandt
>[email protected]


Dear Jobst,

However, Doug can be sure of quick, clear answers here on
rec.bicycles.tech, as long as he's willing to put up with
unprovoked snotty remarks.

Carl Fogel
 
D

Doug Goncz

Guest
As I go through my day as a recovering schizophrenic and self-employed
experimental machinist, I eat large quantities of quick, clear answers mixed
with unprovoked snotty remarks. I find the combination to be a more interesting
feed than the bland oatmeal some prefer, so I have no problem with any of the
replies on this thread.

>Dear Jobst,
>
>However, Doug can be sure of quick, clear answers here on
>rec.bicycles.tech, as long as he's willing to put up with
>unprovoked snotty remarks.
>
>Carl Fogel


I'll post the latest SRAM gearset now.


Yours,
Doug Goncz ( ftp://users.aol.com/DGoncz/incoming )
Student member SAE for one year.
I love: Dona, Jeff, Kim, Mom, Neelix, Tasha, and Teri, alphabetically.
I drive: A double-step Thunderbolt with 657% range.