Most of the Friction In A Bicycle Chain

John Dacey writes:

ISTR that an MIT research project, published in the last few
years, showed that chain efficiency increased with tension rather
than decreasing, rather counterintuitively.

They didn't say on what basis this relied. Was this constant bicycle
speed or was it percentage loss of input.

I doubt that, because as tension increases, lubrication films
decrease and friction increases. However, that me be the result of
there being loss even with a slack chain and that overhead becomes
insignificant at higher loads.

Three things are varying in these comparisons, angular articulation of
the chain, chain tension, and chain speed. As I see it, a chain
running between two 20t sprockets in comparison to one running on two
40t sprockets, transmitting the same rotational torque and speed to
the rear wheel have these effects:

chain tension 2:1
chain bend 2:1
chain speed 1:2

Since it is chain articulation that causes friction in the links, the
smaller sprocket pair has larger bend angle under higher tension
although at half the speed. It still worse than the larger sprocket
pair. Besides, lubrication failure is greater at higher tension.

Is the type of chain construction much of a factor? In what ways
will a chain with bushings for its rollers be better/worse than its
bushingless counterpart?

Bushings give roughly four times the bearing area to the pins than
side plates with upset collars give. This alone causes higher wear,
but in addition, water intrusion and lubricant loss is accelerated by
a fairly direct path into the bearing area of the pin through the gap
under the roller.

Jobst Brandt

Joe Riel writes:

Terms
-----
Nr = number of teeth of rear sprocket
Nf = number of teeth of front chainwheel
mu = coefficient of friction in bushing
p = chain pitch
pi = 3.14159...
Pl = power loss in chain
Ptot = total power transfer
Rb = inner radius of chain bushing
Rr = radius of rear sprocket
T = chain tension
wr = angular velocity of rear sprocket
wf = angular velocity of front sprocket


(6) Pl/Ptot = 2*pi*mu*Rb/p*(1/Nr + 1/Nf)

While this formula is rather simple, it does
give results that are consistent with my
crude knowledge of chain efficiency.

Consider that

Rb ~ 0.11 inch
p = 0.50 inch
mu ~ 0.16 (lubricated steel on steel)

Then

Pl/Ptot = (0.22)(1/Nr + 1/Nr)

The extremes for a typical road bike are

Pl/Ptot|min = (0.22)(1/13 + 1/39) = 2.3%
Pl/Ptot|max = (0.22)(1/23 + 1/53) = 1.4%


which is about what I would expect, probably
lower than achievable.


Joe Riel

Jim Cronin writes:

Bushings give roughly four times the bearing area to the pins than
side plates with upset collars give. This alone causes higher
wear, but in addition, water intrusion and lubricant loss is
accelerated by a fairly direct path into the bearing area of the
pin through the gap under the roller.

Are there any chains with bushings for 7, 8 or 9 speed drivetrains
in current production? Are they any good?

No. As I mentioned, with 20t chainwheels and heavy riders, a
5-element derailleur chain one with full sleeves, is probably not
safely possible, the sleeve cutting a large hole in the inner side
plates.

The ones I have are excellent but I can only put less that half the
tension in these chains with the gears I ride. I don't have a 20t
chainwheel.

Jobst Brandt

Joe Riel writes:

Terms
-----
Nr = number of teeth of rear sprocket
Nf = number of teeth of front chainwheel
mu = coefficient of friction in bushing
p = chain pitch
pi = 3.14159...
Pl = power loss in chain
Ptot = total power transfer
Rb = inner radius of chain bushing
Rr = radius of rear sprocket
T = chain tension
wr = angular velocity of rear sprocket
wf = angular velocity of front sprocket

(6) Pl/Ptot = 2*pi*mu*Rb/p*(1/Nr + 1/Nf)

While this formula is rather simple, it does give results that are
consistent with my crude knowledge of chain efficiency.

Consider that

Rb ~ 0.11 inch
p = 0.50 inch
mu ~ 0.16 (lubricated steel on steel)

Then

Pl/Ptot = (0.22)(1/Nr + 1/Nr)

The extremes for a typical road bike are

Pl/Ptot|min = (0.22)(1/13 + 1/39) = 2.3%
Pl/Ptot|max = (0.22)(1/23 + 1/53) = 1.4%


which is about what I would expect, probably lower than achievable.

There are so many constants floating around in these equations that it muddles
the picture. Items Nr Nf mu p pi Rb Rr are fixed for the obvious test two
cases I proposed, that of a 20t to 20t pair and a 40t to 40t drive train.
This gets rid of most of the fog and gets right down to the issue of power
loss due to sprocket size... for the same ratio.

This would be like a 52t-13t and a 44t-11t for instance but far
simpler to analyze in the 20 and 40 arrangement. So what's your take on that?

Jobst Brandt

In article ,
wrote:

Tim McNamara wrote:

: Much better than a belt drive both in terms of measurement and
: real-life use. However, chain drives have been measured with
: efficiency as high as 98%. These are under ideal conditions with
: clean and properly lubricated components, I'd expect, and
: real-life efficiency is probably rather less.

If we shield the chain from road dirt, will it give us the optimum
efficiency?

Well, there are a number of issues besides cleanliness, as has been
discussed in other posts. The roller chain was intended by Mr.
Renolds (sp?) to run in an oil bath, if I understand correctly. So a
chain in a chain case with an oil bath, over largish cogs and a
straight chainline ought to give you the best efficiency. Not to
mention lasting much, much longer than exposed bicycle chains.

writes:

This would be like a 52t-13t and a 44t-11t for instance but far
simpler to analyze in the 20 and 40 arrangement. So what's your take on that?


for the 52/13
Pl/Ptot = (0.22)(1/13 + 1/52) = 2.1%

for the 44/11

Pl/Ptot = (0.22)(1/11 + 1/44) = 2.5%


So the 52/13 is somewhat better. Probably more so,
since the chain angle is better and my simplistic
formula doesn't consider that.


Joe Riel

Tim McNamara writes:

If we shield the chain from road dirt, will it give us the optimum
efficiency?

Well, there are a number of issues besides cleanliness, as has been
discussed in other posts. The roller chain was intended by Mr.
Renold to run in an oil bath, if I understand correctly. So a chain
in a chain case with an oil bath, over largish cogs and a straight
chainline ought to give you the best efficiency. Not to mention
lasting much, much longer than exposed bicycle chains.

http://www.renold.com/

Automotive timing chains as well as drive transfer chains last for
more than 100000 miles of running... at thousands of RPM. They run in
a filtered oil bath.

Jobst Brandt

Joe Riel writes:

This would be like a 52t-13t and a 44t-11t for instance but far
simpler to analyze in the 20 and 40 arrangement. So what's your
take on that?


for the 52/13
Pl/Ptot = (0.22)(1/13 + 1/52) = 2.1%

for the 44/11

Pl/Ptot = (0.22)(1/11 + 1/44) = 2.5%


So the 52/13 is somewhat better. Probably more so, since the chain
angle is better and my simplistic formula doesn't consider that.

That wasn't the question. It was 20t and 40t, one to one transfer.

for 20/20

Pl/Ptot = (0.22)(1/20 + 1/20) = 2.2%

for 40/40

Pl/Ptot = (0.22)(1/40 + 1/40) = 1.1%

Something doesn't work here!

Jobst Brandt

Peter Cole writes:

This would be like a 52t-13t and a 44t-11t for instance but far
simpler to analyze in the 20 and 40 arrangement. So what's your
take on that?

for the 52/13
Pl/Ptot = (0.22)(1/13 + 1/52) = 2.1%

for the 44/11

Pl/Ptot = (0.22)(1/11 + 1/44) = 2.5%

So the 52/13 is somewhat better. Probably more so, since the chain
angle is better and my simplistic formula doesn't consider that.

That wasn't the question. It was 20t and 40t, one to one transfer.

for 20/20

Pl/Ptot = (0.22)(1/20 + 1/20) = 2.2%

for 40/40

Pl/Ptot = (0.22)(1/40 + 1/40) = 1.1%

Something doesn't work here!

Looks OK to me, since articulation losses are inversely proportional
to sprocket size, half the size means twice the loss, what doesn't
work?

That's the point. By having large chainwheels with 50+ teeth, they
are practically out of the picture as they obscure the losses at the
other end. We should be looking at the losses in small sprockets. By
always changing both CW and SPKT's the linear relationship of
efficiency to sprocket size is lost. The 20 - 20 and 40 - 40 example
demonstrates that.

Therefore, other things being equal, a sprocket half the size has half
the efficiency.

Jobst Brandt

writes:

By having large chainwheels with 50+ teeth, they
are practically out of the picture as they obscure the losses at the
other end. We should be looking at the losses in small sprockets. By
always changing both CW and SPKT's the linear relationship of
efficiency to sprocket size is lost. The 20 - 20 and 40 - 40 example
demonstrates that.

Therefore, other things being equal, a sprocket half the size has half
the efficiency.

Actually, it has twice the *inefficiency*, a different thing altogether.
Half the efficiency would be around 0.5, which would be rather bad.
Efficiency = 1 - inefficiency.

The efficiency of power transfer from a chain to sprocket is approximately

E = 1 - 2*pi*mu*Rb/p/N

where

mu = coefficient of friction
Rb = inner radius of bushing
p = chain pitch
N = number of teeth in sprocket

For a bike chain this is approximately

E = 1 - 0.22/N

When we consider both the front and rear together we get the total efficiency

Etot = Ef*Er = (1-0.22/Nf)(1-0.22/Nr) ~= 1 - 0.22*(1/Nf + 1/Nr)


Joe Riel