EBike DriveSystems Chain
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The most simple type of reduction is the chain. Still more compact than belts in most cases. If lubricated and separated from dirt by a chain guard, this is the non-plus-ultra in DIY environment. Gains up to 98% efficiency.
Link to technical reference by spinningmagnets: 
D.I.D chain strength and dimensions of small chains (pdf) 
chain drive design
There are two common ways of using an electric motor to drive a bicycle's rear wheel using a chain.
- One option is driving the front cranks with a motor, and then transmitting the motor power through the bicycle's standard drive train. This is called a Middrive.
- The other option is driving the wheel by an extra chain. This config is called a Non-Hub Rear Drive. This is often implemented on the left side, via a sprocket that is attached to the wheel hub disc brake holes. This allows a much larger driven sprocket on the rear wheel, which means that you can have a smaller reduction on the bike or a faster spinning motor. However, this method requires a driving sprocket that is strongly attached to the frame, and if the frame used has rear suspension, the chain requires a tensioner unless the driving sprocket rotates on the same axis as the suspension pivot.
crossbreak wrote: this text is misleading, since it tells that there is no need for a tensioner on un-suspended bicycles. Also it's redundant since there is already a Non-Hub-Rear article
chains need tensioners if driven faster than a few inch per second. Types of tensioners are:
- spring loaded rollers
- spring loaded friction guides (often made of PTFE)
- snail cams and
- other design elements, that vary center-to-center distance between sprockets.
The last two mentioned ones add the least drag to the drive.
Average chain load should be not more than 1/6 of the tensile strength of the used chain []. For e-motor drives, the average load can be assumed by calculating with half of the stall torque of the used motor setup. For normal derailleur chains, tensile strength is around 10.5kN, so they should not see more than 1.75kN in average.
- When designing chain drives, one has to take the polygon effect into account. This effect induces chain oscillation. Sprockets should not be very small because of this effect, especially at higher speeds. []
- Max chain speed for roller chains is about is 18m/s or 800inch/s. It's mentioned in the original Wiki article about chains, which is something worth reading [].
Calculating chain load
Chain pull [Newton or lbs]= sprocket torque [Nm or lbs*ft] / driving sprocket radius [meters or ft]
Calculating chain power
max power you can push through it can be calculated by P = F * v
here P is Power (in kW), F is Force (in kN) and v is velocity (in m/s)
So max power you really can push through any normal 6-8 speed derailleur bike chain with the figures mentioned above is at least: 1.75 kN * 18 m/s = 31.5 kW Just keep in mind that chain speed must be fast enough to get some serious power though and that you should not exceed the 1.75kN in average and double of that in peak.
Tensile limit of chains
The tensile limit depends heavily on the quality of the chain. There are lower and higher priced ones of the same size
- 1/2 x 1/8 bicycle chain: 8000 -11500 N
- 1/2 x 3/32 derailleur bicycle chain about 7000 -10500 N
- 1/4 x 1/8 #25 ANSI chain: about 4000 - 5600 N
- #219 chain: 5000 - 10000 N
- 8mm chain like the t8f: 5000-10000 N
derailleur chains and sprockets
There are 3/32" wide chains for up to 8-speed, 11/128" for 9-speed derailleurs and others for 10-and 11-speed. For a full list, view the wiki books article 
Sprocket cassettes of different brands use different spacers which do not always match, for more detail view this table from Sheldon Brown: []