chain efficiency analysis

Hi, got a few questions on chains.

What is the general efficiency for a chain drive?
Which type of loss is more significant for a chain drive?

1. Sprocket tooth/chain sliding friction (engagement/disengagement)
loss

2. Chain segment bending loss.

or are they about equal?

As a follow up question, can you tell me if the following type of
analysis is valid:

a gear pair is inheritantly more efficient than a chain drive
because there is only ONE teeth to teeth interface for a pair of
gears. In another word, one gear can drive the other gear DIRECTLY.

A chain drive requires TWO interface. First the sprocket drives a
chain, then, the chain drives a different sprocket. So in another
word, a sprocket cannot drive another sprocket directly. Since there
is 2 interface/steps, I think a chain drive (even those silent
types) should be at least twice as inefficient as gears.

And that's not counting the bending loss at the links.

That means, if the gear pair has an efficiency of 99. Then the chain
can not have more than an efficiency of 98. Of course this is
assuming there is no bending loss at the links and the sprocket to
chain meshing is just as efficient as the regular gear tooth
meshing, which is unlikely.

Thanks for the help guys.

Chain/sprocket arrangements are typically more efficient than gear pairs. ~98% for a straight chain vs. somewhere in the low 90% range for a gear pair. The number of interfaces doesn't affect the efficiency so much as the amount of sliding friction at the interface. An extreme example is pushing a heavy box across the floor vs. putting it on a wheeled cart. The number of interfaces went from one to four (more if you're counting bearings in the wheels), but the work requirement went down considerably. In a gear pair, the faces of the teeth are sliding against each other while being pressed together. With a chain, the sliding friction occurs at the pins, which depending on the amount of wrap at each end aren't carrying all that much load. The chain/sprocket interface is mostly static, which doesn't affect efficiency. You can however lose upwards of 10% efficiency from large chain crosses, but that's a combination of friction from bending the chain, and friction from rubbing the chain plates against the sprockets. There is also a drop in chain efficiency with very large gear ratios (~6:1 and higher). Faired recumbents are often built with two stage drive trains to avoid this.

So the main source of efficiency losses of roller chain drives and the main reason it needs periodic lubrication is due to the friction between the pin and the bushing as the chain segment bend around a sprocket.

The roller/sprocket mesh is mostly static with very little sliding, and therefore lubrication aren't nearly as critical nor does it affect efficiency as much. ?