# How Much Efficiency is Lost in a Gear Train

I want to get a rough estimate for the transmission efficiency of two different gear trains. One is a one-stage gear train with 11.67:1 ratio (140/12 teeth) and the other is a compound two-stage gear train with overall gear ratio of 18:1 (72/12 + 36/12 teeth).

I read in a forum that one can expect a 10% loss per stage of gear train in this case but I wanted a second opinion. Any help would be greatly appreciated.

• Are the bearings and oil the same? Dec 18, 2019 at 10:13
• Yes, just an approximation is what I'm curious about Dec 18, 2019 at 10:16
• So, what's wrong with 10% for the single stage and 20% for the two stage? That's a rough estimate, until you have exactly what will be there what more do you expect? Dec 18, 2019 at 10:21
• 10/20% may overestimate actual loss vastly, perfectly valid question. usual engineering approach is o call a sales person for the drives, but OP may want to look for independent sources.
– mart
Dec 18, 2019 at 10:41
• Was that forum definitely describing bicycle transmissions? Dec 18, 2019 at 23:02

Generally gear trains with lower ratios are more efficient due to reduced amount of sliding action between the gear teeth in mesh, so the compound gear train would probably be a better solution. That also depends on the quality of the gears, center distances, bearings, lubrication and thermal considerations, but short answer is two stage would probably be more efficient. If all of the components are of "good" quality, you could expect 95% or better efficiency. AGMA standard 917 goes into a lot more detail if you want to do analytics. Edit- Caveat: typically gears with fewer than 24 teeth have modified geometry to avoid undercutting the involute profile, so this could affect sliding action as well. If you change to a finer diametral pitch or module you could avoid that.

In the book Bicycling Science by David Gordon Wilson, it says the following:

When new, clean, and well-lubricated, and when sprockets with a minimum of 21 teeth are used, a chain transmission is highly efficient (at a level of maybe 98.5 percent or even higher)

(Third Edition, chapter 9: Mechanics and Mechanisms: Power Transmission, page 318)

It goes on to describe that efficiency inevitably suffers due to wear, dirt, and poor maintenance and adds "it is not known by how much the efficiency of chain drives decreases in adverse conditions,".

Later, on page 342 it provides some other factors which influence efficiency:

1. Transmission efficiency decreases as the size of the rear sprocket is reduced.

2. Efficiency diminishes as the amount of torque transferred (or chain tension) is decreased.

3. The maximum efficiency attained is at relatively high power (175 W) and low pedal rpm (60) and in the lowest gear (meaning the largest- diameter rear sprocket, with twenty-one teeth) and is just over 98 percent.

4. The additional losses because of chain offset (the two sprockets not being in line) are negligible.

5. The type of lubrication, or even whether there is lubricant present, has almost no effect on efficiency

And finally some typical gearing ratios are matched against some other factors to estimate efficiency:

Table 9.3:

Based on personal riding experience I would find it hard to believe a 20% loss was not an overestimate, but I have no other sources with quantified data to back that up.

Assuming you mean gears and not chain and sprocket systems, it really depends on the size and cost and duty of the gear reduction.

The simplest case is a colinear drop box that has a propshaft input and a propshaft output with no side loads at all. For modest ratios, the reduction should be around 3 percent of the maximum rated torque. For example, if the gearbox is rated for 1000 ft lbs, because your 600 ft lb diesel requires a 30% derating, and you are operating at around 400 ft lbs most of the time, you still loose 3% of 1000, or 30 ft lbs. That's 7.5%.

Other load factors and physical arrangements can further reduce this. Overhung loads (side load associated with a spocket on the input or output shaft) may require additional bearings or a lower rating and tend to be a bit less efficient.