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Alternatively what you could do is just hang a weight off the output pulley and then slowly pour sand into a bucket hanging off the input pulley until the output weight starts to rise. That would give you a measure of the static friction rather than the dynamic friction of the gears when running, but it is much easier to obtain. Of course, you can also do the reverse where you hang a weight off the input shaft and remove sand from a bucket hanging off the output pulley until it starts to rise. If doing this, don't discount tapping the gearbox a bit to determine how close you are to the threshold. Friction torque does not not necessarily stay constant though in a gearbox and may vary with RPM and load torque (just like motors and generators do).

It should be easier to measure small differences in efficiency if you Yeah, load the gears more in terms of RPM and torque should make the differences more pronounced and easier to detect. A difference of 2W is difficult to measure. A difference of 100W is much easier. So run more power through it.

Another thing you should really do is cascade the same gears setup to increase the losses which makes them larger easier to measure. So if you intended to test one pair of gears A-B, repeatedly cascade that pair with itself A-B-A-B-A-B-A-B-A-B which will make the losses larger and easier to measure. So instead of needing to increase the weights by five times and/or the the fall distance by five times you can increase the number of repeated gear stages by fives times.

It should be easier to measure small differences in efficiency if run more power through the gears which would increase the losses. A difference of 2W is difficult to measure. A difference of 100W is much easier. So run more power through it.

Another thing you should really do is cascade the same gears setup to increase the losses which makes them larger easier to measure. So if you intended to test one pair of gears A-B, repeatedly cascade that pair with itself A-B-A-B-A-B-A-B-A-B which will make the losses larger and easier to measure.

If you make a clutch with a lever arm (called a prony brake) you can connect the arm of the prony break to a fixed surface using a linear force scale 90 degrees to the arm. With arm length and the force scale you can calculate torque. So this would allow you to measure output torque without pulleys and string. I found prony brakes are surprisingly difficult to make though. It's difficult to get a consistent smooth interface with constant pressure without stiction so it runs smoothly for a stable reading.

But I know of no equivalent device to allow a linear force gauge to be used to measure the rotation of a motor for input torque.

You take an reading of the instantaneous RPM and calculate the input/output power and efficiency.

This is inconvenient in that you cannot run continuously and you need more fall height to accelerate to higher RPMs if you want to test at those RPMs. You also cannot run at constant speed so gear inertia will play into things but this influence can be reduced with heavier weights relative to the gears.

One weakness of this setup is you are always measuring an accelerating load rather than a constant speed load but if you're really, really lucky and have enough fall height with just the right masses the system will reach an equilibrium where the speed will become constant. You might want to tinker with the masses until can achieve this equilibrium in your fall available fall height.

If you want to use a motor for input torque or generator for output torque for continuous operation, constant speed testing, or variable input/output torque convenience, you need torque sensors. For each motor or generator you use, you need a torque sensor. You cannot get around not using torque sensors if you want the convenience of using a motor for input torque or generator for load torque. You cannot use calculations to avoid a torque sensor.

The whole point of using a falling mass on the input shaft pulley and a rising mass on the output shaft pulley is that you don't need torque sensors because you aren't using motors and generators which have unknown electrical-mechanical efficiencies which also vary under load and RPM. If using falling masses you measure instantaneous power via an instantaneous RPM reading. You can use timing and distance/height to calculate work and divide by the time for power, as long as the time doesn't include impact which dissipates all the energy regardless, but this is needlessly inconvenient.

  The whole point of using a falling mass on the input shaft pulley and a rising mass on the output shaft pulley is that you don't need torque sensors because you aren't using motors and generators which have unknown electrical-mechanical efficiencies which also vary under load and RPM. If using falling masses you measure instantaneous power via an instantaneous RPM reading. You can use timing and distance/height to calculate work and divide by the time for power, as long as the time doesn't include impact which dissipates all the energy regardless, but this is needlessly inconvenient.

If you want to use a motor for input torque or generator for output torque for continuous operation, constant speed testing, or variable input/output torque convenience, you need torque sensors. For each motor or generator you use, you need a torque sensor. You cannot get around not using torque sensors if you want the convenience of using a motor for input torque or generator for load torque. You cannot use calculations to avoid a torque sensor.

The whole point of using a falling mass on the input shaft pulley and a rising mass on the output shaft pulley is that you don't need torque sensors because you aren't using motors and generators which have unknown electrical-mechanical efficiencies which also vary under load and RPM.

But this pulley mass setup is inconvenient in a number of ways. The most obvious is that that you cannot run continuously and you need more fall height to accelerate to higher RPMs if you want to test at those RPMs.

But the biggest weakest of this setup is that you mostly cannot run at constant speed. Unless you have enough fall height and the appropriate balances of masses, your falling and rising masses won't reach equilibrium where they achieve a constant speed. The problem then is that the weight of the masses (multiplied by pulley radius) is not actually the torque. The falling mass applying the input torque will apply less tension to the string than the weight of the mass while the rising mass acting as the load torque will have more tension on the string than the weight of the mass.

That means that you need some way to measure instantaneous acceleration. Since you already need an RPM sensor it might not be that big a deal but it does mean your RPM sensor needs to be able to give discrete readouts at sufficient bandwidth so you can calculate instantaneous RPM. Then you can calculate the string tension which will give you the actual force on the pulley which can be used to compute torque.

Alternatively, you can provide enough fall distance and select your input and output weights appropriately so that the system does reach constant speed, and at that point you can take the RPM measurement and use the weights and pulley diameter to calculate input and output power.