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DKNguyen
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Use a pulley with spooled string on it dropping a weight on the input shaft for input torque, and a pulley spooling up a string with a weight on the output shaft for load torque. With pulley radius and mass you can calculate input and output torques. You then need an RPM sensor on one of the shafts and you can use the gear ratio to calculate the RPM on the other shaft.

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 testing gear setups that are very similar where differences might be small, it's going to be pretty tough either way if the only difference is material. Even motor-generator setups with torque sensors can be very finnicky.

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.

DKNguyen
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