# Would friction forces impact a torque measurement transmitted through a gear box

I want to be able to detect very small torques placed on the end of a cantilever beam. These torques are very small - 1mg by 10cm. I am trying to make this on the cheap and use a load cell.

I plan to amplify the torque by running it through a self made very high stage planetary gear box, say like 250:1. I would apply the resulting torque to the sensor by having a rigid beam of known length hit the load cell.

Now this is essentially a static test. I will have the apparatus so that the torque on the output would be resisted so it could be measured.

Will friction be a problem in terms of accuracy? Is there an initial threshold I would need to meet for the torque to make it through the gear box?

Would I be better off with maybe using a worm gear setup?

The forces associated with this torque will be of order of 10 micronewtons. It takes NASA level equipment to measure such forces (look up EM Drive tests). Your breath at a meter distance will exert this sort of disturbances.

The general approach to measuring forces of this order is using a mirror and a laser beam to detect displacement/rotation: a tiny mirror attached on a long arm, a laser beam aimed at it, and reflecting onto a scale placed a considerable distance from the test rig; minuscule displacements will make the point move a measurable distance. This is the simple measurement rig, but the real difficulty is in eliminating external disturbances - even minor air movement, vibrations from distant vehicles, steps of operators, dynamic pressure from audible noise - that all can introduce forces of that order and spoil your measurement.

Don't even begin to dream torque of $10^{-4}$ Nm can be transmitted by any kind of macroscopic gear mechanism (it's different with nanomechanics, but can you make your planetary gear with sub-millimeter gears?)

• The best way to isolate the experiment from airborne disturbances is put it in a vacuum chamber. If you mount the rig on a very low compliance suspension (e.g. an air bag) and increase its mass artificially if necessary, you can eliminate other disturbances except at very low frequencies (e.g. of the order of 0.01 Hz) which is usually enough to filter them out of the measured data. Jun 6, 2017 at 20:52
• @alephzero thanks for the comment. We are going to try and leverage this idea. We are going with an optical approach to detect deflection Jul 7, 2017 at 22:40

Yes, friction will be a serious problem. So will backlash in the gears, the clearance in the gearbox bearings, the general flexibility of all the gearbox parts (including the casing), etc, etc.

A worm gear will probably be even worse. Unless it is designed to operate in either direction (i.e. if you push on the rack, the gear will turn) the friction is intentionally large to hold the gear in position with no external loads.

You would probably be better making a flexible cantilever and measuring its deformation with a strain gauge or an accelerometer if you want a "cheap" solutions - or use more sensitive measurement device like a laser based system if you want high accuracy and can afford it.