# How do gears multiply the torque

## Nicodemos´ hobby site

The infinity machine!

This machine should - as the name actually suggests - symbolize infinity.
For me personally it represents the conflict between theory and practice. Because theoretically it cannot work and yet you can prove the opposite by replicating it or just by calculating the speed of the last gear.

Basically, the infinity machine is a gear. Take a motor and reduce it around 20 times with z. B. 7: 1. The last gear is then simply poured in concrete and the engine started. Here for me is the conflict between theory and practice. Theoretically, a gearbox that has been cemented in place cannot run. And yet it does. Take, for example, an electric motor with 6000 rpm. The pinion on the motor axis rotates 360,000 times per hour. The 5th gear only rotates at approx. 115 revolutions per hour. The 10th gear only with approx. 0.037 rev / h. At this point, the gear needs more than 27 hours to turn once.

At the twentieth gear you can no longer speak of rev / hour, since there are already 8 zeros after the decimal point! In other words, we are here at over 30,000 years for one revolution of the gear! So that the twentieth gear can move by only one millimeter, we need approx. 192 years ... (The basis for calculation was gear wheels with a diameter of 50mm from the model making sector) That then goes beyond any mortality table and the durability of the engine. At this point, at the latest, it should be clear why you can set the last gear in concrete without the gearbox stopping. This example calculation does not yet take the backlash between the gears into account.

The same calculation can of course now also be made with the torque of the motor. The electric motor used for my calculation had a torque of 1.4 Nm. Everyone should now be able to multiply that by 7 in their heads. A theoretical torque of around 480 Nm is then applied to the third gear, which corresponds roughly to that of a large passenger car diesel engine. With the 4th we have already reached the (theoretical!) Torque of a truck. On the 6th, we already exceed the torque of the largest engine in the world, which is currently manufactured by MAN and is a gigantic marine diesel. The theoretical torque at the 20th gear can no longer be expressed with numbers or examples, only this much: it is an 18th digit number. Precisely this torque calculation is gray theory. I very much doubt that my small plastic gears could even transmit the 50 Nm, let alone the torque on the 20th gear ... If you consider the problems that the automobile manufacturer VW had in making the Bugatti Veyron's transmission steadfast, you understand also, why you have to write the word "theory" very big here and this vehicle had "only" 1250 Nm ...