Gear Ratios: what happens to the force?

[infamous_Q]

Ok here's a fairly simple question (I hope) i know that with different gear ratios you can trade off torque for speed, (ie. big to small = lower torque higher speed, small to big = higher torque lower speed) but what happens to the force applied to the original gear? is it a constant throughout (because of gear ratios and such)?

 

[Chi Meson]

You are confusing torque with force. It the is the force that "trades off" with distance. Torque is the product of force times the distance from the point of application to the center of rotation. The input torque on a gear equals the output torque, but if the distance (radius) is greater on the input side, then the force will be greater on the output side.

With a bike, the force from your legs is "magnified" by the front pedal/chainring gear. The force is transferred to the rear wheel where another torque is applied. The large force/small distance at the rear sprocket is turned into a small force/large distance at the edge of the wheel, but again, torque in = torque out.

 

[faust9]

I think the easiest way to explain this is that power in equals power out. The force applied to the drive gear (be it a pinion or gear) will be proportional to the forces applied to the driven gear such that the power you put into the system equals the power out of the system.

Are the forces uniform in a meshing gear. No. Real gears are not flat planes in contact with each other. The force profile across a gear changes as the gear rotates. The line of force contact moves a little. The number of gear teeth in contact at any given time is usually not 1---you can have 'partial' gear contact where a small portion of the total contact available is actually in contact on one or more of the secondary gear meshes.

All of that is painfully complicated. Most gear analysis was done in the 50's and 60's and is still in use today because of how complex these little buggers actually are.

The underlying concept though is that the power you put into the system will equal the power out of the system. Not all of the power in will translate to mechanical power out. You get noise and heat generation and some shearing of the gear face as the line of contact moves across the gear. But, the power you put into the gear will equal the power you get out of the gear.

You can apply any input force you like. The input force doesn't have to be constant---the forces on the gear faces will not be constant by any means; however, you can always balance the powers.