Help Gear Ratios !!!!!!! Help

[sanddrag]

I really got myself confused and I need some help.

For example....

Everthing on shafts is affixted to drive (e.g. pin, key, weld)
Say a motor has 5Nm torque.
There is a 10 tooth gear on the output shaft of this motor called "shaft A".
It drives a 40 tooth gear on another shaft called "shaft B"
Would the torque output by this last shaft be 20Nm?

Also, lets say there was also a 10 inch diameter wheel on "shaft B"
What torque would the wheel place on the ground??? for driving the robot.

I hope you know what I mean. If not ask a specific question so I can try to help you further understand my questions.

Thanks for the help.

[Gary Dillard]

1) Yes, the resultant ideal torque on shaft B would be 20Nm, and it would turn 1/4 as fast as shaft A. Input power x efficiency (1.0 for ideal) = output power, so Ta x Na = Tb x Nb. The tooth stresses are the same in both gears since the forces are equal - the torque is different because the distance at which it is applied is different (the radius).
2) The Wheel doesn't apply a "torque" on the ground, it applies a force on the ground, equal to the torque on the shaft divided by the distance (the wheel radius). This would be 20 Nm /[5 in x (.0254 m/in)] = 157.48 N. The linear speed would be (Nb rpm) x (Pi x 10 in/rev) x (1 min/60 sec) x (1 ft/12 in) = Nb x Pi/72 fps.

Hope that helps and I hope I got my units right.

[Mike Gray]

Two answers:

The gear ratio is 1:4 so the shaft B torque is 4 times shaft A. The speed of shaft B is 1/4 that of shaft A.

The torque is the same regardless of wheel diameter, but the tractive effort where the wheel meets the floor depends on wheel radius. A 10 inch wheel has a 5 inch radius. Since we're working is SI (metric) units, we'll need to convert to meters:

5 inches/39.37=0.127 meters

Then divide the torque by the distance to the reaction surface(radius):

40 Nm / .127 meters = 315 Newtons

315 Newtons is equal to about 70 pounds so you could tow a 70 pound load IF the coeficient of friction (Mu) is less than one. A 70 pound trailer would move easily. A 70 pound bag of doughnuts wouldn't move at all...unless the grease leaked through the bag and reduced the Mu.

[sanddrag]

Thanks for the help. This is really great. What I meant was the force applied by the wheel not the torque.

Mike, I think the resultant torque was 20Nm not 40Nm. Check Gary's figuring.

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[Mike Gray]

Thanks. I don't know where the 40 came from. Must have confused it with 40 teeth.

[sanddrag]

One more question. Take the figure we calculated for force applied by the wheel, 157.48 N. Say that this wheel was connected by sprockets and chains to another identical wheel, no gear reduction (for connection only). Would the force (157.48 N) be shared between the wheels or would each wheel have that force.

Thanks.