compound gears formulae

[cervantes]

Hi all,

I needed to go through essentials of gear calculations.
I found nice tutorial here

http://www.societyofrobots.com/mechanics_gears.shtml

During my studies I found a possible mistake that it was so obvious that I start to feel that maybe I was thinking wrong?

Please go to compound gear section:

Final formulae for compound gears does not have identical units.
torque_motor=weight*radius_gear3 / radius_gear1 so then Nm = N ???

this mistake (or am I wrong?) comes from wrong basic equation few lines
above in text:

torque_gear3 * radius_gear3 = weight * radius_gear3 so once again N*m =
kg*m so N=kg ? (torque = weight ???)

Am I right?

Anyway if it is correct - could someone explain me why, if not - what is the correct method to determine motor torque there?

 

[kiwitom235]

no it should be this:

Power in = Power out
Torquemotor*rpmmotor=Torquegear*rpmgear
Torquemotor*rpmmotor=Weight*radiusgear*rpmgear

 

[cervantes]

you're sure about that? still have doubts

 

[Occupant]

No, he's right, but kg=mass, N=mass*g or you could use 1kgf=9.807N

 

[3DDave]

cervantes,

The page is correct.

Weight is a force and is measured in Newtons, mass is measured in kg.

Your mistake is assuming that weight is measured in kg. In English units scales report pounds-force; it's metric scales that are incorrect and report kg. On the moon a person would apply 1/6th their usual weight on a scale, but their mass would be unchanged.

 

[drawoh]

3DDave,

I don't think that is the best possible explanation.

If you treat pounds and newtons as units of force, and kilograms and slugs as units of mass, you have a consistent system of equations.

m = w/g

F = ma = w/g [×] a

If you have a weight hanging from a lever arm...

T = wr = gm [×] r

If you are not methodical about your units, you need some other way to figure out when and where to insert g in your equations. Good luck!

--
JHG

 

[tbuelna]

I'd first suggest going back and re-reading the section on "gear efficiency" before you complain too much about the units of measure used. The contact conditions at bearings and gears can have a significant effect on the relationship between input/output torque and power.

 

[rb1957]

going back to the reference, we have ...
"writing down the equations:
torque_motor * radius_gear1 = torque_gear2 * radius_gear2
torque_gear2 * radius_gear2 = torque_gear3 * radius_gear3
torque_gear3 * radius_gear3 = weight * radius_gear3

simplifying, we get:
torque_motor * radius_gear1 = weight * radius_gear3"

the picture of this is torque_motor is driving a gear train to raise a weight. i think the whole set of equations is messed, no? what is "torque_gear3 * radius_gear3" ? = weight * radius_gear3" is wrong. i'd've thought torque = weightmass*accel*radius3.

note, this guy is playing very quick and roughly with units ...
"rps_gear3 * 2*pi*radius_gear3 = velocity_weight" is right for "rps" in rev/sec and "velocity" in ft/sec.
normally v=w*r, with w in rad/sec, so the 2pi corrects rev to radians.

another day in paradise, or is paradise one day closer ?

 

[rb1957]

that'd be torque_gear3 = weight*radius_3 (assuming static, as stated)
then motor_torque/radius_1 = torque_gear3/radius_3 = weight (because, confusingly, he has radius_2 = radius_3);
motor_torque (for static equilibrium) = weight*radius_1.

another day in paradise, or is paradise one day closer ?