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# SLOWING DOWN AN ELECTRIC MOTOR USING GEARS ONLY? Answered

i have a motor with an input voltage of 12vDC and  the final drive RPM is 172. i need to create a winch to lift a specific weight at a specific speed. ( 1kg in 70 seconds) from 1 meter off the ground. can someone tell me how to do this or explain gear ratio and drum diameter. i am completely lost and don't know what to do. your help will be very much appreciated and you will be rewarded

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Rewarded? Rewards are kind of useless to me, because, like the Three Amigos, my reward is knowing that justice is done!

Yeah. I think this problem would make sense if you converted some of the units, like.

Weight:

Weight is a force, equal to M*g, so a 1 kg mass has a weight of

(1.00 kg)*(9.8 m/s/s) = 9.8 N

The N stands for newtons, the SI unit of force.

I am sort of imagining this weight is attached to a string, and it is being pulled up vertically. So the weight pulls downward on the string, and the string pulls upward on the weight.

Speed:

To move the weight through a distance of 1 meter, in 70 seconds, requires an average speed of v = (1.00 m)/(70 s) = 0.014 m/s. Also it is probably safe to assume v is also a constant speed.

Power:

Power required to pull against some constant force, at some constant speed.

P = F*v = (9.8 N)*(0.014 m/s) = 0.14 J/s = 0.14 W

Can your 12 volt motor throw this much mechanical power? I dunno. This number seems believable to me.

Angular speed:

Revolutions per minute, also called "rpm" is sort of traditional measure of angular speed, a measure of how some rotating thing is rotating. A better, but less understood, unit is radians per second. So I want to convert 172 rev/min, to whatever that is in radians per second.

omega = (172 rev/min)*(2*pi/rev)*(1 min/60 s) = 18 rad/s

The lowercase Greek letter omega is the usual symbol used for angular speed, but this editor doesn't have Greek letters, so I just spell it out, and use that whole five letter word as my variable.

The reason radians per second is convenient is because there is a simple formula relating the angular speed (in rad/s) of a wheel to the translational speed (in m/s) of a point at distance r from the center of the wheel.

v = omega*r

And you can maybe sort of see why this is true. The circle at the edge of the wheel has a circumfrence of 2*pi*r, and one of those circles unrolls for every 2*pi of angle, in radians.

Anyway, if I take that formula above, v=omega*r, and solve for r, using your numbers, I get,

r = v/omega =

(0.014 m/s)/(18 rad/s) = 0.000777 m = 0.777e-4 m = 0.777e-3 m

So that a drum with very, very tiny radius: 0.78 mm, or 1.06 mm diameter.

So I am guessing that your angular speed is too big, too fast, for a practical sized drum. However, if you slow it down, by maybe a factor of 10, then you could increase the size of the drum by the same factor, giving you a drum with diameter of around 10 mm, or 1.0 cm. At least then the drum will be bigger than the string.

So. Yeah. Kind of a long story I guess, but I think you do want to slow down the angular speed of your drum, which is kind of what you were suspecting in the first place, I think. So maybe the lesson is to trust your intuition. Maybe.

I hope some of the formulas I have mentioned are useful to you.