# Understanding electric DC gear motor for project

I would like to build an Arduino controlled coin sorter and counter. I want to use a spinning angled disk with holes in them to pick up individual coins.

I have been looking at some 3V DC geared motors on Ebay. I understand that high torque will be important so that it will be able to turn the disk with money pushing against the disk.

How will I find out if a 5-8 RPM motor will be able to turn the disk? These small motors usually have no torque measurement given.

Is there even a DC motor that runs at 3V that would be able to turn the disk?

• I don't use an arduino, but I wouldn't assume that it could meet the current requirements of a 3v motor, so you might need a driving circuit in any case. Sep 5, 2012 at 13:59
• Do they provide any other statistics such as power, stall current, etc.? You might be able to estimate a torque upper limit if given these figures. You can also try contacting the seller, they might know the torque. I agree with Scott, you likely can't drive the motor directly from the Arduino and will need a motor driver. Sep 5, 2012 at 21:12
• @helloworld922 I have found some specs. NO idea how to calculate anything though. The motor itself has these specs: Rated Load mN·m: 0.39. RPM: 2200. Starting torque mN·m: 1.47. Max current: 80mA. After the gears. 5RPM. Current of 60mA. I would love to know how to calculate the after gear torque, if that is even possible with this information. Sep 6, 2012 at 11:29
• @michael, its pregear torque times the gear ratio, which here is 2200/5 Sep 6, 2012 at 12:20

Assuming that you can find a gear reducer with an effective moment of inertia within the motor's range, you can probably crush soda cans with a 3v motor. At some point you're so geared down that the actual load is all but invisible to the motor, and you're simply driving the gear reducer. BUT, to crush a soda can this way, it might take an extremely long time.

It can take some effort to get this right. You might check out http://en.wikipedia.org/wiki/List_of_moments_of_inertia, and calculate the moment of inertia of a cylinder, maybe a quarter inch high with the density of copper and diameter of your hopper, as a first approximation of what you need to drive. The idea is that there will come a point where if you make your coin stack high enough, you won't be able to drive it. Of course, this is an approximation-- you're only trying to move the bottom layer of coins, and there's a mass sitting on top of that, yadda yadda yadda. We're ballparking here, not trying for an exact physical model.

To find the inertial range of a hobby motor, try http://www.mabuchi-motor.co.jp/en_US/product/p_0303.html. Mabuchi seems like a pretty typical "hobby" motor. Enter the diameter of the motor you're thinking about, and 3 Volts, and take a look at the ratings page that comes up. You're interested in the torque at maximum efficiency.

If you can't get there with a "regular" gearhead, other options might be something like a planetary gear, which would be very geared down, or maybe a worm gear drive.

The opposite approach is to shop online, look for something that you think will work, buy it, wait for it to arrive, and see if it works. Repeat as necessary

The right approach for you lies in between these two extremes, and has to do with how much money you want to put into it, whether returns are possible, whether you need to go way overkill just to make sure you meet a deadline, and all sorts of other factors.

Lastly, look at the current specs for the motor you're about to buy, and spec out whether you can drive it without a driving circuit. As a guess, looking at some of the Mabuchi specs, I suspect you'll want something that can source about 300 mAmps to feel comfortable, maybe a half amp.

An Arduino's IO pins are rated for 40mA. This is below what you stated current of the motor is rated for. My guess is that the 80mA is the stall current and 60mA is the current the motor can handle over an extended period of time (i.e. don't stall it for too long or the motor will malfunction). This means you'll need a motor driver. Depending on if you need bi-directional control (spin both ways) or just uni-directional, you can buy or build one. Bi-directional controllers are usually H-bridges and uni-directional controllers can be as simple as a MOSFET (I prefer N-MOS on the low side).

The starting torque is likely the stall torque so the motor can produce at most 1.47 mN*m. It has a no-load speed of 2200 rpm, and is geared down to 5 rpm. This means that the final stall torque is roughly:

$$(1.47 mN * m) * 2200 / 5 = 646.8 mN*m$$

So assuming a friction-less system, how long does it take your motor to spin the wheel up to speed?

I'm assuming the tray is a thin solid cylinder, so it has a moment of inertia of:

$$I = mass * radius ^ 2 / 2$$

For a 0.25 m diameter, 2mm thick acrylic disc weighing 115.8 g, this translates into a moment of inertia of I = 1.809 g * m^2. For people use to archaic units of measurement, that's a 0.82 ft diameter disk that's ~0.08 in thick.

Using Newton's laws of motion: $$\sum Torque = I * angular~acceleration$$ $$angular~speed = \int angular~acceleration * dt$$

The torque the motor can produce linearly decreases as it speeds up, and is 0 when the engine is at the no load speed.

$$Torque = Torque_{stall} * ( 1 - (5 rpm) / angular~speed)$$

The problem is a first-order ordinary differential equation, and the solution is:

$$angular~speed = (5 rpm) * ( 1 - e^{-Torque_{stall} * time / I / (5 rpm)})$$

Plotting this for my disk I get the following curve:

You also mentioned that the rated torque is 0.39 mN * m. This means that your motor can sustain at most:

$$(0.39 mN * m) * 2200 / 5 = 171.6 mN*m$$

This occurs at a speed of 3.67 rpm. For my disk this takes about 1 second to reach, which would probably be fine. You can calculate what it would be for your wheel.

A few remarks:

1. I've completely neglected how many coins are on the disk. They could be on the disk before it starts to spin, or they could be added later. Either way these will increase the moment of inertia of the wheel.

2. There's no friction in this analysis. Friction can either be really small, or it can be large. Either way, it will make it longer to get the wheel up to speed (if it ever does).

edit:

Mis-calculated the moment of inertia of spinning disc (darn calculator :P). Re-ran example calculations with the corrected moment of inertia. Motor might work, though personally I still have reservations about using this motor especially if you expect the motor to be in use for long periods of time or being repeatedly turned on/off.