Motor needed to turn a Drum....

[Will_SPHS]

I had posted a thread several months ago about a similar problem on the same project, but the parameters have changed and my question has slightly as well.

Background:

For a high school engineering class, each group must design and create a prototype of a solution to an environmental related problem. My group is looking to automate the process of turning compost, thereby speeding up the process.

We designed a compost tumbler that consists of a drum (shown below as gray) and motor housing (shown below as green) around an axle mounted onto supports with ball bearings. The final design (not shown) has struts, uses less hinges, and is smaller, but the image gives a rough idea. The motor has room to be geared down to increase the torque if need be.

Calculations:

Drum Radius = 5.625"
Drum Height = 12.50"
Drum Volume = 0.704 ft³ = 5.27 gallons
Compost Weight (when full of compost at 76 lb per cubic foot) = 53.5 lb
Drum Weight = 15 lb

Torque (I was told to use Weight*Radius) = (53.5 lb + 15 lb)*.469 ft = 32.13 lb*ft
Moment of Inertia of Drum (I = 1/2*mr^2) = .5 * 23 kg * (0.02045 m^2) = 0.235 kg*m^2
Power (P = Tω) = 32.13 lb*ft * 0.52 rad/s = 16.71 lbft/s = 22.66 Watts

For the power calculation, I used 5 rpm (.52 rad/s), but I suppose this speed could be reduced as the turning speed isn't something that needs to be precise.

Questions:

How would I factor in the moment of inertia of the drum into the motor selection, and would the frictional force be large enough where I would have to take it into consideration, considering I am using bearings?

How would I decide what motor I would need to use? I suppose with a safety factor, the moment of inertia, and friction (not calculated), I could used a motor around 50 Watts. Does that seem correct? I feel like I am missing something, because motors (ex: http://www.mcmaster.com/#6409k15/=11jetjs) with very little horsepower (in this case, 0.0077 HP / 5.74 Watts) and RPM (12) seem to cost a lot of money (>$50 with this motor example). I could gear down the motor regardless to decrease the RPM and increase the torque.

Thanks for any help you can give!

 

[Merlin3189]

The motor looks a bit under powered. If you did need 32 ft ib as you say, this motor says it is 40 inch pounds or about 3.3 ft lb' (about 10% of 32 ft lb).
But you're right, you could gear it down further, say 10x, then you'd have the torque you asked for, but at 1.2 rpm, which sounds good to me. That's turning the heap over 1500 times a day, which I reckon is at least 100,000 times more often than I turn my heaps! I think you could get away with even much lower turning rates than 1rpm. (This one suggests turning their drum once a day: though that's probably several revolutions.)

And BTW, I think you should be able to get a motor like that for a lot less. Have you tried looking on robot building sites? They do carry expensive stuff for the real enthusiasts, but plenty of cheap gear for those who just want to build something that works. Some also have advice pages which might help you.

But I am not saying you need as much torque as you say. You seem to have used a model which tends to overestimate the work required to turn the drum in the absence of friction. This is ok for a very conservative estimate and leaves an allowance for the friction you haven't included. But if your power budget were tight, a more accurate estimate could be useful.

If the drum were evenly full, there is no movement of the centre of gravity as it rotates, so no work to do! So what is the worst case for lifting the contents? And how much work is that?

You seem to have assumed the drum is full. If you want to aerate the compost, I'd have thought you need to leave a reasonable air gap. (I'm assuming the tumbling is for aeration, but I think any tumbling needs a gap.) I'd have guessed half full, but maybe 3/4 is ok. Have you looked at commercial designs to see what they recommend?

If the drum rotates on ball bearings, I'd guess the torque needed to overcome friction is small compared to that needed to lift the compost. But I've no idea how to get a good estimate of this, other than measuring something similar.

 

[Nidum]

Worst case for load is when compost is compacted into one half only of drum and does not redistribute when drum turned over .

 

[Will_SPHS]

Thanks for the help! By the way, I forgot to mention that we created an Arduino circuit that puts the motor on a timer so we have it rotating for a few minutes a day as opposed to thousands of times a day. This is also because we will have a solar panel charging a battery that powers the motor. Additionally, the axle will also serve as an aeration tube.

Another question (I know it might seem obvious but I don't know): At what point of filling the drum would the required torque to turn it be at a maximum (1/2, full, etc), and how would I go about calculating it? Would I need to factor in the angle of repose of dirt as it slides against the side of the drum or is that over-complicating things?

 

[Will_SPHS]

Worst case for load is when compost is compacted into one half only of drum and does not redistribute when drum turned over .

We have ridges on the inside of the drum (think like in a dryer) to turn over the compost and preventing it from getting stuck on one side. However, I suppose I would still need to calculate the torque needed at this point anyway. How would I go about doing that? If I multiply the weight (1/2 of full capacity) by the distance of the center of compost mass to the axle (about 3"), I will get a torque less than what I previously calculated for full capacity. Did I do something wrong in my calculations earlier?

 

[Merlin3189]

Yes, I'd think your ridges should do the trick - which is fortunate, as finding the angle of repose for compost in varying states of decomposition, sounds difficult!

Nidum's picture shows you what looks like the worst case. Look up the CG of a half circle and see how far the half load is lifted from bottom half to top half. Since it should fall before it gets to the top, you still have a conservative estimate, but better than your previous one.

I don't think of your first calculation as wrong. It was on the safe side. Now you can do a better one. But it is still based on a model which you know is not perfect. The material you are putting in will vary in density and distribution in unpredictable ways. You are never going to know exactly what torque will be required. You need to be covering the worst case, but the further you go beyond that, the greater cost you may incur.

Since your rate of turn is very flexible, you can get more torque by gearing the motor down, so there is not a lot of cost in being generous with your torque.

 

[Baluncore]

To find the stability or rest angle for compost, make a conical pile as steep as possible, then measure that angle. For some mixtures the surface angle may be vertical or possibly overhang.

You should think of the compost as being a living community of organisms. It should not need to be turned more than once per day. If you turn it too often it will cool and the conversion process may be slowed. Your motor controller should really be programmed to stop it turning too much. As explained in the above post, the motor can be very small with a high ratio gearbox.

You might consider throwing out the original axial ball bearing idea and drive mechanism, by supporting the drum on four small wheels close to the floor. If those small wheels were driven, (two shafts, each with two wheels), you would get an advantageous reduction in the speed and torque requirement of the motor and gearbox. That would reduce the height, weight and price of the support structure. It would also be safer to assemble and have a smaller footprint on the floor.

 

[Will_SPHS]

Nidum's picture shows you what looks like the worst case. Look up the CG of a half circle and see how far the half load is lifted from bottom half to top half. Since it should fall before it gets to the top, you still have a conservative estimate, but better than your previous one.

I apologize if I'm being dense, but wouldn't calculating the distance the CG will be moved be calculating the work and not the torque? I'm probably just not understanding something about work/torque though.
Anyway, the CG when half full is exactly .2 feet away from the axle, so it will move .4 feet from top to bottom. At half capacity the total weight will be 41.75 pounds. How would I get the motor specifications from this?
Also, your suggestion about robot building websites was spot on. I found motors that would produce close the right amount of torque when geared down to 1 RPM (ex: http://www.robotshop.com/en/cytron-12v-17rpm-277oz-in-spur-gearmotor.html). One question I have though is that despite having the correct amount of torque and rotational speed, they are all around 3.4 Watts, nowhere near the 20 something I previously calculated. Is that an issue? Thanks for the help!

 

[Nidum]

Weight of the half cylinder of compost * distance of CoG to axle centre = balancing torque .

Balancing torque is that torque which can just hold the half cylinder of compost static in position .

You need to supply an input torque greater than the balancing torque to cause movement .

Note that there is a big cyclic variation of input torque needed for a complete revolution of drum and that for part of the revolution you may actually need a retarding torque .

 

[Merlin3189]

Yes, you're right. I was thinking work and power. Nidrum has sorted it for you.

 

[Will_SPHS]

Thank you! So with 41.75 pounds of weight and .2 feet, the balancing torque will be 8.35 lb*ft. That is much less than I previously calculated and makes identifying a motor much easier. I suppose that instead of applying a torque to slow it down, we could consider having the motor turn it once, not using ball bearings, and letting friction slow it down. I don't know if that is a good idea, but I'll do some research. Thanks again for the help!