### Author Topic: Motor Calculations - some help  (Read 5338 times)

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#### icius

• Jr. Member
• Posts: 9
##### Motor Calculations - some help
« on: December 20, 2006, 10:59:47 PM »
Hello all,

I have been attempting to do some calculations based on the link http://www.societyofrobots.com/mechanics_dynamics.shtml and I'm a bit unclear about some aspects of it.

The parameters I am using are:

Mass = 27 lbs.
Acceleration = 10 in./s (or .83 ft/s)
Velocity = 20 in./s (or 1.67 ft/s)
Efficiency = .75

So I do the equation:

Torque * rps = 27 * .83 * 1.67 * (1 + .75) / 2 * pi

The answer I get is ~:

10.44

Since I am using differential drive I will be using two motors.  So the RMF for one motor should be:

5.22

So that is saying some rps times some torque (in lb-in.) equals 5.22 right?

So now I am looking around a various motors and it occurs to me that I'm obviously going to have some gears between the motor and the axle (assuming a non-geared DC
motor).  So how do you factor gear reduction into the equation?  For instance, look at the motor on this page called "Mabuchi Speed-550 motor".

http://www.robotmarketplace.com/marketplace_motorsmisc.html

It's specs are:

Stall Torque: 91.65 oz-in
RPM: 24,000 rpm

I don't want to stall the motors so let's say operating torque would be 45 oz-in or .234 lb-ft.  RPS would be RPM/60 so RPS would be 400.  So this particular motor would give me an RMF of:

93.6

So it seems this motor is massively over powered right?  However, I wouldn't be hooking the motor up directly to the wheel.  So how does gear reduction play into this?  Or is it somehow already taken into account?  Any info on whether or not my calculations/conclusions are right would be greatly appreciated.

• Supreme Robot
• Posts: 11,657
##### Re: Motor Calculations - some help
« Reply #1 on: December 21, 2006, 08:26:01 AM »
ok two things . . .

first, i found an error in my equation. instead of:
Torque * rps > = Mass * Acceleration * Velocity * (1 + efficiency) / (2 * pi)

Torque * rps > = Mass * Acceleration * Velocity * (2 - efficiency) / (2 * pi)

sorry!!! ill correct that as soon as i can . . .

ok so your RMF with the correction should be 7.44 ft lb / sec (the RMF for one motor should be half that, since its differential drive)

referring to this datasheet:
http://www.robotmarketplace.com/images/mabuchi550.pdf

now looking at the motor . . . so for torque, you dont want to calculate for stall torque, what you want is torque between maximum efficiency (58mNm at 21840rpm) and maximum power (407mNm at 12000rpm), depending on your application. If power or motor overheating is a problem, you want maximum efficiency. If torque or motor cost is an issue, you want maximum power.

So the RMF for the motor would be either 15.57 lb ft / sec at maximum efficiency or 59.99 lb ft / sec at maximum power. It looks like you can run at maximum efficiency with no problem. What happened was the speed you listed is for zero torque, and the torque you listed is for zero speed (not possible  ).

Gearing is when you change the torque to speed ratio, so the RMF is unaffected. If your output will have half the rpm, but twice the torque, RMF doesnt change. However, since you have added gears, you have decreased the efficiency (reducing effective RMF). In my experience, homemade gear setups are low efficiency, so its better to buy a motor with a built in gear head.

in case you havnt seen this, here is where I give efficiency estimates for different types of gearing:
http://www.societyofrobots.com/mechanics_gears.shtml

hope that helps!
« Last Edit: December 21, 2006, 08:35:18 AM by Admin »

#### icius

• Jr. Member
• Posts: 9
##### Re: Motor Calculations - some help
« Reply #2 on: December 21, 2006, 02:16:45 PM »
Thanks for the great explanation!

I had a sneaking suspicion that the RMF would be unaffected by gearing.  I do have one more question though.   Your revised calculations indicate that I would need an RMF of 3.72 per motor.

So at maximum efficiency, the motor I was looking at would have an RMF of 15.57.  Almost 5 times the RMF I need.  Am i right in thinking that this motor is excessive for this application, or is it a "meets or exceeds" the RMF situation I am looking for?  I want my robot to have motors that are "big enough" as opposed to "PLENTY big!"  if you know what I mean.

• Supreme Robot
• Posts: 11,657
##### Re: Motor Calculations - some help
« Reply #3 on: December 21, 2006, 02:28:59 PM »
Calculating RMF is just to find motors that will do the job . . .

but there are really even more issues to consider:
cost of the motor
power requirements of the motor (lower voltages are better)
weight of the motor (lighter robots are always better)
motor size and space requirements (does your robot need to be small?)
terrain (robot going uphill or over bumps?)

and even deeper questions:
how easy is it to mount the motor to wheels and the chassis? when you are finished this project, and scrap this robot, would the motors be useful in the future?

I perfer to rate my motors with a 1.5 safety factor, meaning multiply the required RMF by 1.5. This gives me play room in case of design changes, unexpected flaws, or a miscalculation - each occuring often in the prototyping stage.

• Supreme Robot
• Posts: 11,657
##### Re: Motor Calculations - some help
« Reply #4 on: December 23, 2006, 10:20:44 AM »
I feel dumb for not doing this before . . .

an excel sheet to do the calculations for you has been added to the tutorial:

Also, I used your robot as the example . . .
I added in calculating for inclines too, and it turns out your robot needs an RMF of ~30 to go up a 5 degree slope.

#### icius

• Jr. Member
• Posts: 9
##### Re: Motor Calculations - some help
« Reply #5 on: December 26, 2006, 10:28:34 PM »
Thanks for the spreadsheet and the help.  I'm finding it is darn hard to find places that sell DC motors that actually give enough specs to do any calculations.  Maybe I'm looking in the wrong places?

Anyway I have a motor in mind with the following specs (all at max efficiency):

Voltage: 7.2
RPM: 12900
Torque (mN-m): 28
Amps: 7.48

So if I convert that torque to lb-ft and do the RMF calculation I get 4.44.  So pretty good for my desired 3.72 per motor requirement right?

So I start thinking about batteries.  I have an arbitrary idea in my head that it would be nice to get 60 minutes of continuous operation from the robot before a recharge is required.

So more math, that's two motors at 7.48 amps each so 14.96 amps for an hour.  Hmm sounds like some heavy juice?  So I am thinking I would need at least 2 of these:

http://www.onlybatterypacks.com/showitem.asp?ItemID=10954.8

Maybe 3?  I dunno.  Is an hour a lot to ask?  So much to consider.

• Supreme Robot
• Posts: 11,657
##### Re: Motor Calculations - some help
« Reply #6 on: December 27, 2006, 10:11:39 AM »
Quote
I'm finding it is darn hard to find places that sell DC motors that actually give enough specs to do any calculations.

unfortunately this is a major problem with motor retailers . . . they think that 'high torque motor with super fast rpm' is a useful spec . . . the higher quality more expensive motors always have good specs, but its hit-or-miss otherwise . . .

the majority of the sites i have listed here have good enough specs
http://www.societyofrobots.com/robot_parts_list_motors_servos.shtml

as for your RMF calculation, i highly recommend calculating it for a slope of a few degrees (so it can go over bumps). otherwise, 4.44 is fine for 3.72 requirement.

as for the batteries, yeap, two of those in parallel would be more than sufficient.

good luck!

#### icius

• Jr. Member
• Posts: 9
##### Re: Motor Calculations - some help
« Reply #7 on: December 27, 2006, 05:33:39 PM »
Ok, I'm a little slow at things sometimes, but the whole slope thing just kicked in.

So RMF 16 per motor eh?

That changes things quite a bit.

So now I am firmly in 12v motor land it seems with motors pulling considerably more current.  Something like:

Voltage: 12
RPM: 16400
Torque (mN-m): 80.8
Amps: 15.7

Much bigger.

So I would need like 4 of these:

http://www.onlybatterypacks.com/showitem.asp?ItemID=10691.7

Two pairs wired in series to get 12v and then the pairs wired in parallel to get 20 Ah?

7 lbs. and \$240.00 worth of batteries.  Not sure if I can even get these motors from the manufacturer or what they cost.  Daunting.

So let me understand what we are really calculating here.  This is worst case right?  This would be the robot going up a 5% grade constantly for an hour with the motors at maximum efficiency right?  Isn't there some room to play on either side of max efficiency?  I mean there is a difference between being "capable" of a 5% grade and doing 5% grades all day long right?  Isn't there some torque between torque at maximum efficiency and stall torque that is usable?  So maybe robot has a bad day and has to go over a lot of bumps and only gets 30 min. of running time, but on a better day has smooth ground the whole time and gets a good hour run time.  I'm ok with that kind of scenario.

Am I reaching the right conclusions here or am I off base? Trying to understand :-)

• Supreme Robot
• Posts: 11,657
##### Re: Motor Calculations - some help
« Reply #8 on: December 27, 2006, 07:00:44 PM »
i highly recommend looking into motors with built-in gearheads. there is no point in getting a 16400 rpm motor when you require less than 200rpm. it really hurts efficiency. motors have the highest efficiency when spinning the fastest, so putting a gear head on it gives you a low output speed, yet keeps a high input motor speed.

its also best to avoid more than 10V power source, for many many reasons - weight, cost, electronics availability, etc.

Quote
So let me understand what we are really calculating here.  This is worst case right? . . . Isn't there some room to play on either side of max efficiency?  I mean there is a difference between being "capable" of a 5% grade and doing 5% grades all day long right?
Not exactly 'worst case', but instead 'maximum capabilities.' The RMF specifies the maximum capabilities (in torque and speed) that is possible. Your robot will not be able to perform better than this. But it can perform worse, or perform under less stressing conditions (such as downhill)

Quote
This would be the robot going up a 5% grade constantly for an hour with the motors at maximum efficiency right? . . . So maybe robot has a bad day and has to go over a lot of bumps and only gets 30 min. of running time, but on a better day has smooth ground the whole time and gets a good hour run time.  I'm ok with that kind of scenario.
yeap. i guess its a 'worst case' scenario for the batteries, meaning highest current draw possible.

#### icius

• Jr. Member
• Posts: 9
##### Re: Motor Calculations - some help
« Reply #9 on: December 27, 2006, 09:36:16 PM »
Something like so perhaps?

http://www.lynxmotion.com/Product.aspx?productID=418&CategoryID=71

Of course all they list is stall torque.  Is there any way to calculate backwards?

• Supreme Robot
• Posts: 11,657
##### Re: Motor Calculations - some help
« Reply #10 on: December 27, 2006, 09:50:54 PM »
google searching LS-550S it appears to be a cordless power tool motor made in china . . .
manufacturer: Leshi Motor and Appliance Co., Ltd.