### Author Topic: 6 wheels, math check please  (Read 1272 times)

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#### Mackattack

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##### 6 wheels, math check please
« on: April 11, 2013, 04:21:42 PM »
Hello,

So here's the deal, I need to drive 6 wheels (12.8" tall each, bot foot print about 3' x 4'), bot weighing 300 pounds, at 10 miles per hour over grass/mud/snow and occasionally up a 45 degree incline. I calculate 378Lb-in torque each motor at 232 rpm!!!!!!!! This sounds high. Not due to the math, just more than I expected. This thing needs to be RC controlled too (and then FPV).

Really, 378in-lbs? per wheel?

I'd like to have brushless motors and drives with gearheads (inline style). So any advice for inline planetary motors and gearheads would be appreciated. And, any advice for motor controls (that could be Arduino'd and/or RC controlled to would be fantastic.

Jim

#### jwatte

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##### Re: 6 wheels, math check please
« Reply #1 on: April 11, 2013, 04:42:07 PM »
Yes. the math works out that way.
Radius of the wheels is 6.4 inches.
Weight per wheel is 75 pounds.
75*6.4 = 480 pound-inches, or 40 foot-pounds. But, as you will only climb a 45 degree hill, 378 pound-inches may allow you to just barely crawl up that -- certainly not at 10 mph.
Now, to have some room to actually move upwards, while overcoming friction, and also assuming you slip on at least one wheel, you'd want more than that. I'd go for 50 foot-pounds per motor to have at least some margin.

Good sources for these kinds of motors may be golf carts, for example.

Can't really recommend a motor driver until you know the voltage and current draw of the motor. You should specify the peak voltage and current of your controller to be at 2x the battery voltage and stall current of your motor, to make sure that you will never exceed it. A motor may draw 2x rated current while reversing direction, and inductive kickback can be estimated at voltage, plus the drive voltage, so 2x voltage total.

What kind of batteries are you looking at? And battery management system?

#### Mackattack

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##### Re: 6 wheels, math check please
« Reply #2 on: April 11, 2013, 05:12:43 PM »
Poop, I was hoping I was wrong...

OK, I'm off to search golf cart motors, or any other reco's like wheel chair motors maybe?

#### Duane Degn

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##### Re: 6 wheels, math check please
« Reply #3 on: April 21, 2013, 08:45:38 AM »
You were a little wrong.

The torque determines you maximum acceleration. As long as you can accelerate you should be able to reach your 10mph speed given enough time.

The 45 degree slope is the killer here. You need enough torque to overcome the force exerted by your robot's weight under the influence of gravity. This force is the weight of your robot times the sine of the slope of the incline.

The sine of 45 degrees is about 0.71, so you'll need your motors to provide 71% of the torque previously calculated.

480 lb*in * 0.71 = 340.8 lb*in

If your robot can take a the slopes with a running start, you could get by with less powerful motors. Using smaller wheels would also reduce the torque required at the cost of reduced speed.

The above calculations don't include friction and assume all six wheels will have good traction.

Do you really need to climb a 45 degree incline? That's awfully steep. You'd only need half the torque if you limited yourself to 20 degree inclines which is still steeper than most roads. Wheel chair ramps generally have less than a 5 degree slope.

#### jwatte

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##### Re: 6 wheels, math check please
« Reply #4 on: April 22, 2013, 03:20:28 PM »
Quote
As long as you can accelerate you should be able to reach your 10mph speed given enough time.

Meanwhile, in reality, there are losses both in the system (motor, transmission, axles, wheels) and vehicle/conditions (road, air drag/wind, etc.)
Not to mention that components may wear, may not meet nominal specifications except under ideal conditions, etc. And you certainly don't want to run an electric motor at its stall current for any significant amount of time; you'll burn the motor out!

Specifying "exactly on the border" numerics is how cheap consumer junk stays cheap, and also keeps disappointing with its inability to actually achieve stated specifications. You need the margins for anything robust.

#### Duane Degn

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##### Re: 6 wheels, math check please
« Reply #5 on: April 22, 2013, 04:47:27 PM »
Specifying "exactly on the border" numerics is how cheap consumer junk stays cheap, and also keeps disappointing with its inability to actually achieve stated specifications. You need the margins for anything robust.

Agreed but you need to know the initial requirements in order to figure out what kind of margin you want. The previous calculations regarding torque were wrong.

480oz*in of torque is what is needed to move the robot up a vertical wall (if the tires could maintain friction). A robot travelling on a horizontal surface (or a 45 degree incline) doesn't require the same amount of torque.

It's good to have more power than the bare minimum but it helps to know what the bare minimum is. 480oz*in is much more than the bare minimum in this case.

I've seen this type of error made many times in hobby robotics. There's a tendency to use the weight of the robot and diameter of the wheel to calculated the torque required to move the robot. If a robot were on a flat surface with little friction on its wheels a very small about of torque could propel the robot forward. The torque doesn't tell you how heavy the robot can be, it tells you what the acceleration of the robot will be. If you want the robot to drive up a slope (without needing a running start) you want to make sure the acceleration is at least as much as the acceleration of gravity pushing against the robot.

Once this bare minimum is calculated, then all the other factors such as friction, traction, etc can be addressed.

#### jwatte

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##### Re: 6 wheels, math check please
« Reply #6 on: April 23, 2013, 11:46:24 AM »
Quote
480oz*in of torque is what is needed to move the robot up a vertical wall (if the tires could maintain friction).

You are right; that wasn't made clear. Another way to put that: With 480 oz*in of torque, you could accelerate your robot at 1g on a lossless, perfectly flat horizontal surface. That's a decent amount of acceleration.
The problem with "what is the absolute minimum" is that, in a lossless system on a flat surface, the absolute minimum is epsilon above zero. This is what trains use to be able to move very heavy loads with comparatively small engines. (The first steam locomotives just had a few horse power of power!)
So, using the 1g number for the estimated torque needed is a decent rule of thumb that lets you ignore all the corner cases. Once you have 1g of torque, you're going to be able to climb any incline you can get your tires to stick on, and you're going to have reasonable stopping power. For heavier robots (over 5 pounds, say,) stopping power is actually more important than starting power!

#### Duane Degn

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##### Re: 6 wheels, math check please
« Reply #7 on: April 23, 2013, 01:09:47 PM »
You are right; that wasn't made clear.

Yes, but I think your last post clarified very nicely. Thanks.

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