Sizing DC Motor for Large Robot (350 lb)

[Northbysouth]

I'm working on a senior design project. Currently I'm having some issues with sizing a motor for a large robot; everywhere I look I get different advice. I have a motor that I think will work but would appreciate some input.

The specs are for our robot are as follows:

mass = 350 lb = 158.8 kg
Max velocity = 4 mph = 1.788 m/s
angle = 4.8 degrees = 0.0837 radians
acceleration = (2*v_max)/t + v_i = 1.788 m/s^2
wheel radius = 10 inches = 0.254 m
time = 5 seconds

Surface = smooth indoor flooring

where v_max is the maximum velocity and v_i is the initial velocity (0 m/s), t is the time it takes for the robot to accelerate from 0 to v_max

I did a free body analysis (FBD) of the robot on an inclined plane (0.0837 radians) and got the following equation for the torque:

Torque = m*r*(a+g*sin(theta))

where m is the mass, a is the acceleration, g is gravity (9.81 m/s^2) and theta is the angle of the inclined plane.

This gives me a torque of 31.7 N-m. I think that this motor:

http://www.superdroidrobots.com/shop/item.aspx/dg-158-24vdc-135-rpm-wheel-chair-motor-pair/1531/

may work (the specs given are for the motors together). But the specs are confusing me a little. I don't understand where the 'Power Output (W) =200' spec is coming from or what the 'Gear Rated Motor Torque = 16.95 N-m)' means. As I understand it:

Power = torque*angular velocity

So, for the specs given for the motor:

w_motor = 135 RPM *2*pi/60 = 14.13 rad/s

Power_motor = 16.95 N-m*14.13 rad/s = 239.5 W

The issues is that for us to move the robot we need the following power:

w_robot= v_max/r = (1.788m/s)/(0.13 m) = 13.75 rad/s

where we rounded the radius of the wheel from 0.254 m to 0.13m.

Power_robot = 31.7 N-m*13.75 rad/s = 435.875 W

Additionally, in the images given for this motor there is a speed (RPM) vs torque graph which plots efficiency, current and speed (RPM). Based on the speed curve I re-plotted the points in excel and used a curve of best fit to find that the stall torque was approximately 60 N-m. So, we'd be operating these motors at 50% of their stall torque, but most sources I've read indicate that you should operate dc motors between 10 and 33% of their stall torque.

Any input about whether I'm looking in the right direction would be appreciated. Thanks

 

[Danger]

I know nothing of math or even actual engineering. When faced with a high-torque application, I always fall back on the good old automobile starter motor.
Also, you could look into the motors used on my power-chair (Jazzy Jet 3). It's like a combination of easy chair and motorized wheelchair. 24VDC gearhead motors. You can get them through eBay for a couple of hundred bucks, but they cost over $1,500 new.