Hi everyone,

I'm an EE student, and I'm designing a robot for a senior design. I'm at the point where I need to design for the motors I'm using, but I'm not great with mechanical systems. Specifically I'm having trouble figuring out the torque I need my motors to provide.

These are the parameters I've worked out.
mass = 2kg
wheel radius = 0.0381m
max velocity robot needs to move = 0.31 m/s
rpm = 90
acceleration to max velocity = 1 m/s^2

I need 2 driving motors based on these specifications, but I'm not sure I'm calculating it correctly. I was assuming the force the motor would have to push would be weight, but this results in a large torque:

torque = force * distance = mass * acceleration (gravity)* distance = 0.748 Nm or 0.374 Nm per motor.

How does the acceleration of the motor play into this calculation? I assumed it would be a sum of gravity and the acceleration of the motor, and when the motor reaches the max velocity, the motor acceleration falls out leaving only the acceleration due to gravity.

Those torque values just seem a little to large to after searching around for motors. Most of the motors on maxonmotors.com are rated for mN*m, so this torque I have is about 100times greater than some of the "average" price motors they have. Can anyone validate or correct my calculation?

 

You are looking at the torque at thousands to tens of thousands RPM. Add a gearhead to the motor and it should be just fine. Maxon sells the gearheads separately.

The one I looked at the top of the list for brushed DC motor had these specs:

Assigned power rating W 0.5 Nominal voltage V 6 No load speed min-¹ 12600 Stall torque mNm 1.63 Max. continuous torque mNm 0.921

When that is geared down to 90 RPM, it will exceed your requirements, be sure to have PWM control for speed. Maxon motors are simply the best, and outperform just about everything else in the same size range.

 

You are looking at the torque at thousands to tens of thousands RPM. Add a gearhead to the motor and it should be just fine. Maxon sells the gearheads separately.

The one I looked at the top of the list for brushed DC motor had these specs:



When that is geared down to 90 RPM, it will exceed your requirements, be sure to have PWM control for speed. Maxon motors are simply the best, and outperform just about everything else in the same size range.

I'm glad you see what I'm dealing with as far as the specs go. My advisor said Maxon's are the best, so thats what I'm going with.

I'm fine for the electronics, I'm just not great at mechanical systems. How can I be sure that when I gear down the motor to meet my rpm, that the torque will be adequate? And how do I know if my torque I calculated is correct? Is there a way mathematically to show me? I kind of need to justify my means before ordering anything.

 

I tend to use the "overkill route". Their lowest priced motors with a gearhead will easily move a 5lb robot at roughly 1 foot per second with the tire size mentioned.

The ME precision route involves finding the absolute minimum possible motor and gearhead, then adding a percentage for failsafe. As you probably do not know the stationary and moving friction of all bearings in the wheels, what incline it may be on, etc, get motors capable of "worse case scenario", then it will run efficiently, and still overcome the worse case.

As far as acceleration, assuming close to instant is best. say 100 mS. This is why I add extra power. I don't like running motors at their max limits. I've run a 0.25kg bot with micro RC Servos modded to continual rotation without issues, and the motors inside the micro servos are only about twice the size of a vibrating pager motor.


Torque vs. RPM is very close to Voltage vs. Current. When the 10k RPM is reduced to 100 RPM, you get a roughly 100 fold increase in torque, sacrificing RPM. This is an ideal condition, but gears are close, so subtract 15% for worse case there.

 

I tend to use the "overkill route". Their lowest priced motors with a gearhead will easily move a 5lb robot at roughly 1 foot per second with the tire size mentioned.

The ME precision route involves finding the absolute minimum possible motor and gearhead, then adding a percentage for failsafe. As you probably do not know the stationary and moving friction of all bearings in the wheels, what incline it may be on, etc, get motors capable of "worse case scenario", then it will run efficiently, and still overcome the worse case.

As far as acceleration, assuming close to instant is best. say 100 mS. This is why I add extra power. I don't like running motors at their max limits. I've run a 0.25kg bot with micro RC Servos modded to continual rotation without issues, and the motors inside the micro servos are only about twice the size of a vibrating pager motor.


Torque vs. RPM is very close to Voltage vs. Current. When the 10k RPM is reduced to 100 RPM, you get a roughly 100 fold increase in torque, sacrificing RPM. This is an ideal condition, but gears are close, so subtract 15% for worse case there.

Ok I see, there is an inverse relationship as speed decreases, torque increases. I think I've pretty much worked out the torque I need, my only problem now is a simple logical question.

What is the torque supplied when the acceleration is 0? Aka it is moving at a constant velocity? I would assume there would have to be some kind of torque because a voltage is applied to the motor. I guess can the torque at that moment be zero, but it has the "capability" to use the torque if need be? Like the torque is there, its just not being used? If that makes any sense lol.

 

Then you are at the "no load RPM" of the motor. It is spinning but not doing much "work". This rarely exists though, as the bearings and tires add a slight load due to that pesky friction thing.

As far as the pure mechanical engineering way to find it, you would need more data on run times, inclines, braking, potential environments, etc. for a precise number to get the lowest cost motor.

 

force= torque / wheel radius
force = mass * acceleration

torque / wheel radius = mass * acceleration
torque = wheel radius * mass * acceleration

(If I got that wrong it would be embarassing)

Obviously the gearbox multiplies the torque by the ratio (ignoring losses).

Is the robot going vertically up? If not, gravity is not part of the equation.