How To Determine Newton Meter Force

[Mr. Nice Guy]

Hello!

How do you calculate or determine Newton meter force requirement and rpm's for an electrical motor in the following example:

A device that utilizes a shaft that is 2 inches in diameter and 6 feet length. It needs to be able to lift 10 pounds and distance of 7 feet in 6 seconds. I need to know the formulas to make these calculations and the requirements needed for this application?

Thanks in advance for any assistance!

Mr. Nice Guy.

 

[theCandyman]

RPM can be found by dividing the distance the mass must travel by the circumference of the shaft. The torque will be equal to the radius of the shaft times the force to lift the weight. I am unsure what you are asking for in the second part of your request.

 

[kyle8921]

Hello Mr. Nice Guy,

Thank you for your question. To determine the Newton meter force requirement for an electrical motor, we need to first understand the concept of torque. Torque is the rotational equivalent of force and is measured in Newton meters (Nm). It is calculated by multiplying force (in Newtons) by the distance from the axis of rotation (in meters). So, in this case, we need to calculate the torque required to lift 10 pounds (4.54 kilograms) at a distance of 7 feet (2.13 meters) in 6 seconds.

The formula for torque is T = F x d, where T is torque, F is force, and d is distance. Plugging in the values, we get:

T = (4.54 kg)(9.8 m/s^2)(2.13 m)

T = 95.8 Nm

This is the torque required to lift the weight. Now, to determine the rpm's for the motor, we need to use the formula:

ω = (2πN)/60, where ω is angular velocity (in radians per second), N is the rpm, and 60 is the number of seconds in a minute.

We know the distance (2.13 meters) and time (6 seconds) for one revolution, so we can calculate the angular velocity as:

ω = (2π)(1 revolution)/(6 seconds)

ω = 1.05 rad/s

Now, we can plug this value into our torque formula to solve for the required rpm:

T = (I)(α), where I is the moment of inertia and α is the angular acceleration. Since we know the torque (95.8 Nm) and the angular velocity (1.05 rad/s), we can rearrange the formula to solve for the moment of inertia:

I = T/α

I = (95.8 Nm)/(1.05 rad/s^2)

I = 91.24 kgm^2

Finally, we can use this moment of inertia to solve for the required rpm:

N = ω/(2π)(I)

N = (1.05 rad/s)/(2π)(91.24 kgm^2)

N = 0.006 rpm

Therefore, the required rpm for the motor is approximately 0.006 rpm. However, keep in mind that this is a simplified calculation and there may be other factors to consider, such as friction