Torque Required For a Roller?

[chopperkirks]

Hello

I have recently started working as a design engineer for a manufacturing industry in Zimbabwe. This is my first job after Uni and unfortunately due to the nature o the country I am the only engineer at the company so my transition into the professional engineering world is coming with a STEEP learning curve with no one around to help when I get a bit lost. At the moment I am designing a product that requires the running of a heavy roller driven by an electric motor and a pulley system. The motor is rated at 50kW and 930RPM (from the data plate). The roller is 250Kg and held in place with two tapered roller bearings. Now assuming the start up time for this is ten seconds and the mass is rolling at 280RPM the start up torque will be ~8N.m. This is where the confusion sets in. How would you go about calculating the power needed to keep this mass rolling at 280RPM. Now

Power=Torque x Angular velocity or T = (9.55 x Power)/RPM ..............(1)

This I understand but how do I find the torque/power to keep the mass moving at a constant speed of 280RPM. The mass is no longer accelerating so I can't use the start up torque. Is it right to say that to move a 250Kg mass the force required is equal the force needed to overcome the friction in the bearings by using

Force = Coeff of friction in bearing x Mass

and then using this force in Torque= Force x Radius (0.15m). I would like to say that the torque is governed by the speed and power of the motor but this would be wrong as the operation does obviously not draw the full 50kW of power available.

another way of looking at it is

if Force = Mass x Radius x Angular Velocity^2

is it right to say that the roller has a

Torque = Mass x Radius^2 x Angular velocity^2 and then using that in one of the equations from line (1).

In short what I am asking is how do I get the power being drawn by a 250kg roller turning at 280RPM?

Thanks in advance for any help, it is much appreciated.

Picture of what i am doing