Calculating Torque: Rotating Axle in a Circular Housing

can you illustrate your assembly?

generally speak touque is related to rotation speed.

we can write as

M= J * dw/dt + Mr(resistance torque)

An illustraion would help immensely, especially to show what is on the endpoints.

Are you referring to the torque on the shaft or housing?

If it the housing, then this would be due to the viscosity of the oil between the shaft & housing? In this regard the torque could be calculated [Formula: me don't know right now], however if it is of small scale then directly measuring the torque would be more accurate: measure the force needed to stop the rotation at distance x then torque = Force*x. The torque value would be a peak soon after start up [cold oil, max viscosity] and decrease as the oil heats up.

Wouldn't load have some influence also?

Show us more illustration, is it something like MRI that hospital use to diagnose brain tumor with x-ray device is mounting inside was created torque sort of speak? vibration?

Torque:F*lenght

Hollow cyclinder(inertia)=1/2*mass(Rinside^2+R outside^2)

and depend on the counter balance of the mass attached. Principle the torque formula in above.