Mechanical vibrations, force applied to the armature

[john.kim]

Homework Statement

FYI - I don't have any knowledge on the mechanical aspects of electric motors.

you're given a 400 hp electric motor that needs to run at varying rpms. The armature is 1200 lbs and is 800mm long with a diameter of 500 mm. the air gap that exists is 2.5 mm. At 800 rpm the air gap was reduced to 1.75 mm (the armature displaced 0.75 mm from its equilibrium position).

I need to find the stiffness of the armature and the rotor unbalance.

- how exactly do I find the force applied to the armature ?

Homework Equations

I don't know any

The Attempt at a Solution

finding the force applied to the armature is something I can't figure out. I want to think that using the centripetal force = mv^2/r. However, since the armature is a mass rotating around its central axis, and not a point mass rotating around a point, I am sure my guess is wrong.

finding the force on the armature as a function of speed will let me find the stiffness of the shaft supporting the armature. with the stiffness and the damping ratio I can find the resulting equation of motion (describing the displacement of the armature from the center) using a response to harmonic excitation

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Valkarie]

The force applied to the armature can be found using Newton's second law of motion. Since the armature is a mass rotating around its central axis, the force applied can be calculated using the following equation: F = ma, where m is the mass of the armature and a is the angular acceleration. To find the angular acceleration, you can use the equation a = ω2r, where ω is the angular velocity and r is the radius of the armature. Therefore, the force applied to the armature can be calculated as F = mω2r.Once you have the force applied to the armature, you can then calculate the stiffness of the shaft supporting the armature by dividing the force by the displacement of the armature from the center. For example, if the force applied to the armature is 400 N and the displacement of the armature from the center is 0.75 mm, then the stiffness of the shaft would be 400/0.75 = 533.3 N/mm. To calculate the rotor unbalance, you can use the equation θ = (F/(2πm))*t, where F is the force applied to the armature, m is the mass of the armature, and t is the time. This equation will give you the angle of rotation of the armature due to the unbalance.