# Mechanical vibrations, force applied to the armature

• john.kim
In summary, to find the stiffness of the armature and the rotor unbalance, you need to first calculate the force applied to the armature using Newton's second law of motion and then use this force to calculate the stiffness of the shaft and the angle of rotation of the armature due to unbalance.
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 ?

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

## The Attempt at a Solution

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.

## What is mechanical vibration?

Mechanical vibration is the back and forth motion of an object or structure due to the application of a force. It can be caused by external forces or internal forces within the object itself.

## What is an armature?

An armature is a component of an electric motor or generator that rotates and interacts with the magnetic field to produce motion or electricity. In mechanical vibrations, an armature refers to the part of a system that experiences the force and vibrates.

## What causes mechanical vibrations?

Mechanical vibrations are caused by the application of external forces to an object or structure. These forces can be in the form of impact, pressure, or oscillations. They can also be caused by internal forces within the object, such as unbalanced forces or resonance.

## How do mechanical vibrations affect the armature?

Mechanical vibrations can affect the armature by causing it to vibrate, which can lead to wear and tear, or even failure, of the component. The force applied to the armature can also affect its motion and performance, leading to changes in speed, direction, or amplitude of the vibrations.

## How can mechanical vibrations be controlled or reduced?

Mechanical vibrations can be controlled or reduced by using damping materials or devices, such as shock absorbers or isolators, to absorb or dissipate the energy of the vibrations. Balancing the object or structure can also help reduce vibrations. Additionally, proper maintenance and regular inspection can help identify and address any issues that may lead to excessive vibrations.

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