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Rotating Imbalances

Internal imbalances arise from rotating components that are not completely symmetric, leading to centrifugal forces. A generic model of a system

The system has a total mass and consists of a primary mass mounted on a spring and a damper, and a imbalance. The imbalance can be modeled as a massless rod connected to a point mass , with the rod and mass rotating with constant angular speed . Horizontal forces between the two masses do not contribute to the dynamics as the horizontal motion of the primary mass is restrained.

Problem: Amplitude of vibration when the point mass is turning at 10 rad/s.

Input:

• Total mass 34 kg

- Point mass 4 kg
- Primary mass 30 kg
- Spring stiffness 800 N/m
- Damping coefficient 0.15
- Massless rod length 60 mm

Questions:

1. (50 Points) The periodic force that causes the motor to vibrate is the centrifugal force

due to the imbalance. Calculate the magnitude of this force. Note: Use cylindrical

coordinates to calculate position, velocity, and total acceleration for the imbalance (simple

circular motion) to obtain the acceleration component necessary to calculate the centrifugal

force.

2. (20 Points) Calculate the natural frequency of vibration.

3. (30 Points) Determine the steady-state amplitude.

with an imbalance is shown above.