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I ATTACHED A PDF
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.
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