Excitation from unbalanced mass

In summary, a rigid body with a mass M is sliding vertically within a frictionless prismatic pair, linked to a fixed frame by a spring with stiffness k and a viscous damper with coefficient c. Alongside the body, a point mass m is rotating at a constant speed w on a circular trajectory with radius r. This problem is similar to those found in many textbooks, such as washing machine models. By visualizing the problem, it can be seen that when the eccentric mass is at Ψ=Π/2, the centrifugal force Fc=mΩ2/r is directed upwards, and when it is at -Π/2, it is directed downwards. The equations of motion for this problem can be
  • #1
Godfather_bek
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Homework Statement


A rigid body of mass M slides vertically inside a friction-less prismatic pair. It is linked to the fixed frame through the spring of stiffness k, and a viscous damper with coefficient c. Beside the body, a point mass m rotates with constant speed w(omega) on a circular trajectory of radius r.(mass M also includes the point mass m)

Homework Equations


I don't know how to be with point mass. How to related vertical displacements with rotational? Can anyone suggest something..?

The Attempt at a Solution

 

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  • #2
Examples this type of problem are to be found in many textbooks .

If you want to solve the problem yourself start by visualising the problem . When the eccentric mass is going around what do you expect to see the whole mechanism doing ?
 
  • #3
Nidum said:
Examples this type of problem are to be found in many textbooks .

If you want to solve the problem yourself start by visualizing the problem . When the eccentric mass is going around what do you expect to see the whole mechanism doing ?
It is like washing machines model. If there was no rotating small mass, it would be much easier. How I realized it, as Ψ=Ωt and if Ψ is equal to Π/2, then centrifugal force Fc = mΩ2/r directed to upward. And if Ψ is -Π/2 it is downward. But how to be with equation of motion?
 

Related to Excitation from unbalanced mass

1. What is excitation from unbalanced mass?

Excitation from unbalanced mass refers to the vibration or oscillation caused by a rotating system that has an unbalanced mass. This unbalanced mass creates a centrifugal force that causes the system to vibrate, which can lead to structural damage if not properly addressed.

2. What are some common examples of excitation from unbalanced mass?

Some common examples of excitation from unbalanced mass include unbalanced rotors in engines, fans, turbines, and other rotating equipment. It can also occur in vehicles, such as cars or airplanes, due to uneven weight distribution or worn out components.

3. How does excitation from unbalanced mass affect the performance of a system?

Excitation from unbalanced mass can cause significant performance issues in a system. It can lead to increased vibration levels, which can cause excessive noise, reduce system efficiency, and even lead to structural damage over time. It can also affect the accuracy of measurements or readings in sensitive equipment.

4. How can excitation from unbalanced mass be prevented or minimized?

To prevent or minimize excitation from unbalanced mass, the unbalanced mass itself should be corrected or balanced. This can be done by adding weights to the rotating system in a way that counteracts the unbalanced force. Proper maintenance and regular inspections can also help identify and address any potential sources of unbalanced mass before they become a larger issue.

5. What are some techniques for analyzing and mitigating excitation from unbalanced mass?

There are several techniques for analyzing and mitigating excitation from unbalanced mass. These include dynamic balancing, which involves measuring and adjusting the mass distribution of a rotating system, and vibration analysis, which uses sensors and software to identify and monitor vibration levels. Other methods include modal analysis, which determines the natural frequency of a system, and active vibration control, which uses sensors and actuators to actively reduce vibration levels.

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