Vibrating Conveyor: Determine Amplitude & Power as a Function of Frequency

[tdeng]

I am doing engineering work on a vibrating conveyor and need help in determining the amplitude and Power as a function of driving frequency.

The system consists of a Motor which rotates an eccentric shaft. There is a rubber flexible element which connects from this eccentric shaft to the Conveyor Trough. This element has a spring constant of K1, a damping factor b1 (proportional to velocity only) and the centers on the Eccentric are distance E apart. To keep the conveyor oscillating we have a series of springs and dampers connected between the conveyor trough and the rigid floor. Call these Ks & bs respectively.

Question #1 - Is the natural frequency of this system = sqrt ((K1+Ks)/m) ?

Question #2 - My Textbook on Vibration and Waves gives equations for forced oscillations with damping based on a driving force of Fo cos (omega t). What would Fo be in this example?

The equation I used for amplitude was:
A(omega) = Fo/((k R ((1/R-R)^2+ 1/Q^2)
where R = frequency/natural frequency & Q is the Quality Factor = nat freq*m/bs
For Fo I used K1 * Eccentric c/c

Question #3 - The amplitude equation above neglects damping between the eccentric drive and the mass. What would be the equation with that included?
(I could fit the curve perfectly without this damping)

Question #4 - The equation I have for power required is based on Fo.
P (omega) = Fo^2 * nat freq / (2 k Q sqrt((1/R-R)^2 +1/Q^2)
Is there another equation that would include the damping between the driver and the eccentric shaft?

Thanks for all your help. I am willing to do more research so if you can point me to some literature that would help.

 

[Achy47]

Hello, I am a scientist and I would be happy to help you with your engineering work on the vibrating conveyor. Based on the information provided, here are my responses to your questions:

1. Yes, the natural frequency of the system can be calculated using the formula you mentioned: sqrt((K1+Ks)/m). This is the frequency at which the system will vibrate without any external force applied.

2. The value of Fo in this example would depend on the specific design and parameters of your system. However, it can be calculated using the equation you mentioned: K1 * Eccentric c/c. This represents the force applied by the motor to the eccentric shaft.

3. To include damping between the eccentric drive and the mass in the amplitude equation, you can use the following formula: A(omega) = Fo/((k R ((1/R-R)^2+ 1/Q^2) * (1 + b1^2*m^2/(k1+Ks)^2)). This takes into account the damping factor b1 and the mass m in the system.

4. The equation for power required can also be modified to include damping between the driver and the eccentric shaft. It would be: P(omega) = Fo^2 * nat freq / (2 k Q sqrt((1/R-R)^2 +1/Q^2) * (1 + b1^2*m^2/(k1+Ks)^2)). This takes into account the damping factor b1 and the mass m in the system.

I would recommend doing further research on forced oscillations with damping, as well as specific equations and parameters for vibrating conveyors. Some useful resources could be textbooks on vibrations and engineering mechanics, as well as research articles on similar systems. I hope this helps and good luck with your work!