Trying to understand two masses connected by a shaft

In summary, the conversation discusses a system from a book that models the dynamics of two masses connected by a shaft. The equations given in the book and the nominal speed are mentioned, with a focus on the deviations from the nominal speed for each mass. The speaker expresses confusion about an equation that equates the rate of change of the angle to the deviation in speed for that mass times the nominal speed. Another person suggests that the notations used may be from an electrical engineering textbook, which can make the concept confusing.
  • #1
anon6912
21
3
I have the following system I got from a book, which models the dynamics of two masses connected by a shaft.

The system is given below:
hTqu6ml.png


And the equations given in the book for this system is below:
krHiOa9.png


The nominal speed is w0.
And the interest here is the deviations from the nominal for mass 1 (Δw1) and mass 2 (Δw2).

I understand all the equations except for the ones below:

tEjMpK8.png

oM2Li72.png


How does it make sense that the rate of change of the angle equates to the deviation in speed for that mass times the nominal speed?
bc331d30-a574-408f-ba6c-0a3d7a71e20b
 

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  • #2
I can't answer your question, but just judging by the notations involved, I'd guess that you got this from an EE textbook. The generally make a hash of rotor dynamics. By the time everything is expressed in "per unit," nothing makes sense anymore.
 
  • #3
anon6912 said:
How does it make sense that the rate of change of the angle equates to the deviation in speed for that mass times the nominal speed?
bc331d30-a574-408f-ba6c-0a3d7a71e20b
Quite - it makes no sense dimensionally.
 

1. How does the shaft affect the dynamics of the two masses?

The shaft serves as a connection between the two masses and plays a critical role in their dynamics. It transmits forces and torques between the masses and helps maintain their relative positions and velocities.

2. What factors influence the behavior of the system?

The behavior of the system is influenced by several factors, including the masses of the two objects, their distance from each other, the properties of the shaft (such as its length and stiffness), and any external forces acting on the system.

3. Can the two masses rotate independently from each other?

Yes, the two masses can rotate independently from each other if the shaft allows for it. This can occur if the shaft is designed to have a flexible or rotating joint, or if the masses are connected by multiple shafts.

4. How does the stiffness of the shaft affect the system's response to external forces?

The stiffness of the shaft plays a crucial role in determining the system's response to external forces. A stiffer shaft will resist deformations and transmit forces more effectively, while a more flexible shaft will allow for more movement and potentially alter the system's response.

5. What are some real-world applications of a system with two masses connected by a shaft?

This type of system can be found in various engineering applications, such as in engines, turbines, and mechanical transmissions. It is also commonly used in robotics, where two masses connected by a shaft can represent the rotational joints between different segments of a robot's arm or leg.

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