Modeling and Simulation of a Rotor with Gear Train Driving a Propeller
Modeling and Simulation of a Rotor with Gear Train Driving a Propeller
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The goal of this project was to understand the effect of different stiffness values of the flexible cylinder connected to the propeller on the system output, which in this case, was the oscillation frequency of the propeller. First, I derived the equations of motion, the transfer function with respect to the rotation speed of the propeller and the applied torque, and the state space representation for the system. Next, I implemented these equations into wolfram mathematica using the state space model function, and plotted the results at different periods of time with two different torque inputs.
Impulse Input
Impulse Input
Step Input
Step Input
The system response for an impulse input reached a steady state as it approached zero.
Steady state was also reached when the torque input is modeled as a step input.
Since the simulation time for the impulse response was set as 2000, the effect of the different stiffness coefficients could not easily be seen. However when limited to the first twenty seconds, it was clear that as the stiffness coefficient increases, the oscillation frequency also increases.
When the time period was narrowed down to twenty second, system response with the step input also clearly exhibited an increase in oscillation frequency with an increase in stiffness coefficient.
The positive correlation between stiffness coefficient and oscillation frequency was also seen during the last twenty second of the impulse response.
Torsional damping of the flexible shaft influences the system response through a few main channels. Damping can lead to the decrease in amplitude, which explains the downward trend before steady state was reached in the system response of the impulse input.
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