Forces, Torques, Power etc. on a Wind Turbine

[physics4life1]

Homework Statement

Homework Equations

P = 0.3*rho*A*V^3
F = 0.44*rho*A*V^2

From what I know that may help:

Shear Stress (Torsion) = T*radius/(Moment of Inertia)

The Attempt at a Solution

When we were given this problem no one in the class had the slightest clue how to solve it. I literally have no idea either but what I would guess to do is this:

Part a)

I would assume I need some formula that will incorporate a radius of the flange? Is that what the question means by flange thickness? In that case I suppose the shape of the flange would be circular? After finding a relevant formula you could distribute the stress over the number of bolts needed/required then solve for how many bolts to have and where to place them.

Part b)

I guess the 3hz would contribute to number of cycles to failure the turbine could withstand and we could solve for a max stress? But I am very confused what this part of the question is asking...any guidance?

Part c)

This part also confused me because in the beginning of the problem it says to neglect weight and inertial effects then our professor gave us numbers to use for this part. In any case I set up a free body diagram of the turbine and solved for the reacting forces. I think I got this part correct assuming he didn't try and trick us!


To anyone that can help, I know you don't do the homework for us and that is not what I am asking, however I have literally never been more confused in my life so any help and guidance will be GREATLY appreciated!

Thanks!

 

[KataKoniK]

Hello,

Thank you for reaching out for help on this problem. I understand that it can be frustrating when the entire class is struggling with a problem and the professor has not provided clear guidance. I will do my best to help you understand the problem and guide you towards a solution.

Part a)

You are correct that the flange thickness refers to the radius of the flange. The shape of the flange can be assumed to be circular. In order to distribute the stress over the number of bolts, you will need to use the formula for shear stress (Torsion) that you provided. This formula relates the torque (T) applied to a shaft to the radius of the shaft and the moment of inertia. In this case, the torque is being applied to the flange by the force (F) acting on the blades of the turbine. So, you will need to find the moment of inertia of the flange and use that in the formula to solve for the number of bolts needed and their placement.

Part b)

The 3hz refers to the frequency at which the turbine is rotating. You are correct that this frequency will contribute to the number of cycles to failure. In order to solve for the maximum stress, you will need to use the formula for stress (F = 0.44*rho*A*V^2) and plug in the given values for density (rho), area (A), and velocity (V). This will give you the maximum stress that the turbine can withstand before failing due to fatigue.

Part c)

It is not uncommon for professors to give numbers to use for a part of the problem, even if they have told you to neglect certain effects. This is often done to give you an opportunity to practice solving problems with different values and to check your understanding of the concepts. In this case, you have correctly set up a free body diagram and solved for the reacting forces. This is a good start to solving the problem. However, you will also need to consider the torque (T) applied to the flange by the force (F) acting on the blades. This will contribute to the overall stability of the turbine and should be included in your analysis.

I hope this helps guide you towards a solution for this problem. Remember to always check your units and make sure they are consistent throughout your calculations. If you are still struggling, I would recommend reaching out to your professor for clarification or seeking assistance