# Homework Help: Power transmission of a multi-stepped shaft

1. Mar 2, 2015

### jasonnaylor

1. The problem statement, all variables and given/known data

Imagine a stepped turbine shaft for a wind turbine.

(See PDF 'Question' for image)
Wind hits the turbine blades with a pressure P Pa in a direction which may be averaged out at 90 degrees to the y-axis, creating a torque Ta, which acts clockwise in the x-direction as we look at the diagram from the left hand side.

We may assume that the transmission shaft L1, L2 and L3 is the same material machined to different diameters d1, d2 and d3 respectively, having a young’s modulus of E (N/m2), and a rigidity modulus of G(N/m2).

The armature housing contains the armature and associated electrical system to generate current for the grid. This armature is housed on bearings having a damping constant of c (N1/2), which provides a resistive torque to the system.

a. Design an equation that describes the power transmission over the length of the shaft up to and including the armature housing. Assume that the blades of the turbine may be modelled as a disc with Mass M , radius r and gyration radius k. Ignore the fillet radii between shafts and simply treat as a 90 degree turn.

b. Derive an equation that describes the maximum displacement of the centre of rotation of the shaft turbine blades from the axis “XX” assuming that the transmission shaft has a weight of W newtons. State clearly in your analysis any assumptions that you have made.

c. A block of ice having a mass β falls from a plane and hits the blades at an angle of https://www.physicsforums.com/file:///C:/Users/jason/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png [Broken] to the vertical y-axis. What happens to the transmission shaft? Explain analytically in detail stating any assumptions that you have made.

2. Relevant equations

P= T.ω

3. The attempt at a solution

(See attached PDF 'solution') Ive been trying to crack this question for days and days and im going knowhere.

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Last edited by a moderator: May 7, 2017
2. Mar 7, 2015