Question

A wind turbine rotor with three blades is to be manufactured from an epoxy composite. The minimum required tensile strength is 600 MPa and the required stiffness is given by an elastic modulus in the range 26 GPa to 30 GPa.

Initially, for testing purposes a small wind turbine with a rotor diameter of 2 m was manufactured. The cross sectional area at the blade root is 0.1 m × 0.1 m, the blade mass is 195 kg and the distance between the centre of gravity and the blade axis is 0.4 m. Using the similarity rules, calculate the maximum rotor diameter knowing that the maximum bending stress that the blade can sustain without failure is 400 MPa. (5 marks)

Answer 1

Total tensile strength on the root of the prototype ( or actual turbine) comprises of maximum bending stress + centrifugal which is equal to 600MPa given in the question. Now from centrifugal stress (Fc) on prototype = [bending moment at the root of the prototype (Mb1) * length of the blade (model)] / cross-section area at the root of model A1.
A1 = 0.1*0.1
on solving the equation we have centrifugal stress equals to 40MPa
now bending stress, Mb1 = 600 - 40 = 560 Mpa
from the relation, Mp = Mm (Rp / Rm)^3
we get the value of Rp = 1.11m
hence the diameter of rotor = 2.22m