Page 319 - Wind Energy Handbook

HUB AND LOW-SPEED SHAFT LOADING 293

range fatigue cycles, which can have a disproportionate effect on fatigue damage
for materials with high m value such as those used for blades. However, this
inaccuracy can be reduced (and quantified) by running several simulations with
different random number seeds at each wind speed – see Thomsen (1998).

5.9.5 Fatigue cycle counting

As noted in Section 5.9.4, the dynamic analysis of turbine behaviour in a simulated
wind field yields time histories of loads or stresses which then need to be processed
to abstract details of the fatigue cycles. There are two established methods of fatigue
cycle counting: the reservoir method and the rainflow method, both of which yield
the same result.
In the reservoir method, the load or stress history (with time axis horizontal) is
imagined as the cross section of a reservoir, which is successively drained from
each low point, starting at the lowest and working up. Each draining operation then
yields a load or stress cycle (see BS 5400 (1980) for a full description).
The rainflow method was first proposed by Matsuishi and Endo in 1968, and its
title derives from the concept of water flowing down the ‘rooves’ formed when the
time history is rotated so that the time axis is vertical. However, the following
description not involving the rainflow analogy may be easier to understand.
The first step is to reduce the time history to a series of peaks and troughs, which
are then termed extremes. Then each group of four successive extremes is examined
in turn to determine whether the values of the two intermediate extremes lie between
the values of the initial and final extremes. If so, the two intermediate extremes are
counted as defining a stress cycle, which is then included in the cycle count, and the
two intermediate extremes are deleted from the time history. The process is contin-
ued until the complete series of extremes forming the time history has been
processed in this way. Then the sequence remaining will consist simply of a
diverging and a converging part from which the final group of stress ranges can be
extracted (see ‘Fatigue Characteristics’ in the IEA series of Recommended Practices
for Wind Turbine Testing and Evaluation (1984) for a full description of the method
and for details of algorithms that can be used for automating the process).
Although, in principle, the fatigue cycles obtained from, say, a 600 s time history
could be listed individually, it is normal to reduce the volume of data by allocating
individual cycles to a series of equal load or stress ranges known as ‘bins’ – e.g.,
2
0–2, 2–4, 4–6 N/mm etc. The fatigue spectrum is then presented in terms of the
number of cycles falling into each ‘bin’.

5.10 Hub and Low-speed Shaft Loading

5.10.1 Introduction

The loadings on the hub consist of the aerodynamic, gravity and inertia loadings on
the blades and the equal and opposite (discounting hub self-weight) reaction from