Page 450 - Wind Energy Handbook

424 COMPONENT DESIGN

(1) Maximum shear method. Here the fatigue evaluation is based on the maximum
shear stress ranges, calculated from either the (ó 1 ó 2 )=2, ó 1 =2or ó 2 =2 time
histories. The effect of mean stress is allowed for using the Goodman relation-
ship:

ô a ô m 1
þ ¼ (7:43)
S SN S Su ª
where ô a is the alternating shear stress, ô m is the mean shear stress, S SN is the
alternating shear stress for N loading cycles from the material S–N curve, S Su is
the ultimate shear strength, and ª is the safety factor.
Having used Equation (7.43) to determine S SN , the permitted number of
cycles for this loading range can be derived from the S–N curve, enabling the
corresponding fatigue damage to be calculated.

(2) ASME Boiler and pressure vessel code method. This is similar to the maximum
shear method, but the shear stress ranges are based on notional principal
stresses calculated from the changes in the values of ó x , ó y , ó z , ô xy , ô yz and ô zx
from datum values occurring at one of the extremes of the stress cycle. Mean
stress effects are not included.

(3) Distortion energy method. In this method, the fatigue evaluation is based on the
fluctuations of the effective or Von Mises stress. In the case of the hub shell, the
stress perpendicular to the hub surface (and hence the third principal stress) is
zero, so the effective stress is given by:
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(ó 1 ó 2 ) þ ó þ ó 2
2
2
ó9 ¼ 1 2 (7:44)
2
As the effective stress is based on the distortion energy, it is a scalar quantity, so
it needs to be assigned a sign corresponding to that of the dominant principal
stress. The effect of mean stress is allowed for in the same way as for the
maximum shear method, except that the stresses in Equation (7.43) are now
direct stresses instead of shear stresses. S–N curves for spheroidal graphite iron
are given in Hu ¨ck (1983).

7.4 Gearbox

7.4.1 Introduction

The function of the gearbox is to step up the speed of rotor rotation to a value
suitable for standard induction generators, which, in the case of fixed-speed
machines or two-speed machines operating at the higher speed, is usually
1500 r.p.m. plus the requisite slip. For machines rated between 300 kW and
2000 kW, with upper rotational speeds between 48 and 17 r.p.m., overall gear ratios