Bearings in wind turbines are subjected to both steady and dynamic loads during normal operation, but especially due to turbulence and wind shear that give rise to significant dynamic loads.
Bearing life estimation methods currently use the Palmgren-Miner law to sum the cumulative effect of such loads. Bearing manufacturers’ catalogues present methods to do so, typically taking the cube root of the load cubed and the life fraction at each load. The principle limitations of the Palmgren-Miner damage summation law are its load-level independence, load-sequence independence and lack of load-interaction capability.
However, in recent years, bearings have been afflicted by issues such as white etching cracking (WSF) and white structure flaking (WSF) in which failures occur at a time much less that the estimated L10 life. Since these failures may be initiated at surface or sub-surface defects (such as inclusions), the validity of the Palmgren-Miner law in predicting life should be questioned. For sub-surface initiated failures, a fundamental understanding of the physical processes at play should lead to better damage summation laws. In the first instance, crack initiation on an inclusion must occur (unless the inclusion and any associated void acts as a crack) followed by crack growth to failure (spalling).
Many alternative laws to Palmgren-Miner have been proposed, mostly to deal with fatigue of structures as opposed to bearings. However, these are principally aimed at homogeneous materials, whereas bearing steels must be considered as inhomogeneous (in this respect, continuum damage models may be more appropriate). As well as Palmgren-Miner’s linear damage rule, early models can be categorised as the damage curve approach (DCA), endurance limit approach, S-N curve modification approach, two-stage damage approach and crack growth approach (according to Fatemi and Yang).
Of these, the two-stage linear damage approach is worthy of consideration because damage due to crack initiation and due to crack growth are separated. High-low or low-high load sequences can be evaluated whereas Palmgren-Miner’s linear damage rule has no such sequencing. The crack growth approach is a similar form to linear elastic fracture mechanics (LEFM) in which crack growth rate is expressed as a constant raised to a power times a function of the loading. This approach ignores crack initiation.
Since cracks from inclusions may be considered to be micro-structurally short or physically small, it is more appropriate to use elasto-plastic fracture mechanics (EPFM) as opposed to LEFM. But there are further complications. There is evidence to suggest that either inclusions act as micro-cracks from the outset or the matrix becomes cracked within the white etching regions formed on inclusions under rolling contact stresses, the so-called butterflies. So there are differences to structural fatigue.
In respect of formation of butterfly wings, an approach using continuum damage mechanics has shown some promise according to Moghaddam et al. Once micro-cracking has occurred within the butterfly wing, then EPFM crack growth laws may prove useful estimate life until crack size becomes large enough for rapid growth to failure.
These approaches have the benefit that load-level dependence, load-sequence dependence and load-interaction capability can be accommodated. So whilst Palmgren-Miner has proven to be useful over many years, more representative life estimations for complex dynamic loading situations such as those experienced by wind turbines will require validation of alternative methods.
In this respect, RGL Associates is researching the applicability of two-stage linear damage, crack growth and continuum damage mechanics approaches in order to develop more accurate life estimates.