13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- (a) (b) Figure 9. Damage factor versus distance from surface for bilinear (a) and original limit curve (b). 4. Conclusions The Dang Van criterion has been applied to a roller bearing for windmill applications and the influence of hardness variations and different residual stresses has been studied. Results have shown that, according to the Dang Van criterion, the highest damage factor is reached below the surface, regardless the safe locus used. This suggests that failure is most likely to initiate in the material a little below the surface, which is consistent with literature that reports subsurface failures of roller bearings for wind turbine applications. The effect of increased hardness, in a thin layer close to the surface, has also been studied, relating the hardness to the fatigue strength of the material. The particular hardness distribution induced is seen to be important in evaluating the safety against fatigue for the bearing. Assuming that a higher fatigue strength corresponds to a higher Brinell hardness, the results indicate that a hardening surface treatment will be beneficial in terms of fatigue damage. However, surface hardening is not really possible for AISI 52100 bearing steel, though some recent work [28] seems to indicate an improvement of fatigue strength, for these steels, by induction heating and repeated quenching. It may be noted also that some steels show a maximum for the curve wሺHBሻ, which would limit the applicability of Eq. (22). In fact, Eq.(22) is valid only for smaller values of hardness. Bearings with different residual stress distributions have also been studied and calculations carried out show, for the Dang Van criterion, a positive effect of compressive residual stresses in the subsurface region according to the original safe locus. No influence of residual stresses has been found with the use of the modified safe locus and for the load case analyzed. Acknowledgements The author would like to thank Prof. Viggo Tvergaard and Associate Prof. Peder Kilt, Technical University of Denmark, for ideas, discussions and comments. This work is supported by the Danish Council for Strategic Research, in the DSF center REWIND. References [1] H. Arabian-Hoseynabadi, H. Oraee, P.J. Tavner, Failure Modes and Effects Analysis (FMEA) for wind turbines. Electrical Power and Energy Systems , 32 (2010) 817–824. [2] Y. Amirat, M.E.H. Benbouzid, E. Al-Ahmar, B. Bensaker, S. Turri, Brief status on condition monitoring and fault diagnosis in wind energy conversion systems. Renew Sust Energ Rev, 13 (2009) 2629–2636. [3] P.J. Blau, L.R. Walker, H. Xu, R.J. Parten, J. Qu, T. Geer, Wear analysis of wind turbine gearbox bearings - Final Report. Oak Ridge National Laboratory 2010. [4] K. Smolders, Y. Feng, H. Long, P. Tavner Reliability Analysis and Prediction of Wind Turbine
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