1. benchmark of bolted bearing connection models in wind turbines Athens, 1 March 2006 Marcel van Duijvendijk Alfred Kalverboer Theo de Gruiter

2. 2 bolted bearing connection pitch bearing yawbearing design driver expensive phenomena 4 models bolt strength reliable & economic connection

3. 3 physical bearing phenomena boundary conditions bending load stiffness distribution blade interaction contact angle varies with load varies along circumference ovalisation pre-stress bearings and bolts deformations contact loss between components  phenomena

4. 4 spring section model Germanischer Lloyd boundary conditions axial load cyclic symmetry contact angle balls as pressure-only springs fixed contact angle pre-stress bolts constant component contact along circumference Germanischer Lloyd Department WE spring section

5. 5 2.5D harmonic axi-symm. model Mecal FEM model and spreadsheet boundary conditions bending Load Non-axi-symmetric stiffness contact angle balls as axial springs, radial forces harmonic loading 0Ø, 1Ø and 2Ø spreadsheet for bearing behaviour up to 2Ø load dependent realistic ovalisation pre-stress bolts constant contact along circumference + 2.5D

6. 6 contact section model boundary conditions axial load cyclic symmetry contact angle balls as solids ball-raceway contact load dependent pre-stress bolts and bearing constant component contact along circum. contact section

7. 7 contact angle Upper raceway Lower raceway High load low load

8. 8 180˚ Mecal extension of contact section boundary conditions axial, bending and shear loads half symmetry assumed contact angle load dependent realistic ovalisation pre-stress bolts and bearing realistic component contact along circumference 180˚

9. 9 model comparison comparison

10. 10 relative axial bearing displacements displacements

11. 11 relative radial bearing displacements displacements

12. 12 bolt stress

13. 13 design strength reserve and costs design

14. 14 conclusion & recommendations bearing connection important reliable cost efficient 4 models different phenomena different results 2.5D is best on conservative side 180˚ model seems most promising further model development and validation required