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

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

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 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 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 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 contact angle Upper raceway Lower raceway High load low load

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 model comparison comparison

10 relative axial bearing displacements displacements

11 relative radial bearing displacements displacements

12 bolt stress

13 design strength reserve and costs design

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