benchmark of

bolted bearing connection models in

wind turbines

Athens, 1 March 2006

Marcel van DuijvendijkAlfred Kalverboer

Theo de Gruiter

2

bolted bearing connection

• pitch bearing• yaw bearing

• 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

Microsoft Office Excel Worksheet

+

2.5D

6

11contact 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 loadlow 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 comparisoncomparison

phenomena

boundary conditions

axial force ++ ++ ++ ++ ++bending moment + ++ ++shear load ++ ++varying stiffness + ++ ++blade interaction ++load dependent ++ ++ ++ ++ovalisation + ++ ++bearing pre-stress ++ ++ ++realistic comp. contact +/- +/- +/- ++ ++

speed calculation speed ++ +/- ++ - ++

pre-stress

contact angle

boundary conditions

10

relative axial bearing displacementsdisplacements

0%

20%

40%

60%

80%

100%

120%

0.0% 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% 70.0% 80.0% 90.0% 100.0%

measurements spring section 2.5D contact section 180 degrees

11

relative radial bearing displacementsdisplacements

0%

20%

40%

60%

80%

100%

-100.0% -80.0% -60.0% -40.0% -20.0% 0.0% 20.0% 40.0% 60.0% 80.0% 100.0%

Measurements spring section 2.5D contact section 180 degrees

12

bolt stressbolt stress

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

-100.0% -80.0% -60.0% -40.0% -20.0% 0.0% 20.0% 40.0% 60.0% 80.0% 100.0%

spring section 2.5D Contact section 180 degrees

13

design strength reserve and costsdesign

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

fatigue extreme

Spring section 2.5D Contact section

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