Figure 1. shows a generalized HUB for the wind turbine. This is a simple model which has been created by ALDOTT and simplified in order to show the Hub strength FEM calculation procedure.

### Utilization of Coordinate Systems to apply the customized ball bearing loads as MACRO to the bearing rings

In the HUB there are 3 blade root connection flanges. In general, the HUB is connected to blades by ball bearings. Therefore, the proper load distributions at the bearing rings are crucial for the HUB extreme strength calculations since three blade root connections make much more complex load distributions on the HUB itself. In this example ALDOTT uses blade root coordinate system to implement sinusoidal radial and axial direction forces. You can find cylindrical coordinate system at each blade root from FIGURE 3 to FIGURE 5. Although the pitch moment loads from pitch drive and blades are not main dimensional loads for HUB, ALDOTT considered them to show the way how to utilize them for extreme strength calculation and they are shown from FIGURE 6 to 8.

### Mesh

The maximum equivalent stress like von-Mises stress has occurred at the outer surface of components. Therefore, hexagonal meshes on the surface give much better results than tetrahedral mesh on the solid body according to FEM theory. ALDOTT uses HEX-DOMINANT mesh scheme of which all outer surfaces of the solid body are composed of hexagonal and internal rest of body has tetrahedral meshes.

Bearing loads MACRO at pitch bearing rings

!****************************************************************** ! The SAMPLE of EXTREME load MACRO !******************************************************************

/PREP7 *AFUN,RAD CSYS,0

CONTACT_ANG= 45 ! maximum loading distribution angle in the ball bearings(o)

PI=4*ATAN(1) !***************************************************** ! EXTREME Load MINIMUM MY at blade 2 !***************************************************** !BLADE 1

MX_1=500e6

MY_1=40e6

FX_1=8e3

FY_1=-50e3

FZ_1=160e3 !******************************************* !BLADE 2

MX_2=-230e6

MY_2=-1050e6

FX_2=-70e3 FY_2=20e3 FZ_2=200e3

!******************************************** !BLADE 3

MX_3=-100e6

MY_3=70e6

FX_3=7e3 FY_3=20e3 FZ_3=160e3

!******************************************** ! MAIN LOADING MACROS !********************************************

*DO,f,1,3,1 CMSEL,S,FLANGE%i%

CSYS,199+i MX=MX_%i%

MY=MY_%i%

FX=FX_%i% FY=FY_%i% FZ=FZ_%i%

*GET,NODE_TOT,NODE,,COUNT *GET,NMIN,NODE,,NUM,MIN

PCD = NX(NMIN)

. . . . .

/SOLU SOLVE FINISH /EOF

### Ball bearing loads

Below FIGURE 10 and 11 show the bearing load distributions on the bearing rings in case above full MACRO which has been developed by ALDOTT is working on the model. The MACRO from ALDOTT gives much more precise bearing load distributions as shown in the below models and gives the chance to get the more reliable stress results on the HUB calculations.