Determination of Preload of Double-Row Tapered Roller Bearing Used for Supporting Direct-Drive Wind Turbine Rotor

Appropriate axial preload is necessary for the double-row tapered roller bearing used for supporting the rotor of the direct-drive wind turbine; its function is to ensure the rolling motions of the rollers and the long fatigue life of the bearing as far as possible. For this purpose, statics model of the preloaded bearing under the combined action of radial load, axial load and tilting moment load was established firstly; then, for a set of selected preload values which are different proportions of the dynamic equivalent axial load of the external bearing loads, the corresponding loaded roller number, maximum roller load and bearing fatigue life were obtained; thirdly, the effects of different preloads on the calculated indicator values were analyzed, result show that preload can improve the uneven load distribution among the rollers, the preload value also influence the rolling roller number and bearing fatigue life. A preload of 0.5 times of the dynamic equivalent axial load was selected as a trade-off between the rolling roller number and bearing fatigue life.


Introduction
In spite of the global economic depression, the worldwide wind capacity reached 254000 MW by the end of June 2012, out of which 16546 MW were added in the first six months of 2012 (World Wind Energy Association, 2012).The reliability of wind turbines has attract more and more attention from the researcher, bearings are the key components of wind turbines, they need to be pay more attention as they have higher costs associated with repair or replacement (Kotzalas & Doll, 2010).In recent years, some research work of the mechanics problems of slewing bearing used for wind turbine have been conducted by the researchers.Such as the calculation of the static load-carrying capacity of four-contact-point slewing bearings used for the pitching system and yawing system of wind turbine (Aguirrebeitia, Plaza, Abasolo, & Vallejo, 2013), the contact fatigue damage of hardened layer of bearing raceway used for the yaw system in wind turbine, this problem was solved by constructing the nonlinear material constitutive equation of hardened layer (Niu, Yang, & Gao, 2013), and the effect of local structure change on the fatigue life of yaw slewing bearing of wind turbine, this problem was analyzed by the FEM software (Feng, Chen, Huang, & Wang, 2013), all the present work mainly aimed at the slewing bearings used for the pitching system and yawing system of the double-fed induction wind turbine.
Direct-drive wind turbine is a new turbine architecture which has been developed in recent years, this kind of wind turbine eliminate the gearbox and connect the rotor directly to a permanent magnet generator.Direct-drive wind turbine offers significant potential because they eliminate the gear-speed increaser, which is susceptible to significant accumulated fatigue torque loading, related reliability issues, and maintenance costs (Bywaters et al., 2007).
The rotor of direct-drive wind turbine is supported by one set of slewing bearing.Double-row tapered roller bearing is deemed as a more suitable selection to support the rotor of direct-drive wind turbine (Lucas & Pontius, 2005), because this kind of bearing can carry the combined actions of radial load, axial load and tilting moment load; and their design is built around the concept of zero slip which minimizes wear over long periods of operation; especially their load distribution among the rollers can be optimized to avoid load losing or exceeding of some rollers through appropriate axial preload.The cross section of double-row tapered roller bearing is shown in Figure1.In the direct-drive wind turbine, the outer ring of the bearing is connected to the nacelle main   ing.As the be sis, subscript " the nacelle.Where, d c is the axial distance between two row roller centers.The axial displacement at the position of jth roller produced by the tilting angular displacement θ is Where, d m is the pitch diameter of the bearing.The radial displacement at the position of each roller is produced by the radial displacementδ r and the tilting angular displacement θ.According to Equation (10) and Equation ( 11), the total radial displacement at the position of jth roller is For the axial displacement at the position of each roller, in addition to the axial displacement produced by the axial displacementδ a and the tilting angular displacement θ, the axial displacement produced by the axial displacementδ a0 should be also considered.Then, the total axial displacement at the position of jth roller is Then, the total displacement at the position of jth roller along the normal direction of the outer raceway is

Displacement of Each Roller Position of Nacelle Side Row
According to the same principle as above, for the nacelle side row rollers, the axial displacement at the position of jth roller produced by the axial displacementδ a is equal to -δ a .
The total radial displacement at the position of jth roller is Similarly, the total axial displacement at the position of jth roller is The total displacement at the position of jth roller along the normal direction of the outer raceway contact is

Equilibrium Equations of "Roller-Inner Ring" Isolated Body
Substituting Equation (15) and Equation ( 18) into Equation ( 6) respectively, the expressions of normal load Q e1(j) and Q e2(j) between the two row rollers and the outer raceway can be obtained, where, j=1,2,3,…,Z.
In the radial direction of the bearing, the equilibrium equation of the "roller -inner ring" isolated body under the actions of external radial load r F and normal Q e1(j) and Q e2(j) is In the axial direction of the bearing, the equilibrium equation of the "roller -inner ring" isolated body under the actions of external axial load a The normal load Q e1(j) acting on the rollers by the outer raceway will produce moment actions on the "roller-inner ring" isolated body.One part of them is the moment produced by the axial component of load Q e1(j) on the bearing center, another part of them is the moment produced by the radial component of load Q e1(j) on the bearing center.The equilibrium equation of the "roller-inner ring" isolated body under the actions of the two part moments and external tilting moment load M is A system of nonlinear equations can be obtained by using the above three equilibrium Equations ( 19)-( 21).If the design parameters of the bearing are given, the values of unknown variable δ r , δ a and θ can be solved corresponding a set of axial preload F a0 and external loads F r , F a and M, and the roller loads can be calculated www.ccsen further.

Exampl
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Figure
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