Load Analysis of pitch bearing considering nonquenching zone
J. X. Gui^{1} , G. B. Wang^{2} , Z. Zhou^{3}
^{1, 2}Hunan Provincial Key Laboratory of Mechanical Equipment Health, Xiangtan, China
^{3}XemcWind Co., Ltd., Xiangtan, China
^{1}Corresponding author
Vibroengineering PROCEDIA, Vol. 25, 2019, p. 712.
https://doi.org/10.21595/vp.2019.20704
Received 31 March 2019; accepted 21 April 2019; published 25 June 2019
39th International Conference on Vibroengineering in St. Petersburg, Russia, June 2526, 2019
The pitch bearing of the MWclass wind turbine has a weak zone which is not quenched. In the complicated service environment of the wind turbine, the pitch bearing often has breakage accidents in the nonquenching zone. Firstly, this paper takes the pitch bearing as the object and establishes the pitch bearing model with weak zone. Subsequently, the load variation law of the pitch bearing considering nonquenching is analyzed in the four extreme conditions. Finally, the feasibility of the model is proved by comparing the simulation data with the data obtained from the theoretical formula.
Keywords: pitch bearing, nonquenching zone, static analysis, load distribution.
1. Introduction
The pitch bearing is an important part of the MWclass wind turbine, and the heat treatment process of the raceway surface is usually quenching. However, the trajectory of the heating head on the raceway cannot overlap (because secondary quenching can lead to cracks), a weak zone will be formed in the non quenching zone. When the product leaves the factory, the position of the weak zone on the workpiece will be marked with the word “$S$” to indicate the specific weak zone position.
In the current literature, the research on the failure mechanism of the weak zone of the wind turbine pitch bearing is still rare, and more concentrated on the analysis of the mechanical properties and bearing capacity of the pitch bearing without considering the weak zone of the bearing. In foreign studies, Zupan and Prebil studied the effects of initial contact angle, tightness, clearance value and the stiffness of the support structure on the bearing capacity of the bearing and the actual contact angle [1]. Aguirrebeitia established a mathematical model for carrying capacity of bearing [2]. Alain Daidié analyzed the distribution of contact forces experienced by rolling elements under different loads [3]. In the domestic research, Li Y. F. gave the suggestions for the selection of the parameters of the largescale pitch bearing [4, 5]; Wang H. used the finite element method to calculate the friction torque of single and double pitch bearings respectively [6]; Mao X. N. verified the strength of the pitch bearing under ABAQUS [7]. In these studies, the influence of the weak zone of the bearing was automatically ignored during the mechanical modeling, and the structural strength and load characteristics of the weak zone were not investigated as the influencing factors during the mechanical analysis.
Therefore, this paper will study the load analysis of pitch bearing considering weak zone.
2. Empirical formula
The maximum contact load calculated by empirical formula is still the main form of design analysis of pitch bearings for most pitch bearing manufacturers at present [8].
When the angular contact radial ball bearing or thrust, bearing is subjected to pure axial force:
When the ball bearing is subjected to pure radial force:
When the twoway thrust ball bearing is subjected to the overturning moment:
The pitch bearing is generally subjected to the combined action of the above three loads. According to the characteristics of the pitch bearing structure itself, the empirical formula of the maximum contact load of the pitch bearing subjected to the combined action of three loads is:
In the formula, the ${F}_{a}$ is axial force, the ${F}_{r}$ is radial force and the M is the overturning moment; the ${D}_{w}$ is diameter of the bearing pitch circle; the $Z$ is number of rolling elements; the $\alpha $ is contact angle.
The design parameters of a pitch bearing are shown in the Table 1.
Table 1. A pitch bearing design parameter
Parameter  Data 
Diameter of outer race mounting hole distribution circle ${D}_{1}$ / mm  2000 
Nominal bore diameter $d$ / mm  1716 
Diameter of rolling element center circle ${D}_{m}$ / mm  1900 
Diameter of inner race mounting hole distribution circle ${d}_{1}$ / mm  1800 
Nominal outer diameter $D$ / mm  2080 
Rolling body diameter ${D}_{w}$ / mm  45 
Inner channel radius of curvature ${r}_{i}$ / mm  23.625 
Outer channel radius of curvature ${r}_{e}$ / mm  23.625 
Ditch row spacing ${D}_{c}$ / mm  80 
Number of mounting holes $N$  54 
Number of rolling elements $Z$  2×120 
Initial contact angle $\alpha $ / (°)  45 
3. Calculation of bearing weak zone by finite element
3.1. Establishment of weak zone model
The hardness of the pitch bearing weak zone is generally around 35 HRC, which is lower than the hardness range of 5562 HRC in the quenching zone, thus it becomes the weakest zone in the pitch bearing. Looking over the hardness and tensile strength table, the common material elastic modulus, Poisson’s ratio comparison table can get the data in the Table 2.
Table 2. Material properties of various parts of pitch bearings
Part  Elastic modulus $E$ (Pa)  Poisson’s ratio $\mu $  tensile strength (MPa) 
Quenching zone  2.12e+011  0.3  2180 
Weak zone  2.00e+011  0.28  1125 
The Fig. 1 shows the finite element analysis geometry model and the physical model of the pitch bearing (without weak zone).
For the establishment of the weak zone of the pitch bearing, the quenching zone and the nonquenching zone are distinguished by establishing a different zone, and then the parameters are set in the material library of the ANSYS WORKBENCH to define the material properties, and the pitch bearing is established (including weak zone) as shown in Fig. 2.
Fig. 1. Pitch bearing (without weak zone)
a) Geometric model
b) Physical model
Fig. 2. Pitch bearing (with weak zone)
Fig. 3. Detail of meshing
3.2. Meshing of weak area
This paper selects the automatic division method. If the geometry cannot be swept, the program automatically generates a tetrahedron, and vice versa produces a hexahedron [9]. Meshing produces a total of 188,054 cells and 355,992 nodes, as shown in Fig. 3.
3.3. Load boundary condition
The pitch bearings are an important part of the wind turbine pitch system. Its outer ring is fixed to the hub, and the inner ring is connected to the blade. According to the actual working condition of the bearing, the outer ring is completely restrained, and the axial load, radial load and overturning moment are applied to the bearing.
The following are the various external loads acting on the pitch bearing under four extreme conditions [10].
Table 3. External load under extreme conditions
Design load condition (DLC)  ${F}_{a}$ (KN)  ${F}_{r}$ (KN)  $M$ (KN·m) 
Extreme running gust  3599  725  942.13 
Extreme turbulence fatigue model  1764  1418  2155.28 
Extreme wind speed model  –252  999  1297.97 
Extreme wind shear model  2053  1418  2210.64 
3.4. Contact pair setting
In this paper, a total of 960 contact pairs need to be defined, as shown in Fig. 4. In these contact pairs, the surface of the steel ball serves as a contact surface, and the four raceway surfaces serve as target surfaces.
Fig. 4. Contact pair setting
3.5. Simulation result of finite element
From the Eqs. (1)(4), the force of the pitch bearing under various working conditions can be obtained, as shown in the Table 4.
The figure below shows the results of finite element calculation.
Table 4. Theoretical load
Working condition  Theoretical value (KN)  Theoretical maximum contact load (MPa) 
Extreme running gust  41.439  1413.26 
Extreme turbulence fatigue model  53.843  1836.29 
Extreme wind speed model  26.390  900.02 
Extreme wind shear model  56.233  1917.80 
Fig. 5. Load on pitch bearing in the first condition
a) Overall load
b) Partial load
Fig. 6. Load on pitch bearing in the second condition
a) Overall load
b) Partial load
Fig. 7. Load on pitch bearing in the third condition
a) Overall load
b) Partial load
Fig. 8. Load on pitch bearing in the fourth condition
a) Overall load
b) Partial load
4. Result analysis
Table 5 shows the deviation of the finite element solution and the theoretical solution. It is easy to see that the error between the finite element value and the theoretical value is less than 5 %.
Table 5. Deviation between theoretical value and simulated value
Working condition  Theoretical maximum contact load (MPa)  Finite element maximum contact load (MPa)  Deviation (%) 
Extreme running gust  1413.26  1394.0  1.4 
Extreme turbulence fatigue model  1836.29  1749.3  4.7 
Extreme wind speed model  900.02  867.92  3.5 
Extreme wind shear model  1917.80  1960.6  2.2 
5. Conclusions
1) Results of the finite element and the theoretical value of the empirical formula have a good consistency.
2) According to the comparative analysis of Figs. 58, the contact stress at the weak zone of the pitch bearing is larger than the contact stress of the quenching zone. The maximum contact stress is at the contact point between the bottom end and the inner and outer raceways. Moreover, under different working conditions, the load distribution law of the bearing weak zone is also different. Therefore, in the actual installation process, the bearing weak zone should be kept away from the force zone.
3) The simulation analysis of the bearing’s weak zone is a very complicated project. This paper only performs a simple load analysis on the weak zone of the pitch bearing. In the next studies, the bearing capacity and fracture mechanism of pitch bearings with weak zones became an urgent problem to be solved.
Acknowledgements
Financial support from National Natural Science Foundation of China (51575178), financial support from Hunan Natural Science Foundation of China (2018JJ2120).
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