Effects of design parameters on carrying capacity of a double-row tapered roller slewing bearing used in wind turbine

Abstract

Mechanical model with detailed design parameters of a rotor slewing bearing with the structure type of double-row tapered roller for supporting the rotor of the wind turbine was presented. The internal geometrical relationships of the rotor slewing bearing were established in the Cartesian coordinate system. The elastic contact deformations between each tapered roller and the raceways were expressed through the geometrical transformation. The mechanical model was established using the equilibrium relations in the rotor slewing bearing. The safety factor and the fatigue life which represents, respectively, the ability of resisting the rolling contact plastic deformation failure and the rolling contact fatigue failure of the rotor slewing bearing were obtained based on the solution of the mechanical model. Effects of the detailed design parameters such as axial clearance, contact angle, and roller semi-cone angle on the carrying capacity of the rotor slewing bearing were analyzed. The results show that right amount of small negative axial clearance, increase in contact angle, and decrease in roller semi-cone angle are advantageous for enhancing the carrying capacity of the rotor slewing bearing. This provides the basis for the reasonable value selection of the design parameters of the double-row tapered roller slewing bearing for supporting the rotor of the wind turbine.

Introduction

In recent years, utilization of renewable energy represented by wind power by countries around the world reached a climax. The world wind capacity reached 435 GW by the end of 2015. ¹ With the emergence of many kinds of faults of the grid connected wind turbines, reliability problem of the wind turbines becomes more and more prominent. Slewing bearings are one of the key components with the most expensive maintenance and replacement cost in the wind turbine, the reliability problem of slewing bearings used in wind turbines is becoming the focus of attention of researchers. The reasonable design of the rotor slewing bearing used in the wind turbine is based on the systemic mechanical analysis of the influencing law of the detailed design parameters on the carrying capacity.

At present, the research work of the slewing bearing used in the wind turbine mainly focused on the pitch slewing bearing or yaw slewing bearing which has the structure form of single-row or double-row four-point contact ball. Gao et al. ² established the nonlinear equations of a single-row four-point contact ball slewing bearing, the sensitivity of some design parameters of the ball, and the raceways which influence the maximum ball load and the slewing bearing service life was discussed. Chen et al. ³ developed a mechanical model of a double-row four-point contact ball slewing bearing and studied the effects of the geometric parameters on the carrying capacity of the slewing bearing. Potočnik et al. ⁴ described the internal geometrical relationship of a double-row four-point contact ball slewing bearing with vectors and established the equilibriums of the slewing bearing. Calculation of the maximum ball load and the fatigue life of the bearing were performed. Glodež et al. ⁵ established a vector-based static equilibrium model of a double-row four-point contact ball slewing bearing, and the fatigue lifetime of the slewing bearing was calculated by stress-life approach and strain-life approach. Aguirrebeitia et al. ⁶ presented a static mechanical model of a single-row four-point contact ball slewing bearing under radial load, axial load, and tilting moment load. A carrying capability surface of the slewing bearing was calculated by solving the model. Wang and Yuan ⁷ established the static mechanical model of a double-row four-point contact ball slewing bearing in the polar coordinates and analyzed the effect of negative clearance on the load distribution of the balls. Daidié et al. ⁸ presented an analysis method of single-row four-point contact ball slewing bearing based on finite element analysis software, and the balls under compression were modeled by nonlinear traction springs between the curvature centers of the raceways. Olave et al. ⁹ proposed the calculation of the ball loads in a single-row four-point contact ball bearing considering the elasticity deformation of the supporting structure based on the finite element model (FEM) analysis and an elastic calculation procedure which considered the stiffness effect of the supporting structure. Gao et al. ¹⁰ calculated the load distribution of a single-row four-point contact ball bearing using FEM which simplified the balls to the springs. Chen and Wen ¹¹ employed finite element analysis of the ball loads of the pitch slewing bearing of the wind turbine with the structure of double-row four-point contact ball and compared the results which considered the whole hub, the partial hub, and the rigid outer ring, respectively. Plaza et al. ¹² studied the load distribution of the pitch slewing bearing of the wind turbine with the structure of single-row four-point contact ball and presented a FEM using the superelements, the model significantly reduced the computational time and nearly without accuracy loss.

Compared with the asynchronous doubly fed wind turbine, the direct-drive wind turbine eliminates the gear-speed increaser, and the rotor is connected directly to a permanent magnet generator, this offers significant advantage because the gear-speed increaser is more susceptible to fail, and only one slewing bearing is needed to support the rotor of this kind of wind turbine. The double-row tapered roller slewing bearing is deemed as a suitable selection to support the rotor of direct-drive wind turbine because the design of the double-row tapered roller slewing bearing is built around the concept of zero slip which minimizes wear over long periods of operation. Related research of mechanical calculation of double-row tapered roller slewing bearing has not been previously proposed.

In the traditional description of internal geometrical relationships of the slewing bearing, a polar coordinate system is set with its origin at the bearing center in the radial plane of the slewing bearing, and the polar angle describes the azimuthal angle of rolling element along the circumference. The Z-axis is in the bearing axis direction. Polar coordinates based method only uses two axes. In this article, the internal geometrical relationship of the double-row tapered roller slewing bearing for supporting the rotor of the wind turbine was described in Cartesian coordinate system. The Cartesian coordinates based method uses three axes to describe the internal geometrical relationships of the rotor slewing bearing, which is more advantageous than the polar coordinates based method which only uses two axes. The displacements of the raceway surface at the roller contact sites after the rotor slewing bearing being loaded were represented through geometrical transformation. The mechanical model including the detailed design parameters was established using the mechanical equilibrium relations in the rotor slewing bearing. Based on the solution of the mechanical model, two carrying capacity indicators, the safety factor and the fatigue life of the rotor slewing bearing, were calculated. The influencing law of the detailed design parameters on the carrying capacity was analyzed; this provides the basis for the reasonable value selection of detailed design parameters of double-row tapered roller slewing bearing for supporting the rotor of the wind turbine.

Mechanics modeling

The mechanical model of the double-row tapered roller slewing bearing was built based on the deformation compatibility conditions and the load equilibrium conditions.

Deformation compatibility conditions

The rotor slewing bearing is mainly composed of inner ring, outer ring, and two rows of tapered rollers. The outer ring is installed on the frame of the wind turbine, and the inner ring is joined with the rotor of the wind turbine. During the operation of the wind turbine, the aerodynamic loads acting on the rotor are passed to the frame through the rotor slewing bearing. The rotor slewing bearing sustains the radial load, axial load, and tilting moment load simultaneously.

For the convenience of the description of the internal geometrical relationships of the rotor slewing bearing, set up a Cartesian coordinate system in the center of the rotor slewing bearing, as shown in Figure 1. The coordinate system has its origin at the center of the rotor slewing bearing, the X-axis is vertically upward, the Z-axis is horizontal in the bearing axis direction, and the Y-axis is horizontally sideways so that X-axis, Y-axis, and Z-axis rotate clockwise.

Figure 1.

Coordinate system of the rotor slewing bearing.

In the axial section of the rotor slewing bearing, draw two dotted lines passing the centers of two tapered rollers and perpendicular to the center line of the tapered rollers, respectively. The dotted lines intersect with the raceway surface and produce the center points of the raceway width, that is, $P_{1i}$ , $P_{1e}$ , $P_{2i}$ , and $P_{2e}$ , as shown in Figure 2. In this article, the subscripts 1 and 2 refer to the first row raceway and the second row raceway, respectively, and the subscripts $i$ and $e$ refer to the inner raceway and the outer raceway, respectively.

Figure 2.

Center points of the raceway width.

Before the rotor slewing bearing being loaded, suppose that the tapered rollers are in the ideal position. That is at each roller position, gaps between each roller and raceways are same and equal to $c$ , as shown in Figure 3.

Figure 3.

Geometrical relationships in the XOZ coordinate plane.

In the XOY coordinate plane, positions of the center point $P_{1i}$ and $P_{1e}$ are shown in Figure 4.

Figure 4.

Geometrical relationships in the XOY coordinate plane.

Use the geometrical relationship in the XOY coordinate plane and the XOZ coordinate plane, refer to Figures 3 and 4, the coordinate of each center point of each raceway can be described. At arbitrary roller azimuth angle $\psi$ on the rotor slewing bearing circumference, the coordinate of the center point $P_{1e}$ of the first row raceway of the outer ring is

$$x_{1e,\psi }=[0.5d_m+(0.5D_{\mathrm{wm}}+c)\cos \left(\frac{{\alpha }_e+{\alpha }_i}{2}\right)]\cos \psi$$

(1)

$$y_{1e,\psi }=[0.5d_m+(0.5D_{\mathrm{wm}}+c)\cos \left(\frac{{\alpha }_e+{\alpha }_i}{2}\right)]\sin \psi$$

(2)

$$z_{1e,\psi }=-0.5d_c+(0.5D_{\mathrm{wm}}+c)\sin \left(\frac{{\alpha }_e+{\alpha }_i}{2}\right)$$

(3)

where $d_m$ is the pitch diameter of the slewing bearing, $D_{\mathrm{wm}}$ is the mean diameter of the tapered roller, ${\alpha }_e$ is the contact angle of the outer raceway, ${\alpha }_i$ is the contact angle of the inner raceway, $\psi$ is the azimuthal angle of the tapered roller in the XOY coordinate plane, and $d_c$ is the distance between the centers of two row rollers along the bearing axis.

The coordinate of the center point $P_{1i}$ of the first row inner raceway is

$$x_{1i,\psi }=[0.5d_m-(0.5D_{\mathrm{wm}}+c)\cos \left(\frac{{\alpha }_e+{\alpha }_i}{2}\right)]\cos \psi$$

(4)

$$y_{1i,\psi }=[0.5d_m-(0.5D_{\mathrm{wm}}+c)\cos \left(\frac{{\alpha }_e+{\alpha }_i}{2}\right)]\sin \psi$$

(5)

$$z_{1i,\psi }=-0.5d_c-(0.5D_{\mathrm{wm}}+c)\sin \left(\frac{{\alpha }_e+{\alpha }_i}{2}\right)$$

(6)

The coordinate of the center point $P_{2e}$ of the second row outer raceway is

$$x_{2e,\psi }=[0.5d_m+(0.5D_{\mathrm{wm}}+c)\cos \left(\frac{{\alpha }_e+{\alpha }_i}{2}\right)]\cos \psi$$

(7)

$$y_{2e,\psi }=[0.5d_m+(0.5D_{\mathrm{wm}}+c)\cos \left(\frac{{\alpha }_e+{\alpha }_i}{2}\right)]\sin \psi$$

(8)

$$z_{2e,\psi }=0.5d_c-(0.5D_{\mathrm{wm}}+c)\sin \left(\frac{{\alpha }_e+{\alpha }_i}{2}\right)$$

(9)

The coordinate of the center point $P_{2i}$ of the second row inner raceway is

$$x_{2i,\psi }=[0.5d_m-(0.5D_{\mathrm{wm}}+c)\cos \left(\frac{{\alpha }_e+{\alpha }_i}{2}\right)]\cos \psi$$

(10)

$$y_{2i,\psi }=[0.5d_m-(0.5D_{\mathrm{wm}}+c)\cos \left(\frac{{\alpha }_e+{\alpha }_i}{2}\right)]\sin \psi$$

(11)

$$z_{2i,\psi }=0.5d_c+(0.5D_{\mathrm{wm}}+c)\sin \left(\frac{{\alpha }_e+{\alpha }_i}{2}\right)$$

(12)

Before the rotor slewing bearing being loaded, the distances between the center points of the inner raceway and the outer raceway at the arbitrary roller azimuth angle $\psi$ are

$$A_{1,\psi }=\sqrt{{(x_{1i,\psi }-x_{1e,\psi })}^2+{(y_{1i,\psi }-y_{1e,\psi })}^2+{(z_{1i,\psi }-z_{1e,\psi })}^2}$$

(13)

$$A_{2,\psi }=\sqrt{{(x_{2i,\psi }-x_{2e,\psi })}^2+{(y_{2i,\psi }-y_{2e,\psi })}^2+{(z_{2i,\psi }-z_{2e,\psi })}^2}$$

(14)

As the rotor slewing bearing being loaded, the outer ring is fixed in the wind turbine, and the inner ring produces the radial displacement ${\delta }_r$ along the positive direction of X-axis, axial displacement ${\delta }_a$ along the positive direction of Z-axis, and angular displacement $\theta$ around Y-axis, under the action of radial load $F_r$ , axial load $F_a$ , and tilting moment load $M$ , respectively, as shown in Figure 5.

Figure 5.

Inner ring displacements.

Thus, the positions of the centers of the inner ring raceway change correspondingly. According to the principle of geometrical transformation, the coordinate of the center point $P_{1i}$ of the first row inner raceway is ¹³

$$\left[\begin{array}{c}\hfill {x\prime }_{1i}\hfill \\ \multicolumn{1}{c}{{y\prime }_{1i}}\\ \multicolumn{1}{c}{{z\prime }_{1i}}\\ \multicolumn{1}{c}{1}\end{array}\right]=\left[\begin{array}{cccc}\hfill \cos \theta \hfill & \hfill 0\hfill & \hfill \sin \theta \hfill & \hfill {\delta }_r\hfill \\ \multicolumn{1}{c}{0}& \hfill 1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \multicolumn{1}{c}{-\sin \theta }& \hfill 0\hfill & \hfill \cos \theta \hfill & \hfill {\delta }_a\hfill \\ \multicolumn{1}{c}{0}& \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \end{array}\right]·\left[\begin{array}{c}\hfill x_{1i}\hfill \\ \multicolumn{1}{c}{y_{1i}}\\ \multicolumn{1}{c}{z_{1i}}\\ \multicolumn{1}{c}{1}\end{array}\right]$$

(15)

Using the same geometrical transformation method, the coordinate $(x{\prime }_{2i},y{\prime }_{2i},z{\prime }_{2i})$ of the center point $P_{2i}$ of the second row inner raceway can be obtained.

After the rotor slewing bearing being loaded, the distances between the center points of the inner raceway and the outer raceway at arbitrary roller azimuth angle $\psi$ are

$$A{\prime }_{1,\psi }=\sqrt{{({x\prime }_{1i,\psi }-x_{1e,\psi })}^2+{({y\prime }_{1i,\psi }-y_{1e,\psi })}^2+{({z\prime }_{1i,\psi }-z_{1e,\psi })}^2}$$

(16)

$$A{\prime }_{2,\psi }=\sqrt{{({x\prime }_{2i,\psi }-x_{2e,\psi })}^2+{({y\prime }_{2i,\psi }-y_{2e,\psi })}^2+{({z\prime }_{2i,\psi }-z_{2e,\psi })}^2}$$

(17)

According to the geometrical relationship in Figure 3, the elastic contact deformations between the tapered roller and the raceways along $P_{1e}{P}_{1i}$ direction caused by the distance change between the inner raceway and the outer raceway are

$${\delta }_{1,\psi }=A_{1,\psi }-A{\prime }_{1,\psi }-2c$$

(18)

$${\delta }_{2,\psi }=A_{2,\psi }-A{\prime }_{2,\psi }-2c$$

(19)

where $c=((\sin {\alpha }_e\sin {\alpha }_i)/(2\cos \varphi (\sin {\alpha }_e+\sin {\alpha }_i)))G_a$ and $G_a$ is the axial clearance of the rotor slewing bearing.

According the internal geometrical relationship of the rotor slewing bearing, the elastic contact deformations between the roller and the raceways along the normal direction of the outer raceway are

$${\delta }_{1n,\psi }={\delta }_{1,\psi }\cos \varphi$$

(20)

$${\delta }_{2n,\psi }={\delta }_{2,\psi }\cos \varphi$$

(21)

where $\varphi$ is the semi-cone angle of the tapered roller.

According to Hertz contact theory, the relationship between the roller load $Q_e$ from the outer raceway and the elastic contact deformation ${\delta }_n$ can be represented as ¹⁴

$$Q_e=\{\begin{array}{cc}\hfill K_{\mathrm{ne}}{\delta }_n^{1.11}\hfill & \hfill {\delta }_n>0\hfill \\ \multicolumn{1}{c}{0}& \hfill {\delta }_n\le 0\hfill \end{array}$$

(22)

where $K_{\mathrm{ne}}$ is the load–deflection contact factor between the tapered roller and the outer raceways. ¹⁵ So the contact loads $Q_{1e,\psi }$ and $Q_{2e,\psi }$ between the roller and the outer raceway at arbitrary roller azimuthal angle $\psi$ can be obtained using equation (22).

Load equilibrium conditions

The entirety composed of the rollers and the inner ring of the rotor slewing bearing is at an balancing state under the external load $F_r$ , $F_a$ , $M$ , and all roller normal loads $Q_{e1,\psi }$ and $Q_{e2,\psi }$ applied by the outer raceway, the equilibrium equations can be obtained as following

$$F_r-\sum _{\psi =-\pi }^{\psi =+\pi }(Q_{1e,\psi }+Q_{2e,\psi })\cos {\alpha }_e\cos \psi =0$$

(23)

$$F_a-\sum _{\psi =-\pi }^{\psi =+\pi }(Q_{1e,\psi }-Q_{2e,\psi })\sin {\alpha }_e=0$$

(24)

$$M-\frac{1}{2}{d}_m[\sum _{\psi =-\pi }^{\psi =+\pi }(Q_{1e,\psi }-Q_{2e,\psi })]\sin {\alpha }_e\cos \psi =0$$

(25)

Equations (23)–(25) constitute a system of nonlinear equations with ${\delta }_r$ , ${\delta }_a$ , and $\theta$ as unknown variables. If the design parameters and the external loads of the rotor slewing bearing are given, the nonlinear equations can be solved using the Newton–Raphson iteration method, and the load $Q_e$ between each roller and outer raceways can be calculated further using equations (13)–(23).

Load analysis for the tapered roller

The tapered roller sustains three loads: they are the normal load from the inner raceway, the normal load from the outer raceway, and end surface load from the guide flange of the inner ring. Suppose the load between the roller and inner raceway, outer raceway, guide flange is $Q_i$ , $Q_e$ , $Q_f$ , respectively, and the corresponding contact angle of each load is ${\alpha }_i$ , ${\alpha }_e$ , ${\alpha }_f$ , respectively, as shown in Figure 6.

Figure 6.

Loads of the tapered roller.

For static equilibrium, the sum of loads in the vertical direction and the horizontal direction is equal to zero, respectively, that is

$$Q_e\sin {\alpha }_e-Q_i\sin {\alpha }_i-Q_f\sin {\alpha }_f=0$$

(26)

$$Q_e\cos {\alpha }_e-Q_i\cos {\alpha }_i+Q_f\cos {\alpha }_f=0$$

(27)

In the above two equilibrium equations, the following can be obtained by eliminating $Q_f$

$$Q_i=\frac{\sin ({\alpha }_e+{\alpha }_f)}{\sin ({\alpha }_i+{\alpha }_f)}{Q}_e$$

(28)

So load $Q_i$ can be calculated according to the load $Q_e$ using equation (28).

Carrying capacity

Two carrying capacity indicators, that is the safety factor and the fatigue life which represents, respectively, the ability of resisting the rolling contact plastic deformation failure and the rolling contact fatigue failure of the slewing bearings are usually used as their design basis.

Safety factor

The rotor slewing bearing in the wind turbine sustains the action of impact loads during operation. Oversize impact loads will cause the permanent plastic deformation of the raceways at the contact sites between the tapered rollers and the raceways. This kind of deformation may affect the running performance of the rotor slewing bearings. According to the test results of Shen et al., ¹⁶ the maximum contact stress between the roller and the raceway surface of the slewing bearing made by the material of 42CrMo should be limited to 3300 MPa. This stress value is used as the allowable contact stress between the roller and the raceway. According to contact mechanics theory, the calculating formula of contact stress between the roller and the raceway is ¹⁴

$$\sigma =190.6{\left(\frac{Q\sum \rho }{L_w}\right)}^{\frac{1}{2}}$$

(29)

where $Q$ is the roller load, $\sum \rho$ is the curvature sum of the contact between the roller and the raceway, and $L_w$ is the length of the roller.

Consider the most loaded roller with the load $Q_{max}$ , the maximum contact stress ${\sigma }_{max}$ between this roller and the raceway can be calculated. Then, the safety factor $f_s$ of the rotor slewing bearing can be calculated as

$$f_s={\left(\frac{[\sigma ]}{{\sigma }_{max}}\right)}^2$$

(30)

where $[\sigma ]$ is the allowable contact stress.

Fatigue life

The basic dynamic load ratings, dynamic equivalent roller loads, and roller load distributions are needed to calculate the fatigue life of the slewing bearing. The basic dynamic load ratings depend on the design parameters of the rotor slewing bearing, while the dynamic equivalent roller loads and the roller load distributions depend on the external loads carried by the slewing bearing. The basic dynamic load rating of the inner raceway and the outer raceway can be calculated using the design parameters of the slewing bearing. The dynamic equivalent roller load on the inner raceway and the outer raceway can be calculated using the calculated roller loads. The fatigue life of inner raceway of each row can be calculated by the following ¹⁴

$$L_{10i}={\left(\frac{Q_{\mathrm{ci}}}{Q_{e\mu }}\right)}^4$$

(31)

where $Q_{\mathrm{ci}}$ is the basic dynamic load rating of the inner raceway and $Q_{e\mu }$ is the dynamic equivalent on the inner raceway.

The fatigue life of outer raceway of each row can be calculated by the following

$$L_{10e}={\left(\frac{Q_{\mathrm{ce}}}{Q_{\mathrm{ev}}}\right)}^4$$

(32)

where $Q_{\mathrm{ce}}$ is the basic dynamic load rating of the outer raceway and $Q_{e\nu }$ is the basic dynamic equivalent on the outer raceway.

Then, the fatigue life of the rotor slewing bearing is

$$L_{10}={(L_{10i1}^{-9/8}+L_{10e1}^{-9/8}+L_{10i2}^{-9/8}+L_{10e2}^{-9/8})}^{-\frac{8}{9}}$$

(33)

Based on the calculated roller loads $Q_i$ and $Q_e$ , the safety factor and the fatigue life of the rotor slewing bearing can be calculated, respectively.

Effect of the design parameters on the carrying capacity

The rolling between the tapered roller and the raceway of the tapered roller slewing bearings is zero slip. The precondition to achieve zero slip is that the generating lines of all tapered rollers and the raceway cones, and the bearing axis intersect with the same point. As designing the double-row tapered roller slewing bearings, design space dimensions (i.e. inside diameter, outside diameter, and width) are given first, detailed design parameters such as clearance (preloaded), contact angle, and roller semi-cone angle need to be determined.

The slewing bearing to be analyzed in this article is a rotor slewing bearing in certain type of 2.0 MW direct-drive wind turbine. During operation, the external loads of the rotor slewing bearing are calculated using bladed wind turbine simulation tool, ¹⁷ as shown in Table 1.

Table 1.

Working condition.

External loads		Value
Extreme loads	Radial load, Fr (kN)	618
	Axial load, Fa (kN)	244
	Tilting moment load, M (kN m)	5670
Fatigue loads	Radial load, Fr (kN)	122
	Axial load, Fa (kN)	45
	Tilting moment load, M (kN m)	1072

The given design space dimensions are as follows: the outside diameter is 2330 mm, the inside diameter is 1890 mm, and the width is 285 mm. According to these given dimensions, the preliminary design parameters of the rotor slewing bearing were determined as shown in Table 2. Based on these preliminary design parameters, select possible values of the detailed parameters such as clearance (preloaded), contact angle, and roller semi-cone angle that meet the zero slip design principle. The effect of these parameters on the safety factor and the fatigue life of the rotor slewing bearing were analyzed, so as to provide the basis for the reasonable value selection of these design parameters.

Table 2.

Preliminary design parameters.

Preliminary parameter	Value
Bearing pitch diameter, $d_m$ (mm)	2030
Two row rollers axial distance, $d_c$ (mm)	120
Inner raceway contact angle, ${\alpha }_i$ (°)	43
Outer raceway contact angle, ${\alpha }_e$ (°)	45
Guide flange contact angle, ${\alpha }_f$ (°)	47
Roller length, $L_w$ (mm)	80
Mean diameter of tapered roller, $D_{\mathrm{wm}}$ (mm)	51
Roller semi-cone angle, $\varphi$ (°)	1
Roller number, $Z$	116

Effect of the clearance

The effect of the axial clearance $G_a$ on the carrying capacity of the rotor slewing bearing is shown in Figure 7. As observed from the results, effect trends of clearance change on the safety factor and the fatigue life of the rotor slewing bearing are roughly consistent. As observed from Figure 7(a), as the axial clearance increases from −0.1 to 0.6, the safety factor of the slewing bearing decreases slowly. As the axial clearance decreases from −0.1 to −0.4 toward the negative direction (preload increases), the safety factor of the rotor slewing bearing decreases rapidly. Maximum safety factor appears as the axial clearance equals to −0.1.

Figure 7.

Effect of clearance on the carrying capacity: (a) effect on the safety factor and (b) effect on the fatigue life.

As observed from Figure 7(b), as axial clearance increases from −0.0125 to 0.6, the fatigue life of the rotor slewing bearing decreases slowly. As the axial clearance decreases from −0.0125 to −0.4 toward the negative direction (preload increases), the fatigue life of the rotor slewing bearing decreases rapidly. Especially smaller the negative clearance is, more obvious this trend is. Maximum fatigue life appears as the axial clearance is near zero and slightly less than zero.

The effect of the axial clearance on the carrying capacity of the rotor slewing bearing can be attributed to the fact that increase or decrease in the clearance changes the roller load distribution. As the axial clearance increases, the rollers sustaining external loads become less and less, roller loads increase with it too, so the safety factor and the fatigue life decrease with it. From this perspective, smaller clearance is more advantageous to the rotor slewing bearing. As the axial clearance decreases toward the negative direction, the roller preloads increase with it, and the roller loads increase with it too, so the safety factor and the fatigue life decrease with it. From this perspective, bigger negative clearance is more disadvantageous to the rotor slewing bearing.

Effect of the contact angle

The effect of contact angle ${\alpha }_e$ on the carrying capacity of the rotor slewing bearing is shown in Figure 8.

Figure 8.

Effect of contact angle on the carrying capacity: (a) effect on the safety factor and (b) effect on the fatigue life.

As observed from the results, effect trends of the contact angle change on the safety factor and the fatigue life of the rotor slewing bearing are roughly consistent. As the contact angle increases from 40° to 60°, the safety factor and the fatigue life of the rotor slewing bearing increase with it. The increase in the contact angle causes the component $Q_e\sin {\alpha }_e$ of the roller load along the bearing axis increases with it, and the component $Q_e\sin {\alpha }_e$ is the load component for balancing the external axial load and the tilting load. Therefore, for slewing bearing that mainly sustains axial load and tilting moment load, the increase in the contact angle will cause the decrease in the roller loads, so the safety factor and the fatigue life of the slewing bearing increase with it.

Effect of the semi-cone angle

The effect of the semi-cone angle $\varphi$ of the tapered roller on the carrying capacity of the rotor slewing bearing is shown in Figure 9. As observed from the results, effect trends of the change of the semi-cone angle $\varphi$ of the tapered roller on the safety factor and the fatigue life of the rotor slewing bearing are roughly consistent. As the roller semi-cone angle increases from 50′ to 1°20′, the safety factor and the fatigue life of the rotor slewing bearing decrease with it slowly. With the increase in the roller semi-cone angle, the large end diameter of the tapered roller increases with it. In the given design space, the number of the tapered roller declines rapidly. So the loads apportioned to each tapered roller increase, the safety factor and the fatigue life of the rotor slewing bearing decrease with it.

Figure 9.

Effect of semi-cone angle on the carrying capacity: (a) effect on the safety factor and (b) effect on the fatigue life.

Conclusion

In this article, the internal geometrical relationships of a rotor slewing bearing in wind turbine were described in Cartesian coordinate system; this is different from the traditional description of internal geometrical relationships of the slewing bearing in the polar coordinates. The geometrical relationships of all raceways are described as a unified form by this means; this makes the calculating model neater and more convenient for computer programming. Mechanical model with detailed design parameters was established using the equilibrium relations in the rotor slewing bearing. Effect laws of the detailed design parameters such as axial clearance, contact angle, and roller semi-cone angle on the carrying capacity of the rotor slewing bearing were analyzed.

As the axial clearance increases toward the positive direction, the safety factor and the fatigue life of the rotor slewing bearing decrease slowly. As the axial clearance decreases toward the negative direction (preload increases), the safety factor and the fatigue life of the rotor slewing bearing decrease rapidly. As the contact angle increases from 40° to 60°, the safety factor and the fatigue life of the slewing bearing increase with it. As the roller semi-cone angle increases from 50′ to 1°20′, the safety factor and the fatigue life of the slewing bearing decrease with it slowly. These results demonstrate that right amount of small negative axial clearance, increase in the contact angle, and decrease in the roller semi-cone angle are advantageous for enhancing the carrying capacity of rotor slewing bearing used in wind turbine.