DOI: 10.5545/sv-jme.2024.1239 231
© The Authors. CC BY 4.0 Int. Licencee: SV-JME  Strojniški vestnik - Journal of Mechanical Engineering   ▪   VOL 71   ▪   NO 7-8   ▪  Y 2025
Comprehensive Performance Evaluation of Sliding-
bearing Wind Turbine Gearboxes
Yao Li
1
  – Longsheng Li
1
 – Gaoxiang Ni
1
 – Xinlong Li
1
  – Jianjun Tan
2
 – Kongde He
1
1 College of Mechanical & Power, China Three Gorges University, China
2 State Key Laboratory of Mechanical Transmission for Advanced Equipment, Chongqing University, China
 yao_li_@outlook.com, Xinlongl@163.com
Abstract Considering the structural characteristics and multi-source excitations of sliding-bearing wind turbine gearboxes, this study constructs a multi-body 
dynamic model of high-power sliding-bearing wind turbine gearboxes. A comprehensive performance evaluation methodology is proposed, integrating the 
analytic network process (ANP) with an improved fuzzy comprehensive evaluation (IFCE). A multidimensional comprehensive performance evaluation framework, 
emphasizing the practicality and cost-effectiveness is developed consisting of target, criterion, and indicator layers. The key evaluation indicators identified 
within this framework include the main shaft bearing support force, transmission system reliability, load-sharing coefficient, vibration characteristics, and power 
density. Utilizing ANP and IFCE methodologies the comprehensive performance of two sliding-bearing wind turbine gearboxes is systematically assessed.
Keywords  sliding-bearing wind turbine gearbox, comprehensive performance evaluation, multidimensional evaluation indicators, analytic network process, 
fuzzy comprehensive evaluation
Highlights
 ▪ A rigid-flexible coupling multi-body dynamics model for a high-power sliding-bearing of wind turbine gearboxes (WTGs) is established.
 ▪ Comprehensive performance evaluation indicators, consisting of 5 primary and 13 secondary indicators, are proposed.
 ▪ Introduced a comprehensive performance evaluation ANP–IFCE-based method to evaluate WTG performance, focusing on cost and practicality.
1 INTRODUCTION
Planetary gear trains offer significant advantages, including high-
power density, large transmission ratio, and compact structure, making 
them widely used in wind turbine gearboxes. Traditionally, planetary 
gear trains often use rolling bearings as supports. However, as wind 
turbine capacity continues to grow, the gearbox power requirements 
also increase, exacerbating the challenge of balancing low-cost and 
high-power-density designs under complex environmental loads. 
Consequently, wind turbine companies have begun adopting sliding 
bearings – characterized by their low cost, simplicity and reliability – 
in wind turbine gearboxes (WTGs). Replacing rolling bearings with 
sliding bearings significantly reduces the gearbox’s size, weight, and 
cost, while simultaneously enhancing gearbox service life and torque 
density. Therefore, this study focuses on developing comprehensive 
performance evaluation methods to validate the actual performance 
of high-power sliding-bearing WTGs.
In recent years, some scholars have performed performance 
evaluations of wind turbine gearboxes. Tan et al. [1,2] studied 
different vibration modes and discussed the impact of internal and 
external excitations on gearbox dynamic response. Bi et al. [3] 
proposed a method for identifying fault modes in tooth root cracks 
using generalized back propagation neural networks. Pan et al. [4] 
proposed a performance degradation evaluation approach employing 
complete ensemble empirical mode decomposition with adaptive 
noise to denoise and fuse vibration signals. Tan et al. [5] analyzed the 
effects of structural flexibility on the dynamic characteristics of the 
planetary gear train. Ghane et al. [6] used spectral analysis to obtain 
characteristic bearing fault signals across six severity levels. Wang [7] 
proposed a performance analysis method for spiral differential gear 
trains. Zhao et al. [8] analyzed the influence of tooth flank clearance 
and eccentricity on the system response. Park et al. [9] built a three-
dimensional dynamic model of the wind turbine drivetrain, assessing 
its dynamic response and tooth contact forces. Shi et al. [10] examined 
how shaft bending influences rotational and translational motion as 
well as gear contact forces within transmission systems. Zhao et al. 
[11] analyzed the dynamic characteristics of a fully flexible wind 
turbine gearbox, focusing on the component flexibility impact. Wang 
et al. [12] analyzed the dynamic response of the transmission system 
of a 10 MW offshore wind turbine transmission system and estimated 
the 20-year fatigue damage of gears and bearings. Xie et al. [13] 
studied the effects of time-varying loads, inter-stage gap fluctuations, 
and crack depth on load-sharing capacity and vibration suppression 
effectiveness of wind turbines. Xie et al. [14] established a multi-body 
dynamic model incorporating passive-tuned mass dampers (TMDs) 
and optimized TMD parameters using genetic algorithms.
Several scholars studied the bearing’s performance of WTGs. 
Koukoura et al. [15] predicted planet bearing failures using vibration 
data. Fuentes et al. [16] proposed an acoustic-emission method for 
detecting surface damage in bearings. Keller et al. [17] found that 
the preloaded tapered roller bearings in WTGs have higher load-
sharing capacity than that of cylindrical rolling bearings with bearing 
clearances, with the expected fatigue life 3.5 times longer. Elasha 
et al. [18] used a multi-layer neural network model to predict the 
remaining service life of bearings. Song et al. [19] solved the dynamic 
load of high-speed shaft bearings using the Newmark integration 
method and obtained the bearing’s fatigue life and dynamic reliability. 
Mokhtari et al. [20] used vibration and acoustic emission technology 
to detect radial bearing faults in wind turbine gears and predict the 
remaining service life of bearings. They built a test bench to conduct 
experiments. Hagemann et al. [21] found that the bearing design 
process requires analyzing the distribution of gear meshing loads to 
determine the critical conditions for bearing operation. At the same 
time, wear phenomena can improve bearings’ circumferential and 

Structural Design
232   ▪   SV-JME   ▪   VOL 71   ▪   NO 7-8 ▪   Y 2025
axial clearance shapes, significantly reducing localized maximum 
pressure. König et al. [22] utilized acoustic emission technology to 
distinguish between critical wear and mixed friction states, applying a 
data-driven wear monitoring method to predict wear and degradation. 
Tang et al. [23] coupled a time-varying linear stiffness damping 
model with an additional eccentricity correction force to establish 
a planetary gear system dynamic model for WTGs using sliding 
bearings. Zhao et al. [24] developed a reliability evaluation method 
for WTG bearings considering the competitive failure between 
degradation and sudden failure. Dhanola et al. [25] studied the 
effects of thermal elasticity on the performance parameters of sliding 
bearings lubricated with degradable nano lubricants. However, most 
research focuses on WTGs with rolling bearings and needs more 
quantitative evaluation research on the comprehensive performance 
of sliding-bearing WTGs. Therefore, conducting comprehensive 
performance evaluation research on high-power sliding-bearing 
WTGs is significant.
This contribution establishes a rigid-flexible coupling multi-body 
dynamics model for a high-power sliding-bearing WTG, considering 
five primary and thirteen secondary performance indicators. It also 
proposes a comprehensive performance evaluation method for 
the sliding-bearing WTGs based on the analytic network process 
(ANP) and improved fuzzy comprehensive evaluation (IFCE). The 
remainder of this paper is organized as follows: Section 2 shows 
the dynamic model of the sliding-bearing WTG. Section 3 gives 
the performance evaluation of the WTG. Section 4 provides the 
quantitative analysis of the comprehensive performance of the WTG. 
Finally, some conclusions are summarised in Section 5. 
2 METHODS & MATERIALS
2.1 Structure and Operating Principle of the WTG
The WTG includes a three-stage transmission structure consisting 
of a low-speed stage, an intermediate stage, and a high-speed stage. 
The low-speed and intermediate stages are planetary helical gear 
transmissions, composed of sun gears, planetary gears, planetary 
carriers, ring gears, and associated components. The high-speed 
stage utilizes a parallel shaft helical gear transmission, composed 
of a gear and a pinion. The sliding bearings are applied to support 
planetary gear shafts. The structural diagram is shown in Fig. 1. The 
low-speed, high-torque mechanical energy from the main shaft end 
is first transmitted to the planetary gear system through the low-
speed stage planetary carrier. The low-speed stage sun gear meshes 
with the planet gears transfers motion and force to the intermediate-
stage planetary carrier through the low-speed shaft. Similar to the 
low-speed transmission mode, the intermediate stage planetary 
gear system transfers motion and force to the high-speed stage gear 
through its sun gear, which finally drives the pinion and the output 
shaft. At this point, the low-speed, high-torque input energy has been 
converted into high-speed, low-torque mechanical energy, which is 
used to drive the generator for electricity production.
2.2 Sliding Bearing Dynamic Modelling
The planet gear sliding bearings of WTGs often operate under low-
speed and heavy-load conditions. During operation, the oil film of 
the bearings will generate heat due to shear forces and pressure. 
Consequently, it is necessary to consider the influence of thermal 
elastic deformation on the bearing behaviour. To this end, the coupled 
Reynolds equation, temperature control equation, and temperature 
viscosity equation are applied to calculate the oil film pressure 
distribution. An iterative calculation method is used to obtain the 
discrete solutions, from which the oil film thickness, load-bearing 
capacity, friction power loss, as well as the stiffness and damping of 
the oil film can be calculated.
Fig. 1. Structural diagram of sliding-bearing WTGs
The planet gear sliding bearings of WTGs operate in a mixed-
friction state under heavy load and low-speed conditions. Considering 
the influence of surface roughness on the fluid film area, the 
generalized average Reynolds equation for laminar flow is expanded, 
and the Reynolds equation is formulated as follows:




























r
F
p
rz
F
p
z
U
r
h
F
j
x
p h
j
z
p h
p
j




22
1 1
0
2 F
U R
r
p qx
s
j




















, (1)
where F
0
, F
1
, and F
2
 represent the lubricant dynamic viscosity 
coefficient; p
h
 is the oil film pressure; h is the thickness of oil film at 
any point; and, Φ
x
p
, and Φ
z
p
, show the x, z-axis pressure flow factor; 
Φ
x
s
 is the shear factor; R
q
 represents the surface roughness; Θ 
represents the lubricating oil density, U
p
 is the planetary shaft speed.
The temperature and viscosity of the lubricating oil are 
inversely proportional. This relationship can be described using the 
temperature-viscosity equation, which reflects how the viscosity 
changes with temperature. The mathematical equation can be 
expressed as:
 T
T
T
 







0
0
1
, (2)
where η and η
0
 represent the dynamic viscosity of the lubricating oil 
when the bearing temperatures are T and T0, respectively.
Combining Eqs. (1) and (2), the distribution of oil film pressure 
can be calculated through the iterative finite difference method. The 
oil film thickness h can be calculated by:
hzCe
zh z
R
xy
 
  
,c os
coss in ,,
   
    
   (3)
where C
R
 is the radial clearance; e represents the eccentricity; γ is the 
attitude angle; ϕ represents the angular coordinate; Δh is the value 
of the oil film thickness at each point minus the minimum oil film 
thickness; φ
x
 and φ
y
 represent the alignment angles between planet 
shafts and bearings.
The total load capacity of the bearing can be calculated by Eq. (4).
PP P
xy

22
, (4)
where P
x
 and P
y
 are the x- and y-direction components of the radial 
bearing load capacity.

SV-JME   ▪   VOL 71   ▪   NO 7-8 ▪   Y 2025   ▪   233
Structural Design
The dimensionless bearing characteristic C
p
 usually represents the 
bearing load capacity, as shown in Eq. (5).
C
p
p
m



2
, (5)
where ψ is the bearing clearance ratio; ω represents the bearing 
speed, and p
m
 is the average pressure of the bearing.
The oil film’s stiffness and damping are key components that 
reflect the bearing’s operating state. The oil film stiffness is defined 
as the derivative of the oil film bearing capacity with respect to the 
eccentricity, and its mathematical description is given in Eq. (6).
K
P
xx
pr dd z
K
P
yy
pr d
xx
x
B
B
xy
x
a
b














 

sin
sin
/
/




2
2
 





dz
K
P
xx
pr dd z
K
a
b
a
b
B
B
yx
y
B
B
yy
 
 










/
/
/
/
cos
2
2
2
2
 


















 

P
yy
pr dd z
y
B
B
a
b
cos
.
/
/



2
2
. (6)
Similar to the calculation of the oil film stiffness, the oil film 
damping is the derivative of bearing capacity with respect to velocity.
Bearings are affected not only by internal excitations, such as 
thermal elastic deformation and installation errors, but also by 
external excitations arising from wind speed fluctuation. According 
to the wind speed statistics from a representative wind farm, a two-
parameter Weibull distribution is used to fit the wind speed. The 
probability density function is given by:
fu
k
c
u
c
e
k u
c
k
() , 














1
 (7)
where k = 8.426, c = 1.708. The corresponding cumulative 
distribution function is:
Fu e
u
c
k
() , 







1 (8)
where u is the wind speed, k represents the shape parameter, and c 
is the scale parameter. Considering the wind shear effect, the wind 
speed at the hub height is calculated by:
uu
z
z
hub
hub







02 .
, (9)
where z
hub
 is the hub height, u
hub
 represents the wind speed at the 
hub, and z is the height at which the wind speed is to be estimated.
The Kaimal model is used to calculate the turbulent wind. The 
spectral densities of the three spatial components of turbulent wind 
velocity are given by:
Sf
L
u
fL
u
k
k
k
() , 







4
1
6
2
5
3

hub
hub
 (10)
where k = u, v, w correspond to the longitudinal, lateral and vertical 
wind directions; u
hub
 is the average wind speed at the hub height; f is 
the cyclic frequency; L
k
 is the integral length scale parameter for each 
wind component. According to the IEC 61400-1 standard [26], the 
integral length scales can be expressed as
L
ku
kv
kw
k
u
u
u









81 0
27 0
06 6
.,
.,
.,
,



 (11)
where Λ
u
 is the turbulence scale coefficient. The correlation model of 
wind speeds at two points k and h in space is expressed as:
SfPfSf Sf
kh kk hh ,, ,
() () () () , 
Coh
 (12)
where P
Coh
(  f) is the spatial coherence.
2.3 Dynamic Model of The Sliding-Bearing WTG
Due to the rigid-flexible coupling structure, the sliding-bearing WTG 
must consider the effects of flexible components on the system’s 
dynamic characteristics. Therefore, the rigid and flexible bodies in 
the system are modeled according to the ISO 6336 standard [27]. The 
housing and gears of the gearbox are considered as rigid bodies with 
six degrees of freedom, while the rolling bearings are represented by 
equivalent spring-damping model, also with six degrees of freedom 
to capture coupling effects. In contrast, the carriers and gear shafts 
are regarded as flexible bodies. The relevant modelling strategies and 
the degree-of-freedom division of each component are detailed in 
Table 1.
Table 1. Modeling standards for sliding bearing gearbox
Component Modeling method Degrees of freedom
Housing Flexible body 6 DOF
Planet carrier Flexible body 6 DOF
Gear shaft Flexible body 6 DOF
Gear Rigid body 6 DOF
Generator coupling Torsional segmented rigid body Rotational DOF 
Generator rotor Rigid body 6 DOF
Generator stator Rigid body 6 DOF
Elastic support Damping nylon element Translational DOF 
Base plate Rigid body 6 DOF
Bearing Damping nylon element Full stiffness matrix 
The stiffness is represented by a 6×6 matrix, as shown in Eq. 
(13). Among them, non-diagonal elements represent the coupling 
relationship between the stiffnesses.
K
KKKKKK
KKKKKK
KKKKKK
bearing
x
y
z

12 13 14 15 16
21 23 24 25 26
31 32 34 35 3 36
41 42 43 45 46
51 52 53 54 56
61 62 63 64 65
KKKKKK
KKKKKK
KKKKKK







 















, (13)
where x, y and z are respectively 3 degrees of translational freedom; 
α, β, and γ are the rotational degrees of freedom corresponding to the 
x, y and z directions, respectively.
Gear meshing is one of the primary sources of internal excitation 
in a gearbox. To model this effect, the slicing method is used to build 
the gear model, and the finite element method is employed to obtain 
the meshing stiffness of gear teeth per unit tooth width. Because the 
number of engaged slices varies during the meshing process, the 
variation of gear meshing stiffness with the meshing phase can be 
simulated. Thus, the load distribution along the tooth width direction 
can be obtained, as shown in Fig. 2.

Structural Design
234   ▪   SV-JME   ▪   VOL 71   ▪   NO 7-8 ▪   Y 2025
Fig. 2. Schematic of gear slicing
Its meshing stiffness is calculated in accordance with the ISO 
6336 standard [27], as follows:
cc C
R max
  , (14)
where c' is the meshing stiffness of a single tooth, while C
R
 is the gear 
tooth structure coefficient. The calculation formula for the meshing 
stiffness of a single tooth can be expressed as:
  cc CC
MB th
cos,  (15)
where c
th
 is the theoretical meshing stiffness of a single tooth; C
M
 is 
the theoretical correction coefficient; C
B
 is the basic rack coefficient; 
β is the helix angle. The theoretical meshing stiffness of a single tooth 
c
th
 is defined as:
c
q
th
=
1
, (16)
q
zz
x
z
nn n
  

0 04723
0 15551 0 25791
0 00635
0 11654
0 001
12
1
1
.
..
.
.
. 9 93
0 24188
0 00529 0 00182
2
2
2
1
2
2
2
x
x
z
xx
n

.
.. , (17)
where z
n1
 and z
n2
 are the equivalent tooth numbers of the driving 
gear, and the driven gear, respectively; x
1
 and x
2
 are the modification 
coefficients of the driving gear, and the driven gear, respectively. The 
time-varying meshing stiffness function of gears can be expressed as:
cc S
s
ss
R
cc
() ()
()
max( ,)
, 

 














max
11
12
2
 (18)
where S
R
 = c
min
 / c
max
 is the gear stiffness ratio, s( φ) = r
g
φ represents 
the contact path coordinate, and s
1
c and s
2
c are the distances from the 
node along the meshing line to the meshing-in point and meshing-
out point, respectively. The calculation formula for transmission error 
can be expressed as:
e
N
N
L
 






 
21 10
1
2
20
() , (19)
where φ
10
 and φ
20
 are the initial rotation angles of the driving gear, 
and the driven gear at the moment of entering meshing, respectively; 
φ
1
 and φ
2
 are the rotation displacement angles of the driving gear, and 
the driven gear, respectively; N
1
 and N
2
 are the number of teeth of the 
driving gear, and the driven gear, respectively.
The topological relationship of the sliding-bearing WTG of the 
floating wind turbine is shown in Fig. 3. It encompasses three key 
aspects, including: the components, the topological relationships, 
and the force elements. The components represent the gearbox 
transmission components, the topological relationships represent 
the connection relationships and motion constraints among these 
components, and the force elements represent the interactions 
between them. Within this system, the components of the sliding-
bearing WTG are constrained by both stiffness and damping effects.
Fig. 3. Topology diagram of sliding-bearing WTGs
According to the connection relationships and topological structure 
among the transmission components, a multi-body dynamics model 
of the sliding-bearing WTG is established. Differential equations 
governing the flexible body motion are established based on the 
Lagrange multiplier method and modal synthesis method, as shown 
in Eq. (20). The flexible body modal reduction model is established 
through the finite element method.
MM KD Q
 


 


 


 


 ,
1
2
() ()
M
f
T
g
 (20)
where M represents the mass matrix, K is the stiffness matrix, 
D represents the modal damping matrix, and f
g
 represents the 
generalized gravity.
2.4 Validation of the dynamic model accuracy
To verify the reliability of the multi-body dynamic model, a sliding-
bearing wind turbine gearbox case reported in the literature [28], 
featuring a similar structural configuration and operating conditions, 
was selected for comparison. Key performance indicators, including 
the generator rotor speed as well as the vibration acceleration of 
both the main shaft and the gearbox output shaft, were analysed 
comparatively.
Fig. 4. Generator rotor speed
Figure 4 illustrates the generator speed response of the dynamic 
model under various wind speeds. The results show that when the 
average wind speed is 8 m/s, the rotor speed exhibits significant 
fluctuations, with frequent and noticeable drops. As the wind speed 
increases, the amplitude of these fluctuations gradually decreases, 
and the system demonstrates improved operational stability. Once the 
wind speed reaches 14 m/s or higher, the generator speed stabilizes 
around 1260 rpm under the influence of pitch control, and the 

SV-JME   ▪   VOL 71   ▪   NO 7-8 ▪   Y 2025   ▪   235
Structural Design
fluctuations are significantly reduced. This dynamic trend closely 
aligns with the results reported in literature [28], indicating that the 
model effectively reflects the system’s steady-state behaviour and 
control response under diverse wind conditions.
Figures 5 and 6 present the main shaft vibration acceleration 
reported in reference [28] and obtained in the present study, 
respectively. As observed, both sets of data exhibit a highly consistent 
trend, showing the amplitude of vibration acceleration progressively 
increasing with rising wind speed. This trend indicates the significant 
impact of wind speed on the system’s dynamic load and structural 
response. The developed model accurately captures the dynamic 
characteristics of the wind turbine gearbox under varying wind speed 
excitations. These findings verify the validity and reliability of the 
proposed model in reflecting the actual operational response of 
sliding-bearing WTGs.
Fig. 5. Main shaft vibration acceleration in reference [28]
Fig. 6. Main shaft vibration acceleration in the present study
It should be noted that due to differences, the absolute vibration 
amplitudes arise due to differences in structural dimensions, 
boundary conditions, and simulation time steps between the model 
and the literature case. However, the overall trends remain consistent, 
and the differences are within an acceptable engineering range. The 
agreement in trend and dynamic behaviour of key indicators further 
validates the accuracy and reliability of the proposed multibody 
dynamic model.
3 RESULTS AND DISCUSSION
ANP is suitable for handling complex decision-making problems 
involving internal dependencies and feedback relationships. It 
employs a network structure integrating both qualitative and 
quantitative analysis to accurately describe connections among 
entities, comprising a control layer as a typical hierarchical structure 
and a network layer where elements mutually influence and 
dominate, as illustrated in Fig. 7. Fuzzy comprehensive evaluation 
(FCE) method uses fuzzy mathematics to comprehensively assess 
multi-objective problems characterized by uncertainty, establishing 
corresponding membership functions and conducting quantitative 
analysis of fuzzy objects through a series of operations and 
transformations. The ANP-IFCE method combines ANP with the 
IFCE, classifying various factors of the evaluation object into 
multiple network levels according to their attributes. Elements 
within each network level mutually influence and dominate, enabling 
comprehensive evaluation of each level before proceeding to 
higher-level synthesis. In the dynamic modelling stage, this method 
establishes a gear slicing model based on the ISO 6336 standard [27] 
and calculates local contact stiffness of each tooth segment using 
the finite element analysis (FEA). By accounting for gear elastic 
deformation, contact nonlinearity, and local stress concentration, it 
outperforms traditional empirical formulas, enhancing prediction 
accuracy for key performance indicators like load distribution and 
vibration response. In the structural design and comprehensive 
performance evaluation stages, physical quantities such as contact 
stress and deformation output by FEA are normalized as inputs to 
membership functions, reducing subjective scoring interference. 
Meanwhile, structural coupling relationships revealed by FEA (e.g., 
meshing errors caused by bearing misalignment) are used to construct 
the ANP network structure, improving both the logical consistency 
and causal interpretability of weight allocation.
Fig. 7. ANP basic framework
3.1 Performance Evaluation Indexes
Based on the practicality and economy of sliding-bearing WTG, the 
paper proposes comprehensive performance evaluation indicators, 
including 5 primary and 13 secondary indicators, as shown in 
Table 2. U is the comprehensive performance, u
1
 is the supporting 
force of the main shaft bearing, u
2
 means the transmission system’s 
reliability, u
3
 represents the load-sharing coefficient, u
4
 means 
vibration characteristics, and u
5
 is the power density. u
11
, u
12
 and 
u
13
 represent the supporting force of the main shaft bearing along 
the x, y and z-direction, respectively. u
21
 represents the time-varying 
reliability of bearings, u
22
 and u
23
 are the gear’s bending and contact 
fatigue reliability, respectively. u
31
 and u
32
 are the low-speed and 
intermediate load-sharing coefficients, respectively. u
41
, u
42
 and u
43
 
represent the vibration acceleration along the x, y and z-direction, 
respectively. u
51
 is the unit megawatt weight, and u
52
 represents the 
torque density.
Table 2. Performance evaluation framework for the WTG
Target layer U
Criterion 
layer
u
1
u
2
u
3
u
4
u
5
Indicator 
layer
u
11
, u
12
, u
13
u
21
, u
22
, u
23
u
31
, u
32
u
41
, u
42
, u
43
u
51
, u
52

Structural Design
236   ▪   SV-JME   ▪   VOL 71   ▪   NO 7-8 ▪   Y 2025
3.1.1 Reliability of Gears
Rolling bearings are standardized mechanical components, and 
their service life generally follows the three-parameter Weibull 
distribution. Based on the life distribution function, the bearing 
reliability function can be derived as follows:
ut
t
L
h
21
09 () expl n. , 




















 (21)
where L
h
 is the basic rating life, and γ and β represent the position and 
shape parameters, respectively.
The wear failure is the primary failure mode for sliding bearings. 
The main factors affecting the performance of sliding bearings are: 
bearing pressure (p), sliding speed (v), and the value of (pv). The pv 
value can be calculated as follows:
pv
Fv
BD
pv = ≤[] , (22)
where F is the radial load of sliding bearings, D represents the 
bearing diameter, B means the effective width of bearings, and [pv] 
is the allowable value.
According to Archard’s wear theory, the wear volume of sliding 
bearings under normal conditions is linearly proportional to the 
sliding distance. Therefore, the wear coefficient K is used to estimate 
the wear volume Δ:
  KplK
F
DB
lK pvt, (23)
where K is the wear coefficient.
The actual clearance of the sliding bearing can be determined by 
the initial bearing clearance (L
0
) and the radial wear (Δ), as shown 
in Eq. (24). Due to factors such as installation error, manufacturing 
tolerances and varying operating conditions, the allowable clearance 
of different sliding bearings is random and can be approximated by 
a normal distribution L
C
 ~ N( μ
L
C
, δ
L
C
). When the actual clearance L
t
 
exceeds the allowable clearance L
C
, the sliding bearing fails due to 
excessive wear.
LL LK pvt
C

00
 , (24)
In engineering practice, the allowable clearance, when used as a 
boundary condition for assessing wear failure, exhibits inherent 
ambiguity. This ambiguity is most significant near the mean value of 
the allowable clearance LC . Therefore, the descending half-normal 
distribution function is used to characterize the uncertainty. When the 
membership degree is 0.5, the mean value of the allowable clearance 
is taken as the corresponding value, and the membership function can 
be mathematically described by Eq. (25), as shown in Fig. 8.
Fig. 8. Schematic diagram of membership function
yL
La
eL a
it
t
La
t
t
Lc
 








 





1

, (25)
where L
t
 is the actual fit clearance, δ
L
C
 represents the allowable 
clearance variance, LC is the mean allowable gap, a means the fuzzy 
upper bound, y(L
C
) = 0.5 and a = LC − δ
L
C
 / 1.2.
The reliability of the sliding bearing can be calculated by the 
transcendental function integral formula as shown in Eq. (26).
ut yL tfLt dLt
Lt
Lt
Lt
Lt
  























=
a

3

 

























1
2 2
2
3
2
22
2
2

a
c
c
c
Lt
Lt
L
LL t
Lc
L




  

Lt
Lt
LL t
2
2
3
2
22
e
a
c

 












, (26)
where f(x) is the probability density function, Φ(x) means the standard 
normal distribution function, LC represents the mean allowable gap, 
Lt is the actual gap mean, δLC is the allowable gap variance, and δL 
represents the actual gap variance.
The fuzzy language is used to describe and evaluate gear 
performance degradation and operation status. Considering the 
strength degradation, the fuzzy reliability function of gears can be 
expressed as follows:
ut tgtd
rt
rt
r
ii ii i
i
ii
2
1
01
11
11
() ,
.( )
.( )
.

  








 

+

i ii
i
i
ii
ii
i
t
S
rt
rt
rt
S
()
.( )
()
()


























 1
01


 


















S
rt
rt
S
r
i
i
ii
i
i
01 2
11
2
2
2
.( )
exp
(. () )
exp
((


 t t
S
i
i
))
,













	
	





2
2
2
 (27)
where μ
i
(.) is the membership degree of fuzzy numbers, g
i
(t) is the 
probability distribution function, Si means the standard deviation of 
allowable stress, g
i
 = σ C
i
, r
i
(t) is the remaining strength of each gear 
at time t, Φ(.) means the standard normal distribution function, and 
σ represents the mean stress.
3.1.2 Load-sharing Characteristics
Due to uneven load distributions, the planetary gear train often cannot 
fully demonstrate its advantages, which seriously affects its working 
performance and service reliability. A load-sharing coefficient closer 
to 1 indicates a more uniform load distribution among the planetary 
gears and thus a higher system load capacity. The closer the load-
sharing coefficient is to 1, indicates a more uniform load distribution 
among the planetary gears and thus a stronger system load capacity. 
In order to quantitatively evaluate the load-sharing characteristics of 
the planetary gear train of the WTG, the load-sharing coefficient can 
be defined as:
u
NF
F
NF
F
i
RP
RPi
i
n
SP
SPi
i
n 3
1
2















 
max
max
max
max
, (28)
where u
31
 and u
32
 represent the load-sharing coefficients for the first 
and second planetary gear transmissions, F
RPi
max
 and F
SPi
max
 are the 
maximum dynamic meshing forces of the i
th
 planet gear of the 

SV-JME   ▪   VOL 71   ▪   NO 7-8 ▪   Y 2025   ▪   237
Structural Design
planetary gear train (i = 1,2, …, N), F
RP
max
 and F
SP
max
 represent the 
maximum dynamic meshing forces for the ring-planet gear pair and 
sun-planet gear pair.
3.1.3 Power Density
Torque density is often used to measure the transmission capacity 
of a gearbox. A higher torque density means that the gearbox can 
withstand greater torque load relative to its size. Defined as the 
torque per unit volume, torque density is typically used to evaluate 
the performance and efficiency of a transmission system. The torque 
density u
51
 can be expressed as:
u
T
V
51
= , (29)
where T is the gearbox torque, and V represents the gearbox volume. 
The unit megawatt weight is an important indicator used to measure 
the power generation capacity of wind turbines. A higher value 
indicates a stronger power output capability relative to the turbine’s 
weight. This characteristic is commonly defined as the power-to-
weight ratio (PWR). Therefore, the specific calculation formula of 
the PWR (R
52
) can be expressed as:
u
P
M
52
= , (30)
where P is the generator power, and M represents the gearbox density.
3.2 Construction of the ANP Supermatrix
ANP consists of the control layer and the network layer, where the 
control layer follows an atypical hierarchical structure, while the 
elements in the network layer influence each other. ANP is mainly 
divided into problem description and analysis, construction of ANP 
hierarchical structure, construction of judgment matrix, consistency 
test of judgment matrix, and determination of the weight of the basic 
elements within the supermatrix and weighted supermatrix to the 
overall goal.
Table 3. Judgment scale of the index importance
Scale value Description
1 The element i is equally essential as the element j
3 The element i is slightly more essential than the element j
5 The element i is more essential than the element j
7 The element i is much more essential than the element j
9 The element i is the most essential than the element j
2, 4, 6, 8 The median of the two adjacent judgments mentioned above
The ANP evaluation indicator network model is built with the 
target layer serving as the control layer, while the criterion layer and 
indicator layer are the network layer, as shown in Table 3. Assume 
that the control layer elements of ANP are represented as: P
1
, P
2
, …, 
P
m
, and the first-level indicators of the network layer are denoted as: 
R
1
, R
2
, …, R
5
, where R
i
 contains the second-level indicators R
i1
, R
i2
, 
…, R
in
.
Table 4. Average random consistency indicator
n 1 2 3 4 5 6 7 8 9 10
RI 0 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49
Taking the control layer element P
S
 (S = 1, 2, …, m) as the 
criterion, and the element R
jk
 (k = 1, 2, …, n
j
) within R
j
 (  j = 1, 2, 
…, 4) as the secondary criterion, the elements in R
i
 are compared 
according to their influence on R
jk
. Based on these comparisons, the 
nine-level scaling method is used to construct the corresponding 
judgment matrix L, where the scoring scale of the nine-level scaling 
method is shown in Table 4.
L 














ll l
ll l
ll l
n
n
nn nn
i
i
ii ii
11 12 1
21 22 2
12


 

. (31)
Since the construction of the judgment matrix involves subjective 
assessments, it is necessary to test its consistency to ensure the 
evaluation results’ accuracy. To this end, the consistency ratio (CR) of 
the judgment matrix calculated as follows:
CI
n
n




max
,
1
 (32)
CR
n
RI n




max
()
,
1
 (33)
where CI is the consistency indicator, RI is a random consistency 
index (with values shown in Table 3), n represents the order of 
the judgment matrix, and λ
max
 is the maximum eigenvalue of the 
judgment matrix. When n = 0, 1, and CI = 0, the judgment matrix 
has complete consistency; when n ≥ 2, and CR < 0.1, the judgment 
matrix can be considered to have satisfactory consistency; otherwise, 
adjustments are required.
Based on the survey results, a judgment matrix is formed. After 
passing the consistency test, the judgment matrix can be identified as 
an unweighted supermatrix W
ij
, as follows:
W
ij
i
j
i
j
i
jn
i
j
i
j
i
jn
in
j
in
j
in
ww w
ww w
ww w
j
j
jj

1
1
1
2
1
2
1
2
2
2
12


 

j j
j
jn














, (34)
where the column vector of W
ij
 represents the ranking vector of the 
influencing factors R
i1
, R
i1
, …, R
ini
. Within the factor layer of the 
evaluation index, this vector reflects the degree of influence of the 
factors R
j1
, R
j2
, …, R
jnj
 in R
j
.
By comparing the importance of the criterion layer indicators R
i
 
with R
j
 (i, j = 1, 2, …, 5) in the evaluation indicators, a weighted 
matrix A of the criterion-layer indicators can be obtained by pairwise 
comparison, which is expressed as follows:
A 












aa a
aa a
aa a
n
n
nn nn
11 12 1
21 22 2
12


 

. (35)
By applying the weighted matrix A to weight the unweighted 
supermatrix W
ij
, the weighted supermatrix W
ij
 is obtained, which 
can be expressed as follows:
W
ij
nn
nn
nn nn
aw aw aw
aw aw aw
aw aw

11 11 12 12 11
21 21 12 22 22
11 22


 
  aw
nn nn












, (36)
where W
ij
 = a
ij
w
ij
, I =1, 2, …, n, j = 1, 2, …, n (n ≥ 6).
The normalized form of the weighted supermatrix yields the limit 
supermatrix W
∞
, whose column vector represents the weight vector 
R
inj
 of the comprehensive performance evaluation factor index W' 
for the sliding-bearing wind turbine gearbox, which is expressed as 
follows:
W'( ,, ,, ,) . = WW WW
iniN nN 11 12

T
 (37)

Structural Design
238   ▪   SV-JME   ▪   VOL 71   ▪   NO 7-8 ▪   Y 2025
The normalized weight vector of each index R
ij
 within its 
corresponding criterion layer index R
i
 is denoted as W'
i
, which is 
expressed as follows:
W
ii ii ni
WW W
'' ''
(,,, ). =
12

T
 (38)
3.3 Improved Performance Evaluation Method for the WTG
The evaluation factors represent the properties and performance of 
the evaluation target, while the evaluation level indicates the degree to 
which these factors influence the target. According to the complexity 
of the target, the factor set U = (u
1
, u
2
, …, u
m
), and the evaluation 
set V = (v
1
, v
2
, …, v
n
) are determined. Membership functions reflect 
the relationship between evaluation factors and evaluation levels. 
Correctly selecting the membership function is critical to ensuring 
the accuracy of fuzzy comprehensive evaluation. Thus, this study 
uses the compound membership function to improve the credibility 
of each indicator’s membership function.
The corresponding membership function is selected according 
to the characteristics of the evaluation index. The single-factor 
judgment is then performed on the factor set u
i
 (i = 1, 2, …, m) to 
obtain the membership rij of ui with respect to the evaluation level  
v
j
 (j = 1, 2, …, n). Following this, the ui judgment set is expressed as  
r
i
 = (r
i1
, r
i2
, …, r
ini
). By repeating this process for all factors, the 
whole evaluation matrix R can be constructed.
R
rr r
rr r
rr r
n
n
mm mn













11 12 1
21 22 2
12


 

. (39)
Assume that the membership values of an indicator in n 
membership functions are r
1
, r
2
, …, r
n
, and the variances of the errors 
relative to r are σ
11
, σ
12
, …, σ
nn
. The errors among the membership 
degrees corresponding to the membership functions are unrelated. 
Given the condition Σ ω
i
 = 1, the Lagrange multiplier is employed to 
minimize Var(e
c
). The weights of various membership functions are 
obtained as follows:


 
i
ii
nn

 






1
11 1
11 22

. (40)
From Eq. (40), it can be observed that the closer the membership 
value is to the average value, the larger its corresponding weight 
becomes. Therefore, the compound membership function can be 
calculated by:
rrrr
cn n
  
11 22
 . (41)
3.4 Comprehensive Performance Evaluation  
of Sliding-Bearing WTGs
According to the evaluation system built in Section 3, the first-level 
indicators are considered independently and only affected by their 
second-level indicators. The second-level indicators have either 
unidirectional or bidirectional influence on each other. By taking the 
target layer as the control layer in ANP, and the criterion layer and 
the indicator layer as the network layer (as listed in Table 5), an ANP 
evaluation indicator network model is constructed, as shown in Fig. 
9.
Based on the ANP model for the comprehensive performance 
evaluation of sliding-bearing WTGs, the expert scoring method is 
adopted to determine the corresponding weights of indicators at each 
level. The first-level indicators are regarded as independent of one 
another and are scored according to the nine-level scaling method.  
This scoring yields the judgment matrix of the first-level indicators in 
the control layer, as shown in Table 5.
From Eqs. (32) and (33), the following results are obtained:  
λ
max
 = 5.24, CI = 0.059, RI = 1.12, CR = 0.053 < 0.1. Thus, the 
judgement matrix passed the consistency requirement. The indicator 
weights of the network layer are then determined based on the 
importance of the first-level indicators. At this stage, the mutual 
influences among the elements of the network layer under each first-
level indicator need to be considered. The judgment matrix for the 
second-level indicators of the network layer is constructed through 
the same method applied for the first-level indicator weights of the 
control layer, followed by a consistency test. As an example, the 
reliability indicator is shown in Table 6.
Table 5. Judgment matrix and weight vectors of the first-level indicators in control layer
R
1
R
2
R
3
R
4
R
5
W
R
1
1 1/3 1 1 1/4 0.096
R
2
3 1 5 3 1/2 0.312
R
˝
1 1/5 1 2 1/2 0.128
R
4
1 1/3 1/2 1 1/4 0.086
R
5
4 2 5 4 1 0.378
Fig. 9. ANP model for the comprehensive performance of sliding-bearing WTGs
Table 6. Judgment matrix and weight vector of the system reliability
R
21
R
22
R
23
W
R
21
1 2 1 0.411
R
22
1/2 1 1 0.261
R
23
1 1 1 0.328
Table 7. Weights for comprehensive performance evaluation of sliding-bearing WTGs
First-level indicators Indicator weight Second-level indicators Local weight
R
1
0.096
R
11
0.224
R
12
0.369
R
13
0.406
R
2
0.312
R
21
0.411
R
22
0.261
R
23
0.328
R
3
0.128
R
31
0.500
R
32
0.500
R
4
0.086
R
41
0.249
R
42
0.326
R
43
0.426
R
5
0.378
R
51
0.500
R
52
0.500

SV-JME   ▪   VOL 71   ▪   NO 7-8 ▪   Y 2025   ▪   239
Structural Design
From Eqs. (32) and (33), the following results are obtained:  
λ
max
 = 3.05, CI = 0.046, RI = 0.58, CR = 0.046 < 0.1. Thus, the 
judgement matrix passed the consistency requirements. The 
remaining secondary indicators of the network layer are then 
calculated sequentially, and the weighted supermatrix and the limit 
supermatrix are calculated to obtain the relative weights of the 
secondary indicators as well as the comprehensive performance 
evaluation weights of the WTGs, as shown in Table 7. The evaluation 
criteria are determined according to the performance levels, and a 
comment set is established, as shown in Table 8.
Table 8. Evaluate the level of membership
Performance level Inferior V
1
General V
2
Good V
3
Excellent V
4
Evaluation criterion 0 to 25 25 to 50 50 to 75 75 to 100
Then, the membership degree matrix is constructed according 
to Subsection 3.3. The matrix elements represent the membership 
degree of each risk factor with respect to each level in the evaluation 
set. Let the membership vector of risk factor U
i
 to the judgment set 
be defined as V
i
 = {V
i1
, V
i2
, V
i3
, V
i4
}. Based on this, the membership 
degree values of the comprehensive performance indicators for the 
6.2 MW sliding-bearing WTG are obtained under three functions, as 
shown in Table 9.
Table 9. Membership degree of performance indicators for the 6.2 MW sliding-bearing WTG
Indicator 
factors
Membership function 1/2/3
Inferior General Good Excellent
R
11
0.00/0.00/0.00 0.00/0.00/0.00 0.67/0.45/0.30 0.33/0.55/0.70
R
12
0.00/0.00/0.00 0.00/0.00/0.10 0.50/0.70/0.75 0.50/0.30/0.15
R
13
0.00/0.00/0.00 0.10/0.05/0.25 0.90/0.80/0.75 0.00/0.15/0.00
R
21
0.00/0.00/0.00 0.00/0.20/0.50 0.70/0.60/0.50 0.30/0.20/0.00
R
22
0.00/0.00/0.00 0.00/0.00/0.10 0.15/0.40/0.50 0.85/0.60/0.40
R
23
0.00/0.10/0.40 0.50/0.60/0.50 0.50/0.30/0.10 0.00/0.00/0.00
R
31
0.00/0.00/0.00 0.00/0.00/0.00 0.10/0.25/0.50 0.90/0.75/0.50
R
32
0.00/0.00/0.00 0.00/0.00/0.20 0.30/0.60/0.60 0.70/0.40/0.20
R
41
0.00/0.00/0.00 0.00/0.00/0.00 0.10/0.33/0.20 0.90/0.67/0.80
R
42
0.00/0.00/0.00 0.00/0.00/0.00 0.33/0.20/0.50 0.67/0.80/0.50
R
43
0.00/0.00/0.00 0.00/0.20/0.00 0.50/0.60/0.95 0.50/0.20/0.05
R
51
0.00/0.00/0.00 0.10/0.20/0.20 0.40/0.50/0.70 0.50/0.30/0.10
R
52
0.00/0.00/0.00 0.10/0.20/0.20 0.40/0.50/0.70 0.50/0.30/0.10
Following this, the variance-covariance method was applied to 
obtain the combined membership degree values of the comprehensive 
performance indicators of the 6.2 MW sliding-bearing WTG. 
Similarly, the combined membership degree values for the 10 MW 
sliding-bearing WTG were also obtained, as shown in Table 10. and 
illustrated in Fig. 10.
Table 10. Membership degree of comprehensive performance indicators for sliding-bearing 
wind turbine gearboxes
Indicator 
factors
6.2/10 MW sliding-bearing WTGs
Inferior General Good Excellent
R
11
0.00/0.00 0.00/0.00 0.46/0.17 0.54/0.83
R
12
0.00/0.00 0.01/0.01 0.68/0.36 0.31/0.63
R
13
0.00/0.00 0.08/0.02 0.81/0.45 0.11/0.53
R
21
0.00/0.00 0.21/0.28 0.60/0.43 0.19/0.29
R
22
0.00/0.00 0.01/0.00 0.39/0.49 0.61/0.51
R
23
0.13/0.31 0.57/0.48 0.30/0.21 0.00/0.00
R
31
0.00/0.00 0.00/0.00 0.26/0.41 0.74/0.59
R
32
0.00/0.00 0.03/0.03 0.56/0.82 0.42/0.15
R
41
0.00/0.00 0.00/0.00 0.28/0.34 0.72/0.66
R
42
0.00/0.00 0.00/0.00 0.26/0.52 0.74/0.48
R
43
0.00/0.00 0.15/0.39 0.63/0.50 0.22/0.11
R
51
0.00/0.00 0.19/0.40 0.51/0.48 0.30/0.12
R
52
0.00/0.00 0.19/0.40 0.51/0.48 0.30/0.12
Matrix multiplication is used to perform fuzzy transformation and 
calculate the fuzzy comprehensive evaluation vector B.
B  WR
2
00 00 04 06 80 28
00 40 28 04 50 24
00 00 01 04 10 58
00 0
....
....
....
.0 00 60 42 05 2
00 00 19 05 10 30
...
....
.
















Afterwards, the secondary comprehensive evaluation is performed 
to obtain the final fuzzy comprehensive evaluation vector B
p
.
BB W
p
  00 10 17 04 90 33 .... .
Lastly, the comprehensive performance evaluation value P
1
 for the 
6.2 MW sliding-bearing WTG is calculated using the formula below.
a)                b)  
Fig. 10. Membership degree of sliding-bearing WTGs: a) 6.2 MW sliding-bearing WTG, and b) 10 MW sliding-bearing WTG

Structural Design
240   ▪   SV-JME   ▪   VOL 71   ▪   NO 7-8 ▪   Y 2025
P
1
25 50 75 100
00 1
01 7
04 9
03 3
78 35   













.
.
.
.
..
According to the membership degree of performance indicators 
shown in Table 9, the 6.2 MW sliding-bearing WTG is evaluated as 
having “excellent” performance. In the same way, the comprehensive 
performance evaluation value P2 of the 10 MW sliding-bearing WTG 
is obtained. Thus, the performance of this 10 MW sliding-bearing 
WTG is evaluated as having “good” performance based on the 
membership degree of performance indicators, shown in Table 9.
P
2
25 50 75 100
00 3
02 5
04 5
02 6
73 40   













.
.
.
.
.
To verify the reliability of the evaluation method, a sensitivity 
analysis was carried out on the weights of key indicators in 
the ANP-IFCE-based evaluation framework. Referencing the 
requirements of ISO 12100 [29] for parameter perturbation 
verification of complex systems, a hybrid sensitivity analysis 
method combining single-factor weight fluctuation testing with 
multi-factor superposition perturbation was adopted to investigate 
the response of comprehensive performance evaluation results to 
index weight perturbations. The first-level index R
5
 with the highest 
weight (power density, weight 0.378) and the second-highest R
2
 
(reliability, weight 0.312) are selected to apply ±20 % weight 
perturbation, respectively. The weights of the remaining indicators 
are proportionally normalized to keep the total weight sum remained 
equal to 1. Keeping the membership matrix B unchanged, the fuzzy 
comprehensive evaluation result vector B'
P
 and the comprehensive 
performance evaluation value P' of the sliding bearing wind turbine 
gearbox were calculated after adjusting the weights. The summary 
results are shown in Table 11.
Table 11. Comparison of fluctuations in comprehensive evaluation value P of 6.2 MW and  
10 MW sliding bearing WTGs under ANP index weight adjustment
Adjustment 
method
6.2 MW 10 MW
P' Variation range [%] P' Variation range [%]
Original value 78.35 – 73.40 –
R
5
 +20 % 79.25 +1.15 75.50 +2.86
R
2
 –20 % 78.25 –0.13 75.00 +2.18
R
5
 +20 %,  
R
2
 –20 %
79.75 +1.79 75.75 +3.20
Within the ±20 % weight disturbance range, the comprehensive 
evaluation value P of the 6.2 MW sliding-bearing wind turbine 
gearbox fluctuates by no more than +1.79 %, while that of the 10 
MW model fluctuates no more than +3.20 %. According to the 
standard verification procedure of multi-criteria evaluation models, 
the fluctuation verification of the comprehensive evaluation value P 
for both 6.2 MW and 10 MW sliding-bearing wind turbine gearboxes 
shows that all P value fluctuations remain within ±5 %, demonstrating 
the reliability of the ANP-IFCE model.
4 CONCLUSIONS
To address the lack of systematic performance evaluation indicators 
and methods for high-power sliding-bearing wind turbine gearboxes, 
this paper proposes a comprehensive performance evaluation method 
that integrates ANP and improved FCE. By combining a multi-layer 
network structure with fuzzy logic, the framework enables coupling 
modelling and weight quantification among multiple indicators, 
thereby overcoming the limitations of traditional AHP and single 
FCE in dealing with inter-indicator correlations and subjective bias. 
A unified quantitative scoring mechanism is established to support 
horizontal comparison among different gearbox models as well as 
customized selection, facilitating structural optimization and multi-
working condition adaptive design. Furthermore, dynamic indicators 
such as load-sharing performance, bearing force, and vibration 
characteristics are introduced to effectively identify structural risks, 
evaluate design rationality, and improve the prediction ability at the 
design stage and thereby improving operational reliability. The main 
conclusions are obtained as follows:
1. The importance of the first-level indicators for comprehensive 
performance evaluation of sliding-bearing WTGs is ranked in 
descending order as follows: power density, reliability, load-
sharing performance, support force of main shaft bearings, 
and vibration characteristics. Among these, both weights of 
power density and reliability exceeding 30 %, indicating that 
improvements in these two factors are the most critical for 
enhancing the overall performance of WTGs.
2. By applying the ANP-IFCE method, which comprehensively 
considers the mutual influences between various indicators, 
several secondary factors are identified as key to performance 
improvement.  These include the bearing support force along 
the z-direction, dynamic reliability of bearings, load-sharing 
coefficient of the low-speed stage, load-sharing coefficient of the 
intermediate stage, vibration acceleration along the y-direction, 
weight per megawatt and torque density. Strengthening these 
factors is particularly effective in enhancing the comprehensive 
performance of sliding-bearing WTGs.
3. The comparative evaluation between the 6.2 MW WTG and 10 
MW WTG reveals that the 6.2 MW model performs better in terms 
of reliability, load-sharing performance, vibration characteristics, 
and power density, but is slightly weaker in the support forces of 
the main shaft bearing. On balance, the overall comprehensive 
performance of the 6.2 MW WTG is superior to that of the 10 MW 
WTG model, confirming its advantages in structural design and 
operational efficiency.
References
[1] Tan, J., Zhu, C., Song, C., Xu, X. Study on the dynamic modeling and natural 
characteristics of wind turbine drivetrain considering electromagnetic 
stiffness. Mech Mach Theory 134 541-561 (2019) DOI:10.1016/j.
mechmachtheory.2019.01.015.
[2] Tan, J., Zhu, C., Song, C., Han, H., Li, Y. Effects of flexibility and suspension 
configuration of main shaft on dynamic characteristics of wind turbine drivetrain. 
Chin J Mech Eng 32 36 (2019) DOI:10.1186/s10033-019-0348-4.
[3] Bi, Y., Zhu, C., Tan, J., Song, H., Du, X. Influence of tooth root crack on 
dynamic characteristics of wind turbine gearbox high-speed stage and 
failure mode identification. Acta Energ Solar Sin 43 284-292 (2022) 
DOI:10.19912/j.0254-0096.tynxb.2020-1251.
[4] Pan, Y., Hong, R., Chen, J., Singh, J., Jia, X. Performance degradation assessment 
of a wind turbine gearbox based on multi-sensor data fusion. Mech Mach Theory, 
137 509-526 (2019) DOI:10.1016/j.mechmachtheory.2019.03.036.
[5] Tan, J., Li, H., Zhu, C., Song, C. Study on dynamics characteristics of planetary 
gear train in wind turbine gearboxes considering flexible structures. J Vibr Eng, 36 
1191-1203 (2023) DOI:10.16385/j.cnki.issn.1004-4523.2023.05.002.
[6] Ghane, M., Nejad, A.R., Blanke, M., Gao, Z., Moan, T. Diagnostic monitoring of 
drivetrain in a 5 MW spar-type floating wind turbine using Hilbert spectral 
analysis. Energ Proced 137 204-213 (2017) DOI:10.1016/j.egypro.2017.10.374.
[7] Wang, C. Study on dynamic performance and optimal design for differential gear 
train in wind turbine gearbox. Renew Energy 221 119776 (2024) DOI:10.1016/j.
renene.2023.119776.
[8] Zhao, X., Chen, C.Z., Liu, J. Gu, Q. Nonlinear dynamic response analysis of high-
level wind turbine gearbox transmission system considering eccentricity. J Solar 
Energ 41 98-108 (2020) DOI:10.19912/j.0254-0096.2020.03.014.

SV-JME   ▪   VOL 71   ▪   NO 7-8 ▪   Y 2025   ▪   241
Structural Design
[9] Park, Y., Park, H., Ma, Z., You, J., Shi, W. Multibody dynamic analysis of a wind 
turbine drivetrain in consideration of the shaft bending effect and a variable gear 
mesh including eccentricity and nacelle movement. Front Energy Res 8 604414 
(2021) DOI:10.3389/fenrg.2020.604414.
[10] Shi, W., Park, Y., Park, H., Ning, D. Dynamic analysis of the wind turbine drivetrain 
considering shaft bending effect. J Mech Sci Technol 32 3065-3072 (2018) 
DOI:10.1007/s12206-018-0609-7.
[11] Zhao, Y., Wei, J., Zhang, S., Xu, Z., Guo, J., Ji, K. Study of effect of structural 
flexibility on dynamic characteristics of large-scale wind turbine gear transmission 
system. Acta Energ Solar Sin 42 174-182 (2021) DOI:10.19912/j.0254-0096.
tynxb.2019-1433.
[12] Wang, S., Nejad, A.R., Moan, T. On design, modelling, and analysis of a 10-MW 
medium-speed drivetrain for offshore wind turbines. Wind Energy, 23 1099-1117 
(2020) DOI:10.1002/we.2593.
[13] Xie, F., Sun, Y., Wu, S., Zhang, Q., Li, X. Research on load sharing performance of 
wind turbine gearbox involving multiple-errors and tooth crack. J Mech Sci Technol 
36 4395-4408 (2022) DOI:10.1007/s12206-022-0804-4.
[14] Xie, S., Jin, X., He, J. Structural vibration control for offshore floating wind turbine 
including drivetrain dynamics analysis. J Renew Sustain Ener 11 023304 (2019) 
DOI:10.1063/1.5079427.
[15] Koukoura, S., Carroll, J., McDonald, A., Weiss, S. Wind turbine gearbox planet 
bearing failure prediction using vibration data. J Physics Conf Ser 1104 012016 
(2018) DOI:10.1088/1742-6596/1104/1/012016.
[16] Fuentes, R., Dwyer-Joyce, R., Marshall, M., Wheals, J., Cross, E. Detection of 
sub-surface damage in wind turbine bearings using acoustic emissions and 
probabilistic modelling. Renew Energ 147 776-797 (2020) DOI:10.1016/j.
renene.2019.08.019.
[17] Keller, J., Guo, Y., Zhang, Z., Lucas, D. Comparison of planetary bearing load-
sharing characteristics in wind turbine gearboxes. Wind Energ Sci 3 947-960 
(2018) DOI:10.5194/wes-3-947-2018.
[18] Elasha, F., Shanbr, S., Li.X., Mba, D. Prognosis of a wind turbine gearbox bearing 
using supervised machine learning. Sensors 19 3092 (2019) DOI:10.3390/
s19143092.
[19] Song, L., Cui, Q., Jin, P., Zhou, J. High speed bearing fatigue life and reliability 
analysis of wind turbine gearbox under random load. Acta Energ Solar Sin 44 
437-444 (2023) DOI:10.19912/j.0254-0096.tynxb.2022-0562.
[20] Mokhtari, N., Grzeszkowski, M., Guhmann, C. Vibration signal analysis for the 
lifetime-prediction and failure detection of future turbofan components. Tech 
Mech E J Eng Mech 37 422-431 (2017) DOI:10.24352/UB.OVGU-2017-118.
[21] Hagemann, T., Ding, H., Radtke, E., Schwarze, H. Operating behavior of sliding 
planet gear bearings for wind turbine gearbox applications part II: impact of 
structure deformation. Lubricants 9 98 (2021) DOI:10.3390/lubricants9100098.
[22] Konig, F., Marheineke, J., Jacobs, G., Sous, C., Zuo, M.J., Tian, Z. Data-driven 
wear monitoring for sliding bearings using acoustic emission signals and long 
short-term memory neural networks. Wear 476 203616 (2021) DOI:10.1016/j.
wear.2021.203616.
[23] Tang, H., Tan, J., Li, H., Zhu, C., Ye, W., Sun, Z. Research on dynamic modeling 
and decoupling methods of planetary gear trains in wind turbine gearboxes 
with journal bearings. Chin Mech Eng 35 591 (2024) DOI:10.3969/j.issn.1004-
132X.2024.04.003.
[24] Zhao, Q. Yuan, Y., Sun, Wang, W., Fan, P., Zhao, J. Remaining useful life analysis of 
gearbox bearing of wind turbines based on competition failure. Acta Energ Solar 
Sin 42 438-444 (2021) DOI:10.19912/j.0254-0096.tynxb.2018-1356.
[25] Dhanola, A., Garg, H.C. Thermo-elasto-hydrodynamic (TEHD) study of journal 
bearing lubricated with biodegradable nanolubricant. J Braz Soc Mech Sci, 43 69 
(2021) DOI:10.1007/S40430-021-02801-3.
[26] IEC 61400-1:2019. Wind Energy Generation Systems - Part 1: Design 
Requirements. International Electrotechnical Commission, London.
[27] ISO 6336-3:2019. Calculation of Load Capacity of Spur and Helical Gears - 
Part 3: Calculation of Tooth Bending Strength. International Organization for 
Standardization, Geneva.
[28] Yu, Z., Zhu, C., Tan, J., Song, C., Wang, Y. Fully-coupled and decoupled analysis 
comparisons of dynamic characteristics of floating offshore wind turbine 
drivetrain. Ocean Eng 247 110639 (2022) DOI:10.1016/j.oceaneng.2022.110639.
[29] ISO 12100:2010. Safety of Machinery-General Principles for Design-Risk 
Assessment and Risk Reduction. International Organization for Standardization, 
Geneva.
Acknowledgements The research work in this paper was supported by 
the National Natural Science Foundation of China (Grant No. 52405067), 
Science and Technology Research Program of the Education Department 
of Hubei Province (Grant No. Q20241205), Hubei Provincial Natural 
Science Foundation of China (Grant No. 2024AFB316) and the Science 
and Technology Innovation Key R&D Program of Chongqing (Grant No. 
CSTB2024TIAD-STX0019).
Received: 2024-12-03, revised: 2025-06-19, accepted: 2025-07-17  
as Original Scientific Paper.
Data availability The data that underpin the results of this research are 
available for use by other researchers. Additionally, the corresponding author 
can provide additional raw data upon reasonable request.
Author contribution Yao Li: Writing - review & editing, Writing - original 
draft, Methodology, Data curation, Project administration; Longsheng Li: 
Writing - original draft, Methodology; Gaoxiang Ni: Writing - review & editing, 
Supervision; Xinlong Li: Investigation, Formal analysis, Data curation; Kongde 
He: Investigation, Formal analysis, Data curation. All authors have contributed 
significantly to this work and thoroughly reviewed and approved the final 
version of the manuscript.
Celovita ocena zmogljivosti zobniških prenosov vetrnih turbin  
z drsnimi ležaji
Povzetek   Ob  upo št e v anju  s trukturnih  značilno s ti  in  v ečizv o rnih  vzbujanj 
zo bniških  preno so v  v e trnih  turbin  z  dr snimi  ležaji  ta  štud ija  o blik uje  v ečt elesni 
dinamični  mo del  viso k o zmo gljivih  zo bniških  preno so v  z  dr snimi  ležaji. 
Predlagana  je  celo vita  me t o do lo gija  za  o cenje v anje  zmo gljiv o s ti,  ki  združuje 
analitični  mrežni  pr o ces  (ANP)  z  izbo ljšano  me t o do   mehk e  celo vit e  o cene 
(IFCE).  Razvit  je  bil  v ečrazsežen  o kvir  za  celo vit o   o cenje v anje  zmo gljiv o s ti,  ki 
po udarja  praktično s t  in  s tr o šk o vno  učink o vit o s t,  t er  vključuje  ciljno ,  krit erijsk o  
in  indik at o r sk o   ra v en.  Ključni  k azalniki  o cenje v anja  v  t em  o kviru  vključujejo  
po dpo rno   silo   ležaja  gla vne  gredi,  zanesljiv o s t  preno snega  sis t ema,  k o ef icient 
delitv e  o bremenitv e,  vibracijsk e  značilno s ti  in  go s t o t o   mo či.  Z  upo rabo  
me t o do lo gij  ANP  in  IFCE  je  bila  sis t ematično  o cenjena  celo vita  zmo gljiv o s t 
dv eh zo bniških preno so v v e trnih turbin z dr snimi ležaji.
Ključne besede   zo bniški  preno s  v e trne  turbine  z  dr snimi  ležaji,  celo vita 
o cena  zmo gljiv o s ti,  v ečrazsežni  k azalniki  o cenje v anja,  analitični  mrežni 
proces (ANP), mehka celovita ocena (FCE)