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Journal of Physics: Conference Series
PAPER • OPEN ACCESS
A physics-, SCADA-based remaining useful life
calculation approach for wind turbine drivetrains
To cite this article: Diederik van Binsbergen et al 2022 J. Phys.: Conf. Ser. 2265 032079
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The Science of Making Torque from Wind (TORQUE 2022)
Journal of Physics: Conference Series 2265 (2022) 032079
IOP Publishing
doi:10.1088/1742-6596/2265/3/032079
1
A physics-, SCADA-based remaining useful life
calculation approach for wind turbine drivetrains
Diederik van Binsbergen1, Marcelo Nesci Soares2, Eilif Pedersen1,
Amir R. Nejad1
1Department of Marine Technology, Norwegian University of Science and Technology
(NTNU), Otto Nielsens veg 10, 7052 Trondheim, Norway
2Federal Center of Technological Education “Celso Suckow da Fonseca” (CEFET/RJ), Rio de
Janeiro, Brazil
E-mail: dirk.w.van.binsbergen@ntnu.no, marcelo.soares@cefet-rj.br
Abstract. This paper describes the development of a physics-, SCADA-based model able to
predict the expected lifetime for wind turbine drivetrains. A real-time coupled torsional gearbox-
generator model is developed using the bond graph approach in the software 20SIM. The model
uses SCADA data with a sampling frequency of one hertz to impose a load reference on the wind
turbine for the simulation model. From the SCADA measurements, rotor torque is estimated
and used as input load to the wind turbine rotor, while generator speed is used as reference
in the control loop for maximum power point tracking. Shaft torsion is used to predict high-
speed shaft radial and axial bearing loads from static equilibrium. The load amplitude and the
number of stress cycles are calculated using the load duration distribution method and damage
is calculated using Miner’s rule. Expected lifetime is predicted by linear extrapolation of the
accumulated fatigue damage to the fatigue limit. Results show that the model can capture the
torsional and electrical dynamics and that the model results agree with the reference input. The
radial bearing loads match well with literature where additional sensors are used to determine
the loads.
1. Introduction
Wind turbine (WT) condition monitoring is becoming increasingly more important due to the
increased cost associated with offshore repairs. WTs have been moving further offshore, causing
longer downtime and higher repair costs. Stehly et al. [1] report that the operational expenditure
(OpEx) for land-based WTs can range between 32 and 54 $/kW/year, while for offshore wind
this can range between 62 and 186 $/kW/year. Faulstisch et al. [2] mention that generator
and gearbox failures cause long downtime and result in high repair costs. Furthermore, Nejad
et al. [3] report that generator and gearbox reliability improvement and condition monitoring
development are especially important. Advancing from corrective to predictive maintenance
strategies can be used for remaining useful life prediction and end-of-life decision-making. This
will subsequently result in a reduction of the OpEx and the levelized cost of energy (LCOE).
Condition monitoring with the use of turbine supervisory control and data acquisition (SCADA)
and condition monitoring systems (CMS) can be used to actively track system properties and
can provide early detection of faults in WTs.
Condition monitoring can be subdivided into data-driven, physics-based and hybrid methods.
The potential of physics-based models is large but these models require additional knowledge
The Science of Making Torque from Wind (TORQUE 2022)
Journal of Physics: Conference Series 2265 (2022) 032079
IOP Publishing
doi:10.1088/1742-6596/2265/3/032079
2
on the WT [4; 5], such as modal parameters [6], which are rarely available to WT operators.
Condition monitoring, both data-driven and physics-based, can require additional sensors. This
increases the cost related to condition monitoring and requires installation before or after the
operational start of the WT and can result in additional downtime. Monitoring properties
based on SCADA measurements is cost-effective since sensors are already installed and can be
implemented directly. Moreover, with historical SCADA data available, the WT status can be
easily exploited since the operational start of the WT. This does not apply when a CMS is added
after the operational start of the WT.
In previous literature, coupled gearbox-generator models have been created [7–9] based
on simulation data, but not based on SCADA measurements. Gear and bearing fatigue life
calculations have been done based on time domain simulations [10–12]. In Gray and Watson [5]
SCADA measurements are used to estimate torque from electrical power and the shaft rotational
speed to further model bearing loads and damage. Here, the torsional dynamics of the drivetrain
are not considered. Remigius and Natajaran [13] show that rotor torque can be estimated
from SCADA data using an inverse approach. They modeled the drivetrain as a two degree
of freedom (DOF) torsional model, consisting of two bodies with inertia and a shaft modeled
as a viscously damped torsional spring and a gearbox ratio to adjust the torsional load and
displacement between the low-speed shaft (LSS) and high-speed shaft (HSS). The state-of-the-
art on physics-, SCADA-based models for WT condition monitoring is therefore limited, while
Helsen [14] mentions that the use of physical simulation models can contribute significantly to
the remaining useful life assessment of the asset. Liu et al. [15] summarized WT bearing failure
modes and mentioned that fatigue fracture, among other failure modes, can occur for all bearings
in the WT. Increasing the accuracy of load calculations based on SCADA measurements will
influence the high cycle fatigue assessment. Thus the need for high accuracy physical models is
of significant importance for future prognostics.
The objective of this work is to develop a real-time physics-, SCADA-based model able to:
(i) calculate torsional loads across the drivetrain and electrical dynamics of the generator
(voltages and currents).
(ii) predict remaining useful life on drivetrain and generator components.
The scope of this work mainly focuses on the development and validation of the coupled
gearbox and generator model and will be used to determine bearing load responses and
deterministic high cycle fatigue damage on the HSS.
In future work, the model can be used in a digital twin framework, where system parameter
estimation due to degradation can be included in combination with stochastic degradation
models, as shown in Moghadam et al. [6]. The model can be used for fault sensitivity analysis
between the mechanical and electrical components of the WT.
The rest of the paper is organized as follows: In section 2 the coupled gearbox-generator,
load estimation and damage accumulation models are presented. Then, in section 3 the model
is validated using SCADA data and previous literature followed by results on the deterministic
damage and remaining useful life results for high cycle fatigue. Finally, in section 4 concluding
remarks are made and future work will be elaborated on.
2. Methodology
The bond graph (BG) [16] approach is used to construct the real-time coupled torsional gearbox-
generator model of the WT since it is well suited for complex multi-domain systems. SCADA
measurements with a sampling frequency of one hertz (Hz) are used to impose a load reference on
the WT for the simulation model. Shaft torsion is calculated across the drivetrain and voltages
and currents of the generator are calculated. Radial and axial bearing loads are calculated on
the HSS using static equilibrium. Stress cycles are counted using the load duration distribution
The Science of Making Torque from Wind (TORQUE 2022)
Journal of Physics: Conference Series 2265 (2022) 032079
IOP Publishing
doi:10.1088/1742-6596/2265/3/032079
3
(LDD) [17; 18] method and Miner’s rule [19] is used to model damage accumulation. Expected
lifetime is predicted based on linear extrapolation. Radial bearing loads on the HSS are compared
to the results of Guo and Keller [20], where strain gauge measurements are used to predict the
bending moment on the HSS in order to solve static equilibrium. The generator model is
validated using the available wound rotor induction machine in Matlab/Simulink [21].
In subsection 2.1 literature and measurement data relevant to the development of the case
study model are mentioned. In subsection 2.2 it is explained how the load reference on the rotor
side is calculated using SCADA data. In subsection 2.3 the bond graph approach is further
introduced and in subsection 2.4 the developed model is discussed. Due to the stiff nature of
the system, subsection 2.5 substantiates the solver choice. Bearing load estimation and fatigue
damage accumulation are discussed in subsection 2.6 and 2.7 respectively.
2.1. Case study data
An approach for developing a physics-based model based on data extracted from measurements
was introduced by van Binsbergen et al. [22]. The considered case consists of a 1.5MW doubly-
fed induction generator (DFIG) WT and its information is available in NREL technical reports
[23–25] and in Guo and Keller [20]. Experimental data is provided by the National Renewable
Energy Laboratory (NREL) [26] and is publicly available. Further information on the gearbox
topology and model parameters can be found in van Binsbergen et al. [22].
2.2. Load reference
The load reference for the model is determined from SCADA measurements, which are denoted
by ∗. The SCADA power production (P∗), rotor speed (Ω∗
r) and generator speed (Ω∗
g) are
used to determine the input references of the 20SIM [27] model. Rotor torque (Tr) is used as
load reference to the wind turbine rotor, while Ω∗
gis used as reference in the control loop for
maximum power point tracking (MPPT). The rotor torque is determined using Equation 1,
which is derived from the equations of motion (EOM) for a torsional 2 DOF drivetrain system:
Tr=Jr˙
Ω∗
r+N(Tg+Jg˙
Ω∗
g),(1)
where Jrand Jgrepresent the rotor and generator inertia respectively. Nis the inverse of the
gearbox ratio and ˙
Ω∗
rand ˙
Ω∗
gare the rotor and generator shaft acceleration respectively. The
generator torque (Tg) is calculated from P∗=TgΩ∗
g. This is a valid assumption when power
is measured either before or after the converter since the converter has a limited influence on
the system dynamics. A Butterworth filter is applied on the rotor torque input and the control
reference with a cut-off frequency of 0.25Hz. This assumption makes the results smoother and
has limited consequences on the available dynamics in the data since the Nyquist frequency is
0.5Hz. Moreover, the power electronic converter has been considered ideal in this model and
therefore the output rotor voltages to control the generator are purely sinusoidal.
2.3. Bond graph approach
The BG modeling approach is used to construct the coupled gearbox-generator model. BGs
are a graphical notation of energy flow in physical systems where half arrows, also called power
bonds, represent the flow of energy between systems or elements. 1- and 0-junctions represent
the distribution of energy, with equal flow and effort respectively, while I-C- and R-elements
represent energy storage (flow storage and effort storage respectively) and energy dissipation.
BGs automatically provide the model equations in state-space form which can be solved through
a variety of integration methods. A thorough description of BG modeling can be found in
Karnopp et al. [16].
The Science of Making Torque from Wind (TORQUE 2022)
Journal of Physics: Conference Series 2265 (2022) 032079
IOP Publishing
doi:10.1088/1742-6596/2265/3/032079
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2.4. Wind turbine model
The coupled WT gearbox-generator model is implemented in 20SIM [27]. Figure 1 shows an
overview of the model. The SCADA submodel contains the reference power production,
reference rotor speed and reference generator speed for the LoadReference and Control
submodel. In the LoadReference submodel, the rotor torque is calculated from SCADA
measurements and is applied on the rotor side of the Gearbox submodel. The Gearbox
submodel is represented as a 7 DOF system and receives the rotor torque and electromagnetic
torque (Te) as input from the LoadReference and Generator submodel respectively and
outputs the mechanical generator speed (Ωg) towards the generator and controller. Here it is
assumed that the electromagnetic torque is the same as the generator torque. The Generator
submodel represents the generator as a DFIG, connected to a 575V/60Hz grid, and the Control
submodel represents the controller for the DFIG. First, the optimal speed reference from SCADA
data is applied in the generator speed control loop. Hence, the control is following the MPPT
power curve of the real wind turbine. Furthermore, the electromagnetic torque and rotor-side
currents are necessary as input to the control loop in order to control the rotor-side voltages of
the generator. From the Gearbox submodel, the HSS torque (Thss) and HSS rotational speed
(Ωhss) are extracted and the gear teeth load (Ft) is calculated from the HSS torque and pinion
base radius (Rb): Ft=Thss
Rb. The axial load (Fa) can then be calculated using the helix angle of
the gear-pinion stage, which is further elaborated in subsection 2.6. In the LoadEstimation
submodel, the radial bearing loads on the HSS are calculated from static equilibrium. The radial
bearing loads are compared to Guo and Keller [20], which uses strain gauge measurements to
predict the bending moment on a specific place of the shaft to solve static equilibrium on the HSS.
In the Damage submodels, damage accumulation is modeled for the rotor side radial bearing
(FRS), generator side radial bearing (FGS) and the 4 point contact ball bearing (4PCBB). The
LDD [17; 18] method is used to count the stress cycles and the Miner’s rule [19] is used to
calculate accumulated damage. Expected lifetime is predicted by linear extrapolation of the
accumulated fatigue damage to the fatigue damage limit.
Figure 1. Case study model overview: Coupled gearbox-generator model including load
reference and controller in blue, load estimation model in green and fatigue damage accumulation
model in red.
2.4.1. Gearbox model: The WT drivetrain is modeled as a lumped parameter model with 7
torsional DOF. Gear meshing is modeled as rigid, while shafts are modeled as flexible beams.
The shaft rotational stiffness (K) is determined geometrically, assuming an ideal cylinder and
constant E-modulus, for each shaft and the equivalent stiffness is equal to the first torsional
natural frequency of the drivetrain for the given rotor and generator inertia.
The Science of Making Torque from Wind (TORQUE 2022)
Journal of Physics: Conference Series 2265 (2022) 032079
IOP Publishing
doi:10.1088/1742-6596/2265/3/032079
5
The EOM are derived using the Lagrange-Hamiltonian [28] method and are represented with
an IC-element [16; 29]. The torque on each inertia element and the rotational speed of each
inertia element is found by solving Equation 2 and 3 respectively.
e≡˙p=δT
δq
−δV
δq +E=e′+E,(2)
f≡˙
q=M−1p,(3)
where eand frepresent the effort and flow respectively, prepresents the generalized
momentum and qrepresents the generalized coordinate. Tand Vare the kinetic and potential
energy respectively and Mis the mass matrix. e′contains all effort terms dependent on
generalized coordinates and Econtains the external effort sources.
e′=−
Klss(θr−θgs,1)
Klss(θgs,1−θr)−Kiss(θgs,2−n1n2θgs,1)
Kiss(θgs,2−n1n2θgs,1)−Kiss,hss(θgs,3−n3θgs,2)
Kiss,hss(θgs,3−n3θgs,2)−Khss(θbd −n4θgs,3)
Khss(θbd −n4θgs,3)−Kbd,c(θc−θbd )
Kbd,c(θc−θbd )−Kc,gs (θg−θc)
Kc,gs(θg−θc)
,E=
Tr
0
0
0
0
0
−Tg
(4)
e′represents the stiffness torque and can be seen in Equation 4. e′is dependent on the
generalized coordinate of the shaft position (θ) and K. Subscript gs, 1,gs, 2and gs, 3are
abbreviations for gear stage 1, 2 and 3 respectively. Subscript bd and crepresent the brake disk
and the coupling respectively. Subscript nrepresents gear ratios of the gearbox, where n1,n2,
n3and n4stand for the carrier-planet, planet-sun, gear-pinion stage 1 and gear-pinion stage 2
ratios respectively. ISS and GS are abbreviations for intermediate-speed shaft and generator
shaft respectively. Damping is not considered since this method is energy conservative. Eis the
external torque on the gearbox, Trand Tg.
M=
Jr0 0 0 0 0 0
0 3n2
1Jpl +n2
1n2
2Jsun 0 0 0 0 0
0 0 n2
3Jpin,1+Jgear,10 0 0 0
0 0 0 n2
4Jpin,2+Jgear,20 0 0
0 0 0 0 Jbd 0 0
0 0 0 0 0 Jc0
0 0 0 0 0 0 Jg
(5)
Mass matrix Mis independent of any generalized coordinates or momenta and is shown in
Equation 5. Jis the moment of inertia around the axis of rotation of the rigid body. Subscript
pl and pin are abbreviations for planet and pinion respectively. Figure 2 shows the Gearbox
submodel. Equation 2 and 3 are solved in the IC-element without the external torque, E.E
is provided to the 1-junction from the left-hand and right-hand multibonds. Tris provided as
signal from the LoadReference submodel and converted to a [7x1] bond using the modulated
effort source, MSe. Similarly, Tgis provided by the Generator submodel as [1x1] bond and is
converted to a [7x1] bond using a transformer, TF. The generator speed (Ωg) is then used in
the control structure of the DFIG.
The Science of Making Torque from Wind (TORQUE 2022)
Journal of Physics: Conference Series 2265 (2022) 032079
IOP Publishing
doi:10.1088/1742-6596/2265/3/032079
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Figure 2. Case study: bond graph gearbox submodel.
2.4.2. Generator model and control structure: The equivalent circuit of the DFIG model [30; 31]
can be seen in Figure 3. Subscript sand rindicate that the circuit elements are part of the
stator-and rotor-side respectively. Subscript dand qindicate that the circuit elements are part
of the direct and quadrature frame respectively. LM,Llr and Lls are the magnetization, rotor
and stator inductances respectively and R,λ,vand iare resistance, flux linkage, voltage and
current respectively. ωis the angular velocity.
RsLls
λsq λrq
dλrd
dt
dλsd
dt
ωdq
LM
Llr Rr
(ωdq-ωm)
vsd vrd
ird
isd
iMd
RsLls
λsd λrd
dλrq
dt
dλsq
dt
ωdq
LM
Llr Rr
(ωdq-ωm)
vsq vrq
irq
isq
iMq
Figure 3. Equivalent circuit of a DFIG in dq frame.
Electromagnetic torque (Te) is calculated using Equation 6, which is obtained by the
simplification of the total instantaneous active power equation of the DFIG in dq frame.
Te=3
2
LM
Ls
Pp(λsqird −λsdir q ), Ls=LM+Lls, Pp: # pole pairs (6)
The DFIG model in Figure 4 is derived from the equivalent circuit of the DFIG model in
Figure 3 and Equation 6. In red the rotor-side electrical bonds and signals are shown, while in
blue the stator-side electrical bonds and signals are shown. At the top and bottom 1-junctions
the rotor-side and stator-side voltages are calculated in direct-quadrature (dq) frame. In green
the flux linkage signals are shown, which are calculated, together with the current, at the M-
element by solving the inductance matrix in dq frame (Ldq) [32] and is given by Equation 7.
The Science of Making Torque from Wind (TORQUE 2022)
Journal of Physics: Conference Series 2265 (2022) 032079
IOP Publishing
doi:10.1088/1742-6596/2265/3/032079
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λsd
λsq
λrd
λrq
=
Rt1
t0vsd dt
Rt1
t0vsq dt
Rt1
t0vrd dt
Rt1
t0vrq dt
,
isd
isq
ird
irq
=L−1
dq
λsd
λsq
λrd
λrq
, Ldq =
Lls +LM0LM0
0Lls +LM0LM
LM0Llr +LM0
0LM0Llr +LM
(7)
In cyan the angular velocity signals are shown. The mechanical generator speed (Ωg) is taken
from the left-hand 1-junction and is used to calculate the electrical angular velocity (ωm) of
the rotor as follows: ωm=PpΩg. The electrical angular rotor velocity (ωr) of the circuit is
calculated as follows: ωr=ωs−ωm, where ωs= 2πfsand the stator frequency (fs) is 60 Hz.ωs
is the electrical angular stator velocity of the circuit and is described as ωdq in Figure 3. Gain K
multiplies the stator flux linkages with constant K=3
2
LM
LsPpto calculate the electrical torque,
shown in the left-hand 1-junction with orange bonds and signals.
Figure 4. DFIG model.
The Park transform [33] and phase-locked loop (PLL) [34] are accommodated in the PLL,
ABC/DQ submodel. The submodel performs the abc to dq transformation, as shown in
Equation 8, and synchronizes the input phase to the grid phase.
xd
xq=2
3cos (ωdqt) cos ωdqt−2π
3cos ωdqt+2π
3
−sin (ωdqt)−sin ωdqt−2π
3−sin ωdqt+2π
3
xa
xb
xc
(8)
The DFIG control [35; 36], shown in Figure 5, consists of PI-controllers in series that have
the purpose to control the rotor-side voltages. The rotor-side direct voltage (vrd), responsible
for controlling the active power, uses the generator speed (Ω∗
g) from SCADA data as a reference
to the speed control loop. The rotor-side quadrature voltage, responsible for controlling the
The Science of Making Torque from Wind (TORQUE 2022)
Journal of Physics: Conference Series 2265 (2022) 032079
IOP Publishing
doi:10.1088/1742-6596/2265/3/032079
8
reactive power, is controlled by the rotor-side quadrature current, i∗
rq , where i∗
rq =−vsd
ωsLM. This
quadrature current will provide a power factor closest to 1 for steady state conditions. Gain K1,
K2and K3are: K1=LM
Ls,K2=K3=Lrσ, where σ=LrLs−L2
M
LrLsand Lr=Llr +LM.
Figure 5. Control structure.
2.5. Integration method
The system is considered to be stiff due to the gearbox and the high ratio between mechanical
inertia and electrical inductance. This will subsequently result in eigenvalues with a large
difference in magnitude. Therefore the Vode Adams solver by Cohen and Hindmarsh [37] is used
with an absolute and relative acceptable error of 10−10 for stability and accuracy considerations.
The applied multistep method and iteration type are the backward differential formula (BDF)
and Newton method respectively, suited best for stiff systems.
2.6. Bearing load estimation
Loads at bearings that support the pinion and the HSS are calculated. The case study WT
shaft is supported by three bearings, mentioned in Guo and Keller [20]:
•NU2326: Radial roller bearing on the rotor-side of the pinion.
•NU232: Radial roller bearing on the generator-side of the pinion.
•QJ328: 4 point contact ball bearing (4PCBB) on the generator-side of the pinion.
SKF states that a 4PCBB in combination with radial roller bearings can carry axial loads
only. It is assumed that the radial roller bearings only provide radial load support. Furthermore,
it is assumed that the radial and axial loads on the bearings are primarily caused by the gear
teeth load and the rotor side of the HSS is assumed to have a free end with zero moment.
The radial bearing loads can then be calculated from static force and moment equilibrium in
radial (Y and Z) direction. Further details on the equilibrium Equations can be found in Guo
and Keller [20]. Radial bearing loads are compared with loads calculated in Guo and Keller
[20]. Similarly, axial bearing loads can be calculated from static load equilibrium as follows:
Fa=Fttan(β), where βis the helix angle of gear-pinion stage 2. The helix angle of gear-pinion
stage 2 is unknown. For further calculations a helix angle of 12◦is assumed.
2.7. Damage accumulation
Accumulated fatigue damage is calculated for the rotor-side, generator-side and 4PCB bearing.
First, the dynamic equivalent load (PR) is calculated [38] as follows: PR=X Fr+Y Fa, where
Xand Yare bearing-specific load factors, given by manufacturers and Frand Faare the radial
and axial load on the bearing.
The Science of Making Torque from Wind (TORQUE 2022)
Journal of Physics: Conference Series 2265 (2022) 032079
IOP Publishing
doi:10.1088/1742-6596/2265/3/032079
9
The load amplitude and number of stress cycles are calculated using the LDD method as
shown in Equation 9 [17; 18]. The total number of cycles to reach failure for a given load
amplitude is calculated using the life Equation as shown in Equation 10 [38].
ni=Ωi
2πdt, (9)
where Ωiis the rotational speed of the HSS for timestep iand dt is the solver timestep.
Ni=C
Pia
,(10)
where Cis the basic dynamic load rating, ais a bearing geometric constant and Piis the
equivalent load for timestep i.
Accumulated fatigue damage is calculated using Miner’s rule [19] as shown in Equation 11.
D= 1 corresponds to a reliability of 90%. Load ratings and dynamic equivalent factors for each
bearing are available at SKF.com. Expected lifetime is predicted by linear extrapolation of the
accumulated fatigue damage to D= 1.
D=
k
X
i=1
ni
Ni
(11)
3. Results and discussion
The results of the coupled gearbox-generator model are validated in subsection 3.1, where
reference values are compared to model outputs and bearing load results are compared to Guo
and Keller [20] for multiple measurement series. Deterministic damage accumulation results on
the HSS bearings can be found in subsection 3.2.
3.1. Validation
The reference SCADA power production, rotor speed and generator speed are compared to the
model results for multiple measurement series. Figure 6 shows these results in the top left-hand,
top right-hand and centre left-hand plots respectively for one measurement series. DRC-uptower
measurements [26] are used as load reference. A good agreement between the reference values
and the model results is found when the turbine is producing power (Pel >0). From Nejad et
al. [39] it can be seen that short-term fatigue damage increases significantly with an increase in
wind speed, thus it is assumed that high cycle fatigue for gears and bearings that provide radial
load support is negligible below cut-in.
The rotor and generator torque are shown in the centre right-hand corner of Figure 6. A clear
difference in torque load behaviour between the rotor and the generator can be seen, implying
that the rotor and generator shaft acceleration should not be neglected when calculating either
rotor or generator torque from the EOM. Bearing loads are compared to Guo and Keller [20]
and results from one measurement series are shown at the bottom of Figure 6. It can be seen
that loads calculated by the model match well with the work done by Guo and Keller [20]. This
means that bearing loads on the case study HSS can be predicted without the additional need
for strain gauges or other sensors when power is produced. Important to consider is that static
equilibrium equations are solved both in this work and in Guo and Keller [20], assuming that
the resultant of all forces acting on the shaft is equal to zero. Furthermore, loads due to other
DOF are not considered. The axial load support by the 4PCBB is not shown in Figure 6 since
no measurements from Guo and Keller [20] are available for this bearing. Also, the axial load
magnitude is highly dependent on the helix angle of the gear-pinion set, which is assumed for the
case study WT. The load magnitude is used for further damage calculations in subsection 3.2.
The Science of Making Torque from Wind (TORQUE 2022)
Journal of Physics: Conference Series 2265 (2022) 032079
IOP Publishing
doi:10.1088/1742-6596/2265/3/032079
10
50 100 150 200 250 300 350
1.7
1.8
1.9
2
50 100 150 200 250 300 350
130
140
150
160
50 100 150 200 250 300 350
0.5
1
1.5
50 100 150 200 250 300 350
200
400
600
800
2
4
6
8
10
12
50 100 150 200 250 300 350
40
60
80
100
120
50 100 150 200 250 300 350
10
20
30
40
50
Figure 6. From top left to bottom right: Reference and model parameter comparison, rotor
and generator torque comparison and radial bearing load comparison.
3.2. Accumulative damage
Bearing accumulative damage and expected lifetime is shown in Figure 7 for each bearing.
It can be seen that for a decrease and increase in bearing load, the gradient of damage
accumulation becomes concave and convex respectively. Furthermore, expected lifetime increases
and decreases for a decrease and increase in mean damage accumulation respectively.
50 100 150 200 250 300 350
0
0.2
0.4
0.6
0.8
1
1.2 10-6
100 150 200 250 300 350
10
20
30
Figure 7. Bearing damage and total lifetime estimation for 90% reliability.
The Science of Making Torque from Wind (TORQUE 2022)
Journal of Physics: Conference Series 2265 (2022) 032079
IOP Publishing
doi:10.1088/1742-6596/2265/3/032079
11
4. Concluding remarks and future work
A real-time physics-based model is developed using the bond graph approach. The model
uses SCADA data with a sampling frequency of one hertz to impose a load reference on the
wind turbine gearbox-generator model. Rotor torque is applied on the wind turbine hub, while
generator speed is used as reference to the control loop for maximum power point tracking.
The model is validated by comparing the rotor speed, generator speed and power production
to the reference values of the model and by comparing the estimated bearing loads to Guo and
Keller [20], where additional strain gauges are used for load estimation. The model can calculate
expected lifetime on high-speed shaft bearings for high cycle fatigue.
Rotor torque can be determined from SCADA measurements when the rotor and generator
inertia are known. The use of an incorrect rotor torque will significantly affect torsional results
across the gearbox and the generator dynamics.
Bearing loads that support the high-speed shaft and pinion can be estimated from SCADA
measurements without requiring additional sensors when operating between cut-in and cut-out
wind speed. This does require additional knowledge on the dimensions of the shaft.
In the future, the model can be used in a digital twin framework, where system parameter
estimation due to degradation can be included in combination with stochastic degradation
models for future prognostics. The model can also be used for coupled fault sensitivity analysis
between the drivetrain and the generator and can be further extended to other failure modes
for gears, bearings, shafts and electrical components.
Acknowledgments
Thanks go to Jonathan Keller and Yi Guo for providing drivetrain properties and load results
for this work.
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