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8/17/2019 Power Loss Prediction Application to a 2.5 MW
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8/17/2019 Power Loss Prediction Application to a 2.5 MW
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Original Article
Power loss prediction: Application to a2.5 MW wind turbine gearbox
Carlos MCG Fernandes1, Maroua Hammami1,2,
Ramiro C Martins1 and Jorge HO Seabra3
Abstract
A 2.5 MW wind turbine gearbox design was considered to perform a power loss prediction using different wind turbinegear oil formulations. A gearbox power loss model, previously validated with experimental results, was used to predictthe efficiency of a full wind turbine planetary gearbox. The power loss model account the gears and rolling bearing losses
using well established models calibrated with a method proposed by the author. The calculations clearly showed thatsignificant energy savings can be achieved by selecting different base oils, modifying gear tooth geometry, or combiningboth.
Keywords
Wind turbine gearbox, gears, rolling bearings, efficiency, power loss, lubrication
Date received: 5 May 2015; accepted: 18 November 2015
Introduction
Wind turbines have a significant contribution to the
electrical power generation from renewal sources
around the world.1 The blades of a wind turbinerotate at very low speeds, typically 20 r/min, which
are not suitable for conventional power generation
using an electrical generator. This constraint is
solved using a multiplying gearbox between the hub
and the electrical generator.
While the main focus of researchers and engineers
for the wind turbine applications is mainly the gear-
box reliability, the energetic efficiency of such
large machines should not be disregarded. The gear-
box efficiency of the car or the bus of daily use is
often considered very high and the power loss prob-
lem is mainly focused on the engine and vehicleweight.2,3 However, wind turbine gearboxes, han-
dle several megawatt and even a small efficiency
increase can save energy useful for several more
households.
The gearbox might have different configurations,
although one of the most used designs has two planet-
ary stages plus a helical gear stage at the end. The
efficiency of these multiplying gearboxes, with such
arrangement or a similar one, is good. Nevertheless,
any efficiency increase will have a significant impact,
reducing the power loss and the operating tempera-
ture. If the efficiency of a 1 MW wind turbine gearbox
is increased by 1%, something like 10 kW of add-itional power would be available in only one machine.
The 1 MW wind turbines are very rare nowadays,
since the current output power is in some cases
above 5 MW.
The power loss reduction has a direct influence on
lubrication quality, increased efficiency, i.e. lower heatdissipation and lower oil operating temperature.
Lowering the operating temperature minimizes oil
oxidation and degradation, which has a large impact
on the lubrication quality and consequently on the
surface protection against failures. Ho ¨ hn et al.4
showed that reducing the oil temperature also reduces
the risk of failure. Even in the case of gearboxes with-
out failure problems overtime, the oil change will be
less frequent contributing for the reduction of the
maintenance costs, related to the cost of fresh oil,
but also to the cost of replacing it in a wind turbine.
The main sources of power loss in a gearbox arethe load-dependent gear and rolling bearings losses.5
In previous works, Hohn suggested5 Palmgren’s
model6 to predict the rolling bearing power losses.
However, more recently Fernandes et al.7 suggested
1INEGI, Universidade do Porto, Campus FEUP, Rua Dr. Roberto Frias,
Porto, Portugal2Laboratory of Mechanical, Modelling and Manufacturing, National
School of Engineers of Sfax, University of Sfax, Tunisia3FEUP, Universidade do Porto, Rua Dr. Roberto Frias s/n, Porto,
Portugal
Corresponding author:Carlos MCG Fernandes, INEGI, Universidade do Porto, Campus FEUP,
Rua Dr. Roberto Frias 400, 4200-465 Porto, Portugal.
Email: [email protected]
Proc IMechE Part J:
J Engineering Tribology
0(0) 1–13
! IMechE 2015
Reprints and permissions:
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DOI: 10.1177/1350650115622362
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8/17/2019 Power Loss Prediction Application to a 2.5 MW
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the use of the new SKF model,8 after a calibration
procedure for each oil formulation.
Ohlendorf’s9 model is currently used to predict
the average gear mesh losses, a constant and average
coefficient of friction along the path of contact is
assumed. The average CoF is usually calculated with
formulations like the ones proposed by Schlenk,10Michaelis et al.,11 and Matsumoto and Morikawa.12
In a previous work,13 the authors showed that a
properly calibrated Schlenk’s model can be used to
accurately estimate the average gear mesh power
losses.7,13,14
The previous works of the authors7,13–23 aimed to
fully characterize wind turbine gear oils in terms of
physical properties and friction, both on gears and
rolling bearings. Experimental tests were performed,
allowing to calibrate each power loss source and then
a gearbox power loss model was developed.
Furthermore, the experimental results clearlyshowed that it is possible to increase gearbox effi-
ciency through an improved gear tooth design or
selecting the most suitable gear oil formulation, or
even, combining these two possibilities.
The present work intends to predict the power loss
of a 2.5 MW wind turbine gearbox lubricated with
different fully formulated ISO VG 320 wind turbine
gear oils. The gearbox and the power loss model con-
sidered allowed to show the influence of rolling bear-
ings, gears, oil formulation, and operating conditions
on a real application.
Wind turbine gear oils
In order to obtain an overview of the different wind
turbine gear oil formulations available on the market,
three fully formulated gear oils were selected. Due to
practical purposes, it is interesting to cover a good
range of possible products, mainly in terms of base
oil. A mineral (MINR), a polyalpholephin (PAOR),
and a polyalkylene glycol (PAGD) oils are included in
this analysis. All wind turbine gear oils selected
have the same viscosity grade, ISO VG 320, and
are expected to have a viscosity of 320 cSt (10%)
at 40
C.According to the manufacturer, the mineral-based
oil (MINR) is formulated with an EP additive system,
providing anti-foam, oxidation, and dispersant prop-
erties as well. It complies to DIN-51517 part 3 (CLP);
Flender Industrial Gear and ISO 12925-1 CKD qual-
ity standards. The polyaphaolephin-based oil, PAOR,
is constituted by 90% of PAO and also with a signifi-
cant amount of ester used to increase additive solubil-
ity and avoid haze. The additive package has
primarily EP function. The lubricant meet the require-
ments of DIN-51517 part 3 (CLP), Flender Industrial
Gear, AGMA 9005-E02 EP, ISO 6743/6 CKT and
U.S. Steel 224. The polyalkylene glycol based oil(PAGD) is a fully formulated oil developed to work
under corrosive media and also to be compatible with
paintings. The chemical and physical characterization
of the wind turbine gear oils can be found in A.
Power loss model
According to Ho ¨ hn et al.,5 as well as several other
authors,24–33 the power loss in a gearbox consists of
gear (PVZ 0 and PV ZP ), bearing (PV L), seals (PV D),and auxiliary (PV X ) losses, as presented in Figure 1.
Load-independent gear losses
Several authors presented works regarding the predic-
tion of the power loss generated by partly immersed
gears.34–41 However, the modes that were proposed
are not able to accurately estimate the actual no-
load losses in cases that deviate from the conditions
that the models were developed for. On the case of
planetary gearboxes, the power loss generated by the
air–oil mixture interaction with the moving mechan-
ical elements presents additional complications. Theplanet gears are animated with a rotational movement
around their own center combined with another rota-
tional movement around the center of the sun gear.
The planet carrier is the element that holds the
planet gears in place and allows the transport
movement of the planets around the sun gear. In a
planetary gearbox, under oil sump lubrication, several
phenomena are prone to create power loss.
Considering a planetary gearbox driven by the
planet carrier but without the sun and internal
gears, the result would be the planet carrier and the
planets rotating as a single element. This movementalone is responsible for the majority of the power loss
generated due to the air–oil mixture interaction with
the moving elements. If the full planetary gearbox is
considered, the power loss due to fluid trapping and
squeezing as well as pumping effects due to the mesh-
ing gears must be considered. The rotation of the
planets around its own center can also create add-
itional power loss.
Recently, Concli et al.42 also proposed a solution
for the problem of the churning power loss in a
planetary speed reducer, which was based on a com-
putational fluid dynamics (CFD) approach. For the
moment the author believes that the CFD is not thebest method to predict the no-load losses due to CFD
models limitations (the relevant effects must be
PV = PVZ0 + PVZP + PVL + PVD + PVX
no-load losses
load dependent losses
power loss gears bearings auxiliaryseals
Figure 1. Power loss contributions.28
2 Proc IMechE Part J: J Engineering Tribology 0(0)
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simulated separately), processing costs and necessity
of experimental validation deviations.43
Load-dependent gear losses
To calculate the meshing gears power losses, the
Ohlendorf equation (1) was used
PVZP ¼ PIN H VL mZ ð1Þ
The local gear loss factor H V L, equation (2), was
considered which was showed to be valid for helical
gears with profile shift.13
H VL ¼ 1
pb
Z b0
Z E A
F N ðx, yÞ
F bt v gðx, yÞ
vtbdxd y ð2Þ
Schlenck10 equation (3) was used to predict the mesh-
ing gears coefficient of friction. The corresponding
lubricant parameter X L (see Table 1) was determined
with experimental results for each oil formulation.
mZ ¼ 0:048 F bt=b
C redC
0:20:05 R0:25a X L ð3Þ
Rolling bearing losses
The SKF model8 considers that the total friction
torque is the sum of four different physical sources
of torque loss, represented as follows
M t ¼ M 0rr þ M sl þ M drag þ M seal ð4Þ
Equations (5) and (6) define the rolling and slidingtorques, respectively
M sl ¼ Gsl sl ð5Þ
M rr0 ¼ ish rs ½Grrðn Þ0,6 ð6Þ
Equation (7) defines the inlet shear heating and equa-
tion (8) shows the replenishment/starvation reduction
factor, both for the rolling element raceway contact.
ish ¼ 1
1 þ 1:84 109 ðn d mÞ1:28 0:64
ð7Þ
rs ¼ 1
eK rsnðd þDÞ
ffiffiffiffiffiffiffiffiffiK z
2ðDd Þ
p ð8Þ
The rolling bearing drag losses are given by equation
(9) for ball bearings or by equation (10) for roller
bearings
M drag ¼ 0:4 V M K ball d 5m n
2 þ 1:093
107 n2 d 3m n d
2
m f t
1:379Rs ð9ÞM drag ¼ 4 V M K roll C w B d
4m n
2 þ 1:093
107 n2 d 3m n d 2m f t
1:379Rs ð10Þ
The seal losses are defined by
M seal ¼ K S 1 d Rs þ K S 2 ð11Þ
The constants Gsl , Grr, K L, K Z K S 1, K S 2, and R are
dependent on the geometry of the rolling bearing.The sliding friction torque (equation (12)) is
dependent on the weighting factor (equation (13))
and on the reference values of the coefficient of fric-
tion (boundary film coefficient of friction— bl and
full-film coefficient of friction— EHD) of each oil.
sl ¼ bl bl þ ð1 bl Þ EHD ð12Þ
bl ¼ 1
e2,6108ðnÞ1,4d m
ð13Þ
The rolling bearing friction torque model, or torque
loss model, only can predict accurate values if theboundary film coefficient of friction bl and the full
film coefficient of friction EHD are representative of
the lubricant used and of the operating temperature of
the rolling bearing. For mineral oils, whatever the
rolling bearing element type, ball or roller, a value
of bl ¼ 0:15 is suggested. Also for mineral oils a
value of EHD ¼ 0:05 is proposed for ball element
bearings, and a value of EHD ¼ 0:02 is proposed
for roller element bearings.8
There are no values of bl and EHD available for
different gear oil formulations, neither for different
operating temperatures. These values must be deter-mined experimentally through rolling bearing tests. In
a previous work, the values of bl and EHD were
determined for different wind turbine gear oil formu-
lations and are presented in Table 2.
Seal losses
Seal power loss is due to friction in the contact zone.
The friction has been the scope of many researchers
but the problem of seal losses is not very well under-
stood yet.44 The contact zone is very small and the
microscopic phenomena is difficult to parametrize.
Freudenberg Simrit performed a large number of measurements and observed that the seal losses are
function of seal diameter and rotational speed.
Table 1. Lubricant parameter for each oil
formulation.13
Oil X L
MINR 0.85
PAOR 0.70
PAGD 0.60
MINR: mineral; PAOR: polyalpholephin;
PAGD: polyalkylene glycol.
Fernandes et al. 3
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The experimental work of Freudenberg culminated in
equation (14) to predict seal losses. The formula onlytakes into account the shaft diameter and the rota-
tional speed while the oil effect is not considered.
PVD ¼ 7:69 106 d 2sh n ð14Þ
Auxiliary losses
The auxiliary losses take into account other dissipa-
tive sources that are not generated by gears, bearings
or the sealing elements.
Application to a 2.5 MW wind
turbine gearbox
A particular wind turbine gearbox design was chosen
to predict its efficiency. The gearbox is presented in
Figure 2(a). It has two planetary stages and a final
stage with a parallel helical pair. It is a very
common type of configuration used in wind turbine
gearboxes, as presented in Figure 2(b). The input
torque and speed on each planetary stage is
made through the planetary carrier and the output
in the sun shaft. Thus, a fixed ring configuration isused.45–47
The gearbox is designed using helical gears in all
stages with a helix angle of z ¼ 10. The total trans-
mission ratio is i 102. The gear properties are
resumed in Table 3: all gears have profile shift and
the safety factors were calculated for an input
torque of 1200 kNm and an input speed of 20 r/min,
assuring the necessary life rating of the gears.
The shafts are supported by the rolling bearings
listed in Table 4.
Operating conditions and specific film thicknessThe test conditions considered for the present study
are resumed in Table 5.
It was assumed the full power capacity of the wind
turbine, i.e. 2.5 MW corresponding to an input speed
on the blades of 20 r/min. The rotational and tangen-
tial speed of each gear mesh are presented in Table 6.
The load conditions produced by a 1200 kNm torque
applied to the input shaft produced the maximum
Hertz pressures presented in Table 6. It is importantto note that in previous works,13,19 the operating con-
ditions used to test fully formulated gear oils in a
FZG gear testing machine were very similar to those
presented here.
In order to know the lubrication regime in each
gear mesh, equation (15), proposed by Hamrock
et al.,48 was used to predict the central film thickness
on the pitch point.
h0 ¼ 0:975 vC ð Þ
0:727R0:364X b E ð Þ0:091
F 0:091nð15Þ
Taking into consideration the inlet shear heating of
the lubricant and corresponding thermal correction
factor (T ), the corrected film thickness is presented
in the following equation
h0C ¼ T h0 ð16Þ
The thermal correction T used was proposed by
Gupta et al.,49 as shown in the following equations
T ¼ 1 13:2 ð p0=E
Þ ðLÞ0:42
1 þ 0:213ð1 þ 2:23 S 0:83Þ ðLÞ0:64 ð17Þ
L ¼ L U S
kLð18Þ
The specific film thickness was then quantified using
equation (19), where ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Rq21 þ Rq22
q and assuming
Rq1 and Rq2 equal to 0.6 mm
¼ h0C
ð19Þ
The specific film thickness was calculated for each
gear mesh, for two operating temperatures (60
Cand 80C) and for the wind turbine gear oils selected.
The results are presented in Figure 3. It can be
observed that the first stage (LSS) operated under
mixed film lubrication conditions (155 2) while
the second (LIS) and the third (HSS) stages per-
formed under full-film conditions at 60 (4 2), no
matter the oil formulation considered. The film thick-
ness predictions allow to conclude that no significant
differences can be found between oil formulations.
At 80C, the first (LSS) and second (LIS) stages
operated under mixed film lubrication conditions
and the gears on the high speed shaft (HSS) operated
under full-film lubrication conditions. The planetarystages (LSS and LIS) presented similar specific
film thickness no matter the contact considered,
Table 2. Coefficient of friction of both TBB and RTB rolling
bearings for an operating temperature of 80C.13
Valid for:3262.5< n d m5 52,200
Bearing type
Oil Parameter TBB RTB
MINR bl 0.058 0.035
EHD 0.056 0.018
PAOR bl 0.049 0.039
EHD 0.044 0.010
PAGD bl 0.054 0.025
EHD 0.044 0.010
MINR: mineral; PAOR: polyalpholephin; PAGD: polyalkylene glycol.
4 Proc IMechE Part J: J Engineering Tribology 0(0)
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i.e. planet/ring or planet/carrier. No matter the oper-
ating temperature considered, the oils allow to keepthe risk of failure below 5%,50 since the specific film
thickness calculated is higher than that required.
Figure 2. Wind turbine gearbox used for the simulation.47
Table 3. Gear geometric properties of the wind turbine gearbox.
Stage 1 Stage 2 Stage 3
Parameter Sun Planet Ring Sun Planet Ring Pinion Wheel
z 21 35 96 23 38 103 117 35
b 320 320 331.5 168.4 168.4 177.4 245 240
i 5.587 5.464 3.343
m 16 9 7 z 20 20 20
z 10 10 10
a0 476 290 550
x z 0.71 0.8031 0.2093 0.6464 0.7693 0.0639 0.769 0.7176
SF 1.68 1.19 1.89 1.98 1.39 2.18 2.74 2.91
SH 1.09 1.15 1.79 1.18 1.22 2.25 2.02 1.99
Table 4. Rolling bearings of the wind turbine gearbox.
Stage Rolling bearing Location Quantity
Stage 1 SKF NU 20/800 ECMA carrier 1
SKF NU 1080 MA carrier 1
SKF NU 2340 ECMA planets 3
SKF NU 2340 ECMA planets 3
Stage 2 SKF NU 244 ECMA carrier 1
SKF NU 1060 MA carrier 1
SKF NNCF 4930 CV planets 3
SKF NNCF 4930 CV planets 3
Stage 3 SKF NU 1060 MA pinion shaft 1
SKF 32960 pinion shaft 1
SKF 32960 pinion shaft 1
SKF NU 1036 ML wheel shaft 1
SKF NUP 236 ECMA wheel shaft 1
NSK QJ1036 wheel shaft 1
Table 5. Wind turbine gearbox conditions for the power loss
simulation.
Condition Value
Input torque 1200 kNm
Input speed 20 r/min
Output speed 2040 r/min
Nominal power 2.5 MW
Operating temperature 60C and 80C
Lubrication method (gears) Oil jet lubrication
Lubrication method (rolling bearings) Dip lubrication
Fernandes et al. 5
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Power loss prediction
To carry on the simulations, the power loss model
presented in section ‘‘Power loss model’’ was used as
resumed in the following equation
PV ¼ PVZ 0 |ffl{zffl}Disregarded
þ PVZP |ffl{zffl}PIN H V mZ
þ PVL |{z}New SKF Model
þ PVD |{z}Disregarded
þ PVX |{z}Disregarded
ð20Þ
The no-load losses of gears and seals were disregarded
for different reasons. In the present study, the no-
load gear losses will not be considered in the simula-
tion since the models available are not independent
of the gearbox configuration. Furthermore, theexperimental and model results presented in previous
works13,19 show that the influence of the no-load gear
losses on the total torque loss of a gearbox, at
low speed, are small. At the same time, the oils
used are ISO VG 320 and the differences between
them, in terms of no-load losses, are expected to
be very small. The auxiliary losses were also
disregarded.
The seal losses were not considered since the seals
used in this particular gearbox are not known.
Furthermore, the Simrit equation (14) does not
account for the influence of different oil formulations.
In a previous work,13 the influence of the seal losses ina gearbox were estimated to be lower than 10% for
loaded conditions.
A simulation was performed for MINR, PAOR
and PAGD gear oils. Two different operating tem-
peratures were considered, 60C and 80C which is
the usual range of operation in a wind turbine gear-
box. The first and second stage were analyzed usingthe concept of mesh-power, while stage 3 of the wind
turbine gearbox, being a parallel helical gear, was
analyzed using equation (1). The input power on
each planetary stage is splitted in three planets and
the tangential force applied on the base plane is cal-
culated by the following equation
F bt ¼ PIN
3 vtð21Þ
The mesh power in each meshing pair should be cal-
culated as presented in equation (22), and so the rela-tive speed was considered. The mesh power (PM )
should be used in equation (1) instead of input
power (PIN ) for the case of planetary gears.
Regarding the coefficient of friction the sum velocities
in the pitch point (vC ) should also be calculated using
the relative velocities.
PM ¼ F bt v0t ð22Þ
The input shaft of stage 3 runs at 610 r/min, which
corresponds to 25 m/s of tangential speed.
Independently of the oil used, the gears will perform
under full-film conditions. The Schlenck equation issuitable for mixed film lubrication conditions and the
coefficient of friction would decrease ad infinitum if
(a) (b)
Figure 3. Specific film thickness calculated at 60C and 80C for each gear mesh and oil formulation.
Table 6. Rotational and tangential speed on the gear mesh of a wind turbine gearbox for an input speed of 20 r/min.
Stage 1 Stage 2 Stage 3
Property Unit P/S P/R P/S P/R Helical
n r/min 111.4 34.9 610.4 190.6 610.4
v t m/s 1.867 0.974 6.302 3.251 24.933p0 MPa 1028 699 921 624 567
P/S: Planet/Sun; P/R: Planet/Ring.
6 Proc IMechE Part J: J Engineering Tribology 0(0)
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the speed is increased without care. To avoid the
underestimation of the meshing gears power loss,
the third stage coefficient of friction was calculated
for ¼ 2, i.e. it was assumed that the coefficient of
friction is better estimated if calculated at the speed
corresponding to the beginning of full film conditions.
The rolling bearing power losses were calculated
using the calibrated power loss model described in
section ‘‘Rolling bearing losses’’. The coefficients of friction (bl and EHD) determined based on the
experimental results are here again used for the
simulation performed, assuming that no significant
difference is found between 60C and 80C.7
Simulation results
Considering the main sources of power loss in each
gearbox stage, gears and rolling bearings, antagonistic
effects were observed, as presented in Figure 4. PAGD
reduced the gears power loss but slightly increased therolling bearing losses. The opposite behavior is
observed for MINR.
MINR PAOR PAGD0
20
40
60
80
100
Oil [−]
P o w e r L o s s [ k W ]
PVZP
PVL
MINR PAOR PAGD0
20
40
60
80
100
Oil [−]
P o w e r L o s s [ k W ]
PVZP
PVL
MINR PAOR PAGD0
20
40
60
80
100
Oil [−]
P V Z P
[ k W ]
Stage 1
Stage 2Stage 3
MINR PAOR PAGD0
20
40
60
80
100
Oil [−]
P V Z P
[ k W ]
Stage 1
Stage 2Stage 3
MINR PAOR PAGD
0
20
40
60
80
100
Oil [−]
P V L
[ k W ]
Stage 1
Stage 2
Stage 3
MINR PAOR PAGD
0
20
40
60
80
100
Oil [−]
P V L
[ k W ]
Stage 1
Stage 2
Stage 3
(a) (b)
(c) (d)
(e) (f)
Figure 4. Power loss prediction for a full wind turbine gearbox.
Fernandes et al. 7
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The temperature also has an opposite effect,
depending if gears or bearings are considered.
Increasing the operating temperature increases the
gear losses, as shown in Figure 4(c) and (d). Raising
the temperature, a more severe lubrication conditionis expected on the gears as shown in Figure 3, which is
in agreement with the power loss predictions.
The rolling bearing losses reduce by increasing the
temperature and consequently lowering the viscosity.
The rolling torque (M rr), in rolling bearings, is the
main source of power loss in stage 3 and it is mainly
dependent on speed and viscosity. Consequently, the
rolling bearings power loss in stage 3 is almost inde-
pendent of the oil formulation.
Simulation results with modified tooth geometry
A different gear tooth geometry was considered for
each gearbox stage. The gear loss factor of the ori-
ginal gear mesh’s is already quite low. In order to
reduce the gear loss factor and achieve a better gear-
box efficiency, the number of teeth was increased and
the module was reduced, keeping the same center dis-
tance.13,51 A positive profile shift was applied in every
gear mesh and the safety factors were slightly reduced,
as presented in Table 7.
The gear loss factors are presented in Table 8 for
both the standard (STD) and modified (MOD) teeth.
The safety factors can be increased by using a
larger face width. This was not done in purpose, inorder to keep the gearbox dimensions and to show
that is possible to reduce the meshing gears power
loss in comparison to the original design. The nominal
pressure angle and the helix angle were also kept inorder to be possible use the same bearings. The pre-
sent work was done for an existent gearbox, but it
would be better to apply it in the early stage of the
gearbox design allowing to modify the helix angle, the
face width, the number of teeth, and select adequate
rolling bearings to achieve the best efficiency without
reducing the safety factors.
Comparing Figure 5(a) and (b) it is clear that the
total power loss decreased and the efficiency
increased, for each oil formulation. The power loss
reduction is due to the gear tooth geometry as pre-
sented in Figure 5(c) and (d). The meshing gears
power loss was reduced by 18 % independently of the oil formulation.
The rolling bearing power losses remain almost the
same as presented in Figure 5(e) and (f), which was
expected since the applied forces were not increased
significantly. Comparing the original gear geometry
lubricated with MINR (Figure 5(a)) and the new one
lubricated with PAGD (Figure 5(b)), the total power
loss can decrease 22%, which corresponds to 21kW.
The main problem of stage 3 is due to the rolling
bearing dimensions and the high operating speed. For
such large bore rolling bearings the only possibility is to
be able to replace them by smaller ones. It implies shaftswith small diameter, which cannot be feasible. The roll-
ing bearing failures are reported in Ruellan et al.52,53 as
a problem in wind turbine gearboxes, so, the rolling
bearing geometry should be addressed with care.
Gearbox efficiency
The efficiency of each gearbox stage is presented in
Table 9 for each gearbox design and for each oil
formulation.
ConclusionsA power loss model previously validated with experi-
mental results was used to perform a power loss
Table 7. Gear geometric properties of the modified (MOD) wind turbine gearbox.
Stage 1 Stage 2 Stage 3
Parameter Sun Planet Ring Sun Planet Ring Pinion Wheel
Z 28 47 128 30 50 135 150 45
B 320 320 331.5 168.4 168.4 177.4 245 240
i 5.587 5.495 3.333
M 12 7 5.5
z 20 20 20
z 10 10 10
a0 476 290 550
x z 0.7742 1.0280 0.2110 0.4330 0.4342 0.9927 0.7464 0.2850
SF 1.29 0.94 1.41 1.64 1.14 1.49 2.23 2.29
SH 1.10 1.16 1.86 1.20 1.24 1.90 2.03 2.00
Table 8. Gear loss factors for the standard (STD) and mod-ified (MOD) wind turbine gearbox.
Stage 1 Stage 2 Stage 3
P/S P/R P/S P/R Helical
HV L (STD) 0.1482 0.1093 0.1391 0.1055 0.0955
HV L (MOD) 0.1132 0.1005 0.1245 0.0676 0.0752
8 Proc IMechE Part J: J Engineering Tribology 0(0)
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simulation with a full-scale wind turbine gearbox. The
power loss model is based on well-established models
for gear losses and rolling bearings. The author sug-
gested a calibration procedure with empirical data for
each power loss source, gears, and bearings, produ-
cing an improved power loss model.The model results show the influence of gear mesh-
ing and rolling bearing losses. It was found that the
rolling bearing losses predominate in very high-speed
conditions while meshing gear power losses are very
important in low and intermediate speeds of stage 1
and 2 planetary sets.
The results showed that a PAGD can promote an
efficiency increase up to 0.6% when compared with aMINR. Combining gear tooth modification and oil for-
mulation 0.8% of efficiency improvement was observed.
MINR PAOR PAGD0
20
40
60
80
100
Oil [−]
P o w e r L o s s [ k W ]
PVZP
PVL
MINR PAOR PAGD0
20
40
60
80
100
Oil [−]
P o w e r L o s s [ k W ]
PVZP
PVL
MINR PAOR PAGD0
20
40
60
80
100
Oil [−]
P V Z P
[ k W ]
Stage 1
Stage 2
Stage 3
MINR PAOR PAGD0
20
40
60
80
100
Oil [−]
P V Z P
[ k W ]
Stage 1
Stage 2
Stage 3
MINR PAOR PAGD0
20
40
60
80
100
Oil [−]
P V L
[ k W ]
Stage 1
Stage 2
Stage 3
MINR PAOR PAGD0
20
40
60
80
100
Oil [−]
P V L
[ k W ]
Stage 1
Stage 2
Stage 3
(a) (b)
(c) (d)
(e) (f)
Figure 5. Power loss prediction for a full wind turbine gearbox.
Fernandes et al. 9
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The power loss model proved to be a valuable tool
to identify the gearbox elements that contribute to
energy dissipation. The power loss quantificationallows to identify which elements (oil formulation,
lubricant viscosity, rolling bearings, and gear geom-
etry) need redesign or alternative selection.
A physical and chemical characterization
of fully formulated wind turbine gear oils
Rheology
Tests at 40C, 70C, and 100C, using an Engler visc-
ometer, were performed in order to measure the kine-
matic viscosity of all the wind turbine gearoils. The kinematic viscosity measurements are
presented in Table 10, showing that all the oils are
in the range acceptable for an ISO VG 320 grade oil
320 32 cSt.
Using ASTM D34154 (equation (23)) it was pos-
sible to calculate the ASTM constants mA and nAkeeping the constant value of aA¼0.7 for all the oils.
log logð þ aAÞ ¼ nA mA logðT Þ ð23Þ
The density was measured with an Anton Par dens-
imeter, a portable unit. The range of temperature
available goes from 15C up to 40C, which isenough to know the density of a fluid under ambient
temperature conditions. It is known that the density
depends on the temperature.55 However, the influence
of the pressure on the density is much more important
than the influence of the temperature.
The density was measured at 15C, which is the
reference temperature ( 0) and the values are pre-
sented in Table 10. Additional measurements
were performed up to the limit temperature of the densimeter. The values measured were used to
evaluate the thermal expansion coefficient (t),
according to the following equation, also presented
in Table 10.
¼ 0 þ t 0 0 ð Þ ð24Þ
The results show that PAOR has lower density than
MINR, 0.859 g/cm3 and 0.902 g/cm3, respectively.
PAGD has a significantly high density (higher than
water and the other formulations).
Pressure–viscosity
Under elastohydrodynamic lubrication conditions,
the formation of the lubricating film is strongly
dependent on the pressure–viscosity behavior of
a lubricating oil, as shown in Dowson and
Higginson.55
The kinematic viscosities measured and presented
in Table 10 may be used to determine the pressure–
viscosity coefficient using Gold’s equation (25). The
pressure–viscosity coefficient can be determined for a
pressure of 0.2 GPa, usual value of the pressure in the
inlet zone of the contact, where the film formationoccurs.55 Depending on the base oil, the s and t
values are provided by Gold et al.56
¼ s t 108 ð25Þ
The pressure–viscosity coefficient can be calculated
with some degree of confidence for MINR (mineral
naphtenic), PAOR (polyalphaolephin), and PAGD
(polyalkylene glycol) using equation (25).
With the ‘‘Gold’’ constants s and t previously pub-
lished56 (Table 11), the pressure–viscosity coefficients
can be calculated at different temperatures. Table 11
shows the values for each wind turbine gear oil at80C. It is possible to verify that the oils have the
following behavior: MINR4PAOR4PAGD.
Table 9. Wind turbine gearbox efficiency (%) and total power loss for each oil formulation and gearbox configuration at 80C.
Oil Gearbox design Stage 1 Stage 2 Stage 3 Global P V (W)
MINR Standard 98.93 99.12 98.20 96.25 93,597
Modified 99.10 99.27 98.25 96.62 84,942
PAOR Standard 99.12 99.28 98.20 96.59 85,043
Modified 99.26 99.39 98.23 96.90 78,009
PAGD Standard 99.26 99.38 98.18 96.82 79,423
Modified 99.38 99.48 98.21 97.07 73,537
MINR: mineral; PAOR: polyalpholephin; PAGD: polyalkylene glycol.
Table 10. Density (), thermal expansion coefficient (t ),
kinematic viscosity (), ASTM constants (m A, n A), and viscosity
index (VI) for the wind turbine gear oils.
Parameter Unit MINR PAOR PAGD
at 15C g/cm3 0.902 0.859 1.059
t 104 5.8 5.5 7.1
at 40C cSt 319.22 313.52 290.26
at 70C cSt 65.81 84.99 102.33
at 100C cSt 22.33 33.33 51.06
m A 9.066 7.351 5.759
n A 3.473 2.787 2.151
VI 85 153 252
MINR: mineral; PAOR: polyalpholephin; PAGD: polyalkylene glycol.
10 Proc IMechE Part J: J Engineering Tribology 0(0)
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Mia et al.57 determined the pressure–viscosity coef-
ficient from high-pressure rheology for a mineral oil
and different PAO wind turbine oil formulations. The
values found are slightly lower than those calculated
through Gold’s equation. Mia et al. values are 15%
lower in the case of mineral oil and 9% lower in the
case of the PAO (Table 12).
Funding
This research received no specific grant from any
funding agency in the public, commercial, or not-for-profit
sectors.
Acknowledgements
This study was funded by:
. National Funds through Fundaça ˜o para a Ciência
e a Tecnologia (FCT), under the project EXCL/SEM-PRO/0103/2012;
. COMPETE and National Funds through
Fundaça ˜o para a Ciência e a Tecnologia (FCT),
under the project Incentivo/EME/LA0022/2014;
. Quadro de Referência Estrate ´ gico Nacional
(QREN), through Fundo Europeu de Desenvolvi-
mento Regional (FEDER), under the project
NORTE-07-0124-FEDER-000009 - Applied
Mechanics and Product Development.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest withrespect to the research, authorship, and/or publication of
this article.
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Appendix
Notation
a0 center distance (mm)
aA ASTM D341 reference kinematic visc-osity (cSt)
b gear face width (mm)
12 Proc IMechE Part J: J Engineering Tribology 0(0)
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B rolling bearing width (mm)
C w drag torque factor for roller bearings
d rolling bearing inner diameter (mm)
d m rolling bearing mean diameter (mm)
D rolling bearing bore diameter (mm)
f t drag torque factor for rolling bearings
F a axial load (N)F N gear normal force per unit contact
length in each meshing position along
the path of contact (N/mm)
F bt gear tangential force on the base plane
(N)
Grr rolling torque factor depending on the
bearing type, bearing mean diameter
and applied load
Gsl sliding torque factor depending on the
bearing type, bearing mean diameter
and applied load
h0 central film thickness (m)h0C corrected central film thickness (m)
H V L local gear loss factor
HSS high speed shaft
i gear ratio
K ball drag torque factor for ball bearings
K roller drag torque factor for roller bearings
K S 1, K S 1 rolling bearing seal losses factors
K rs starvation constant for oil bath
lubrication
K Z bearing type related geometry constant
LSS low speed shaft
LIS low intermediate shaft
m gear module (mm)mA ASTM D341 viscosity parameter
M 0rr rolling friction torque (Nmm)
M sl sliding friction torque (Nmm)
M drag friction torque of drag losses ([Nmm)
M seal friction torque of seals (Nmm)
M t internal bearing friction torque (Nmm)
n rotational speed (r/min)
nA ASTM D341 viscosity parameter
pb gear transverse pitch (mm)
P / S planet/sun meshing contact
P / R planet/ring meshing contact
PIN input power (W)PV total power loss (W)
PVZ 0 no-load gears power loss (W)
PV ZP meshing gears power loss (W)
PV L rolling bearings power loss (W)
PV D seals power loss (W)
R1 geometry constant for rolling friction
torque
Ra average surface roughness (m)Rs drag torque factor for rolling bearings
s pressure–viscosity parameter
S 1 geometry constant for sliding friction
torque
S F root stress safety factor
S H flank stress safety factor
t pressure–viscosity parameter
v g gear sliding velocity in each meshing
position along the path of contact (m/s)
vtb gear tangential velocity on the base
plane (m/s)
v
C sum of the gear surface velocities on thepitch point (m/s)
V M drag torque factor depending on the
bearing type
xz gear profile shift
z gear number of teeth
pressure–viscosity coefficient (Pa –1)
t thermal expansion coefficient
z gear pressure angle ()
thermoviscosity coefficient (K1)
R rolling bearing seal losses factor
z gear helix angle ()
dynamic viscosity (Pas)
specific film thicknessbl coefficient of friction in boundary film
lubrication
EHD coefficient of friction in full film
lubrication
sl sliding coefficient of friction
bearing coefficient of friction
kinematic viscosity (cSt)
bl sliding friction torque weighting factor
ish inlet shear heating reduction factor
rs kinematic replenishment/starvation
reduction factor
density (g/cm3
)
Fernandes et al. 13