Power Loss Prediction Application to a 2.5 MW

8/17/2019 Power Loss Prediction Application to a 2.5 MW

1/14

Page Proof Instructions and Queries

Journal Title: Journal of Engineering Tribology, Proceedings of the Institution of

Mechanical Engineers Part J [PIJ]

Article Number: 622362

Greetings, and thank you for publishing with SAGE. We have prepared this page proof for your review. Please respond to each of

the below queries by digitally marking this PDF using Adobe Reader.

Click “Comment” in the upper right corner of Adobe Reader to access the mark-up tools as follows:

For textual edits, please use the “Annotations” tools.

Please refrain from using the two tools crossed out

below, as data loss can occur when using these tools.

For formatting requests, questions, or other

complicated changes, please insert a comment

using “Drawing Markups.”

Detailed annotation guidelines can be viewed at: http://www.sagepub.com/repository/binaries/pdfs/

AnnotationGuidelines.pdf

Adobe Reader can be downloaded (free) at: http://www.adobe.com/products/reader.html.

No. Query

Please confirm that all author information, including names, affiliations, sequence,

and contact details, is correct.

Please review the entire document for typographical errors, mathematical errors,

and any other necessary corrections; check headings, tables, and figures.

Please confirm that the Funding and Conflict of Interest statements are accurate.

Please ensure that you have obtained and enclosed all necessary permissions for the

reproduction of artistic works, (e.g. illustrations, photographs, charts, maps, other

visual material, etc.) not owned by yourself. Please refer to your publishing

agreement for further information.

Please note that this proof represents your final opportunity to review your article

prior to publication, so please do send all of your changes now.AQ: 1 Please provide venue of the conference for ref [12]

AQ: 2 Please provide venue of the conference for ref [37]

AQ: 3 Please provide venue of the conference for ref [42]

AQ: 4 Please provide year of publishing for ref [45,46,47]

http://www.sagepub.com/repository/binaries/pdfs/AnnotationGuidelines.pdfhttp://www.sagepub.com/repository/binaries/pdfs/AnnotationGuidelines.pdfhttp://www.adobe.com/products/reader.htmlhttp://www.adobe.com/products/reader.htmlhttp://www.sagepub.com/repository/binaries/pdfs/AnnotationGuidelines.pdfhttp://www.sagepub.com/repository/binaries/pdfs/AnnotationGuidelines.pdf


2/14

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:

sagepub.co.uk/journalsPermissions.nav

DOI: 10.1177/1350650115622362

pij.sagepub.com


3/14

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)


4/14

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


5/14

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.



6/14

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


7/14

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.


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.



8/14

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 [−]


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


9/14

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.


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.


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



10/14

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 [−]


PVZP

PVL

MINR PAOR PAGD0

20

40

60

80

100

Oil [−]


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


11/14

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


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




12/14

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.

References

1. Agency EE. Europe’s onshore and offshore wind energy

potential- An assessment of environmental and eco-

nomic constraints. EEA Technical report No 6, 2009,

p. 91.

2. Sprei F and Karlsson S. Energy efficiency versus gains

in consumer amenities: An example from new cars soldin Sweden. Energy Policy 2013; 53: 490–499.

3. Team U. UK team creates Ech2o fuel cell car for effi-

ciency record bid. Fuel Cells Bull 2005; 9: 7–8.

4. Ho ¨ hn BR and Michaelis K. Influence of oil temperature

on gear failures. Tribol Int 2004; 37: 103–109.

5. Ho ¨ hn BR, Michaelis K and Vollmer T. Thermal rating

of gear drives: Balance between power loss and heat

dissipation. AGMA Technical Paper, 1996.

6. Palmgren A. Ball and roller bearing engineering. SKF

Industries, 1959.

7. Fernandes CMCG, Marques PMT, Martins RC, et al.

Gearbox power loss. Part I: Losses in rolling bearings.

Tribol Int 2014.

8. SKF General Catalogue 6000 EN. SKF, November2005.

9. Ohlendorf H. Verlustleistung und Erwa ¨ rmung von

Stirnra ¨ dern. Dissertation, TU Mu ¨ nchen, 1958.

10. Schlenk L. Unterscuchungen zur Fresstragfa ¨ higkeit von

Grozahnra ¨ dern. Dissertation, TU Mu ¨ nchen, 1994.

11. Michaelis K, Ho ¨ hn BR and Hinterstoiber M. Influence

factors on gearbox power loss. Ind Lubric Tribol 2011;

63: 46–55.

12. Matsumoto S, Morikawa K. The new estimation for-

mula of coefficient of friction in rolling-sliding contact

surface under mixed lubrication condition for the power

loss reduction of power transmission gears. In:

International gear conference, 2014 1.13. Fernandes CMCG, Marques PMT, Martins RC, et al.Gearbox power loss. Part II: Friction losses in gears.

Tribol Int 2014.


Gearbox power loss. Part III: Application to a parallel

axis and a planetary gearbox. Tribol Int 2015.

15. Fernandes CMCG, Martins RC and Seabra JHO.

Friction torque of cylindrical roller thrust bearings

lubricated with wind turbine gear oils. Tribol Int 2013;

59: 121–128.


Friction torque of thrust ball bearings lubricated with

wind turbine gear oils. Tribol Int 2013; 58: 47–54.

17. Fernandes CMCG, Amaro PMP, Martins RC, et al.Torque loss in thrust ball bearings lubricated with

wind turbine gear oils at constant temperature. Tribol

Int 2013; 66: 194–202.

18. Fernandes CMCG, Amaro PMP, Martins RC, et al.

Torque loss in cylindrical roller thrust bearings lubri-

cated with wind turbine gear oils at constant tempera-

ture. Tribol Int 2013; 67: 72–80.


Torque loss of type C40 FZG gears lubricated with

wind turbine gear oils. Tribol Int 2014; 70: 83–93.

20. Gonçalves DEP, Fernandes CMCG, Martins RC, et al.

Torque loss in a gearbox lubricated with wind turbine

gear oils. Lubric Sci 2013; 25: 297–311.

21. Marques PMT, Fernandes CMCG, Martins RC, et al.

Power losses at low speed in a gearbox lubricated with

Table 12. Chemical composition in ppm of the wind turbine

gear oils through ICP analysis.

Parameter Unit MINR PAOR PAGD

Sulphur (S) ppm 11200 5020 362

Phosphorus (P) ppm 354.3 415.9 1100

Boron (B) ppm 22.3 28.4 1.0Calcium (Ca) ppm 2.5 0.5 0.8

Zinc (Zn) ppm 0.9 3.5 1

Magnesium (Mg) ppm 0.9 0.5 1.4


Table 11. Constants of Gold equation at 0.2 GPa and

pressure–viscosity coefficient at 80C for each wind turbine

gear oil.

Parameter MINR PAOR PAGD

s 0.9904 0.7382 0.5489

t 0.1390 0.1335 0.1485 108 (1/Pa) 1.677 1.279 1.061


Fernandes et al. 11


13/14

wind turbine gear oils with special focus on churning

losses. Tribol Int 2013; 62: 186–197.

22. Marques PMT, Fernandes CMCG, Martins RC, et al.

Efficiency of a gearbox lubricated with wind turbine

gear oils. Tribol Int 2014; 71: 7–16.


Film thickness and traction curves of wind turbine gear

oils. Tribol Int 2015.

24. Michaelis K. Die Integraltemperatur zur Beurteilung

der Fresstragfa ¨ higkeit von Stirnra ¨ dern. TU Mu ¨ nchen,

1987.

25. Michaelis K and Ho ¨ hn BR. Influence of lubricants on

power loss of cylindrical gears. Tribol Trans 1994; 37:

161–167.

26. Ho ¨ hn BR, Michaelis K and Wimmer A. Gearboxes

with minimised power loss. VDI Berichte 2005; 1904

II: 1451–1465.

27. Ho ¨ hn BR, Michaelis K and Otto HP. Influence of

immersion depth of dip lubricated gears on power

loss, bulk temperature and scuffing load carrying cap-

acity. Int J Mech Mater Des 2008; 4: 145–156.28. Ho ¨ hn BR, Michaelis K and Hinterstoißer M.

Optimization of gearbox efficiency. Goriva i Maziva

2009; 48: 462–480.

29. Changenet C and Velex P. A model for the prediction of

churning losses in geared transmissions—preliminary

results. J Mech Des 2007; 129: 128–133.

30. Changenet C and Velex P. Housing influence on churn-

ing losses in geared transmissions. J Mech Des 2008;

130: 062603.

31. Csoban A and Kozma M. Tooth friction loss in simple

planetary gears. In: 7th international multidisciplinary

conference, Baia Mare, Romania, 17–18 May 2007,

pp.153–160.

32. Martins R, Seabra J, Seyfert C, et al. Power loss in

FZG gears lubricated with industrial gear oils:

Biodegradable ester vs. mineral oil. In: D Dowson

and AA Lubrecht (eds) Tribology and interface engin-

eering series. vol 48, New York: Elsevier, 2005,

pp.421–430.

33. Martins RC, Cardoso NFR, Bock H, et al. Power loss

performance of high pressure nitrided steel gears. Tribol

Int 2009; 42: 1807–1815.

34. Terekhov AS. Hydraulic losses in gearboxes with oil

immersion. Vestn Mashinostroeniya 1975; 55: 13–17.

35. Lauster E and Boos M. Zum Wa ¨ rmehaushal

Mechanischer Schaltgetriebe fu ¨ r Nutzfahrzeuge. VDI-

Ber 1983; 488: 45–55.36. Mauz W. Zahnradsehmierung - Leerlaufverluste. FVA-

Forschungsheft Nr. 185, 1985.

37. Boness RJ. Churning losses of discs and gears running

partially submerged in oil. In: Proceedings of ASME

international power transmission gearing conference,

1989, pp.355–359 .

38. Luke P and Olver AV. A study of churning losses in

dip-lubricated spur gears. Proc IMechE, Part G: J

Aerospace Engineering 1999; 213: 337–346.

39. Changenet C, Oviedo-Marlot X and Velex P. Power

loss predictions in geared transmissions using thermal

networks-applications to a six-speed manual gearbox.

J Mech Des 2006; 128: 618–625.

40. Changenet C, Leprince G, Ville F, et al. A note on flowregimes and churning loss modeling. J Mech Des 2011;

133: 121009.

41. Seetharaman S and Kahraman A. Load-independent

spin power losses of a spur gear pair: Model formula-

tion. J Tribol 2009; 131: 022201.

42. Concli F and Gorla C. Computational and experimen-

tal analysis of the churning power losses in an industrial

planetary speed reducer. In: 9th international conference

on advances in fluid mechanics-advances in fluid mech-

anics IX , WIT Transactions on Engineering Sciences,

vol. 74, 2012, pp.287–298 3.43. Marques PMT, Camacho R, Martins RC, et al.

Efficiency of a planetary multiplier gearbox: Influence

of operating conditions and gear oil formulation. Tribol

Int 2015; 92: 272–280.

44. Croes J and Iqbal S. D2.1 Document 3: Literature

survey: Seal losses. ESTOMAD.

45. Dinner H. Uncertainties in the static calculation of

wind turbine gearboxes. KissSoft.

46. Dinner H. Gearing analysis for wind turbine, seen as a

process. KISSsoft.

47. Dinner H. Wind turbine gearbox calculation. KissSoft 4.

48. Hamrock BJ, Schmid SR and Jacobson BO.Fundamentals of fluid film lubrication. New York:

Taylor & Francis, 2004.

49. Gupta PK, Cheng HS, Zhu D, et al. Viscoelastic effects

in MIL-L-7808-type lubricant, Part I: Analytical formu-

lation. Tribol Trans 1992; 35: 269–274.

50. Association AGM. Effect of lubrication on gear surface

distress. AGMA information sheet. American Gear

Manufacturers Association, 2003. https://books.goo

gle.pt/books?id¼H5tuAgAACAAJ.

51. Ho ¨ hn BR, Michaelis K and Wimmer A. Low loss gears.

Gear Technol 2007; 6: 28–35.

52. Ruellan A, Ville F, Kleber X, et al. Understanding white

etching cracks in rolling element bearings: The effect of

hydrogen charging on the formation mechanisms. Proc

IMechE, Part J: J Engineering Tribology 2014.

53. Ruellan A, Kleber X, Ville F, et al. Understanding

white etching cracks in rolling element bearings:

Formation mechanisms and influent tribochemical dri-

vers. Proc IMechE, Part J: J Engineering Tribology

2015; 229: 886–901.

54. ASTM D341 – 09. Standard practice for viscosity-

temperature charts for liquid petroleum products. West

Conshohocken, PA: ASTM.

55. Dowson D and Higginson GR. Elasto-hydrodynamic

lubrication: the fundamentals of roller and gear lubrica-

tion. The Commonwealth and International Library.

Oxford: Pergamon Press, 1966.56. Gold PW, Schmidt A, Dicke H, et al. Viscosity-pres-

sure-temperature behavior of mineral and synthetic oils.

J Synth Lubric 2001; 18: 51–79.

57. Mia S, Mizukami S, Fukuda R, et al. High-pressure

behavior and tribological properties of wind turbine

gear oil. J Mech Sci Technol 2010; 24: 111–114.

Appendix

Notation

a0 center distance (mm)

aA ASTM D341 reference kinematic visc-osity (cSt)

b gear face width (mm)


https://books.google.pt/books?id=H5tuAgAACAAJhttps://books.google.pt/books?id=H5tuAgAACAAJhttps://books.google.pt/books?id=H5tuAgAACAAJhttps://books.google.pt/books?id=H5tuAgAACAAJhttps://books.google.pt/books?id=H5tuAgAACAAJhttps://books.google.pt/books?id=H5tuAgAACAAJ


14/14

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

Documents

Power Loss Prediction Application to a 2.5 MW