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Friction torqueofthrustballbearingslubricatedwithwindturbinegearoils

Friction torque of thrust ball bearings lubricated with wind turbine gear oils

Carlos M.C.G.Fernandes a ,n ,Ramiro C.Martins a ,Jorge H.O.Seabra b

a INEGI,Universidade do Porto,Campus FEUP,Rua Dr.Roberto Frias 400,4200-465Porto,Portugal b

FEUP,Universidade do Porto,Rua Dr.Roberto Frias s/n,4200-465Porto,Portugal

a r t i c l e i n f o

Article history:

Received 21May 2012Received in revised form 7September 2012

Accepted 9September 2012

Available online 16September 2012Keywords:Gear oils

Rolling bearings Friction torque Ef?ciency

a b s t r a c t

Planetary gearboxes used in wind turbines very often have premature bearing and gear failures,some of them related to the lubricants used.Five fully formulated wind turbine gear oils with the same viscosity grade and different formulations were selected and their physical characterization was performed.The lubricant tribological behaviour in a thrust ball bearing was analyzed.A modi?ed Four-Ball Machine was used to assemble the bearings.They were submitted to an axial load and the tests were performed at velocities ranging between 150and 1500rpm.Experimental results for the operating temperatures and for the internal friction torque are presented.

1.Introduction

As proven source of clean and affordable energy,wind resources clearly have a vital role to play in energetic sustain-ability [1].In this sense it is necessary to have wind turbines that maximize the use of eolic energy and achieve their design life goals with minimal maintenance.

Gearboxes have plagued the wind power industry [2–5].Wind turbine failures can be extremely costly in terms of repair costs,replacement parts and lost power,and the gearbox is the most likely component to have a major effect on the turbine avail-ability.Since the establishment of the wind energy industry large failure rates of the gearboxes have been observed.Windmills,often placed in hostile environments,have premature bearing and gear failures,and the performance of the gear oils used for their lubrication also have an important role in gearbox reliability.Most wind turbine gearbox failures are rooted to the bearings [6–9].The most signi?cant fatigue wear phenomena is micropit-ting and smearing caused by large amounts of roller/raceway sliding in situations in which speci?c ?lm thickness (L )is low,leading to high stresses and temperatures in the contact [10].

Due to economic and environmental constraints it is mandatory to increase the ef?ciency of windmills,to reach the highest ef?ciency of planetary gear drives and their parts (gears,rolling bearings,seals,y )and to minimize the heat generation in the gearboxes [11].In order to increase gearbox ef?ciency it is important to identify the main sources of power loss.The most common wind turbine gearboxes

have planetary gears and the main losses occurring are:friction loss between the meshing teeth [12–17],friction loss in the bearings [12,18,19],friction loss in the seals [12],lubricant churning losses [20,21]and energy loss due to air-drag [11].

Friction generated between the meshing teeth is the main source of power loss in a planetary gear.On the other hand,rolling bearing friction is also very important because it can reach about 30%of total power loss occurring within the mechanism [22].In this sense,understand the friction torque generated within rolling bearings is essential in order to reduce their contribution to the overall power loss.There are four physical friction sources inside a rolling bearing:rolling friction,sliding friction,seal friction and drag losses [23].The most important ones in the case of windmill applications (high torque and low speed)are the friction occurring in the contact between the rolling elements and raceways (sliding friction)and the friction due to the lubricant ?ow between the bearing elements (rolling friction).These energy loss mechanisms are highly depen-dent on the lubricant ability to generate an effective oil ?lm between the rolling elements and the raceways and on the physical properties of the gear oils.

The identi?cation of the loss mechanisms occurring in rolling bearings lubricated with wind turbine gear oils are the main purpose of this work.For that purpose the friction torque losses in thrust ball bearings (51107)were identi?ed and compared when different lubricants are used.Five different fully formulated gear oils were characterized and tested on a thrust ball bearing (51107)submitted to an axial load of 7000N and rotational speeds between 150and 1500rpm.The tests were performed on a modi?ed Four-Ball Machine (Cameron-Plint TE 82/7752)using a special assembly for the thrust ball bearings (51107).

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Tribology International

Corresponding author.Tel.:t351225082212.

E-mail address:cfernandes@inegi.up.pt (C.M.C.G.Fernandes).

Tribology International 58(2013)47–54

2.Lubricant properties

All the lubricants tested are fully formulated gear oils have a viscosity grade ISO VG320and their base oils are:Ester(ESTF and ESTR),Mineral(MINR),Polyalkyleneglycol(PAGD)and Polyalphao-le?n(PAOR).Table1displays the physical properties of the?ve lubricants as well as their chemical composition.

2.1.Chemical composition

Using the ICP method according to ASTM D5185,the chemical composition of the lubricants was determined and presented in Table1.The elements identi?ed were Zinc(Zn),Magnesium(Mg), Phosphorus(Ph),Calcium(Ca),Boron(B)and Sulfur(S).It is clear that the formulations are signi?cantly different,both in terms of base oil and additive package.

2.2.Physical properties

A complete characterization of physical properties of the lubricants was performed.A detailed description are presented in Appendix A and the results are in Table1.

3.Rolling bearing assembly and test procedures

The rolling bearing tests were performed on a modi?ed Four-Ball machine,where the Four-Ball arrangement was replaced by a rolling bearing assembly,as shown in Fig.1.This assembly was developed to test several rolling bearings and measure the friction torque and the operating temperature in several different points.

A detailed presentation of this assembly can be found in[24].

The rolling bearing assembly is divided in two parts:the shaft adapter(6),directly connected to the machine shaft and support-ing the bearing upper race(5);a lower race support(2)and the bearing lower race(3),both clamped to the bearing housing(1). In operation,the internal bearing torque(or friction torque)is transmitted to the torque cell(11)through the bearing housing (1).The friction torque was measured with a piezoelectric torque cell KISTLER9339A,ensuring high-accuracy measurements even when the friction torque generated in the bearing was very small compared to the measurement range available.

This assembly has?ve thermocouples(I–V),measuring tem-peratures at strategic locations(see Fig.1)which are used to monitor the temperature inside the bearing assembly(IV), near to the rolling bearing and the lubricant(III)and to eva-luate the heat evacuation from the bearing housing into the surrounding environment(I,II and V).The system is also monitored by two thermocouples to quantify the chamber and room temperatures.

When assembled in the modi?ed Four-Ball machine the rolling bearing assembly is submitted to a continuous air?ow,forced by two38mm diameter fans running at2000rpm,cooling the chamber surrounding the bearing house.

For the axial load applied(7000N)each contact element(ball) reach a Hertz pressure of2.483GPa and the half-width of contact area is123.87?10à3mm.

The rolling bearing is lubricated by an oil volume of14ml.This volume was selected so that the oil level reaches the centre of the ball,such as advised by the manufacturer.

Notation and units

T operating temperature(1C)

T ref reference temperature(1C)

D T stabilization temperature(1C)

a t thermal expansion coef?cient(–)

b thermoviscositye1Kà1T

r densityeg=cm3T

density at reference temperatureeg=cm3T

C0Ellipticity in?uence parameter(–)

d m bearing mean diameter(mm)

E n equivalent Young’s Modulus(Pa)

Fa axial load(N)

G material in?uence parameter(–)

G rr factor that depends on the bearing type,bearing

mean diameter and applied load(–)

G sl factor that depends on the bearing type,bearing

mean diameter and applied load(N mm)

H0centred?lm thickness(m m)

K rs starvation constant for oil bathe3?10à8T

K Z bearing type related geometry constant(3.8)

L thermal parameter of lubricant(–)

m calculated according ASTM D341[28](–)

M exp bearing friction torque measured experimentally (N mm)

M rr rolling friction torque(N mm)

M sl sliding friction torque(N mm)

M drag friction torque of drag losses(N mm)

M seal friction torque of seals(N mm)

M t total bearing friction torque(N mm)

Z kinematic viscosity at the operating temperature emm2=sTn rotational speed(rpm)

n calculated according ASTM D341[28](–)

D P power loss(W)

R1geometry constant for rolling frictional torque e1:03?10à6T

S1geometry constant for sliding frictional torque(0.016) s parameter depending on lubricant package according to[29](–)

S sliding rate(–)

t parameter depending on lubricant package according to[29](–)

U speed in?uence parameter(–)

U1linear speed of ball(m/s)

U2linear speed of ring(m/s)

VI viscosity index(–)

W load in?uence parameter(–)

sliding frictional torque weighting factor(–)

ish

inlet shear heating reduction factor(–)

kinematic replenishment/starvation reduction factor

(–)

starvation?ow reduction factor(–)

thermal reduction factor(–)

roughness reduction factor(–)

m dynamic viscosity(Pa s)

coef?cient depending on the additive package in the

lubricant(–)

EHD

friction coef?cient in full?lm conditions(–)

sliding friction coef?cient(–)

n kinematic viscosity(cSt))

L speci?c?lm thicknessem mT

t shear stress(Pa)

C.M.C.G.Fernandes et al./Tribology International58(2013)47–54 48

The?ve different rotational speeds were chosen considering the available range of our machine and also the rotational speeds usually used in the wind turbines.

3.1.Start-up friction torque procedure

After mounting the rolling bearing assembly and connecting the thermocouples and the torque cell,a static axial load of 7000N was applied.The rolling bearing monitoring system[24] and the Four-Ball machine were turned on and the speed was increased from rest to150rpm in60s,at room temperature, while the bearing friction torque is monitored.The starting friction torque is the maximum friction torque recorded during this period.3.2.Total friction torque procedure

All thrust ball bearing tests were performed applying an axial load of7000N and rotation speeds in the range150–1500rpm.A detailed presentation of the test procedure can be found in[24].

The machine was started at the desirable speed and run until it reached a constant temperature.Under these conditions,four friction torque measurements were performed:three values are stored and the most dispersed one was disregarded.Due to the ‘‘drift effect’’,which affects the measurements of the piezoelectric sensors after long periods of operation,the friction torque measurements should be made in a short period of time(less than120s)and at constant temperature(721C).

4.Experimental results

4.1.Start-up friction torque

The start-up friction torque is the minimum torque necessary for the rolling bearing to start rotating from rest.The measure-ments were performed in the same conditions for all gear oils,at almost the same operating temperature,see Table2.The start-up friction torques of the thrust ball bearings(TBBs)lubricated with each oil are presented in Table2:the MINR oil generated the highest TBB start-up friction torque,followed by PAOR.ESTF and ESTR oils generated very similar TBB start-up friction torque,276 and240,respectively.The TBB lubricated with PAGD generated the lowest start-up friction torque,210N mm.

Table1

Physical properties of lubricants used.

Parameter Unit ESTF ESTR MINR PAGD PAOR

Base oil(-)Ester Ester Mineral Polyalkyleneglycol Polialphaole?n Chemical composition

Zinc(Zn)(ppm)0.7 6.60.91 3.5 Magnesium(Mg)(ppm) 1.3 1.30.9 1.40.5 Posphorus(Ph)(ppm)449.4226.2354.31100415.9

Calcium(Ca)(ppm)n.d.14.4 2.50.80.5

Boron(B)(ppm)33.6 1.722.3 1.028.4

Sulfur(S)(ppm)5030406112003625020

Physical properties

Density@151C(g=cm3)0.9570.9150.902 1.0590.859 Thermal expansion coef?cient(a t)(/)à6:7?10à4à8:1?10à4à5:8?10à4à7:1?10à4à5:5?10à4 Viscosity@401C(cSt)324.02302.86319.22290.26313.52 Viscosity@701C(cSt)88.0977.4865.87102.3384.99 Viscosity@1001C(cSt)36.0634.8522.3351.0633.33

m(/) 2.695 2.682 3.459 2.752 2.049

n(/)7.1267.0889.0317.266 5.505 Thermoviscosity@401C(b?10à3)[1Kà1]49.9049.0963.8837.3450.68 Thermoviscosity@701C(b?10à3)[1Kà1]35.7835.2542.8328.3636.16 Thermoviscosity@1001C(b?10à3)[1Kà1]26.5526.1930.0722.1226.72

s@0.2GPa(/) 6.605 6.6059.904 5.4897.382

t@0.2GPa(/)0.1360.1360.1390.1490.134 Piezoviscosity@401C(a?10à8)(Paà1) 1.450 1.437 2.207 1.278 1.590 Piezoviscosity@701C(a?10à8)(Paà1) 1.220 1.212 1.774 1.105 1.339 Piezoviscosity@1001C(a?10à8)(Paà1) 1.076 1.071 1.5270.988 1.182

VI(/)15916285241153

1 - Bearing house;

2 - Lower race support;

3 - Bearing lower race;

4 - Rolling element and cage assembly;

5 - Bearing upper race;

6 - Shaft adapter;

7 - Retainer;

8 - Cover;

9 - Upper protecting plates;

10 - Upper connection pins;

11 - Torque cell;

12 - Lower connection pins;

13 - Lower protecting plates;

I - Cover temperature;

II - Bearing house temperature;

III - Oil temperature;

IV - Internal temperature;

V - Inferior temperature;

P - Load

n - Rotational speed

Fig.1.Schematic view of the rolling bearing assembly.Table2

Operating temperature,kinematic viscosity and start-up friction torque@150rpm.

Base oil ESTF ESTR MINR PAGD PAOR

Operating temperature(1C)26.827.425.125.726.4 Kinematic viscosityemm2=sT686.84619.58927.13527.40669.64 Start-up friction torque(N mm)276240306210302

C.M.C.G.Fernandes et al./Tribology International58(2013)47–5449

4.2.Operating and stabilization temperatures

The operating temperature is the one measured in the thermo-couple (III),shown in Fig.2.The operating temperature of the TBB increases when the operating speed increases,whatever the gear oil considered,as shown in Fig.1.At 150rpm the operating temperatures of the TBB lubricated were very similar,between 29.31C for PAOR gear oil and 30.21C for MINR oil.At 1500rpm the operating temperatures of the TBB were signi?cantly higher:y PAGD ?64:51C,y MINR ?66:11C,y ESTF ?67:21C,y ESTR ?68:81C and y PAOR ?71:21C.

The stabilization temperatures of the TBB,de?ned as the differ-ence between the operating and chamber temperatures,that is,y s ?y ày c ,are presented in Fig.3.As in the case of the operating temperature,the stabilization temperature of the TBB increased when the operating speed increased.The TBB lubricated with the MINR gear oil always had the highest stabilization temperature.At low speed (150–300)the other lubricants had very similar stabiliza-tion temperatures with a maximum difference of 0.71C.

The TBBs lubricated with the PAOR,ESTR and ESTF oils had very similar stabilization temperatures,lower than those obtained for MINR and PAGD oils (see Fig.3).At 1500rpm the following TBB

stabilization temperatures were measured:y ESTF s ?33:31C,y ESTR

s ?

33:11C,y MINR s ?36:21C,y PAGD s ?36:01C and y PAOR

s ?31:61C.

These results clearly show that gear oil formulation had a very signi?cant in?uence on the stabilization temperatures of the 51107TBB.

4.3.Friction torque and power loss

The internal friction torque of the TBB,measured at different rotating speeds (150–1500rpm)and for each gear oil tested is plotted in Fig.4.

The TBBs lubricated with MINR and PAGD oils always gener-ated the highest friction torques.Depending on the operating

speed,the friction torques generated by TBBs lubricated with ESTF and PAOR oils were close either to the MINR and PAGD oils (higher values)or to the ESTF oil (lower values).

Knowing the internal friction torque and the operating speed it is possible to calculate the power loss (D P )in the TBB,using Eq.(1),P ?M exp áo

e1T

The power loss results are plotted in Fig.5.The power loss

increased when the operating speed increased,reaching a max-imum of 31–39W at 1500rpm,depending on the gear oil considered.At 1500rpm,the TBB lubricated with the MINR oil had the highest power loss and the TBB lubricated with PAOR the lowest one.

5.Film thickness in the ball-raceway contact

The centre ?lm thickness in the ball-raceway contact can be determined using Eqs.(2)–(8)for elliptical contacts,derived by Hamrock and Dowson [25].The geometry of the ball-raceway contact in the TBB was used as well as the oil properties at the corresponding operating temperatures.H 0?1,345áR X áC 0áU 0,67áG 0,53áW à0,067e2T1X ?11X 1t1X 2

e3T

1R Y ?121R Y 1t1R Y 2

e4T

C 0?1à0:61e ?à0:752eR Y RX T

0:64

R X o R Y

010203040506070800

250

500750100012501500

O p e r a t i n g T e m

p e r a t u r e [°C ] Rotational Speed [rpm]

ESTF ESTR MINR PAGD PAOR

Fig.2.Operating temperature vs.rotational speed.

0510152025303540

250

500750100012501500

S t a b i l i z a t i o n T e m p e r a t u r e [°C ]

Rotational Speed [rpm]

ESTF ESTR MINR PAGD PAOR

Fig.3.Stabilization temperature vs.rotational

speed.

150

175200225250275300M t [N .m m ]

Rotational speed [rpm]

ESTF ESTR MINR PAGD PAOR

Fig.4.Friction torque vs.rotational

speed.

010********

P o w e r L o s s [W ]

Rotational Speed [rpm]

ESTF ESTR MINR PAGD PAOR

Fig.5.Power loss vs.rotational speed.

C.M.C.G.Fernandes et al./Tribology International 58(2013)47–54

U?Z

eU1tU2T

2R X E n

e6T

G?2a E ne7T

W?2F n

E n

e8T

The theoretical?lm thickness H0was corrected using the thermal reduction factor(f T)due to inlet shear heating,as shown in Eqs.(9)–(12).The speci?c?lm thickness was computed with Eq.(13),taking into account the composite roughness of the thrust ball bearinges?0:18m mT.

Knowing the speci?c?lm thickness in the ball-raceway con-tact,it is possible to evaluate the corresponding lubrication regime.

h0C?f TáH0e9T

?f1t0:1e1t14:8S0:83TL0:64gà1e10T

L?b Z0eU1tU2T2

e11T

S?9U

àU29

U1tU2

e12T

h0C

????????????????

ts22

qe13T

Fig.7shows the evolution of speci?c?lm thickness in the ball-raceway contact with the rotational speed.Gear oils ESTF,ESTR and PAOR had a similar behaviour for all the speed range, reaching the maximum speci?c?lm thickness at300rpm.The speci?c?lm thickness calculated for all gear oils were in the range 1.10–1.94,typical of mixed?lm lubrication.

PAGD gear oil had a slightly different behaviour,generating the highest speci?c?lm thickness of all oils at1000rpm and above that speed.This different behaviour of the PAGD gear oil is explained by its very high Viscosity Index(241),meaning that its viscosity drops signi?cantly less than the other lubricants when the operating speed and temperature of the TBB increased(see Fig.6),although it had the lowest pressure–viscosity coef?cient (see Table1).Below1000rpm PAGD promoted the lowest speci?c ?lm thickness.

The MINR gear oil had the opposite behaviour of the PAGD oil, generating the lowest speci?c?lm thickness of all oils for the highest speed tested.This behaviour of the MINR oil is explained by its low Viscosity Index(85),meaning that its viscosity drops signi?cantly more than the other lubricants when the operating speed and temperature of the TBB increased(see Fig.6),although it had the highest pressure–viscosity coef?cient(see Table1).Fig.7also shows that TBB lubricated with the MINR gear oil has

the highest?lm thickness below500rpm,with L41:74.

6.Friction torque model and discussion

In order to understand the friction torque behaviour of the TBB lubricated with each gear oil the model proposed by SKF[19]was used.The friction torque model used allow to quantify the different components of the friction torque.

The model considers that the total friction torque is the sum of four different physical sources of torque loss,represented by Eq.(14),

M t?M0

tM sltM dragtM seale14TThe thrust ball bearing(51107)does not have seals and so the M seal torque loss term was disregarded.The drag losses were very small because the operating speeds and the mean diameter of the TBB are small and,consequently,the drag torque loss term was also disregarded.Thus,the total internal friction torque of the thrust ball bearing had only two terms:the rolling and sliding

torques,respectively,M0

and M sl,as represented in Eq.(15),

M exp?M t?M0

tM sle15TSince the total friction torque was measured experimentally (M t?M exp),it was possible to calculate the sliding torque once the rolling torque was known,see Eq.(16),

M sl?M tàM0

?M expàM0

e16TEqs.(17)–(24)de?ne the rolling and sliding torques,

M rr0?f isháf rs?G rrenánT0,6 e17T

ish

1t1:84?10à9end mT1:28n0:64

e18T

e K rs n nedtDT

????????????????

K z

2eDàdT

se19T

G rr?R1ád1,83

áF0,54

e20TM sl?G slám sle21T

G sl?S1ád0,05

áF4=3

e22T

?f blám blte1àf blTám EHDe23

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1.8

0250500750100012501500 S

[

]

Rotational Speed [rpm]

ESTF ESTR MINR PAGD PAOR

Fig.7.Speci?c?lm thickness vs.rotational

speed.

100

200

300

400

500

600

700

0250500750100012501500

[

]

Rotational Speed [rpm]

ESTF ESTR MINR PAGD PAOR

Fig.6.Kinematic viscosity vs.rotational speed.

C.M.C.G.Fernandes et al./Tribology International58(2013)47–5451

f bl ?

e 2,6?10en áu T1,4

d m

e24T

The constants S 1and R 1for TBB are equal to 0.016and 1:03?10à6,respectively.

The rolling torque (Eq.(17))is mainly in?uenced by the viscosity of the gear oil at the operating temperature,and by the rotational speed (en án T0:6).The product of the ‘‘kinematic replenishment factor’’by the ‘‘inlet shear heating factor’’(f rs áf ish ),decreases when the operating speed increases.

The sliding torque is highly affected by the load weighting factor and by the coef?cient of friction in full ?lm EHD lubrica-tion,f bl and m EHD ,respectively.The load weighting factor f bl increases when the speci?c ?lm thickness decreases and this affects the sliding coef?cient of friction,m sl ,and the sliding torque.

6.1.Rolling friction torque

The rolling friction torque M 0rr inside the thrust ball bearing was determined using Eqs.(17)–(20)and the operating tempera-tures measured during the TBB tests were considered to deter-mine the kinematic viscosities.The results obtained are shown in Fig.8.The TBBs lubricated with synthetic gear oils (ESTF,ESTR and PAOR)had similar rolling friction torques behaviour.Further-more the values determined are not signi?cantly in?uenced by the rotating speed,meaning that for these gear oils with high Viscosity Index the product n án ,remained almost constant when the rotating speed increased.In fact,higher speed generates higher operating temperature and,consequently lower operating viscosity and n án ?const .

The TBB lubricated with the MINR gear oil had a signi?cantly different behaviour,where the rolling friction torque decreased continuously while the rotating speed increased,above 300rpm.This behaviour is typical of TBBs lubricated with low Viscosity Index mineral ?uids.For a very high Viscosity Index like the PAGD lubricant when speed increases n áu becomes higher and the rolling torque increases.

6.2.Sliding friction torque

Since the total friction torque (M t ?M exp )was measured and the rolling friction torque M 0rr was calculated,the sliding friction torque can be determined using Eq.(16).

Fig.9shows the sliding friction torque inside the TBB,at the operating speed and for each gear oil.The TBB lubricated with the PAGD gear oil always had the highest sliding friction torque at speeds below 1000rpm.The TBBs lubricated with ESFT,ESTR and PAOR gear oils generated signi?cantly smaller sliding friction torques than the MINR and PAGD oils.

The TBBs lubricated with ESTF,ESTR and PAOR oils,with similar viscosity index,have very similar sliding friction torque behaviour in all speed range.Above 500rpm the TBB lubricated with MINR has a different behaviour of the other lubricants and their sliding friction torques increases with speed due to lower viscosity index.At 1500rpm PAOR had the lowest sliding torque (66N mm),only 53%of the value calculated for MINR oil.6.3.Sliding coef?cient of friction

Knowing the sliding friction torque,it is possible to calculate the sliding coef?cient of friction corresponding to each gear oil at the operating speed,using Eqs.(22)and (25),that is,

m sl ?

M sl G sl

e25T

The sliding coef?cient of friction (sliding COF)follows exactly the same trend of the sliding friction torque,because G sl is constant for the same TBB geometry and constant axial load (Fa ?7000N),both are shown in Fig.9.

At low speed (below 500rpm),the high sliding coef?cients of friction calculated for the TBB lubricated with PAGD gear oil can be explained both by the lower viscosity (see Fig.6).This behaviour changes for higher speeds where their higher viscosity resulting in a decrease of sliding torque and then in the sliding coef?cient of friction.

According Brand ~a

o [26],for the same viscosity grade and the same temperature and speed,mineral oils generate higher coef?-cients of friction than Ester,PAO and PAG ?uids.At higher speeds the TBB lubricated with MINR gear oil had lower viscosity than the other oils,justifying the high sliding coef?cient of friction obtained.

At 1500rpm the TBBs lubricated with synthetic gear oils (ESTF,ESTR,PAOR and PAGD)had very similar sliding torques and,consequently,very similar sliding COF.At 150rpm the sliding COF show the following trend,m PAGD sl 4m MINR sl 4m ESTF sl 4m PAOR sl 4m ESTR sl .7.Conclusion

Above 500rpm,the total friction torque inside the TBB

decreased when the operating speed and temperature increased for the synthetic lubricants (ESTF,ESTR,PAGD and PAOR).

The TBBs operated in mixed ?lm lubrication (1:10r L r 1:95T.

The TBBs lubricated with high VI gear oils had an almost constant rolling friction torque for operating speeds equal or above 500rpm.Above 300rpm,the rolling torque of the TBB lubricated with mineral oil decreased as the operating speed

increased.

0.02

0.03

0.040.050.06

0.070.085075100125150175

2000

250500750100012501500

μs l

M s l [N .m m ]

Rotational speed [rpm]

ESTF ESTR MINR PAGD

PAOR Fig.9.Sliding friction torque and sliding coef?cient of friction vs.rotational speed.

50751001251501752000

250

5007501000

1250

1500

M r r [N .m m ]

Rotational speed [rpm]

ESTF ESTR MINR PAGD PAOR

Fig.8.Rolling torque vs.rotational speed.

C.M.C.G.Fernandes et al./Tribology International 58(2013)47–54

The polyalkyleneglycol oil generated higher sliding coef?cient of friction than the other lubricants,below1000rpm.Above 1000rpm mineral oil generated signi?cantly higher sliding COF than other lubricants.

None of the oils is the best across the speed range.A wind turbine only uses a single oil,so the choice must be for the best commitment.

The study of the oils was also extended to gearboxes to fully understand their behaviour.

Acknowledgments

The authors acknowledge to‘‘Fundac-~a o para a Ci?e ncia e Tecnologia’’for the?nancial support given through the project ‘‘High ef?ciency lubricants and gears for windmill planetary gearboxes’’,with research contract PTDC/EME-PME/100808/2008. Appendix A.Physical properties

In a previous work[27],the physical properties were characterized and are now included in the present work.

A.1.Density

The densities of the gear oils at151C are presented in Table1. The gear oil densities were measured at40,70and1001C using a DMA35N densimeter.The values measured were used to calcu-late the thermal expansion coef?cient a t of the gear oils,accord-ing to Eq.(A.1).The results are presented in Table1.

r?r

ta tár0eTàT refTeA:1TA.2.Kinematic viscosity

The kinematic viscosities of each oil were measured using an Engler viscometer.The measurements were performed at40,70 and1001C according to ASTM D341[28]and are displayed in Table1.At401C all the kinematic viscosities were very similar, since all the gear oils had the same viscosity grade.However,at 1001C the kinematic viscosities were signi?cantly different:22.3 cSt for the MINR oil,51.6cSt for the PAGD and33.3,34.9and36.6 for the PAOR,ESTR and ESTF,respectively.

The kinematic viscosities were used to determine the Viscosity

Index of each lubricant.The MINR gear oil had the lowest VI(85) while the PAGD oil had the highest value(241).The PAOR,ESTR, ESTF gear oils had intermediate values,respectively,153,162 and159.

A.3.Dynamic viscosity

The dynamic viscosities of the oils were also measured using a Contraves Rheomat115rheometer with a rotary viscometer with coaxial cylinders.The measurements were performed at40,70 and1001C,and several shear strain rates(6.387,26.786,112.477, 472.479and967.280).The results are displayed in Fig.A1.The corresponding kinematic viscosities are presented in Fig.A2.

At401C the dynamic viscosity was not independent of the shear strain rate,indicating that the lubricant behaviour was non-Newtonian.At higher temperatures(70and1001C)such non-Newtonian behaviour was no longer observed and the dynamic viscosity was constant whatever the shear strain rate.This behaviour was observed for all the gear oils.A.4.Thermoviscosity

The kinematic viscosities were used to determine the thermo-viscosity of the oils,using Eq.(A.2),

eutaTlneutaT

eA:2TThe constants m and n(ASTM D341)as well as the thermo-viscosity values calculated for each oil are presented in Table1. The constant a is0.7according the standard.The thermoviscosity values follow the inverse trend of the Viscosity Index(high Viscosity Index imply a low thermoviscosity value).

A.5.Piezoviscosity

Gold et al.[29]proposed Eq.(A.3)to calculate the piezo-viscosity of oils formulated with different base oils,

a?s n teA:3T0

100

150

200

250

300

350

400

[

]

Rate of shearing strain,du/dy

ESTF ESTR MINR PAGD PAOR

Fig.A1.Dynamic viscosity vs.shearing strain rate.

100

150

200

250

300

350

400

020040060080010001200?

[

]

Rate of shearing strain,du/dy

ESTF ESTR MINR PAGD PAOR

@ 40°C

@ 100°C

@ 70°C

Fig.A2.Kinematic viscosity vs.shear strain rate.

C.M.C.G.Fernandes et al./Tribology International58(2013)47–5453

The constants s and t as well as the piezoviscosity values calculated for each oil are presented in Table1.The MINR gear oil had the highest piezoviscosity at401Ce2:207?10à8Paà1Twhile the PAGD oil had the lowest value(1:278?10à8Paà1T.The PAOR, ESTR,ESTF gear oils had intermediate values,respectively, 1:590?10à8Paà1,1:437?10à8Paà1and1:450?10à8Paà1.

The piezoviscosity has a very signi?cant in?uence on lubricant ?lm thickness between ball and raceways in a thrust ball bearing. References

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Friction torqueofthrustballbearingslubricatedwithwindturbinegearoils

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