Friction Moment in Oil and Kerosene Mist Lubricated All-Steel and Hybrid Ball Bearings Viorel PALEU Technical University “Gh. Asachi” of IASI, Dept. of Machine Elements and Mechatronics, Iasi, Romania vpaleu@yahoo.com Spiridon CRETU Technical University “Gh. Asachi” of IASI, Dept. of Machine Elements and Mechatronics, Iasi, Romania Daniel NELIAS Institut National des Sciences Appliquées, Lyon, France Summary A theoretical model for friction moment computation in high-speed oil and kerosene mist lubricated ball bearings is presented. This model is based on Houpert’s model [6], developed for low and moderate speed ball bearings, extending the model for the high-speed domain and oil mist lubrication method. For oil mist lubrication the friction model is vali-dated, the theoretical and experimental results obtained for pairs of face-to-face mounted all-steel and hybrid ball bear-ings from 7206C series being in good agreement. For the 7206C face-to-face mounted hybrid ball bearings lubricated by kerosene mist accelerated tests were carried-out at different speeds and loads, the monitored parameters being the friction moment and the developed temperature. Theoretical and experimental results on the friction moment developed in hybrid ball bearings with silicon nitride balls lubricated by kerosene mist are also presented herein.

1 Introduction The research on hybrid bearings began quite late at the international level, but in the last 10 years they reached great proportions. For example, the Japanese company NSK supplies at the present moment more than 60% of the special machines tools only with hybrid ceramics ball bearings, on account of silicon nitride Si3N4 balls (which posses about 40% of the density of the bearing steel, as well as the advanced rigidity and thermal stability). The kerosene is employed from many years for the lubrication of the rolling bearings in turbo-pumps. The work of Tevaarwerk [1] presents an experimental study on the rheology of the rocket propellant RP1 (a kerosene based fuel). In order to reach the optimum design of the hybrid rolling bearings in limited-life gas turbine applications (missiles, drones and other unnamed air vehicles), the results from [1] were used by Schrader and Pfaffenberger [2] as input data in the SHABERTH advanced computer code. Also, endurance tests on oil and JP-10 fuel lubricated all-steel and hybrid ceramic ball bearings with split inner ring were carried at different heavy loads and high speeds [2]. The

hybrid silicon nitride ball bearings under-race lubricated by JP-10 resisted in good state for 25 hours, a slightly more heat being generated when used as lubricant JP-10 fuel instead of MIL-L-23699 oil. Ohta and Satake [3-4] studied the vibration level in kerosene lubricated all-steel, hybrid and all-ceramic ball bearings. They found the greatest level of vibration in hybrid bearings, and the least vibrations in all-ceramic bearings. The tests were carried-out at low speed (maximum value 3 000 rpm) and light load (maximum value 95 N). Recently, Hui et al. [5] determined by tests on ball-on-disk machine the friction coefficient of JP-8+100 fuel lubricated steel ball on steel plate contacts. Also, endurance tests were developed on a three-ball-on-rod rolling contact fatigue machine using different combinations of steel and silicon nitride tribological systems. As lubricant, Mil-L-23699 turbo-jet oil and JP-8+100 fuel were employed. The rolling fatigue life of tribological systems operating in the presence of jet fuel was less than that of the similar oil-lubricated systems. Hui et al. [5] present results on friction moment and developed temperature in hybrid silicon nitride ball

bearings lubricated by jet fuel and oil. The results indicate that the fuel gives lower friction torque and developed temperature than oil. The friction moment and the developed temperature in the bearings are important factors at high speed; they can dictate the reliability of the bearings. If the jet fuel is used in the same time as lubricant for rolling bearings, the trend is to minimize the fuel consumption [2], but assuring a good lubrication. The mist lubrication uses only a small amount of lubricant supplied in a draught of pressurized air.

F

b

Si

F

F

F

F

F

F

F

S

S

e

e

eeP

Peb

Re

RF e

Pi i

FPib

FSi

R i

FR ii

Q

Q

i

e

δe'

δ 'i

2δ

'

F

F

RFR F

' 1δ

22 1

FR 1 FR

S FS

P 2FPc2 FPFP 1bb

FS2

SF 2

Q2 Q2

Q1 Q1

ϖ

ς

FB

)

In this paper, in order to predict the friction moment in kerosene-mist lubricated steel and hybrid ball bearings, a friction model and a computer code were developed. The theoretical results are validated with experimental results by tests on a high-speed rolling bearing testing machine. 2 Friction model for high-speed ball bearings lubri-cated by fluid-lubricant mist Despite of its simplicity, a rolling bearing is a complex tribological system, multiple interactions taking place between their elements: (i) rolling elements and rings, (ii) rolling elements and cage, (iii) rings and cage, (iv) rolling elements and lubricant, (v) and cage and lubricant interactions. The interactions within the tribological system of the rolling bearing generate a variety of forces and moments acting on its elements. In Fig. 1a and 1b, the forces and moments acting on the elements of an angular contact ball bearing are represented. We started from the friction models proposed by Houpert and Leenders [6], further developed by Houpert [7]. The sliding forces acting on a ball of a rolling bearing are computed as resultants of the other forces and moments acting on rolling bearing elements. The forces and moments introduced by Houpert [7] will not be presented herein, but only the forces and moments generated by the high-speed effect [8-9]. 2.1. Ball and cage normal contact forces, Q1 and Q2, and of the braking force, FB

The next relationship exists between the ball-cage contact forces, Q1,2, and the braking force, FB [10]:

21 QQFB −= (1) In pure axial loaded angular contact ball bearings, the balls are pushing the cage, except the case when skidding appears on balls and inner ring contacts.

ZO

aα

a

α

α

i

ea

MERMER

MC

MC

MC

MC

MP

MP

i

i

ii

e

eee e

MER i

MEReMPiMPe

MB + MDb*

Fig. 1: Forces and moments acting on ball and

contacts of an angular contact ball bearing, (a) arespectively

In this case FB is a resistant force acting on balis 0Q2 = ), superposing to the drag force, FD. To model the testing conditions employed in the paper (pure axial load, oil-mist lubrication andspeed), we considered that the contact forces beach ball and the cage are equal. Using the equaequilibrium of moments on cage, the brakingacting on a single ball, FB, can be determifollows:

021

=−⋅ ∑∑=

cm

Z

jj M

dFB

∑ cM = represents the sum of the moments ac

cage [11]. Zj ..1= , Z=numbers of balls;

dm= pitch diameter. 2.2. Drag force acting on ball, FD

The generally formula, necessary for the computadrag ball force, FD, are presented by Gupta [11].and kerosene mist lubrication, the density mixture, ρam, was computed in this paper as follo

(a

1

1

c1

(b)

races nd (b)

ls, (that

current high-etween tion of force

ned as

(2)

ting on

tion of For oil of the ws:

100oil) % - (100 oil % oil air

amρρ

ρ⋅+⋅

= (3)

where the air density is 2.1≅airρ [Kg/ m3]. For oil and kerosene mist lubrication, the mean percent of fluid found in the testing device, that is the house of the testing bearings, was estimated as:

% oil= % 100* ⋅h

dropdrops V

VN (4)

where: Ndrops= means the number of oil drops per minute;

3

34

dropdrop RV ⋅⋅= π , (5)

Vdrop represents the volume of a drop, Rdrop = is the radius of the oil drop (~ 1.0 mm);

Vh= ( )hiLdD

⋅−

⋅4

2π (6)

where: D= outer diameter of the rolling bearing, d= inner diameter of the rolling bearing, Lhi= distance between the to face to face tandem of rolling bearings (about 20.0 mm). The drag force acting on one ball is given by:

2

21

cDam VAcbCFD ⋅⋅⋅⋅= ρ (7)

where: CD = coefficient of ball drag;

bb DLwc

DAcb ⋅−

⋅=

4

2π, (8)

Acb represents the surface area of the ball; Lwc= thickness of cage;

cm

cd

V ω⋅=2

, tangential speed of cage. (9)

The coefficient of ball drag, CD, was obtained as a

function of Reynolds number, η

ρ bcam DV ⋅⋅=Re ,

where =η dynamic viscosity of lubricant, by interpolating the Schlichtig’s data, presented in [11]. 2.3. Friction force between the asperities of the contact surfaces, Fa To estimate the friction force between the asperities of an elliptical contact roller end – flange, Aihara [12] used the model of Patir & Cheng, considering EHD conditions, contact pressures smaller than 0.4 GPa , and relative longitudinal roughness. Aihara approximated the Patir & Cheng curve with the equation:

( )2.18.1exp λ⋅−=Q

Qa (10)

where: Qa = contact force on asperities; Q=total load on the considered contact;

2211.1 abac

c

RR

h

+=λ , (11), represents the

lubrication parameter;

ch =lubricant central film thickness;

acR = raceway roughness;

abR = ball roughness. Bercea et al. [13] recommend for the computation of the friction coefficient in mixed regime the next formula:

QFFRFS

QFF

QF asolidfluidf ++

=+

==µ (12)

where: Ff =friction force on contact;

fluidF =FS+FR (13), represents the fluid friction force, within the lubricant film; FS= sliding friction force; FR= rolling friction force; Fsolid= Fa= aa Qµ (14), represents the asperity friction force. For the friction coefficient on asperities, Aihara [12] recommends the value aµ =0.2. Houpert [7] take into consideration for the computation of the friction coefficient in mixed regime only the forces FS and Fa. In ball and races contacts, the contact loads are very high (hundreds or thousands of Newtons). For an exact analysis it was considered that the contact force, Q, divides in two components: the force acting on the lubricant fluid film, Qfluid, and the force acting on contact asperities, Qa . Therefore:

afluid QQQ −= (15) From Aihara equation results: ( )[ ]2.182.1exp1 λ⋅−−⋅=−= QQQQ afluid (16)

The remaining load, (17), acts on asperities and produces the friction force between asperities, Fa.

fluida QQQ −=

In this paper, the lubricant film thickness was computed with Hamrock and Dowson formula for EHD contacts [14-16], thermally corrected by Murch and Wilson thermal correction coefficient [17]. The sliding speed on ball and races contact surface of the contact bodies were estimated using a vectors-and-matrix model presented on large in [9]. This model is closed by Gupta’s model [11], but use the outer race control assumption to avoid the integration of the equations of motion for the rolling elements and for the cage. The fluid friction force, Ffluid, was computed using the lubricant shear stresses. The shear stresses in the

kerosene film were estimated with the thermally corrected Johnson’s model, further developed and presented by Houpert [18]. 2.4 Computation of braking moment, MB To find the braking moment MB, the sliding and rolling forces on ball and cage contacts must be appreciated taking into account the lubrication regime and the contact geometry [10]:

21 MBMBMB += (18) where: ( ) bRFSFRMB )2(1)2(1)2(1 += (19)

1, 2= index corresponding to the ball and cage front and rear contacts. This method is very sophisticated, not all of the input data for the problem being available. In our case the rolling bearings are pure axially loaded, and the braking moment MB can simply be computed if considering a constant friction coefficient on ball and cage contacts. For this friction coefficient, Rumbarger et al. [19] recommends a value 1.0<bcµ . In this paper

we considered that . As the braking force was previously determined, the braking moment can be computed with the next relationship:

08.0bc =µ

2b

bcD

FBMB ⋅⋅= µ (20)

Db is the ball diameter. All the other forces and moments represented on Fig. 1a and Fig. 1b have the relationships indicated by Houpert [6-7]. 3 Experimental section 3.1 Testing machine Hybrid silicon nitride ball bearings from 7206C series were tested on the test rig described in [10], [11], and [23]. A general view of the test rig and the sketch of testing device are given in Fig. 2a, 2b and Fig. 3, respectively. The box bed of the test rig weights about 3 tones, assuring a good stiffness and vibration damping capacity. Belts on the box bed fix a rigid metallic vertical support (1). A dovetail guide (2) and an elastic hub (3) support the motor spindle (4). A back-to-back precision tandem of 2 angular ball bearings from small series sustains the caned coil motor spindle. These rolling bearings of the motor spindle are lubricated by textile oil-mist, supplied by a first oil-mist device and lubrication circuit (6). The cooling of the motor spindle house is realized by a return cooling system (7), assuring a continuously flux of could tap water. The spindle of the testing device (5) is clamped by screwing up at the end of the motor spindle (4). Both the motor spindle and the spindle of the tested device were

equilibrated as the maximum run out to be less than 2 micrometers (µm).

(a)

Figure 2: General view of the test rig

(b)

To measure the friction moment at the outer race level within the tested bearings, a metallic elastic leaf (9), with two resistive strain gages brazed on it, was screwed in the vertical support (1). This metallic leaf blocks a pin, fixed in the house of the rotating testing device (5). There is no direct contact between the block of house - charging pieces - outer rings of testing rolling bearings, and the block of spindle – inner rings, the movement from the spindle to the house being transmitted only by balls/ races and cage/ races contacts. To avoid the touch between the nozzle and the house, a 25 degrees circular slit was executed into the house. The speed of the motor spindle (4) was varied by a frequency static converter equipped with overcharge protectors.

Fig. 3: Testing device 3.2. Data acquisition Data acquisition chain allows the monitoring of the friction moment at the outer race level of the face-to-face testing rolling bearing. The acquisition chain, schematically shown in Fig. 4, is composed by: • The mechanical structure: rolling bearings’ house, a

blocking pin, an metallic elastic leaf and two strain gages of 120 Ω electrical resistance brazed on each side of the metallic leaf.

• The strain gages bridge SC-2043-SG National Instruments directly connected the strain gages to the acquisition board.

• The data acquisition board for laptop, DAQCard 6062E, 16 chanals, 12 bits, 500 000 samples/sec.

• Graphical interface (a LabVIEW made Virtual Instrument).

• Laptop. • Terminals (CANON LBP-800 printer).

Figure 4: Data acquisition chain 3.3. Materials All-steel and hybrid angular contact rolling bearings from 7206CTAP4 series were tested on a high-speed test rig, the only difference between the two types of bearings being the balls’ material: AISI 52100 rolling bearing steel and silicon nitride (Si3N4), respectively. The dimensional precision of rolling bearing elements and their physical properties are indicated in Table 1. The chemical composition of AISI 52100 steel is: C: 0.95 - 1.1 %, Si: 0.17 - 0.37 %, Si: 0.17 - 0.37 %, Mn: 0.25 - 0.45 %, Cr: 1.30 - 1.65 % (in wt. %). For the HIP

Si3N4 balls, the chemical composition is: Si3N4 @93% and Y2O3 + Al2O3 @ 7 %. In addition, it must be no-ticed that the cage was made from textile-reinforced phenolic resin and is outer race guided. Cage to outer and inner ring radial clearances are:

e cJ ( )252.0 ..2.0∈ mm, mm, respectively. Ball to cage clearance is

i cJ 1.725) ..65.1(∈

bcJ ( )0.162 ..137.0∈ mm. Rolling bearing

Steel and hybrid rolling bearings

Steel rolling

bearings

Hybrid rolling

Bearings Material Rolling bearing steel

(AISI 52100) Silicon nitride

(HIP Si3N4) Ball grade 3

Parameter and unit system

Inner ring

Outer ring

Balls

Diameter, [mm]

30 62 9.525

Roughness, Ra [µm]

0.07.. 0.1

0.065.. 0.1

0.018.. 0.035

0.01.. 0.014

Poisson coefficient, ν

0.3 0.25

Density, ρ [Kg/ m3]

7800 3200

Elasticity modulus, E [GPa]

208 314

Hardness @ 20 0C, HV10 [Kg/ mm2]

700 1700

Thermal conductivity @ 20 0 C, λ, [W/m/0C]

43 30.7

Specific heat, c [J/Kg/0C]

460 810

Table. 1: Rolling bearing materials

3.4. Experimental and semi-empirical determination of the kerosene rheology A lubricant must be able to create a separating film between the contact bodies. For a good running of the rolling bearings, this lubricating film must assure a low friction at low and medium speeds, and high traction at high speeds (to avoid the skidding). The term friction refers to an undesirable phenomenon which must be reduced, while the traction refers to a desired process (e.g. in friction gears and couplings). For a given application, the lubricant is chosen to optimize the energy efficiency of the device. This is not always possible. An example is given in [1], the bearings used in rocket motor turbo-pumps must be

lubricated by the process liquid (a kerosene based low-viscosity fuel as RP1, or a cryogenic substance as liquid oxygen or hydrogen). If used as a lubricant, the chemical composition and the main rheological properties of the kerosene must be known. To establish the chemical composition of commercial kerosene in this work, a sample was tested by Nuclear Magnetic Resonance spectroscopy (NMR). The next composition was found (expressed in percents from the entire mass of the sample): - Aromatic hydrocarbons (benzene, toluene,

xilene, trimetil benzene): 24.1 %; - C9 (nonan) – C14, with maximum of C11

(undecan): 42.1 %; - C4 (butane), C5 (pentane), C6 (hexane), C7

(heptane) and C8 (octane): 11.2 %; - C14-C18: 9.18%; - 2,2,4-trimetil pentane (isooctane with calorific

power 100): 5.75%; - isoprenoid (2,6,10-trimetil undecan): 2.56%. Following the analysis, the kerosene seems to be a JET-A1 type (a paraffin oil-based fuel), used in modern jet engine aircrafts and turbine helicopters from civil aviation. The similar military kerosene is JP-8, which is less flammable, in order to assure the safety during combats. The JP-8 posses an increased lubricity and contains other additives (ice inhibitors, anti-oxidants etc.). The performed tests on viscosimeters and densimeters offered the viscosity and density values of the kerosene sample referred in the paper (see Table 3):

Temperature, 0C

Density, Kg/m3

Dynamic viscosity, Pa*s

Kinematic viscosity, cSt

15 867 1.79*10-3 2.06 40 758 0.88*10-3 1.15

Table 3: Density and viscosity of the tested kerosene For the JP-8 kerosene a larger temperature database for the density and viscosity is available. The density and the viscosity of the JP-8 kerosene manifests versus temperature according to Figure 5. The density of the JP-8 kerosene depends on temperature according the formula (21), determined by median-median regression of the experimentally database.

( 20718.020 −⋅−= T )ρρ (21) The variation of thermal conductivity, and specific heat of the kerosene as a function of temperature are obtained by interpolation of data given in [21]:

30 20 70 120 1700

1

2

3

4

5

6

7

650

700

750

800

850ViscosityDensity

Temperature, C deg.

Kin

emat

ic v

isco

sity

, cSt

Den

sity

, Kg

/ m^3

Figure 5: Density and viscosity of JP-8 kerosene versus temperature

( )2010711.1 420 −⋅⋅−= − Tλλ , [W/m/0C] (22)

( )20815.420 −⋅+= TCC , [J/Kg/0C] (23) In the above equations, 20ρ , 20λ , and represent density, thermal conductivity and specific heat of the kerosene at 20 0C, T being the temperature in 0C.

20C

At T=20 0C, the JET-A1 and JP-8 kerosene have 125.0≈λ [W/m/0C] and C ≈ 1890 [J/Kg/0C]. For

comparison, at T=20 0C a mineral oil has 14.0≈λ [W/m/0C] and C ≈ 2 000 [J/Kg/0C].

For the computation of the shear stress in the lubricant film the most employed rheological model is that of Johnson and Tevaarwerk [1]. To apply this model we must know the fluid shear modulus, G, and the limiting shear stress (the so-called Ree-Eyring shear stress). Tevaarwerk [1] found an empirical formula for the compliance corrected fluid shear modulus of RP1, Gc.

( )Dv

UGPGGUPGc

+

⋅+⋅+=

θθ

321,, , [GPa] (24)

G1, G2, and G3 are specific parameters for each fluid. For the RP1 (Rocket Propellant 1), the mentioned parameters are: G1=1.0 [GPa.0C]; G2=0.25 [0C]; G3=-0.005 [GPa. 0C.s/m]; Dv=143 [0C] viscosity solidification temperature parameter; θ = represents the local temperature, in [0C]; U= rolling speed, in [m/s], and P= mean Hertz pressure on the contact, in [GPa]. The non-linear stress parameter, sτ , for the RP1 can be found using the relationship (25).

CDs

s+

=θτ (25)

51075.2 −⋅=C [0C/Pa], represents the non-linear shear stress constant;

Ds=143 [0C] is the solidification constant for Eyring equation.

A pure axially load was applied to the device in three steps: 100 N, 200 N and 400 N. The limit running speed for all steel bearings was 35 000 rpm for oil lubrication and about 20 000 rpm for kerosene lubrication, while for the hybrid bearings the maximum attended speed was 40000 rpm for both oil and kerosene lubrication.

Finally, the dependence of the kerosene viscosity on pressure and temperature can be approximated with the Roelands-Barrus formula, or using the formula deduced for RP1 from kerosene experimental data [1]. Both relationships give close viscosity values for the JET-A1, JP-8 and RP1. In this paper we used the connected Roelands-Barrus formula:

To establish the equilibrium temperature of the testing device in the case of the hybrid bearings lubricated by kerosene mist, the rolling bearings were 200 N axially loaded and the running speed was kept at a constant value of 20 000 rpm. ( ) ( )

2.41351 lg)( lg

1010 −+⋅−

=TFE

Tη (26) ( ) ( ) ( )PTTP p ⋅⋅= αηη exp, (27)

5.Results and discussions. Theoretical model valida-tion

where the constants E and F can be found for each fluid knowing the viscosity values at two different temperatures, and P is the mean Hertz pressure.

5.1. Oil-mist lubrication For the piezo-viscosity coefficient of the kerosene, pα ,

from Barrus formula, a mean value was chosen from [22]: [Pa-1] 8101.1 −⋅≈pα

For oil mist lubrication of the testing rolling bearings, an mineral oil was used. The kinematic viscosity of the mineral oil is 31.3 cSt at 30oC, and 6.9 cSt at 75oC. The results of comparative tests (see Figure 6), developed on geometrically identical all-steel and hybrid ball bear-ings, have shown that the measured friction moment was lower in hybrid bearings for the high speed range (speed parameter greater than 0.46 x 106 mm x rpm).

With all the rheological parameters of the kerosene determined, the viscous friction in the kerosene film can be computed.

4. Test description The greater the speed and applied load, the greater the friction moment. The centrifugal forces acting on ce-ramic balls are smaller than those acting on steel balls, because of the lower density of silicon nitride. Accord-ingly, there are diminished contact loads and friction forces on ceramic balls and outer race contacts.

Tests were carried out on tandems of face-to-face mounted all-steel and hybrid ball bearings from 7206CTAP4 series. Before the test, a running-in was made for each tandem of rolling bearings, at a speed of 9 000 rpm and 200 N axial preload, until the monitored friction moment be-came stable.

Also in comparison with the steel balls, the silicon ni-tride balls have a better surface quality (see Tab. 1), creating improved lubricating conditions in ceramic ball and races contacts.

During all the tests, the lubricant was supplied into the rolling bearings’ house as follows:

5.2. Kerosene-mist lubrication - the oil-air mixture was composed by feeding 16 drops of H9 mineral oil in a draught of air at 3.0 Bars.;

For accelerated tests at @28 0C the all-steel bearings lubricated by kerosene-mist ran well for an axial pre-load of 200 N and 10 000 rpm, the evolution of the friction moment being almost constant during about 2 minutes (Fig. 7).

- the kerosene-air mixture was composed by feeding 60 drops of kerosene in a draught of air at 3.0 Bars.

It was considered as a valid experimental data, the mean value of friction moment of three identically repeated experiments.

At 35 000 rpm and 200 N axial preload the friction moment and the temperature in the all-steel bearings increased continuously and abruptly (Fig. 8), the test being interrupted at 60 0C, temperature measured on the house of the testing device.

To estimate the mean temperature of the testing device the temperature was measured on the house by a SKF-TMDT type magnetic thermocouple. Accelerated tests were carried-out varying the running speed and keeping constant all the other parameters, until the same temperature was reached on the house of the testing device.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 5 10 15 20 25 30 35 40 45 50

N [rpm] x 10 3

Mt [

N x

m]

S - N (Fa=400 N) S - E (Fa=400 N)

S - N (Fa=200 N) S - E (Fa=200 N)

H - N (Fa=400 N) H - E (Fa=400 N)

H - N (Fa=200 N) H - E (Fa=200 N)

Figure 6. Friction moment for one ball bearing versus running speed and axial load for oil-mist lubrication [9]

S - N = numerical results for all-steel rolling bearing; S - E = experimental results for all-steel rolling bearing; H - N = numerical results for hybrid rolling bearing; H - E = experimental results for hybrid rolling bearing;

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 0.5 1 1.5 2 2.5

Time

3

, t [min]

Mt [

N x

m]

Figure 7: Friction moment evolution for kerosene-mist lubricated all-steel bearings (10 000 rpm, 200 N axial load, T=25 0C )

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.5 1 1.5 2 2.5

Time, t [min]

Mt [

N x

m]

3

Figure 8. Friction moment evolution in kerosene-mist lubricated all-steel bearings (35 000 rpm; 200 N axial load)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Time, t [min]

Mt [

N x

m]

Figure 9. Seizure of kerosene-mist lubricated all-steel bearings (25 000 rpm; 200 N axial load, T@65 0C) After the test at 35 000 rpm the all-steel bearings ran at 25 000 rpm and the same axial preload of 200 N, the friction moment value had normal value during 1 min-ute, but increased suddenly after, indicating that the rolling bearings failed by scuffing at this high speed (Figure 9). It must be noticed that the latest test was started at 60 0C. For the hybrid ball bearings lubricated by kerosene mist tests were carried-out at different speeds and loads (Fig. 10 and Fig. 11). The friction moment increase with both axial preload and speed, being more dependent on speed (Fig. 11).

A comparison for the friction moment values between Fig. 10, Fig. 11, and Fig. 6 shows that the kerosene-mist assure a good lubrication, the friction moment having the same magnitude. In Fig. 6 the friction moment val-ues were divided by two, corresponding to a single ball bearing. Anyway, at 40 000 rpm and 200 N axial preload the temperature and the friction moment in the hybrid ball bearings increase continuously, the temperature arriving in few minutes at 60 0C. An equilibrium temperature around 48 0C was found for the hybrid ball bearings running at 20 000 rpm and 200 N axial preload.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 50 100 150 200 250 300 350 400 450Axial preload, Fa [N]

Fric

tion

Mom

ent,

Mt [

N x

m]

ExperimentalNumerical

N=10 000 [rpm] T=28 0 C

Fig. 10 : Friction moment in kerosene-mist lubricated face-to-face tandem of hybrid ball bearings versus axial preload

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 5 10 15 20 25 30

Speed, N [rpm x 10 3]

Fric

tion

Mom

ent,

Mt [

N x

m]

Experimental

Numerical

Fa=100 [N]T=28 0 C

Fig. 11 : Friction moment in kerosene-mist lubricated face-to-face tandem of hybrid ball bearings versus speed

As observed during the tests, the kerosene-mist lubrica-tion give good results for light load and a speed parame-

ter (mean diameter of the ball bearing multiplied by the shaft speed) up to 1 million mm x rpm. For the tested

7206C ball bearings the corresponding shaft speed is about 20 000 rpm. Above this speed it seems that thermal effects in the kerosene film of ball and races contacts become impor-tant, the lubrication regime passing from mixed elasto-hydro-dynamic to a limit one. This could be explained by the low viscosity of the kerosene, about 10 percents from that of the mineral oil. The obtained experimental results are promising. The future tests must be focused on the optimum density of the kerosene-air lubricating mixture, as the friction moment and the temperature in the ball bearings to be maintained at low values, even for high speed and heav-ier loads. Another solution for the lubrication of the rolling bear-ings used in the various machinery of the turbo-jets could be the lubrication of the ball bearings by an emul-sion of kerosene and oil (a small percent), in order to increase the viscosity index of the kerosene. 6 Conclusions A theoretical model for the estimation of the friction moment in fluid-mist (oil and kerosene) lubricated ball bearings is proposed. In order to experimentally evaluate the performances of kerosene-mist lubricated all-steel and hybrid ball bear-ings, the friction torque and the developed temperature were monitored using a test rig and adequate equip-ment. The results of comparative tests carried-out on geometrically identical all-steel and hybrid ball bearings from 7206C series have shown that the measured friction moment was lower in hybrid bearings. The friction moment increase with both axial preload and speed, being more dependent on speed. For kerosene mist lubricated hybrid ceramic ball bearings and oil-mist lubricated similar all-steel and hybrid ball bearings the friction moment values have the same magnitude, prooving that the kerosene-mist assure a good lubrication for the test conditions used in this paper. The all-steel ball bearings lubricated by JET-A1 kero-sene-mist failed at high speed (25 000… 35 000 rpm), especially because of the high temperature (60 0 C). At 40 000 rpm and 200 N axial load the temperature and the friction moment in the hybrid ball bearings increase continuously, the temperature arriving in few minutes at 60 0C. An equilibrium temperature around 48 0C was found for the hybrid ball bearings running at 20000 rpm and 200 N axial load.

As observed during the tests, the kerosene-mist lubrica-tion give good results for light load and a speed parame-ter (mean diameter of the ball bearing multiplied by the shaft speed) up to 1 million mm x rpm. For the tested 7206C ball bearings the corresponding shaft speed is about 20 000 rpm. The obtained theoretical and experimental results are in good agreement, the measured and the predicted values of the friction moment having the same trend. The future tests must be focused on the optimum den-sity of the kerosene-air lubricating mixture, as the fric-tion moment and the temperature in the ball bearings to be maintained at low values, even for high speed and heavier loads. 2 References [1] Tevaarwerk, J. L.: The Measurement, Modeling,

and Prediction of Traction for Rocket Propellant 1, report NASA/CR-185186, 1989.

[2] Schrader, S.M., Pfaffenberger, E.E.: Performance

of Hybrid Ball Bearings in Oil and Jet Fuel, Tribol. Trans., 35 (1992) 3, 389 – 396.

[3] Ohta, H., Kobayashi, K.: Vibrations of Hybrid

Ceramic Ball Bearings, J. Sound Vibr., 192 (1996), 2, 481-493.

[4] Ohta, H., Satake, S.: Vibrations of the All-Ceramic

Ball Bearing, ASME J. Tribol., 124 (2002), 3, 448-460.

[5] Hui, T., Sadeghi, F., Rateick Jr., R. G.,. and Frank,

M. C.: Performance Characteristics of Jet Fuel in Heavily Loaded Contacts, Tribol. Trans., 50 (2007) 2, 154 – 164.

[6] Houpert, L., and Leenders, P.: A Study of Mixed

Lubrication Conditions in Modern Deep Groove Ball Bearings, Proc. of 11th Leeds-Lyon Symposium, Sept. 9-12, 1984, Leeds.

[7] Houpert, L.: Ball Bearing and Tapered Roller

Bearing Torque: Analytical, Numerical and Experimental Results, Tribol. Trans., 45 (2002) 3, 345-353.

[8] Paleu, V., Cretu, Sp., and Nelias, D.: Behavior of

Hybrid and All-Steel Angular Contact Ball Bearings in Oil Shut - Off Conditions: Experimental and Theoretical Results, Society of Tribology and Lubrication Engineers' 58th Annual Conference (STLE Annual Meeting), 27 April -1 May 2003, New York.

[9] Paleu, V.: Theoretical and Experimental Research on Hybrid Rolling Bearings' Dynamics and Reliability, PhD Thesis (in Romanian), Iasi, 2002.

[10] Houpert, L.: Piezoviscous-Rigid Rolling and

Sliding Traction Forces, Application: The Rolling Element- Cage Pocket Contact, ASME J. Tribol., 109 (1987), 363-370.

[11] Gupta, P.K: Advanced Dynamics of Rolling

Elements, Springer-Verlag, New-York, 1984. [12] Aihara, S.: A New Running Torque Formula for

Tapered Roller Bearings Under Axial Load, ASME J. Tribol., 109 (1987), 471-478.

[13] Bercea, I., Cretu, Sp., Bercea, M., and Olaru, D.N.:

Simulating Roller - Cage Pocket friction in a tapered roller bearing, Eur. J. Mech. and Env. Eng., 43 (1998) 4, 189-195.

[14] Hamrock, B.J., and Dowson, D.: Isothermal

Elastohydrodynamic Lubrication of Point Contacts. Part I – Theoretical Formulation, J. Lub. Tech., 98 (1976) 2, 223-229.

[15] Hamrock, B.J., and Dowson, D.: Isothermal

Elastohydrodynamic Lubrication of Point Contacts. Part II – Ellipticity Parameter Results, J. Lubr. Tech., 98 (1976) 3, 375-383.

[16] Hamrock, B.J., Dowson, D.: Isothermal

Elastohydrodynamic Lubrication of Point Contacts.

Part III – Fully Flooded Results, J. Lubr. Tech., 99 (1977) 2, 264-276.

[17] Murch, L.E., Wilson, W.R.: A Thermal

elastohydrodynamic inlet zone analysis. J. Lubr. Tech., 97 (1975) 2, 212-216.

[18] Houpert, L.: Fast Numerical Calculations of EHD

Sliding Traction Forces; Application to Rolling Bearings, J. Tribol., 107 (1985) 2, 234-240.

[19] Rumbarger, J.H., Filetti, E.G., Gubernick, D: Gas

Turbine Engine Mainshaft Roller Bearing- System Analysis, J. Lubr. Tech., (1973), 401-416.

[20] Paleu, V., Cretu, Sp., Dragan, B., and Balan, R.M.:

Test Rig For Friction Torque Measurement in Rolling Bearings, The Annals of “Dunarea de Jos” University of Galati, Fascicle VIII, Tribology, 2004, 86-93.

[21] Edwards, T., Stricker, J.M., Harrison III, W.E.:

Coordinating Support of Fuels and Lubricant Research and Development (R&D) 2, Handbook of Aviation Fuel Properties, 3rd Edition, S.A.E., 2004.

[22] Pascovici, M.D., Cicone, T. : Elemente de

Tribologie, Ed. BREN, Bucuresti, 2001. [23] Paleu, V., Cretu, Sp., Dragan, B., and Balan, R.M.:

Test Rig For Friction Torque Measurement in Rolling Bearings, The Annals of “Dunarea de Jos” University of Galati, Fascicle VIII, Tribology, 2004, 86-93