Influence of polyalkylmethacrylate and sulphurized ester on oil film thickness in an elastohydrodynamic point contact

Wear, 115

(1987)

223

223

- 234

INFLUENCE OF POLYALKYLMETHACRYLATE AND SULPHURIZED ESTER ON OIL FILM THICKNESS IN AN ELASTOHYDRODYNAMIC POINT CONTACT*

ERIK HtiGLUND Division

of Machine

Elements,

Luleii

University

of Technology,

S-951

8 7 Luleb

(Sweden)

Summary

The aim of this investigation is to determine how additives in a base oil affect the central oil film thickness in an elastohydrodynamic rolling point contact. The experiments have been carried out using a sapphire disc and a steel ball and the film thickness has been measured by means of optical interferometry. A detailed description of the apparatus is given. Two different additives have been used, polyalkylmethacrylate (PMA) and sulphurized ester (SE). Each of them have been mixed in a superrefined naphthenic base oil at five different concentrations. The results show that the central oil film thickness increases with increasing concentration of additive. This is because the additives increase the oil viscosity. If this effect is compensated for, 0.1 wt.% PMA or 0.63 2.5 wt.% SE give the best relative oil film build-up. There is consequently no reason to use more additive in the base oil unless one wants to have a thicker oil film because of the viscosity-increasing effect.

1. Introduction

The oil film thickness between two moving surfaces plays an important role when the endurance of a lubricated machine element is to be calculated. If the oil film is too thin the asperities of the moving surfaces will come into contact and cause high friction which leads to loss of energy or, in extreme cases, breakdown of the machine element. Alternatively, if the oil is too viscous the oil film becomes too thick and there is unnecessary heating of the oil owing to shear. The desired oil is one that gives an oil film that is just thick enough to prevent asperity contact, *Paper Technology,

presented at the Nordic Symposium LuleSI, Sweden, June 15 - 18, 1986.

0043-1648/87/$3.50

@ Elsevier

on Tribology,

Sequoia/Printed

LuleP

University

in The Netherlands

of

224

The viscosity of a lubricating oil is of major importance for the oil film thickness. However, viscosity changes considerably with temperature and an oil giving a satisfactory oil film thickness at one temperature may give too thin an oil film at a higher temperature. A remedy for this sensitivity to temperature is to incorporate additives into the oils. The additives, such as polymers, may help to keep the viscosity high in spite of the increasing temperature and others may help to form a surface layer on the moving parts that help keep them apart. Extreme pressure additives are of this latter type. The study of elastohydrodynamic (EHD) point contacts has been the subject of many authors. An EHD point contact is, for example, a lubricated contact between two balls or a ball and a flat surface. A typical feature of an EHD point contact is shown in Fig. 1. It is characterized by a central region with almost constant film thickness and three lobes of thinner oil film, two at the sides of the contact and one near the outlet connecting the two side lobes. Both theoretical predictions and experimental measurements of the oil film thickness in point contact have been made by many authors. The predominant theory for the prediction of oil film thickness in EHD contact is that of Hamrock and Dowson [ 1 - 41. An experimental evaluation of this theory has been made by Koye and Winer 151. This work is also an experimental investigation to determine how the central oil film in EHD point contact under pure rolling conditions is affected by the rolling speed and concentration of additives in the oil (similar work has been carried out earlier by the author [6]). One oil with different concentrations of polyalkylmethacrylate (PMA) and sulphurized ester (SE) is tested. It was believed from the manufacturer of the oil that the additives could form a surface layer on the rolling parts. This surface layer should give a thicker oil film than an oil without additives. Mrnimum f llm thickness

Central

Inlet

thickness

Rolling Fig. 1. Typical feature face. From ref. 6.

f llxl

direction of a lubricated

EHD point

contact

between

a ball and d flat su-

225

2. Experimental

apparatus

The most important parts of the experimental apparatus (Fig. 2) are a polished steel ball and a sapphire disc. The steel ball is a 50.003 mm ball-bearing ball made of special steel SIS 142258 which has a Rockwell hardness of 62 HRC. The ovality of the ball is less than 2 pm and the surface roughness is less than 0.04 pm rms. The sapphire disc is synthetic and has a diameter of 100 mm and a thickness of 6.3 mm. Young’s modulus is 390 000 MPa and Poisson’s ratio

Air

pressure

and

regulator

gauge

Oil

feed

I Oil

supply

+li I

Insulation

Heating

device

K-motor

Adjustable microscope JariableSapphire

speed lrive

in

steel

mounting

Fibre

optics

Y I

bundle -i

White

_d light

t

Ej Fig. 2. Sketch

I::::::::]jl’lii:::‘] of sapphire

and steel ball apparatus.

226

is 0.23. The surface roughness of the sapphire is less than 0.009 pm rms. The sapphire disc makes it possible to reach pressures of the same magnitude (1 - 2 GPa) as those present in a roller bearing or between gear teeth. This is not possible with a disc made of glass. The sapphire disc is mounted in a steel disc with its circumference shaped as a chain wheel. This steel disc is supported by a large ball-bearing which enables the disc to rotate about a fixed centre. The steel disc with the sapphire disc is driven by an electric motor and a variable-speed gear drive via a chain drive. The speed of the gear drive ranges from 0 to 1200 rev min I, thus giving a maximum rolling speed at the contact point of about 6 m s ~‘. A tachometer measures the speed of the drive chain wheel and the chain gear ratio then gives the rolling speed at the contact point. The steel ball is placed in a polished steel tube. The diametral clearance is 13 pm. The steel ball is pressed against the sapphire disc by a variable hydrostatic oil pressure. A small amount of oil leaks out through the clearance between the steel ball and the tube. This oil is then dragged into the contact zone as the sapphire disc and the steel ball start to roll against each other. The frictional force between the steel ball and the steel tube is of the order of p*N where N is the normal force between the ball and the sapphire, and 1-1is the coefficient of friction for the ball-sapphire lubricated contact. Thus it can be assumed that almost pure rolling conditions are present at the contact. The oil in the steel tube is supplied from a reservoir which can be pressurized by compressed air. The necessary pressure is obtained by using a precision pressure gauge together with a regulator valve, thus making it possible to keep the pressure constant at the contact within a very narrow range. The oil reservoir is insulated and the temperature of the oil can be adjusted by means of a heating device and a regulator. To heat the steel tube containing the ball and the oil, a thermocord is wound around it and attached to a regulator. The temperatures in the reservoir and in the steel tube are registered by thermocouples which are connect,ed to a recorder. The contact zone between the steel ball and the sapphire disc is observed through a Zeiss microscope with 100 times magnification. The con tact zone is illuminated with white light. The light is led through a fibre optics bundle to a glass prism which is used to direct the light down through the sapphire on to the contact. The light reflected from the contact is then observed through the microscope. A camera is mounted on the microscope and photographs of the contact zone are taken. The film thickness can then be calculated from the colours on the photograph. The film used has a sensitivity of 100 ASA and the exposure time is l/60 s. After each test the parts of the experimental apparatus which had been in contact with the oil being tested were disassembled and cleaned in an ultrasonic washer, first with toluene and then with acetone. The parts were then reassembled and the next oil tested.

227

3. Method of measurement

The method used to determine the oil film thickness in the contact zone between the steel ball and the sapphire disc was interferometry. Interferometry can be used when the thickness of a thin transparent film is to be measured. This technique is well known and was first used by Cameron and Gohar [7]. Optical interferometry was also used by Koye and Winer and Hoglund [ 5, 61. To make use of the interference technique, one surface of the sapphire had to be coated with a thin layer of chromium. This was necessary in order to obtain enough reflected light from the underside of the sapphire. The sapphire was first thoroughly cleaned in an ultrasonic washer with toluene and acetone and then put into a vacuum chamber. The pressure in the chamber was reduced to about 1O-2 Pa (1.45 X 10e6 lbf in2). A small piece of chromium, about 15 mg, was vaporized on to the surface of the sapphire. It was rather difficult to produce an even chromium layer on the surface and it was also easily worn off. However, thorough cleaning made it possible to obtain a layer that stuck to the surface. It was also possible to compensate for the wear of the chromium layer by moving the steel tube with the ball radially, relative to the sapphire disc, to give a new contact surface with no wear. By directing a light beam through the sapphire onto the contact zone, the incident light was reflected both from the chromium layer on the sapphire and from the surface of the steel ball. The reflected light beams have a phase difference depending on the distance between the reflecting surfaces and the refractive index for the oil between the surfaces. The distance between the ball and the sapphire is given by

(1) In order to confirm the validity of eqn. (1) an experiment was carried out. The contact pressure between the steel ball and the sapphire disc was decreased until the deformation of the surfaces in the contact zone was negligible. Photographs of the coloured interference fringes (Newton’s rings) were then taken through the microscope. Knowing the magnification of the optical system and the camera, the diameters of the different colours in the rings were determined. These diameters were then compared with the diameters obtained from the equation which gives the distance between a flat surface and a ball when the contact deformation is negligible h=

dP2 sR

p = 1, 2,3, ,..

(2)

The comparison gave the results shown in Table 1. The theoretical and experimental values showed good agreement, therefore eqn. (1) was used to determine the oil film thickness for the oils tested. In the tests of the oils white light was used because the reflected light from the contact is then split up into different colours, depending

228 TABLE

1

Comparison coiour)

between

theoretical

and

Theoretical diameter d, = (8Rh)” ‘I (mm)

experimental

diameters

Experimental (mmi _-ll___l^

11.7

12.5

16.6 20.3 23.5 26.2

16.5 20.5 Es.5 26.5

for

Newton‘s

rings (red

diameter _...-- __...- _..,__.._..

on the oil film thickness, Thus different colours were used, giving a finer resolution of the estimated film thickness. If n~~nochromatj~ light was used, only reflected light of this colour would be seen as light fringes in the contact zone. The reflected colours used in the measurements were blue, green and red with ~~avelen~hs of 0.410 pm, 0.535 pm and 0.620 ~_trnres~~~~tivei~. To determine the film thickness of the oils, their refractive indices are needed. They were measured at 20 “C with an Abbe refractometer. The influence of pressure on the refractive index was neglected in the film thickness calculations, since the change in refractive index with pressure is small [S, 81. 4. Experiments

Data for the oils tested are given in Table 2. The base oil was a superrefined mineral oil with naphthenic structure. It contained no additives. The tests were run at 20 “C with a contact pressure of 1.5 GPa and were carried out as follows. The desired oil temperature and contact pressure were set. A photograph was then taken of the stationary contact zone. The rolling speed of the sapphire and ball was increased until the first calour (blue) appeared as the central film thickness. A photograph was taken of the contact zone and the oil temperature, rolling speed and contact pressure were recorded. The rolling speed was then increased further until the first red colour appeared in the eentre of the contact. Temperature, speed and pressure were recorded, The speed was increased until the second green colour appeared, parameters were recorded and so on for progressively higher rolling speeds. 5, Results and discussion An example of the test results is shown in Fig. 3. The central oil film thickness h is plotted against the square root of viscosity times rolling speed

229

TABLE

2

Data for the oils tested

Additive

Kinematic

(wt.%)

(mm*

Refractive index

Density

viscosity

s-l)

(kg me3) (15 “C)

20 “C

40 “C

Base oil 0

40.53

16.14

869.8

1.4739

PMA 0.1 0.3 0.9 2.7 8.1

41.13 42.03 44.5 52.85 91.93

16.30 16.72 17.83 21.32 35.55

869.7 869.6 869.6 870.9

873.8

1.4739 1.4739 1.4740 1.4741 1.4741

38.9 39.9 40.8 45.6 53.0

16.2 16.5 17.0 18.2 20.8

872 873 874 877 881

1.4747 1.4748 1.4751 1.4756 1.4760

SE 0.63 1.25 2.5 5 10

h

I ,.m,

2. 0

1.6

_

Fig. 3. Oil film thickness at 20 “C for pure kinematic viscosity (h = 76.2(~U)“~ - 0.133).

base oil as a function

of rolling

speed

and

230

(vU)“~. By using this combination of viscosity and rolling speed as the coordinate on the x axis, changes in these variables can be expressed in a single diagram for each oil. For each set of test points a linear regression analysis has been made resulting in an equation for the oil film thickness, see Table 3. From the equations it can be seen that the oil film thickness does not change much with type or concentration of additive, The equations must not be extrapolated outside the range of measurement. In Fig. 3 the regression line intersects the h axis on the negative side. This is due to the fact that the regression line is a straight line and should not be interpreted to mean that the central oil film thickness 1‘; tlegat,ive for small values of (VU)“*. Of course, from a physical point of view, il. is clear that when (VU)“* equals zero the oil film thickness is also zero. Under normal service conditions the value of (~li’)“~ usually exceeds 5 J 10 3 and the straight line approximation then gives a good estimate of the oil film thickness. Some tests were also made with a contact pressure of 1 C:Pa, this had very little influence on the film thickness. This has also been found by others [ 1 - 51. Another way of presenting the results is shown in Fig. .i, Here the oil film thickness is plotted vs. six different rolling speeds, 7 - 6 m s ‘. II can be clearly seen that 8.1 wt.% PMA and 10 wt.% SE give a significantly thicker oil film. This is due to the large concentration of additive which gives an increased oil viscosity, resulting in a thicker oil film. From Fig. 4 it is also seen that 5 wt.92 SE gives a thinner oil film than oil with different percentages of SE at low speeds. For the rest, the results give almost the same oil film t,hicknesses. In Figs. 5 and 6 the oil film thickness is divided by the viscosity v and LJO.~respectively. The reason for this can be explained in the following way. TABLE Equations

3 for o11 film thickness -.______---__

Additive

-

(wt .% )

-__

h (pm

_. ._....-.._ - .--. --.

i

Base oil

$6.%(vU)

1

0,138

PMA 0.1 0.3 0.9 ‘2.7 8.1

‘76.7(Uc:) ;5,6(vCi)’ ?3.3(VU) 70.9(UU) 63.6(VU)’

3 ’ -L -2 -?

0.: 14 0.098 0.112 0.119 0.139

79,qvu) ‘iS.l(UU)’ 79,6(vU)’ 79.4(W) 75.6(vU)“* _~____

2 - 0.119 ? --~ 0.113 ’ -- 0.117 ? 0.209 - 0.088 ____.

SE 0.63 1.25 2.5 5 10

~~-

._._

_-

.~ --

-----

231

h

0.2

_

Additive 13

0

-Base

P .

P Y

P m

p-' ? .I .

weight

Additive

%

p

:

p

8

K

UT

01

;;

D

P "

P w

P LD

Iu u

weight 9: ID -

L

P!0

NM s

ln

/

;;-

I

1.I PMA

SE

oil

Fig. 4. Oil film thickness

as a function

Base oil

PMA

of roiling speed and concentration

SE

of additive.

Assume that two oils of the same kind, one with a certain concentration of additive and the other with no additive, have different viscosities and film thicknesses at the same rolling speed. If, for example, one oil gives an oil film thickness of 1 X 1O-6 m at a viscosity of 10 X lop6 m2 s-’ and the second oil gives a thickness of 2 X 1O.-6 m at a viscosity of 15 X 10W6m2 s i, then, by dividing the thicknesses by the viscosities, we obtain the values 0.1 and 0.13 respectively. Since the oils are of the same kind the difference in film thickness must depend on the additives and a higher value of the ratio h/v should then indicate a better oil film build-up. If the oil film thickness is proportional to v’*~“, as suggested by [ 1 - 41, the co~esponding values of ~~v”.67 will be 2.24 X low3 and 3.41 X 10p3. That is, a higher value of the ratio h/v**47 will still indicate a better oil film build-up. Figures 5 and 6 show that 0.1 - 0.3 wt.% PMA and 0.63 - 2.5 wt.% SE give the highest values of relative oil film thickness, with 0.63 - 2.5 wt.% SE giving the slightly higher value of the two. Larger concentrations of additive do not give a thicker relative oil film. It is also seen that 10 wt.% SE gives a thicker oil film, both absolute and relative, than 2.7 wt.% PMA, although they both have about the same viscosity.

232

~“---1----1-__

--.L_L_L_

Fig. 5.

Oil

;r

PMA

Base nil film

thickness

speed and concentration

divided

ikdii ,.

by kinematic

viscosity

_. -

ihi~)

as a t’unctwl;

6. Error analysis points

can be split into

two parts

(1) The error in x = (VU)“” (2) The error in h=

‘2

p = 1, 2, 3, . . .

The relative Ax X

errors

can be written

as

1
and Ah Ax __=---+h

X

An n

A reasonable Au = 0.01 V

estimation

= 0.15

from

an experimental Ah

-

h

2 0.06

__.

PM;

of additive.

The errors in the experimental

._...

point

of view is

An -2 n

0

oi ioiling

233

8.0

’ I

6.0

.

4.0

.

2.0

-

’

Additive 0

P -

P w

I

0

weight

P

r

.m

m

.I

-

I

P

B

Additive

% 7

c:

.N

m ;; I

.P I

P

P

N

m

P

7

N

w

(D

u

c

8

g

Ll

I

I

ln

;,

I

-I

-I Base 011

0

Lo

I

weight %

PMA

Fig. 6. Oil film thickness speed and concentration

SE

divided by kinematic of additive.

Base 011

viscosity

SE

PMA

(h/~‘.~~)

as a function

of rolling

The relative errors of U and X should not be regarded as errors but are caused by the fact that the colours used in the measurements had a certain band width. The errors in the experimental values are then 8% in (vU)~‘~ and 6% in h. 7. Conclusions The central oil film thickness in an EHD point contact can, for the additives tested, be represented by straight lines in a (VU)“‘-h diagram and corresponding equations can be derived. Large concentrations of additive give thicker oil films owing to the increasing viscosity of the base oil. 0.63 - 2.5 wt.% SE gives the highest value of the relative oil film thickness. Also 0.1 - 0.3 wt.% PMA gives a thicker relative oil film compared with pure base oil. Acknowledgments The author wishes to thank Mr. &ten Uusitalo for assisting in the experimental work. The work has been sponsored by the Marten E. Liander foundation which the author also wishes to acknowledge.

234

References 1 B. J. Hamrock and D. Dowson, Isothermal elastohydrodynamic lubrication of point contacts, part I -theoretical formulation, J. Lubr. Technol., 98 (2) (1976) 223 _ 229. 2 B. J. Hamrock and D. Dowson, Isothermal elastohydrodynamic lubrication of point contacts, part II - ellipticity parameter results. J. Lubr. Technol., 98 (3) (1976)

375 - 378. 3 B. J. Hamrock 4 5

6

7

8

and D. Dowson, Isothermal elastohydrodynamic lubrication o/‘ point contacts, part III - fully flooded results, J. Lubr. Technob, 99 (2) (1977) 264 276. B. J. Hamrock and D. Dowson, Isothermal elastohydrodynamic lubrication of point contacts, part IV --starvation results, J. Lubr. Technol.. 99 (1) (1977) 1.5 23. K. A. Koye and W. 0. Winer, An experimental evaluation of the Hamrock and Dowson minimum film thickness equation for fully flooded EHD point contacts, J. Lubr. Technol., 103 (2) (1980) 284 - 294. E. Hiiglund, Elastohydrodynamic lubrication. Interferometric measurements, Lubricant rheology and subsurface stresses, Doctoral Thesis, LuleP University of Technology, 1984, 32D. A. Cameron and R. Gohar, Theoretical and experimental studies of the oil film in lubricated point contact, Proc. R. Sot. London Ser. A, 291 (1966) 520 636 A. Cameron, personal discussion, 1978.

Appendix

41 h

it P

R

u h I-1

V

A: Nomenclature

diameter of Newton’s ring with ordinal p (m) central oil film thickness (m) refractive index of the oil (dimensionless) normal force between ball and sapphire (N) ordinal (1, 2, 3, . . .) radius of steel ball (25 mm) rolling speed (m s ‘)

wavelength of light (m) coefficient of friction (dimensionless) kinematic viscosity (m* s ~~’ )