The properties of elastohydrodynamic grease films

Wear, 77.( 1982) 277 - 285

THE

PROPERTIES

WLODZIMIERZ

277

OF ELASTOHYDRODYNAMIC

GREASE

FILMS

JONKISZ and HENRYK KRZEMINSKI-FREDA

Institute of Machine Resign, Technical University, Lodz (Poland) (Received April 6,198l;

in revised form September 26,198l)

The results of investigations of elastohydrodynamic grease films are reported. The elastic deformation of the rolling elements and changes in the grease properties due to pressure were considered. The theoretical results were confirmed by optical interference measurements of the film thickness. A formula for the film thickness as a function of the rheological grease parameters is given. The effects of breakdown of the grease structure and of starvation conditions on the film thickness are discussed.

1. Introduction The behaviour of grease in rolling contact differs from that of oil. The Herschel-Bulkley equation [l] is one of the more accurate mathematical models for grease:

where rP = rp, exp(op),

nSn = rlS’ = rlS, exp(ep)

and

The rheological parameters of this equation can change with the working time as a result of temperature effects and of the breakdown of the grease structure. It is difficult to estimate these changes, and little information about them is available although they play a dominant role in reducing the thickness of the grease film. The second factor which acts to decrease the film thickness is lubricant starvation. Experimental results [ 2, 31 show that the combined effect of these two factors is to reduce the equilibrium film thickness to about half its initial value. Theoretical and experimental investigations of grease films have been reported elsewhere f4 - 6 3 . The basic equations and a method for the solution of the elastohydrodynamic (EHD) grease film problem were given in ref. 5. The pressure dist~bution was 0043-1648/82/0000-0000/$02.75

@ Elsevier Sequoia/Printed in The Netherlands

278

(2)

x

and the film shape was 2h = 2/z, + f-

-~~eptslln(

E,)

(3)

ds

The grease properties p , 7p and qS were assumed to be func~ons of pressure. The simult~eous solution of these equations provided the pressure distribution and the shape of the grease film. The pressure distribution obtained was similar to that for oil [ 5] . The film thickness and the velocity distribution in a grease layer were obtained for given load, grease properties and rolling element material, so that the thickness of the grease film was found as a function of the material, the load, the speed and the grease properties [4] . When the method of Jonkisz and Krzeminski-Freda [ 51 was used to calculate the thickness of the grease film, the effects of randomly chosen grease rheological parameters and of grease starvation were shown. To save computer time most of the calculations of the effect of grease rheology were carried out by ~suming that the film shape was that predicted by the G~bin-Eel hypothesis. It was assumed that the film shape was similar to that obtained when two elements were in static contact except that the film thickness was increased by 2h,, and.thus the film shape was described by 2h = 2h,

+

2h = 2h,

n --a
The results for the dimensionle~ film thickness obtained by the method described in ref. 5 and those obtained by the method based on the Grubin-Ertel hypothesis correlated according to h,/h,, = CUos7, and the differences between them did not exceed 8%. Thus the application of the much simpler and quicker method based on the Grubin-Ertel hypothesis is justified. 2. Results of the calculation Construction parameters based on their variation in robing bearings were chosen for the calculations (Table 1). Average bearing working conditions were assumed.

279

TABLE1 PH

(MN y-‘)

1400 496.7 15.52x10+'

700 124.18 3.88x~O-~ 9.064 353 x103

YkNm) R (mm) E'(MNme2)

2100 1117.6 34.93x10-6

M=aE'

(1) 7060 (2) 9969 (3)13545

2b Wm)

0.05,0.15,0.5 0.6,0.7,0.82,0.9,1 24,48,100,200,400,800,900,1600

R

T,,

(N mW2)

2800 1986.8 62.1x10+

The grease yield 7p had a negligible effect on the film thickness but the exponent n and the grease viscosity Q, had a significant effect. The following formulae for the thickness of the grease film were derived from the theoretical results : H,=C,----

lYMb

H min a 0.85H,

G’

where

G=?

H,

E’R

R=

RI Rz RI

2hm

=-

R

up = u1 = u2

+R2

In eqn. (5)) C, and the exponents

a, b and c are functions

c, = 1.9 x 101o(n-l)

nn E (0.8 - 1)

c, = 3 x lOll(n-1)

r-mE (0.68 - 0.8)

C, = g x 1012.W-1)

nn E (0.6 - 0.68)

of the parameter

n:

(6)

a = 0.43 + 27n b = 1.24 - 0.63n c = 0.21 - 0.09n

(7)

280

3. Experiments To verify the theoretical predictions, the thicknesses of fresh grease films and of base oil films were measured by an optical interference technique [ 71. The interferograms were monitored and photographed at different rolling element velocities for three types of greases and base oils. Their flow curves are shown in Fig. 1. The experimental results are shown in Figs. 2 - 4. The solid curves indicate the grease film thickness calculated according to eqn. (5). The broken curves indicate the theoretical base oil film thickness calculated using the EHD theory for oil [8]. The experimental thicknesses of

Fig. 1. Flow curves for greases and their base oils obtained at 25 “C.

I

1

27.10 -*

$4. to-”

ZLB~lo-”

27.fO_”

(J_w -?#

Fig. 2. Comparison of theoretical and experimental results for grease LT12.

experiment&

points

r

!lSM‘ff

&V0-"

&wo-”

0,s

do-”

u-$f

Fig. 3. Comparison of theoretical and experimental results for grease LT4S2.

t WV-*

fP*

IO‘”

qvo-ffll+j

21.fO‘ff

Fig. 4. Comparison of theoretical and experimental results for Litol grease.

the grease films and of the oil films are represented by crosses and by circles respectively. The speed parameter U was calculated from

% ugrease = vs, E’R

uoil _ QOUP E’R

and hence two different U ordinates are shown in Figs. 2,3 and 4.

282

Figures 2 - 4 show that the experimental results confirm the theoretical predictions. The thickness of a fresh grease film under fully flooded conditions is roughly 1.5 times greater than that of its base oil. This is in agreement with the results of earlier studies [2]. The ratios XH of the grease film thickness to the oil film thickness hn =

grease film thickness base oil film thickness

are in the following ranges for greases 1,2 and 3 (from the data on Figs. 2 - 4): hn, = 1.6 - 1.3 Xn, = 1.25 - 1.05 hn, = 1.6 - 1.3 This ratio decreases as the speed parameter U increases. A possible explanation for this behaviour is that as du/dy increases, the grease flow curve approaches that of its base oil (Fig. 1). Hence we postulate that the film thickness calculated using the EHD formula for the grease base oil is a good approximation to the thickness of a grease film. This is a significant result, because the constitutive equation for fresh grease is not always known and is difficult to obtain for presheared grease. The grease structure is destroyed during shearing, and if the shear stress is removed the grease structure is partially rebuilt. Under the shear stress produced by the working conditions, the structure of the grease thickener breaks down and the thickness of the grease film decreases to that of its base oil. For example, for presheared grease with the constitutive equation [l] du 0.82 r=48+1.6 i dy 1 and base oil with viscosity no = 0.13 N s mF2, the ratio hn is 1.2 - 0.9 depending on the value of du/dy. 4. Effect of grease starvation Grease is removed from the working surfaces of rolling bearing8 during operation, and as the grease supply is poor only a thin layer of grease is left on the surfaces. Thus starvation conditions exist. The pressure build-up in the lubricant film moves toward8 the middle of the static contact area and the film thickness decreases. Dowson [9] reported that the oil film begins at the point where the reverse flow of lubricant vanishes and that the thickness of the oil film under starvation condition8 is 0.7 of that for fully flooded conditions. The film thickness hi at which the pressure build-up commences is related to the film thickness h, . The equilibrium film thickness exists for newtonian oil starvation [9] if hi/h,

= 3

283

For grease starvation the approximate position of this point can be calculated theoretically. The speed distribution in any cross section is described by the relation n

a{#

-

YP)

(n*l)/*

_

ty

_yp)(n+l)/n)

(8)

The thickness yP of the plug flow relative to the thickness hi is negligible, and consequently y,/h q 0 and h - yP = h. At the same time, as the reverse flow disappears u becomes zero for &I< yp . Thus eqn. (8) becomes (T&Up)* =

$ is1 jnh”“l

(9)

and, assuming that pm = p, we obtain from eqn. (1) n (h-h,)” hb+l

(10)

Substitution of eqn. (9) in eqn. (10) and of h by hi shows that grease starvation occurs at the point where hi 2n + 1 -=(11) h, n Results of peculations of the equ~ibrium film thickness for grease st~ation are given in Table 2. The ratio of the thickness H, of the grease film under starvation conditions to the thickness Hf under fuIly flooded conditions is about 0.7, which is similar to that found for oil. TABLE2

0.15 0.15 0.15

n

Xila

U=q&,IE'R

%I%

0.6 0.82 1

-1.18 -1.16 -1.15

1.9x~O-~ 1.04x 10-10 8 x~O-~"

0.69 0.74 0.73

M= aE'= 7060 PH =1400%'iNM-2

5. Conclusions The thickness of the grease film can be calculated from eqn. (5) by using its constitutive equation, or by using its base oil viscosity. In the latter case the EHD formula for oil is used, and the film thickness for fresh grease is found to be about 1.5 times greater than that calculated for oil. The structural breakdown of the grease thickener decreases the film thickness to the value calculated for the base oil. Grease starvation decreases the film thickness to 0.7 of that obtained under fulfy flooded conditions.

264

The combined effect of starvation and structural breakdown is to decrease the real thickness of the grease film (for bearing operation conditions) to 0.5 of that calculated using the constitutive equation for fresh grease and 0.7 of that calculated using the base oil viscosity.

Nomenclature a

E G 2h H M n P P R S cl u UP x7 Y

2yn 01 t7 7)s

V P 7 TP

semiaxis of the static contact area Young’s modulus dimensionless load parameter film thickness dimensionless thickness parameter dimensionless material parameter rheological parameter pressure load per unit length reduced cylinder radius pressure coordinate velocity dimensionless velocity parameter cylinder velocity coordinates plug flow thickness pressure viscosity coefficient oil viscosity grease viscosity Poisson ratio density shear stress grease yield value

Subscripts G m min 0

Grubin static contact minimum environmental

median conditions

References 1 J. A. Greenwood and J. J. Kauzlarich, EHD lubrication with Herschel-Bulkley model greases, ASLE Trans., 4 (1972) 269 - 277 2 S. Y. Poon, An experimental study of grease in EHL, J. Lubr. Technol., 94 (1) (1972) 27 - 34. 3 S. Aihara and D. Dowson, A study of film thickness in grease lubricated elastohydrodynamic contacts, Proc. 5th Leeds-Lyon Symp. on Tribology, Leeds, 1978, Mechanical Engineering Publishers, London. 4 W. Jonkisz and H. Krzeminski-Freda, Pressure distribution and shape of EHD grease film, Proc. 5th Leeds-Lyon Symp. on Tribology, Leeds, 1978, Mechanical Engineering Publishers, London.

285 5 W. Jonkisz and H. Krzeminski-Freda,

6 7 8 9

Pressure distribution and shape of EHD grease film, Wear, 55 (1979) 81 - 89. W. Jonkisz and H. ~zeminski-Freda, Thickness of EHD films as a function of grease rheological parameters, Tribal. Lubrificazione, 24 (March 1979) 12 - 14. C. A. Foord, L. D. Wedwen, F. G. Westlake and A. Cameron, Optical elastohydrodynamics, Proc., Inst. Mech. Eng., London, 184 (1) (1969 - 1970) 487 - 506. H. Krzeminski-Freda, Druckverlauf und Oelfilmform bei elastohydrodynamischer Schmierung eines Waeltzlagers, Schmierungstechnik, 2 (1971) 327 - 332. D. Dowson, W. Y. Saman and S. Toyoda, A study of starved EHD fine contacts, Proc. 5th Leeds-Lyon Symp. on ~~boiogy, Leeds, 1978, Mechanical engineering Publishers, London.