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A study of wear characteristics of journal bearings operating under mixed-lubrication conditions
11
Wear, 172 (1994) 11-22
A study of wear characteristics mixed-lubrication conditions A. Ramam~ha~a Department of ~ec~~~j~~l
of journal bearings operating
under
Rao and P.V. ~~hanram En&eeting,
Indian Inst&ute of Techmbgy,
Madras 600 0%
(;mdia)
(Received January 79, 1993; accepted October 21, 1993)
Abstract A comprehensive set of experiments incorporating some of the significant factors affecting wear under mixed lubrication of journal bearings has been carried out following Taguchi’s technique. Using carburized plain carbon steel like-pair bearing materials, wear characteristics and surface topography changes have been studied. Statistical analysis of mean and variance of test results reveals that, among the different factors considered, frequency of starts and stops, journal surface velocity, load and hardness influence the specific wear rate of the bush to a large extent. Hydrodynamic and asperity load computations correlate well with the experimental results. In addition, surface topography changes occurring during the wear process, related to power spectra1 density and fractal dimension, yield quantitative info~at~on regarding cha~cteri~tion of the wear process.
1. Introduction When the lubricant film that separates two loaded members becomes thin enough, the asperities on the surfaces begin to interfere. Hydrodynamic journal bearings invariably experience this phenomenon, which is called mixed lubrications during starting and stopping. In this case, a part of the applied load is carried by the hydr~~arni~ action of the fluid film and the remainder through asperity contacts. In recent years, Christensen El] and Berthe and Godet [2] proposed mixed-lubrication theories. These theories involve modification of Reynolds’ equation wherein the statistical parameters of surface topography have been incorporated. Wu 133 improved the theoretical base by pro~sing a truncated normal distribution for surface roughness. Rao et al. f4] reported that sursulf-treated like-pair steel bearings perform satisfactorily, substituting for bronze with economic advantages. The objective of the present investigation is to study the factors influencing the wear of carburized plain carbon steel like-pair journal bearings operating under mixed-lubrication conditions. A comprehensive set of experiments employing Taguchi’s technique [5] was carried out to establish wear characteristics under vary ing combinations of different parameters, i.e. load, surface velocity, surface roughness of journal and bush, surface hardness pairing of mating members, clearance ratio of bearing, and frequency of starts and stops, An optimum set of values of these parameters resulting
~3-1~~~4/$~?.~ Q 1994 EIsevier Sequoia. AD rights reserved XX@ U~43-~648(93)~~3~9-F
in minimum specific wear rate of the bush has been established. Relative grading of various factors influencing specific wear rate has been presented. A detailed surface topography analysis based on changes in asperity radius of curvature, power spectral density and fractal dimension has been carried out to characterize the wear process in the above experiments.
Dimensional details of test specimens, each consisting of two parts (bush and journal), are shown in Fig. 1. The materials used for the bush and journal were plain carbon steei with carbon content of 0.17% and 0.25% respectively. The manganese content was approximately 0.6%. The test specimens were case-carburized and hardened. The experimental set-up used to test the specimens is shown in Fig. 2. The drive shaft 1 which carries the test journal was supported by two self-aligning ball bearings 2 and driven by a variable-speed d,c. motor 6 through V-belts. The test bearing 3 was a full journal bearing mounted in a floating bracket 9, which was loaded by means of the loading arrangement 17, 18, 10 and 11. Frictional torque was measured using strain gauges 7 mounted on a cantilever which engages with the floating bracket. A gravity-feed arrangement 4 and 16 supplied lubricating oil to the bearing assembly through an oil groove in the floating bracket and an
12
A.R.Rao und P.Y Mohanram i Joumai bearing wear under mixed iuhricur~orz
spiine
I-
L x 16 X20
63Lh6 (al
Fig. 1. Test specimens:
Ib)
(a) bush, (b) journal.
oil hole in the bush located diagonally opposite to the loading side. For the measurement of frictional force, strain gauges were provided, the output voltage of which was amplified with a carrier-frequency amplifier 14 and recorded using an X-Y plotter 13. A trial was conducted to obtain the Stribeck curve for the test specimens. In this test, a load of 508 N was applied to the bearing and it was run for 2 h at a speed of 50 rev min -I. At the end of this period the speed was varied, keeping the load on the bearing constant. At each speed, the specimen was run for 5 min, and at the end the frictional force was measured. From this frictional force, the coefficient of friction f
was calculated by taking the ratio of the frictional force to the normal load on the bearing. The coefficient of friction was then plotted against the bearing characteristic number S, (= qw/$) to yield the Stribeck curve, as shown in Fig. 3. Here, r] is the dynamic viscosity of the lubricating oil, w is the angular velocity of the journal and pi is the load per unit projected area of the bearing. From the Stribeck curve, the test values of bearing load F and journal surface velocity U were selected so that the operating conditions fell in the mixed-lubrication zone. The test specimens were carefully segregated and paired to meet specific combinations of longitudinal surface roughness value, R, (centre line average value, c.l.a.), surface hardness H, and clearance ratio of bearing !P. In this work, suffix b is used for the bush and j for the journal. A summary of test factors together with their levels and operating loads and surface velocities are provided in Table 1. With the objective of studying the effect of frequent starts and stops on wear characteristics, it was decided to conduct experiments with intermittent stops followed by immediate restarting. 50% of the experiments were conducted with time duration t between successive stops equal to 15 min, and the rest at 1 h intervals. Experiments using special matrices, called orthogonal arrays, allow the effect of several parameters to be determined efficiently, and this is an important technique in robust design. Taguchi developed the foundations of robust design and validated its basic philosophies by applying them in the development of many products. In the present study, plann~g of experiments and analysis of test results was carried out as per the steps outlined by Taguchi [4]. The matrix experiments selected, taking into account the different factors and their levels, are provided in Table 2. The matrix experiments consist of 18 individual experiments corre-
Fig. 2. Experimental set-up: (1) drive shaft, (2) support bearing, (3) test specimen, (4) oil supply hose, (5) revolution counter, (6) d.c. motor, (7) strain gauge, (8) oil collector, (9) floating bracket, (10) loading lever, (11) loading pan, (12) concrete base, (13) X-Y recorder, (14) carrier-frequency ampllffer, (15) speed control panef, (16) oii tank, (17) connecting link, (18) central plate.
A.R.
Mixed
lubrication
Bearing
Rao and P.K
Mohanram
I Journal
number,Sox107
Fig. 3. Stribeck curve. TABLE
1. Test factors
and their levels
Factor
Unit
1
2
t
(min)
15
R.b
bm)
R,
(pm) cl *0.10 1.60 1350
(MPa)
H”b
Wpa) F
(N)
u
TABLE
0.65 IL-0.10
2.70 f 0.20
0.27 * 0.02
0.33 f 0.02
2.10 *0.10
2.60 *0.10
f200
2250 *200
2250 f 220
4500 f 300
0.063
2. Experimental
arrays
5400 cl It300
464
(3771
(m SC’)
3
160
0.40 cl zto.10
572
0.079
13
levels of factors. The settings of each experiment can be conveniently read from Tables 1 and 2. In determining the wear characteristics, the following procedure was adopted. The test specimens were assembled after thorough cleaning and run under no load at the required test speed for 5 min. Then the experimental load was gradually applied and the test was run for 4 h at full load. Weight loss and surface roughness measurements were taken by dismantling the arrangement at 1 h intervals. Lubricating oil was plain mineral oil Cab01 32 (7 = 27 X 10e3 N s mm2 at 30 “C). Roughness of test specimens was measured using a perthometer interfaced with a personal computer. The digitized surface profile data provided by the perthometer were analysed by a computer program for statistical parameters. A total of 5760 points at sampling intervals A of 0.7 pm were used for the computational work.
zone
chorocteristic
bearing wear under mixed lubrication
10.0941
Experiment No.
1
2
3
4
5
6
7
t
R,b
R,
$
Hvb
Hvi
F
8 u
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2
1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 2 3 1 3 1 2 2 3 1 3 1 2
1 2 3 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1
1 2 3 2 3 1 3 1 2 2 3 1 1 2 3 3 1 2
1 2 3 3 1 2 2 3 1 2 3 1 3 1 2 1 2 3
1 2 3 3 1 2 3 1 2 1 2 3 2 3 1 2 3 1
sponding to the 18 rows. The eight columns of the matrix experiments represent the eight factors indicated. The entries in the matrix experiments represent the
3. Results and discussion 3.1. Determination of conditions favouring minimum specific wear rate It is desirable that a good bearing material has a low specific wear rate. The specific wear rate k is calculated as the wear loss in cubic millimeters per unit load per unit sliding distance of the bearing [6]. The specific wear rate of bush k, is relatively higher than that of journal kj; it also depends on the time. Hence, in the analysis presented here, the specific wear rate of the bush is considered and for the purpose of comparison, it is chosen at the fourth hour of testing. Signal-to-noise ratio (Y~expressed in decibels (dB) for the ith experiment for the present case of a “the smaller the better” type of problem is given by (Yi= - 10 lOgl0[(kb)?]
(1) where (&Ji is the mean value of specific wear rate of the bush determined from the ith experiment. In the present analysis, the term “signal” represents the target value of the specific wear rate, and the term “noise” corresponds to the effect of various factors responsible for the variation in the observed value of &,. It may be noted that the objective of minimizing the specific wear rate is equivalent to maximizing the signalto-noise ratio. The overall mean value of LY~ for the 18 experiments, m, is given by
(2) The average value of signal-to-noise ratio when the time duration between successive stops t (referred to as the time interval factor) is fixed at level 1, i.e. 15 . . mm, 1s called m(,),. The same was estimated from the test data of experiments 1 to 9 of Table 2 and is given by
14
A.R. Rao and P.V. Mohanram
I Journal
the columns of matrix experiments used in the computations of the entries in Table 3, is given in Table 4. Wherever summation [C] is indicated, it is for i= I
(3)
Similarly, the average signal-to-noise ratios for the other factors corresponding to their respective levels were evaluated and are shown in Fig. 4. The corresponding equivalent average specific wear rate of the bush, k,,, can be read from the scale on the right. The primary goal of the matrix experiments is to determine the optimum level for each of the factors under study. The appropriate optimum levels of different factors which yielded maximum average signal-to-noise ratio, i.e. minimum specific wear rate, were obtained and are indicated with filled circles in Fig. 4; the same are indicated in boxes in Table 1. Analysis ofvariance provides quantitative information about the relative influencing capability of various factors on specific wear rate. The difference (m(,), -m) is a measure of deviation caused by the time interval factor t at level 1 from the overall mean, and it is termed as the effect of time interval factor at level 1. The individual effects of various factors at their respective levels for the different experiments are indicated by shaded areas in Fig. 5; a large shaded area implying a larger influencing power of the corresponding factor on specific wear rate. Hence, it might be observed that time interval factor, surface velocity factor, load factor and journal hardness factor seem to introduce significant deviations of the signal-to-noise ratio from the overall mean, while the contribution from the other factors is relatively small. Quantitative information related to the above could be obtained by computing the sum of squares Es2 due to various factors. The sum of squares due to the time interval factor t is equal to the total squared deviation of the wave for t (Fig. 5(c)) from the line representing the overall mean (Fig. Sim5(b)) and is given by 9[(m,,,, -m)‘+ (mCrjz-m)‘] ilarly, the sum of squares due to other factors was established and listed in Table 3. A summary of the different relationships, based on the orthogonality of
l
Levels
Fig. 4. Variation
in average
of
signal-to-noise
different
ratio
bearing weor under mired lubncurion
to 18. It may be observed
that the variance ratio of the time interval factor (5.12) is the maximum, followed by the variance ratios of journal surface velocity (3.69), load (1.16) and journal hardness (0.98) factors. Hence, it can be concluded that these four factors have significant influence on the specific wear rate in relation to the others. The validity of this approach was confirmed by conducting a verification experiment and ensuring that the measured value of signal-to-noise ratio lies within the predicted range. The predominant nature of the time interval factor in influencing specific wear rate is due to the severe mixed-lubrication conditions prevailing during frequent starting and stopping. The observed reduction in average specific wear rate of the bush (Fig. 4) at high journal velocities (velocity factor, level 3) and low loads (load factor, level 1) may be attributed to reduction in coefficient of friction (f) because of an increase in the bearing characteristic number (S,) within the mixedlubrication zone, as evident from the Stribeck curve (Fig. 3). 3.2. Sulfate topography analysis 3.2.1. Conditions favouring mixed lubrication
A close observation of surface topography changes occurring in the above experiments can be expected to provide an insight into the wear process. A summary of the different concepts required for this investigation associated with bearings operating under mixed-lubrication conditions is presented below. Details of the geometry of a journal bearing presented in polar coordinate system r, 0, z with O=o” aligned with the line of centres are shown in Fig. 6. The bearing dimensions are: 6, the length of the bearing; r,, the radius of the bush; rj, the radius of the journal; c, the radial clearance, equal to (rh-r,). The clearance ratio ?P is given by c/rj. Under stable conditions, with an
Optimum
levels
factors
with
different
levels
of various
factors.
A.R. Rao and P.V. Mohanram
I Journal
124
124
116
116
108
108
100
100
12 4
r
=114,67
Overallmean
dB
124
(b)
15
bearing wear under mixed lubrication
r
Effect
of bush
hardness
factor
(g)
I
116 108 -
108 _
m 0
100 124
r
Effect
of time
interval
I
(cl
factor
2
5 L
108r
*
.;
I 5 2
5 ._ m
$
124
.: e f ._
116
124
r
Effect
of bush
roughness
2
100 124
5 &
116
;7,
108
I
Cd)
factor
108 -
108
4
lOOl!l
I
100
h
Effect
of load
factor
124
124
Effect
of journal
roughness
factor 116
116
108
0
6
3
9
Experiment
Fig. 5. Effect
TABLE
12
15
0
18
of individual factor
Ss2
V
1 2 2 2 2 2 2 2 2
162.72 6.16 18.34 13.67 38.20 62.06 73.79 234.50 63.56
162.72 3.08 9.17 6.84 19.10 31.03 36.89 117.30 31.78
5.12 0.10 0.29 0.22 0.60 0.98 1.16 3.69 -
17
673.00
-
_
t R R:p * H”b Hvi F u Error Total
applied load F, and journal speed n, the bearing operates with an eccentricity e, the eccentricity ratio E being given by e/rj. The film thickness is dependent on 0 and has the value h(e)=c(l+Ecos
e)
9
12
15
18
number
levels relative to the overall mean m.
cs’
DOF
6 Experiment
3. Analysis of variance
Factor
3
number
(4)
In the present work, it is assumed that the bearing surfaces are covered with one-dimensional roughness in the z direction, the roughness remaining constant in the 0 direction. The roughness profiles are char-
acterized as shown in Fig. 7. Thus, for each value of z, the effective film thickness H shown at Fig. 7(a) is given by H=h(e)+R
(5)
where R, represented in Fig. 7(b), is the statistical summation of profile heights of the bush R, and the journal Rj and is referred to as the profile sum. R is assumed to have a truncated normal distribution as at Fig. 7(c), where R,, the cut-off value of R, is given by R,= 3s. Here s is the standard deviation given by S=m
(6)
Further, it may be noted that mixed lubrication can be expected to prevail under the following condition (l-R,/c)<~
(7)
3.2.2. Gaussian d&ribution parameters A typical set of test results of experiment no. 6 (Table 2), which was terminated owing to bearing failure (seizure) at the end of 4 h of testing, was selected for the present study. The surface roughness recordings of (a) bush and (b) journal as a function of time of
TABLE 4. ______. Summation of squares Grand total Mean Total
(cf’)
due to
Error
=Summation
Degrees of freedom (DUF) of Summation of squares: grand total Uveratl mean Summation of squares: total Each factor
= Number of experiments I = Number of experiments=Number of levels-l
Summation
=DOF
of squares
due to error
Others Mean sum of squares (Cr2) Variance due to error Variance ratio, V
of summation
bearing
(total)-summation
of squares due to factor effects
I
of squares (total)-sum
of DOF of factor effects
= Sum of squares/DOF =Mean sum of squares due to error =Mean sum of squares/variance due to error
,ectian
Fig. 6. Journal
of squares
nomenclature.
testing 1”are shown in Fig. 8. A ~or~~g~ ~n~estiga~~o~ into the changes in surface topography was carried out to correlate the latter with the test results of matrix experiments. Analysis of digitized profile data pertaining to these profiles is presented in the following paragraphs. Cumulative ~robabili~ plots on normal probabili~ paper confirmed the gaussian nature of the distribution of profile heights of the mating parts. The 95% upper
and Iower confidence limits of the standard deviation of the bush and journal profiles of experiment 5 (Fig. 8) fime.sbu, s blf and Sj”,Sjl, respectively) were determined for different test times and are shown in plots in Figs. 9(a) and 9(b). The figure also shows the corresponding mean values sb and sj- The test specimen parts - bush as weh as journal - showed an initial decrease in standard deviation typical of the running-in process, and towards the end of the fourth hour of testing there was a sharp rise. Higher values of standard deviation of mating profiles result in increased probability of asperity interaction; hence, these Iimits (sbrr, Sj”) have been considered in the subsequent analysis. With respect to the profile sum, the mean I* and standard deviation s (using eqn. (6)) were determined and are shown in Fig. 9(c)_ The standard deviation plot of the profile sum was found to be approximately similar to that of the bush, owing to the fact that the standard deviation of the bush was very much greater than that of the journal. It may be noted that the Probability density,
f fR>
t
R=Rj
lRt,
(b)
Fig. 7, Characterization of rough surfaces: (a) roughness distribution of profile sum R.
Height
of profile
sum,
R
(cl
of bush Rb and journal I$; (bf combined
roughness
R; G+ truncated
normat
17
A.R. Rao and P.V. Mohanram / Journal bearing wear under mired lubrication
BL =$-f
Ll+L2*t3+L~+...Ln)X
o
distance
BL
length
Lt
trace
below of
5%
bearing
100
reference line
tine
( pm)
‘1.
length
I b)
(0)
Fig. 8. Surface roughness recordings of (a) bush and (b) journal.
-2 -
-51
lnitiol
I
I
I
I
LO
60
60
% ,.*, t
1
I
1
5
20
Length of bearing
line
1
%,BL
Fig. 10. Nomenclature (a) and bearing Iine curves (b) of bush and (c> of journal as a function of test duration, 7’.
0.0 1.2
L 0
I 1 Test
I
I
2
3
durotion
,
1 4
T (h)
Fig. 9. Variation in mean and 95% confidence limits of measured vahtes of standard deviation with test duration T, for (a) bush (So, rbr sbl); (b) journals (Sj”, si, sir). (c) Variation in standard deviation s and mean p of profile sum R with test duration 7’.
standard deviation of the profile sum (s) was the highest at 1.48 Frn, corresponding to the end of testing; the estimated mean value of the profile sum was close to
zero for most of the test duration and it became increasingly negative (i.e. -0.8 pm) towards the end of testing, indicating progressive surface deterioration. A study of the bearing line curves of the above profiles shown in Fig. 10 provides evidence for this observed phenomenon; they indicate that 100% bearing lines are available at increased depth below the 5% reference line towards the end of testing, i.e. 4 h. 3.2 3. Hyd~~n~~ic load Under mixed lubrication, load is shared between hydrodynamic action and asperity interaction. Procedures for determining the loads supported by the hydrodynamic action of the fluid film considering the surface roughness effects F,, and the asperity contacts Fa have been presented by the authors elsewhere [7,8].
A. R. Rao nnd P. VI Mohanrum
18
/ Journal
The hydrodynamic load computations require the inputs s, E, II and 77in addition to the geometry of the bearing. Hydrodynamic computations are reported in Fig. 11. A comparison of hydrodynamic loads F, that can be supported by the bearing at the end of third and fourth hours of testing for various eccentricity ratios E,confined to the mixed-lubrication zone, is shown in Fig. 11(a). It can be clearly seen that, to support a constant hydrodynamic load, a bearing operates at a higher eccentricity ratio as the standard deviation increases owing to surface degradation with increased time of running. The inference is that a rough bearing has a greater probability of asperity interaction compared to a relatively smooth bearing. Hence, a rough bearing can be expected to undergo premature failure. This might be one of the causes for the observed higher value of specific wear rate of mating members (kb, k,) Z
1200
(0) T=3h,
s-0.60pm
-,
Eccentricity
ratio,
/
E
-6
7 2x10
4
(b) 4 lx 10-6
3
2 .l x 10-6
4
3
11. (a) E. (b) fourth VI for
[Journol-ki]
1.4 x 10-6 0
I 2.5
1 5
Specific
weor
rate
Cleoronce
Fig. ratio and ratio
[Bush_1
,
I 7.5
k
b’
k.
ratio,
I
x lo6 (mm3
10 N-‘m-l)
q~
Variation in hydrodynamic load Fh with eccentricity Specific wear rate of bush and journal kb ki for third hours of testing. (c) Variation of Fh with clearance s= 1.48 pm, c=O.95, U=79 mm s-‘.
bearing wear under mixed lubricurion
of experiment no. 6 (Table 2), measured at the fourth hour when compared to that at the end of the third hour. This is indicated by the bar chart in Fig. 11(b). The experimental results reveal that an increase in clearance ratio P from level 1 to level 3 resulted in an increase in average specific rate kb (decrease in average signal-to-noise ratio) as shown in Fig. 4. The influence of clearance ratio on specific wear rate can be estimated analytically by determining the hydrodynamic load-carrying capacity of the bearing using the fourth-hour surface topography data of experiment no. 6 (s = 1.48 pm) for various clearance ratios. The results are plotted at Fig. 11(c). The computation is for a given eccentricity ratio of 0.95. It can be observed that an increase in clearance ratio reduces the hydrodynamic load-carrying capability. Hence, for a constant hydrodynamic load to be supported, a loose bearing (high value of ?P) will be forced to operate at a higher E within the mixed-lubrication zone, thus leading to an increase in specific wear rate as discussed in the preceding paragraph.
3.2.4. Asperity load The procedure for the computation of asperity load has been outlined by the authors in ref. 8. The inputs required (apart from s, E and H,,) are: mean asperity radius p of profile sum; the number of asperities per unit area N,; and the equivalent Young’s modulus of elasticity E. A better understanding of the sequence of events leading to the seizure of the bearing in experiment no. 6 can be had by making a comparative study of estimated asperity load-carrying capacity at the third and fourth hours of testing shown in Fig. 12. The changes in surface topography parameters related to the asperity load computation, i.e. p and N, of the profile sum are shown in Fig. 12(a), plotted with respect to test duration. Initially there was an increase in equivalent mean asperity radius and a reduction in the number of asperities of profile sum per unit area, characteristic of the running-in process. The above data corresponding to the third and fourth hours of operation were used in the computation of asperity load-carrying capability (F.) together with the ratio of real and apparent areas of contact (A,/‘,) for various eccentricity ratios E and are shown in Figs. 12(b) and 12(c). It can be seen that the asperity loadcarrying capability is significantly less for the fourth hour compared to the third. This is in agreement with the observed fact that there was seizure in the fourth hour owing to excessive plastic deformation. The ratio of A, to A, within the mixed-lubrication zone also showed a decrease in the fourth hour of testing when compared to the third hour, thus indicating that real contact took place at a reduced number of asperities
19
A.R. Rao and P.K Mohanram I Journal bearing wear under mixed lubrication
‘1400 Test
duration
(h)
2400
3400
Hordness
of bush,
4400
541
H, b (MPo)
Fig. 13. Variation in asperity load F, with hardness of bush Hvc for s=1.48 pm, l=O.95, p=O.22 mm, N,=387 mm-*.
Fig. 12. Variation in (a) equivalent mean asperity radius p and number of asperities per unit area N. with test duration T; and variation of (b) asperity load F. and (c) ratio of real and nominal areas of contact AC/A, with eccentricity ratio c for third and fourth hours of test duration T.
average specific wear rate; whereas the experimental results did not show a consistent trend in the measured average value of specific wear rate of the bush (average signal-to-noise ratio) when the bush hardness was varied from level 1 to level 3 (Fig. 4). The corresponding variance ratio of the bush hardness factor was low, i.e. 0.60, which implies that the variation in the experimentally observed values of average signal-to-noise ratio due to the bush hardness factor was comparatively small, i.e. 60% of that ,due to the error component in the experiment. Therefore, it can be seen that no concrete inference relating the effect of bush hardness factor on the measured values of average specific wear rate (and hence average signal-to-noise ratio) can be derived from the above matrix experiments (Table 2). Thus it may be concluded that exclusive experiments with bush hardness as the primary variable may have to be undertaken to validate the above predicted decrease in &, with increase in Hvb. Furthermore, it must be noted that a high hardness of the bush greatly reduces the conformability and compatibility characteristics of the bearing.
at the end of the fourth hour; this might be responsible for the observed surface deterioration. The influence of the hardness of the bush (which is soft in comparison to the journal) on estimated asperity load-carrying capacity and possible correlation with the experimentally observed values of average specific wear rate are discussed below. The variation of the estimated asperity load-carrying capacity with the hardness of the bush using the fourth-hour surface topography data of experiment no. 6, i.e. s= 1.48 w, p=O.22 mm, and N, =387 mn-*, for l equal to 0.95 is shown in Fig. 13. The figure clearly reveals that when the bush hardness increases there is a corresponding increase in asperity load-supporting capability. Hence it can be expected that bearings with higher bush hardness will have less plastic deformation, leading to a reduction
3.2.5. Power spectral density A study of wear topography using power spectral density G, furnishes information about the variation in amplitudes of the different constituent surface wavelengths [9]. Each surface wavelength component of the profile is designated by its frequency fk and is referred to as the spatial frequency. Analysis of recorded digitized profile data of mating components of experiment no. 6 (Fig. 8) with respect to time of testing reveals the predominance of low spatial frequencies (large surface wavelengths). The surface profiles were considered as stationary ergodic random processes. The stationary nature of the surface profiles was verified by the reverse arrangement test, and a single record of surface topography was found to be adequate in describing the statistical parameters. In addition, the fast Fourier transform (FFT)
in
,011
’
0.879
t 0.909
I 0.999
Eccentricity
rotio,
I 0.969
I 0.999
E
20
A.R. Rao and P. V. Mohanram
I Journal bearing wear under mired lubrication
procedure for the analysis of discrete stationary ergodic random data was employed to obtain the power spectral density G, corresponding to the different spatial frequenciesf,. The complete record of surface profile data was subdivided into 100 sub-records to ensure that the standard error of the power spectral density was small. The appropriate equations used to obtain power spectral density have been taken from ref. 10. It is well known [9] that a large value of power spectral density G, in the neighbourhood of spatial frequency f, implies a high mean-square value of the amplitude of the appropriate surface wavelength. Plots of power spectral density are shown in Fig. 14. The power spectrum plots in Figs. 14(a) and 14(b) reveal that the powers of low spatial frequencies (0.045 to 0.270 pm) are higher. The plots also indicate an increase in the power of the low spatial frequencies towards the end of the fourth hour. Thus it could be
After
0.001
I
T I lh
3.2.6. Fractal analysis A unique property of rough surfaces is that, if a surface is repeatedly magnified, increasing details of roughness are observed. In recent work [ll] it was established that such a behaviour could be characterized by scale-independent fractal geometry. In the present study, an attempt has been made to establish the fractal characteristics of wear surfaces. The basic idea behind fractal geometry is that it aims at characterizing the order behind the disorder of surface roughness. The essence of fractal analysis is: the number of measuring units M required to cover the length (or area) of an irregular line (or surface) depends on the size of the relative measuring unit B,. Small measuring devices resolve finer details than larger devices, requiring disproportionately greater numbers. A graphical representation of log(M) of a fractal curve against log(l/B,) yields a straight line described by the power law relation
, ‘. -,--_,___
I 1 I I 1I
m
O.Ol‘\
,001
6
I
I
(
I
inferred that the mean-square value of the amplitude corresponding to low spatial frequencies in the range of 0.045 to 0.270 pm increased at the time of bearing failure (i.e. the fourth hour). In order to highlight the influence of surface roughness on power spectral density, a comparative study of power spectral plots of bushes with varying degrees of surface roughness, that is, sb = 0.63, 1.60 and 3.40 pm, measured at the end of the first hour of testing under similar test conditions (experiments 1, 5 and 9 of Table 2) is provided in Fig. 14(c). The predominance of power spectral estimates corresponding to low spatial frequencies in the case of bush profiles with coarse roughness is distinctly evident. In either situation, i.e. surface failure or relatively coarse finish of mating profiles, the power spectral estimates corresponding to low frequencies showed an increasing trend. Hence, it might be concluded that surface degradation at the end of wear life is associated with coarsening of the surface finish, characterized by an increase in the power of the low spatial frequencies (large surface wavelengths).
-e-o-
*J
I
log(M) = K+ D log( l/B,)
O.OOll ’
t
t
0.04
Spatial
SC1 0 10 frequency,
I 0.20
0.30
fk
(pm-’
0.70
1Log
Fig. 14. Variation in power spectral density Gk with respect to spatial frequency!, for (a) bush and (b) journal with test duration T for experiment no. 6 and (c) for different bushes with varying initial surface roughnesses at T=l h.
(8)
where D is the fractal dimension and K is the fractal scale factor. Stupak et al. [12] suggested that a constant value of fractal dimension observed during wear tests on rubber surfaces could be attributed to the similarity of microscopic wear mechanisms; the fractal scale factor correlated well with the relative scale of wear surfaces. The digitized profilometry data was analysed following Dubuc’s “variational method” fractal algorithm [13]. In practice, computational limitations required that the digitized data be analysed using sample data files consisting of 450 points.
2.0
I
I
(0)
Bush
I
Y
6 -“.2
5
, 1
ij
“u -0.8 ,o
Lt.
-l.Ol1
f
*
2
Test
3 duration
I
J
4
(h)
Fig. 15. Variation in (a} fractal dimension L) and (b) fractal scale factor K with test duration T for bush and journal of experiment no. 6.
The results of fractal analysis of the digitized surface profile data of experiment no. 6 are displayed in Fig. 15. The variation in the fractal dimension of the bush and journal profiles with test duration is shown in Fig. 15(a). It can be observed that the fractal dimensions of the bush traces are consistently larger than the fractal dimension of the journal traces. Furthe~ore, it can be seen that the fractal dimension remained almost constant during the initial hours of testing, indicating that the wear mechanism was practically the same during that period; a sudden decrease in fractal dimension close to the fourth hour of testing might be attributed to a change in wear mechanism. The associated variation in fractal shift factor K with test duration is shown in Fig. 15(b). A sharp rise in K for both the mating members is seen towards the fourth hour of the test duration, indicating a corresponding increase in severity of wear as was observed in the experiments. Thus, a sudden change in fractal dimension together with an increase in fractal scale factor could be used as an index of impending failure of the specimens.
4. Conclusions The major conclusions derived from the experimental programme based on Taguchi’s technique and the surface topography analysis related to mixed lubrication of plain carbon steel like-pair journal bearings are listed below.
Minimum specific wear rate of the bush can be expected to occur under conditions of minimum number of starts and stops, maximum journal surface velocity, minimum load and maximum journal hardness. Surface degradation was associated with an increase in the standard deviation of the profile sum, which resulted in a decrease in hydrodynamic load-carrying capacity of the bearing, leading to further intense m~ed-lub~cation ~nditions. During the running-in period, equivalent mean asperity radius of the profile sum increased, while the number of asperities per unit area decreased. Surface deterioration and increase in bush hardness resulted in a decrease and an increase respectively of the asperity load-carrying capacity Spatial frequency analysis of wear surfaces could be carried out using the stationary ergodic random process approach. Failure of the bearing was characterized by an increase in power spectral density ~~esponding to low spatial frequencies (large surface wavelengths). Monitoring of fractal dimension and fractal scale factor could be used to predict impending failure of journal bearings.
Acknowledgments The authors thank the Indian Institute of Technology, Madras, and the P.S.G. College of Technology, Coimbatore, for providing an oppor~~i~ and necessary facilities to carry out this research work. In addition, the authors wish to acknowledge the computational assistance provided by Shri P. Satya Sai I&mar in the analysis of surface topography.
References H. Christensen, A theory of mixed lubrication, Proc. Insf. Eng, f86 (1972) 41-72. D. Berthe and MA. Godet, A more general form of Reynolds’ equation application to rough surfaces, Wear, 186 (1972) 41-72. M.E. Weyler and Wu Chih, A Numerical Method for the Calculation of Lubricant Pressures in Bearings with Mixed Lubrication, T&ol. Znt., I3 (1982) 89-95. A.R. Rao, R. Marappan and P.V. Mobanram, Performance studies on treated steels as substitutes for conventional bearing materials, Wear, 155 (1992) 15-29. MS. Phadke, Qua& L%gineeringUsing Robust Lksign, Prentice-Hall, Englewood CM%, NJ, 1989. 6 A. Be8ihnger and A.W.J. De Gee, Friction and wear tests on metallic hearing materials for oil lubricated bearings, Wear, 69 (1981) 43-54. Me&
22
A.R. Rao and P.V. Mohanram I Journal bearing wear under mixed lubrication
7 A.R. Rao and P.V. Mohanram, Load distribution analysis of journal bearings operating under mixed lubrication conditions, Proc. 6th ASME Int. Co@ on Power Transmission and Gearing, Advancing Power Transmission into the 21st century, Vol. 1, ASME, Phoenix, AZ, 1992, pp. 299-306. 8 A.R. Rao and P.V. Mohanram, A study of mixed lubrication parameters of journal bearings, Wear, in press. 9 T.R. Thomas, The characterization of changes in surface topography during running-in, in D. Dowson (ed,), Proc. 4th Leeds-Lyons Symp. on Tribology, Lyon, France, 1977, The Institute of Tribology, Leeds, 1978, pp. 99-108. 10 J.S. Bendat and A.G. Piersol, Random Data Ana&sis and Measurement Rocedures, Wiley, NY, 1986. 11 A. Majumdar and 3. Bhushan, Role of fractal geometry in roughness characterization and contact mechanics of surfaces, ASME J. Tkibol., 112 (1990) 205-216. 12 P.R. Stupak, J.H. Kang and J.A. Donovan, Fractal characteristics of rubber wear surfaces as a function of load and velocity, Wear, 141 (1990) ‘73-84. 13 B. Dubuc, C. Quiniou, C. Roques-Carmes, C. Tricot and SW. Zucker, Evaluating the fractal dimension of profiles, Phys. Rev. A, 39 (1989) 1500-1512.
N
Hvb,Hvj
h(O) Kb, Kj
k, kj (lb)i
Lt A4
GA n
P
R Rb,Rj R,
R r, 0,
Appendix: Nomenclature
rb, ‘i
& s
true area of contact nominal contact area distance below 5% reference line size of relative measuring unit bearing length (%) length of the bearing radial clearance fractal dimension equivalent modulus of elasticity eccentricity journal load asperity load hydrodyna~c load coefficient of friction probability density function of R spatial frequency power spectral density
effective film thickness Vickers surface hardness of bush and journal film thickness at any angular position 0 fractal scale factor specific wear rate mean specific wear rate of bush for the ith experiment trace length number of measuring units overall mean value of signal-to-noise ratio combined number of asperities operating speed of journal load per unit projected area combined surface profile height of bush and journal (profile sum) profile height variables of bush and journal half the range of the profile sum variable
sb,
sj
sbb
Sjl
Sbu,
sju
T t t.7
ai
2
centre line average value polar co-ordinates radii of bush and journal bearing characteristic number standard deviation of profile sum R standard deviation 95% lower confidence limit of standard deviation 95% upper confidence limit of standard deviation test duration time interval between successive starts surface velocity of journal observed signal-to-noise ratio of ith experiment sampling interval of digitized profile data eccentricity ratio lubricant viscosity (constant) combined mean asperity radius of curvature mean asperity radii of curvature angular velocity of journal clearance ratio
Wear, 172 (1994) 11-22
A study of wear characteristics mixed-lubrication conditions A. Ramam~ha~a Department of ~ec~~~j~~l
of journal bearings operating
under
Rao and P.V. ~~hanram En&eeting,
Indian Inst&ute of Techmbgy,
Madras 600 0%
(;mdia)
(Received January 79, 1993; accepted October 21, 1993)
Abstract A comprehensive set of experiments incorporating some of the significant factors affecting wear under mixed lubrication of journal bearings has been carried out following Taguchi’s technique. Using carburized plain carbon steel like-pair bearing materials, wear characteristics and surface topography changes have been studied. Statistical analysis of mean and variance of test results reveals that, among the different factors considered, frequency of starts and stops, journal surface velocity, load and hardness influence the specific wear rate of the bush to a large extent. Hydrodynamic and asperity load computations correlate well with the experimental results. In addition, surface topography changes occurring during the wear process, related to power spectra1 density and fractal dimension, yield quantitative info~at~on regarding cha~cteri~tion of the wear process.
1. Introduction When the lubricant film that separates two loaded members becomes thin enough, the asperities on the surfaces begin to interfere. Hydrodynamic journal bearings invariably experience this phenomenon, which is called mixed lubrications during starting and stopping. In this case, a part of the applied load is carried by the hydr~~arni~ action of the fluid film and the remainder through asperity contacts. In recent years, Christensen El] and Berthe and Godet [2] proposed mixed-lubrication theories. These theories involve modification of Reynolds’ equation wherein the statistical parameters of surface topography have been incorporated. Wu 133 improved the theoretical base by pro~sing a truncated normal distribution for surface roughness. Rao et al. f4] reported that sursulf-treated like-pair steel bearings perform satisfactorily, substituting for bronze with economic advantages. The objective of the present investigation is to study the factors influencing the wear of carburized plain carbon steel like-pair journal bearings operating under mixed-lubrication conditions. A comprehensive set of experiments employing Taguchi’s technique [5] was carried out to establish wear characteristics under vary ing combinations of different parameters, i.e. load, surface velocity, surface roughness of journal and bush, surface hardness pairing of mating members, clearance ratio of bearing, and frequency of starts and stops, An optimum set of values of these parameters resulting
~3-1~~~4/$~?.~ Q 1994 EIsevier Sequoia. AD rights reserved XX@ U~43-~648(93)~~3~9-F
in minimum specific wear rate of the bush has been established. Relative grading of various factors influencing specific wear rate has been presented. A detailed surface topography analysis based on changes in asperity radius of curvature, power spectral density and fractal dimension has been carried out to characterize the wear process in the above experiments.
Dimensional details of test specimens, each consisting of two parts (bush and journal), are shown in Fig. 1. The materials used for the bush and journal were plain carbon steei with carbon content of 0.17% and 0.25% respectively. The manganese content was approximately 0.6%. The test specimens were case-carburized and hardened. The experimental set-up used to test the specimens is shown in Fig. 2. The drive shaft 1 which carries the test journal was supported by two self-aligning ball bearings 2 and driven by a variable-speed d,c. motor 6 through V-belts. The test bearing 3 was a full journal bearing mounted in a floating bracket 9, which was loaded by means of the loading arrangement 17, 18, 10 and 11. Frictional torque was measured using strain gauges 7 mounted on a cantilever which engages with the floating bracket. A gravity-feed arrangement 4 and 16 supplied lubricating oil to the bearing assembly through an oil groove in the floating bracket and an
12
A.R.Rao und P.Y Mohanram i Joumai bearing wear under mixed iuhricur~orz
spiine
I-
L x 16 X20
63Lh6 (al
Fig. 1. Test specimens:
Ib)
(a) bush, (b) journal.
oil hole in the bush located diagonally opposite to the loading side. For the measurement of frictional force, strain gauges were provided, the output voltage of which was amplified with a carrier-frequency amplifier 14 and recorded using an X-Y plotter 13. A trial was conducted to obtain the Stribeck curve for the test specimens. In this test, a load of 508 N was applied to the bearing and it was run for 2 h at a speed of 50 rev min -I. At the end of this period the speed was varied, keeping the load on the bearing constant. At each speed, the specimen was run for 5 min, and at the end the frictional force was measured. From this frictional force, the coefficient of friction f
was calculated by taking the ratio of the frictional force to the normal load on the bearing. The coefficient of friction was then plotted against the bearing characteristic number S, (= qw/$) to yield the Stribeck curve, as shown in Fig. 3. Here, r] is the dynamic viscosity of the lubricating oil, w is the angular velocity of the journal and pi is the load per unit projected area of the bearing. From the Stribeck curve, the test values of bearing load F and journal surface velocity U were selected so that the operating conditions fell in the mixed-lubrication zone. The test specimens were carefully segregated and paired to meet specific combinations of longitudinal surface roughness value, R, (centre line average value, c.l.a.), surface hardness H, and clearance ratio of bearing !P. In this work, suffix b is used for the bush and j for the journal. A summary of test factors together with their levels and operating loads and surface velocities are provided in Table 1. With the objective of studying the effect of frequent starts and stops on wear characteristics, it was decided to conduct experiments with intermittent stops followed by immediate restarting. 50% of the experiments were conducted with time duration t between successive stops equal to 15 min, and the rest at 1 h intervals. Experiments using special matrices, called orthogonal arrays, allow the effect of several parameters to be determined efficiently, and this is an important technique in robust design. Taguchi developed the foundations of robust design and validated its basic philosophies by applying them in the development of many products. In the present study, plann~g of experiments and analysis of test results was carried out as per the steps outlined by Taguchi [4]. The matrix experiments selected, taking into account the different factors and their levels, are provided in Table 2. The matrix experiments consist of 18 individual experiments corre-
Fig. 2. Experimental set-up: (1) drive shaft, (2) support bearing, (3) test specimen, (4) oil supply hose, (5) revolution counter, (6) d.c. motor, (7) strain gauge, (8) oil collector, (9) floating bracket, (10) loading lever, (11) loading pan, (12) concrete base, (13) X-Y recorder, (14) carrier-frequency ampllffer, (15) speed control panef, (16) oii tank, (17) connecting link, (18) central plate.
A.R.
Mixed
lubrication
Bearing
Rao and P.K
Mohanram
I Journal
number,Sox107
Fig. 3. Stribeck curve. TABLE
1. Test factors
and their levels
Factor
Unit
1
2
t
(min)
15
R.b
bm)
R,
(pm) cl *0.10 1.60 1350
(MPa)
H”b
Wpa) F
(N)
u
TABLE
0.65 IL-0.10
2.70 f 0.20
0.27 * 0.02
0.33 f 0.02
2.10 *0.10
2.60 *0.10
f200
2250 *200
2250 f 220
4500 f 300
0.063
2. Experimental
arrays
5400 cl It300
464
(3771
(m SC’)
3
160
0.40 cl zto.10
572
0.079
13
levels of factors. The settings of each experiment can be conveniently read from Tables 1 and 2. In determining the wear characteristics, the following procedure was adopted. The test specimens were assembled after thorough cleaning and run under no load at the required test speed for 5 min. Then the experimental load was gradually applied and the test was run for 4 h at full load. Weight loss and surface roughness measurements were taken by dismantling the arrangement at 1 h intervals. Lubricating oil was plain mineral oil Cab01 32 (7 = 27 X 10e3 N s mm2 at 30 “C). Roughness of test specimens was measured using a perthometer interfaced with a personal computer. The digitized surface profile data provided by the perthometer were analysed by a computer program for statistical parameters. A total of 5760 points at sampling intervals A of 0.7 pm were used for the computational work.
zone
chorocteristic
bearing wear under mixed lubrication
10.0941
Experiment No.
1
2
3
4
5
6
7
t
R,b
R,
$
Hvb
Hvi
F
8 u
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2
1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 2 3 1 3 1 2 2 3 1 3 1 2
1 2 3 2 3 1 1 2 3 3 1 2 3 1 2 2 3 1
1 2 3 2 3 1 3 1 2 2 3 1 1 2 3 3 1 2
1 2 3 3 1 2 2 3 1 2 3 1 3 1 2 1 2 3
1 2 3 3 1 2 3 1 2 1 2 3 2 3 1 2 3 1
sponding to the 18 rows. The eight columns of the matrix experiments represent the eight factors indicated. The entries in the matrix experiments represent the
3. Results and discussion 3.1. Determination of conditions favouring minimum specific wear rate It is desirable that a good bearing material has a low specific wear rate. The specific wear rate k is calculated as the wear loss in cubic millimeters per unit load per unit sliding distance of the bearing [6]. The specific wear rate of bush k, is relatively higher than that of journal kj; it also depends on the time. Hence, in the analysis presented here, the specific wear rate of the bush is considered and for the purpose of comparison, it is chosen at the fourth hour of testing. Signal-to-noise ratio (Y~expressed in decibels (dB) for the ith experiment for the present case of a “the smaller the better” type of problem is given by (Yi= - 10 lOgl0[(kb)?]
(1) where (&Ji is the mean value of specific wear rate of the bush determined from the ith experiment. In the present analysis, the term “signal” represents the target value of the specific wear rate, and the term “noise” corresponds to the effect of various factors responsible for the variation in the observed value of &,. It may be noted that the objective of minimizing the specific wear rate is equivalent to maximizing the signalto-noise ratio. The overall mean value of LY~ for the 18 experiments, m, is given by
(2) The average value of signal-to-noise ratio when the time duration between successive stops t (referred to as the time interval factor) is fixed at level 1, i.e. 15 . . mm, 1s called m(,),. The same was estimated from the test data of experiments 1 to 9 of Table 2 and is given by
14
A.R. Rao and P.V. Mohanram
I Journal
the columns of matrix experiments used in the computations of the entries in Table 3, is given in Table 4. Wherever summation [C] is indicated, it is for i= I
(3)
Similarly, the average signal-to-noise ratios for the other factors corresponding to their respective levels were evaluated and are shown in Fig. 4. The corresponding equivalent average specific wear rate of the bush, k,,, can be read from the scale on the right. The primary goal of the matrix experiments is to determine the optimum level for each of the factors under study. The appropriate optimum levels of different factors which yielded maximum average signal-to-noise ratio, i.e. minimum specific wear rate, were obtained and are indicated with filled circles in Fig. 4; the same are indicated in boxes in Table 1. Analysis ofvariance provides quantitative information about the relative influencing capability of various factors on specific wear rate. The difference (m(,), -m) is a measure of deviation caused by the time interval factor t at level 1 from the overall mean, and it is termed as the effect of time interval factor at level 1. The individual effects of various factors at their respective levels for the different experiments are indicated by shaded areas in Fig. 5; a large shaded area implying a larger influencing power of the corresponding factor on specific wear rate. Hence, it might be observed that time interval factor, surface velocity factor, load factor and journal hardness factor seem to introduce significant deviations of the signal-to-noise ratio from the overall mean, while the contribution from the other factors is relatively small. Quantitative information related to the above could be obtained by computing the sum of squares Es2 due to various factors. The sum of squares due to the time interval factor t is equal to the total squared deviation of the wave for t (Fig. 5(c)) from the line representing the overall mean (Fig. Sim5(b)) and is given by 9[(m,,,, -m)‘+ (mCrjz-m)‘] ilarly, the sum of squares due to other factors was established and listed in Table 3. A summary of the different relationships, based on the orthogonality of
l
Levels
Fig. 4. Variation
in average
of
signal-to-noise
different
ratio
bearing weor under mired lubncurion
to 18. It may be observed
that the variance ratio of the time interval factor (5.12) is the maximum, followed by the variance ratios of journal surface velocity (3.69), load (1.16) and journal hardness (0.98) factors. Hence, it can be concluded that these four factors have significant influence on the specific wear rate in relation to the others. The validity of this approach was confirmed by conducting a verification experiment and ensuring that the measured value of signal-to-noise ratio lies within the predicted range. The predominant nature of the time interval factor in influencing specific wear rate is due to the severe mixed-lubrication conditions prevailing during frequent starting and stopping. The observed reduction in average specific wear rate of the bush (Fig. 4) at high journal velocities (velocity factor, level 3) and low loads (load factor, level 1) may be attributed to reduction in coefficient of friction (f) because of an increase in the bearing characteristic number (S,) within the mixedlubrication zone, as evident from the Stribeck curve (Fig. 3). 3.2. Sulfate topography analysis 3.2.1. Conditions favouring mixed lubrication
A close observation of surface topography changes occurring in the above experiments can be expected to provide an insight into the wear process. A summary of the different concepts required for this investigation associated with bearings operating under mixed-lubrication conditions is presented below. Details of the geometry of a journal bearing presented in polar coordinate system r, 0, z with O=o” aligned with the line of centres are shown in Fig. 6. The bearing dimensions are: 6, the length of the bearing; r,, the radius of the bush; rj, the radius of the journal; c, the radial clearance, equal to (rh-r,). The clearance ratio ?P is given by c/rj. Under stable conditions, with an
Optimum
levels
factors
with
different
levels
of various
factors.
A.R. Rao and P.V. Mohanram
I Journal
124
124
116
116
108
108
100
100
12 4
r
=114,67
Overallmean
dB
124
(b)
15
bearing wear under mixed lubrication
r
Effect
of bush
hardness
factor
(g)
I
116 108 -
108 _
m 0
100 124
r
Effect
of time
interval
I
(cl
factor
2
5 L
108r
*
.;
I 5 2
5 ._ m
$
124
.: e f ._
116
124
r
Effect
of bush
roughness
2
100 124
5 &
116
;7,
108
I
Cd)
factor
108 -
108
4
lOOl!l
I
100
h
Effect
of load
factor
124
124
Effect
of journal
roughness
factor 116
116
108
0
6
3
9
Experiment
Fig. 5. Effect
TABLE
12
15
0
18
of individual factor
Ss2
V
1 2 2 2 2 2 2 2 2
162.72 6.16 18.34 13.67 38.20 62.06 73.79 234.50 63.56
162.72 3.08 9.17 6.84 19.10 31.03 36.89 117.30 31.78
5.12 0.10 0.29 0.22 0.60 0.98 1.16 3.69 -
17
673.00
-
_
t R R:p * H”b Hvi F u Error Total
applied load F, and journal speed n, the bearing operates with an eccentricity e, the eccentricity ratio E being given by e/rj. The film thickness is dependent on 0 and has the value h(e)=c(l+Ecos
e)
9
12
15
18
number
levels relative to the overall mean m.
cs’
DOF
6 Experiment
3. Analysis of variance
Factor
3
number
(4)
In the present work, it is assumed that the bearing surfaces are covered with one-dimensional roughness in the z direction, the roughness remaining constant in the 0 direction. The roughness profiles are char-
acterized as shown in Fig. 7. Thus, for each value of z, the effective film thickness H shown at Fig. 7(a) is given by H=h(e)+R
(5)
where R, represented in Fig. 7(b), is the statistical summation of profile heights of the bush R, and the journal Rj and is referred to as the profile sum. R is assumed to have a truncated normal distribution as at Fig. 7(c), where R,, the cut-off value of R, is given by R,= 3s. Here s is the standard deviation given by S=m
(6)
Further, it may be noted that mixed lubrication can be expected to prevail under the following condition (l-R,/c)<~
(7)
3.2.2. Gaussian d&ribution parameters A typical set of test results of experiment no. 6 (Table 2), which was terminated owing to bearing failure (seizure) at the end of 4 h of testing, was selected for the present study. The surface roughness recordings of (a) bush and (b) journal as a function of time of
TABLE 4. ______. Summation of squares Grand total Mean Total
(cf’)
due to
Error
=Summation
Degrees of freedom (DUF) of Summation of squares: grand total Uveratl mean Summation of squares: total Each factor
= Number of experiments I = Number of experiments=Number of levels-l
Summation
=DOF
of squares
due to error
Others Mean sum of squares (Cr2) Variance due to error Variance ratio, V
of summation
bearing
(total)-summation
of squares due to factor effects
I
of squares (total)-sum
of DOF of factor effects
= Sum of squares/DOF =Mean sum of squares due to error =Mean sum of squares/variance due to error
,ectian
Fig. 6. Journal
of squares
nomenclature.
testing 1”are shown in Fig. 8. A ~or~~g~ ~n~estiga~~o~ into the changes in surface topography was carried out to correlate the latter with the test results of matrix experiments. Analysis of digitized profile data pertaining to these profiles is presented in the following paragraphs. Cumulative ~robabili~ plots on normal probabili~ paper confirmed the gaussian nature of the distribution of profile heights of the mating parts. The 95% upper
and Iower confidence limits of the standard deviation of the bush and journal profiles of experiment 5 (Fig. 8) fime.sbu, s blf and Sj”,Sjl, respectively) were determined for different test times and are shown in plots in Figs. 9(a) and 9(b). The figure also shows the corresponding mean values sb and sj- The test specimen parts - bush as weh as journal - showed an initial decrease in standard deviation typical of the running-in process, and towards the end of the fourth hour of testing there was a sharp rise. Higher values of standard deviation of mating profiles result in increased probability of asperity interaction; hence, these Iimits (sbrr, Sj”) have been considered in the subsequent analysis. With respect to the profile sum, the mean I* and standard deviation s (using eqn. (6)) were determined and are shown in Fig. 9(c)_ The standard deviation plot of the profile sum was found to be approximately similar to that of the bush, owing to the fact that the standard deviation of the bush was very much greater than that of the journal. It may be noted that the Probability density,
f fR>
t
R=Rj
lRt,
(b)
Fig. 7, Characterization of rough surfaces: (a) roughness distribution of profile sum R.
Height
of profile
sum,
R
(cl
of bush Rb and journal I$; (bf combined
roughness
R; G+ truncated
normat
17
A.R. Rao and P.V. Mohanram / Journal bearing wear under mired lubrication
BL =$-f
Ll+L2*t3+L~+...Ln)X
o
distance
BL
length
Lt
trace
below of
5%
bearing
100
reference line
tine
( pm)
‘1.
length
I b)
(0)
Fig. 8. Surface roughness recordings of (a) bush and (b) journal.
-2 -
-51
lnitiol
I
I
I
I
LO
60
60
% ,.*, t
1
I
1
5
20
Length of bearing
line
1
%,BL
Fig. 10. Nomenclature (a) and bearing Iine curves (b) of bush and (c> of journal as a function of test duration, 7’.
0.0 1.2
L 0
I 1 Test
I
I
2
3
durotion
,
1 4
T (h)
Fig. 9. Variation in mean and 95% confidence limits of measured vahtes of standard deviation with test duration T, for (a) bush (So, rbr sbl); (b) journals (Sj”, si, sir). (c) Variation in standard deviation s and mean p of profile sum R with test duration 7’.
standard deviation of the profile sum (s) was the highest at 1.48 Frn, corresponding to the end of testing; the estimated mean value of the profile sum was close to
zero for most of the test duration and it became increasingly negative (i.e. -0.8 pm) towards the end of testing, indicating progressive surface deterioration. A study of the bearing line curves of the above profiles shown in Fig. 10 provides evidence for this observed phenomenon; they indicate that 100% bearing lines are available at increased depth below the 5% reference line towards the end of testing, i.e. 4 h. 3.2 3. Hyd~~n~~ic load Under mixed lubrication, load is shared between hydrodynamic action and asperity interaction. Procedures for determining the loads supported by the hydrodynamic action of the fluid film considering the surface roughness effects F,, and the asperity contacts Fa have been presented by the authors elsewhere [7,8].
A. R. Rao nnd P. VI Mohanrum
18
/ Journal
The hydrodynamic load computations require the inputs s, E, II and 77in addition to the geometry of the bearing. Hydrodynamic computations are reported in Fig. 11. A comparison of hydrodynamic loads F, that can be supported by the bearing at the end of third and fourth hours of testing for various eccentricity ratios E,confined to the mixed-lubrication zone, is shown in Fig. 11(a). It can be clearly seen that, to support a constant hydrodynamic load, a bearing operates at a higher eccentricity ratio as the standard deviation increases owing to surface degradation with increased time of running. The inference is that a rough bearing has a greater probability of asperity interaction compared to a relatively smooth bearing. Hence, a rough bearing can be expected to undergo premature failure. This might be one of the causes for the observed higher value of specific wear rate of mating members (kb, k,) Z
1200
(0) T=3h,
s-0.60pm
-,
Eccentricity
ratio,
/
E
-6
7 2x10
4
(b) 4 lx 10-6
3
2 .l x 10-6
4
3
11. (a) E. (b) fourth VI for
[Journol-ki]
1.4 x 10-6 0
I 2.5
1 5
Specific
weor
rate
Cleoronce
Fig. ratio and ratio
[Bush_1
,
I 7.5
k
b’
k.
ratio,
I
x lo6 (mm3
10 N-‘m-l)
q~
Variation in hydrodynamic load Fh with eccentricity Specific wear rate of bush and journal kb ki for third hours of testing. (c) Variation of Fh with clearance s= 1.48 pm, c=O.95, U=79 mm s-‘.
bearing wear under mixed lubricurion
of experiment no. 6 (Table 2), measured at the fourth hour when compared to that at the end of the third hour. This is indicated by the bar chart in Fig. 11(b). The experimental results reveal that an increase in clearance ratio P from level 1 to level 3 resulted in an increase in average specific rate kb (decrease in average signal-to-noise ratio) as shown in Fig. 4. The influence of clearance ratio on specific wear rate can be estimated analytically by determining the hydrodynamic load-carrying capacity of the bearing using the fourth-hour surface topography data of experiment no. 6 (s = 1.48 pm) for various clearance ratios. The results are plotted at Fig. 11(c). The computation is for a given eccentricity ratio of 0.95. It can be observed that an increase in clearance ratio reduces the hydrodynamic load-carrying capability. Hence, for a constant hydrodynamic load to be supported, a loose bearing (high value of ?P) will be forced to operate at a higher E within the mixed-lubrication zone, thus leading to an increase in specific wear rate as discussed in the preceding paragraph.
3.2.4. Asperity load The procedure for the computation of asperity load has been outlined by the authors in ref. 8. The inputs required (apart from s, E and H,,) are: mean asperity radius p of profile sum; the number of asperities per unit area N,; and the equivalent Young’s modulus of elasticity E. A better understanding of the sequence of events leading to the seizure of the bearing in experiment no. 6 can be had by making a comparative study of estimated asperity load-carrying capacity at the third and fourth hours of testing shown in Fig. 12. The changes in surface topography parameters related to the asperity load computation, i.e. p and N, of the profile sum are shown in Fig. 12(a), plotted with respect to test duration. Initially there was an increase in equivalent mean asperity radius and a reduction in the number of asperities of profile sum per unit area, characteristic of the running-in process. The above data corresponding to the third and fourth hours of operation were used in the computation of asperity load-carrying capability (F.) together with the ratio of real and apparent areas of contact (A,/‘,) for various eccentricity ratios E and are shown in Figs. 12(b) and 12(c). It can be seen that the asperity loadcarrying capability is significantly less for the fourth hour compared to the third. This is in agreement with the observed fact that there was seizure in the fourth hour owing to excessive plastic deformation. The ratio of A, to A, within the mixed-lubrication zone also showed a decrease in the fourth hour of testing when compared to the third hour, thus indicating that real contact took place at a reduced number of asperities
19
A.R. Rao and P.K Mohanram I Journal bearing wear under mixed lubrication
‘1400 Test
duration
(h)
2400
3400
Hordness
of bush,
4400
541
H, b (MPo)
Fig. 13. Variation in asperity load F, with hardness of bush Hvc for s=1.48 pm, l=O.95, p=O.22 mm, N,=387 mm-*.
Fig. 12. Variation in (a) equivalent mean asperity radius p and number of asperities per unit area N. with test duration T; and variation of (b) asperity load F. and (c) ratio of real and nominal areas of contact AC/A, with eccentricity ratio c for third and fourth hours of test duration T.
average specific wear rate; whereas the experimental results did not show a consistent trend in the measured average value of specific wear rate of the bush (average signal-to-noise ratio) when the bush hardness was varied from level 1 to level 3 (Fig. 4). The corresponding variance ratio of the bush hardness factor was low, i.e. 0.60, which implies that the variation in the experimentally observed values of average signal-to-noise ratio due to the bush hardness factor was comparatively small, i.e. 60% of that ,due to the error component in the experiment. Therefore, it can be seen that no concrete inference relating the effect of bush hardness factor on the measured values of average specific wear rate (and hence average signal-to-noise ratio) can be derived from the above matrix experiments (Table 2). Thus it may be concluded that exclusive experiments with bush hardness as the primary variable may have to be undertaken to validate the above predicted decrease in &, with increase in Hvb. Furthermore, it must be noted that a high hardness of the bush greatly reduces the conformability and compatibility characteristics of the bearing.
at the end of the fourth hour; this might be responsible for the observed surface deterioration. The influence of the hardness of the bush (which is soft in comparison to the journal) on estimated asperity load-carrying capacity and possible correlation with the experimentally observed values of average specific wear rate are discussed below. The variation of the estimated asperity load-carrying capacity with the hardness of the bush using the fourth-hour surface topography data of experiment no. 6, i.e. s= 1.48 w, p=O.22 mm, and N, =387 mn-*, for l equal to 0.95 is shown in Fig. 13. The figure clearly reveals that when the bush hardness increases there is a corresponding increase in asperity load-supporting capability. Hence it can be expected that bearings with higher bush hardness will have less plastic deformation, leading to a reduction
3.2.5. Power spectral density A study of wear topography using power spectral density G, furnishes information about the variation in amplitudes of the different constituent surface wavelengths [9]. Each surface wavelength component of the profile is designated by its frequency fk and is referred to as the spatial frequency. Analysis of recorded digitized profile data of mating components of experiment no. 6 (Fig. 8) with respect to time of testing reveals the predominance of low spatial frequencies (large surface wavelengths). The surface profiles were considered as stationary ergodic random processes. The stationary nature of the surface profiles was verified by the reverse arrangement test, and a single record of surface topography was found to be adequate in describing the statistical parameters. In addition, the fast Fourier transform (FFT)
in
,011
’
0.879
t 0.909
I 0.999
Eccentricity
rotio,
I 0.969
I 0.999
E
20
A.R. Rao and P. V. Mohanram
I Journal bearing wear under mired lubrication
procedure for the analysis of discrete stationary ergodic random data was employed to obtain the power spectral density G, corresponding to the different spatial frequenciesf,. The complete record of surface profile data was subdivided into 100 sub-records to ensure that the standard error of the power spectral density was small. The appropriate equations used to obtain power spectral density have been taken from ref. 10. It is well known [9] that a large value of power spectral density G, in the neighbourhood of spatial frequency f, implies a high mean-square value of the amplitude of the appropriate surface wavelength. Plots of power spectral density are shown in Fig. 14. The power spectrum plots in Figs. 14(a) and 14(b) reveal that the powers of low spatial frequencies (0.045 to 0.270 pm) are higher. The plots also indicate an increase in the power of the low spatial frequencies towards the end of the fourth hour. Thus it could be
After
0.001
I
T I lh
3.2.6. Fractal analysis A unique property of rough surfaces is that, if a surface is repeatedly magnified, increasing details of roughness are observed. In recent work [ll] it was established that such a behaviour could be characterized by scale-independent fractal geometry. In the present study, an attempt has been made to establish the fractal characteristics of wear surfaces. The basic idea behind fractal geometry is that it aims at characterizing the order behind the disorder of surface roughness. The essence of fractal analysis is: the number of measuring units M required to cover the length (or area) of an irregular line (or surface) depends on the size of the relative measuring unit B,. Small measuring devices resolve finer details than larger devices, requiring disproportionately greater numbers. A graphical representation of log(M) of a fractal curve against log(l/B,) yields a straight line described by the power law relation
, ‘. -,--_,___
I 1 I I 1I
m
O.Ol‘\
,001
6
I
I
(
I
inferred that the mean-square value of the amplitude corresponding to low spatial frequencies in the range of 0.045 to 0.270 pm increased at the time of bearing failure (i.e. the fourth hour). In order to highlight the influence of surface roughness on power spectral density, a comparative study of power spectral plots of bushes with varying degrees of surface roughness, that is, sb = 0.63, 1.60 and 3.40 pm, measured at the end of the first hour of testing under similar test conditions (experiments 1, 5 and 9 of Table 2) is provided in Fig. 14(c). The predominance of power spectral estimates corresponding to low spatial frequencies in the case of bush profiles with coarse roughness is distinctly evident. In either situation, i.e. surface failure or relatively coarse finish of mating profiles, the power spectral estimates corresponding to low frequencies showed an increasing trend. Hence, it might be concluded that surface degradation at the end of wear life is associated with coarsening of the surface finish, characterized by an increase in the power of the low spatial frequencies (large surface wavelengths).
-e-o-
*J
I
log(M) = K+ D log( l/B,)
O.OOll ’
t
t
0.04
Spatial
SC1 0 10 frequency,
I 0.20
0.30
fk
(pm-’
0.70
1Log
Fig. 14. Variation in power spectral density Gk with respect to spatial frequency!, for (a) bush and (b) journal with test duration T for experiment no. 6 and (c) for different bushes with varying initial surface roughnesses at T=l h.
(8)
where D is the fractal dimension and K is the fractal scale factor. Stupak et al. [12] suggested that a constant value of fractal dimension observed during wear tests on rubber surfaces could be attributed to the similarity of microscopic wear mechanisms; the fractal scale factor correlated well with the relative scale of wear surfaces. The digitized profilometry data was analysed following Dubuc’s “variational method” fractal algorithm [13]. In practice, computational limitations required that the digitized data be analysed using sample data files consisting of 450 points.
2.0
I
I
(0)
Bush
I
Y
6 -“.2
5
, 1
ij
“u -0.8 ,o
Lt.
-l.Ol1
f
*
2
Test
3 duration
I
J
4
(h)
Fig. 15. Variation in (a} fractal dimension L) and (b) fractal scale factor K with test duration T for bush and journal of experiment no. 6.
The results of fractal analysis of the digitized surface profile data of experiment no. 6 are displayed in Fig. 15. The variation in the fractal dimension of the bush and journal profiles with test duration is shown in Fig. 15(a). It can be observed that the fractal dimensions of the bush traces are consistently larger than the fractal dimension of the journal traces. Furthe~ore, it can be seen that the fractal dimension remained almost constant during the initial hours of testing, indicating that the wear mechanism was practically the same during that period; a sudden decrease in fractal dimension close to the fourth hour of testing might be attributed to a change in wear mechanism. The associated variation in fractal shift factor K with test duration is shown in Fig. 15(b). A sharp rise in K for both the mating members is seen towards the fourth hour of the test duration, indicating a corresponding increase in severity of wear as was observed in the experiments. Thus, a sudden change in fractal dimension together with an increase in fractal scale factor could be used as an index of impending failure of the specimens.
4. Conclusions The major conclusions derived from the experimental programme based on Taguchi’s technique and the surface topography analysis related to mixed lubrication of plain carbon steel like-pair journal bearings are listed below.
Minimum specific wear rate of the bush can be expected to occur under conditions of minimum number of starts and stops, maximum journal surface velocity, minimum load and maximum journal hardness. Surface degradation was associated with an increase in the standard deviation of the profile sum, which resulted in a decrease in hydrodynamic load-carrying capacity of the bearing, leading to further intense m~ed-lub~cation ~nditions. During the running-in period, equivalent mean asperity radius of the profile sum increased, while the number of asperities per unit area decreased. Surface deterioration and increase in bush hardness resulted in a decrease and an increase respectively of the asperity load-carrying capacity Spatial frequency analysis of wear surfaces could be carried out using the stationary ergodic random process approach. Failure of the bearing was characterized by an increase in power spectral density ~~esponding to low spatial frequencies (large surface wavelengths). Monitoring of fractal dimension and fractal scale factor could be used to predict impending failure of journal bearings.
Acknowledgments The authors thank the Indian Institute of Technology, Madras, and the P.S.G. College of Technology, Coimbatore, for providing an oppor~~i~ and necessary facilities to carry out this research work. In addition, the authors wish to acknowledge the computational assistance provided by Shri P. Satya Sai I&mar in the analysis of surface topography.
References H. Christensen, A theory of mixed lubrication, Proc. Insf. Eng, f86 (1972) 41-72. D. Berthe and MA. Godet, A more general form of Reynolds’ equation application to rough surfaces, Wear, 186 (1972) 41-72. M.E. Weyler and Wu Chih, A Numerical Method for the Calculation of Lubricant Pressures in Bearings with Mixed Lubrication, T&ol. Znt., I3 (1982) 89-95. A.R. Rao, R. Marappan and P.V. Mobanram, Performance studies on treated steels as substitutes for conventional bearing materials, Wear, 155 (1992) 15-29. MS. Phadke, Qua& L%gineeringUsing Robust Lksign, Prentice-Hall, Englewood CM%, NJ, 1989. 6 A. Be8ihnger and A.W.J. De Gee, Friction and wear tests on metallic hearing materials for oil lubricated bearings, Wear, 69 (1981) 43-54. Me&
22
A.R. Rao and P.V. Mohanram I Journal bearing wear under mixed lubrication
7 A.R. Rao and P.V. Mohanram, Load distribution analysis of journal bearings operating under mixed lubrication conditions, Proc. 6th ASME Int. Co@ on Power Transmission and Gearing, Advancing Power Transmission into the 21st century, Vol. 1, ASME, Phoenix, AZ, 1992, pp. 299-306. 8 A.R. Rao and P.V. Mohanram, A study of mixed lubrication parameters of journal bearings, Wear, in press. 9 T.R. Thomas, The characterization of changes in surface topography during running-in, in D. Dowson (ed,), Proc. 4th Leeds-Lyons Symp. on Tribology, Lyon, France, 1977, The Institute of Tribology, Leeds, 1978, pp. 99-108. 10 J.S. Bendat and A.G. Piersol, Random Data Ana&sis and Measurement Rocedures, Wiley, NY, 1986. 11 A. Majumdar and 3. Bhushan, Role of fractal geometry in roughness characterization and contact mechanics of surfaces, ASME J. Tkibol., 112 (1990) 205-216. 12 P.R. Stupak, J.H. Kang and J.A. Donovan, Fractal characteristics of rubber wear surfaces as a function of load and velocity, Wear, 141 (1990) ‘73-84. 13 B. Dubuc, C. Quiniou, C. Roques-Carmes, C. Tricot and SW. Zucker, Evaluating the fractal dimension of profiles, Phys. Rev. A, 39 (1989) 1500-1512.
N
Hvb,Hvj
h(O) Kb, Kj
k, kj (lb)i
Lt A4
GA n
P
R Rb,Rj R,
R r, 0,
Appendix: Nomenclature
rb, ‘i
& s
true area of contact nominal contact area distance below 5% reference line size of relative measuring unit bearing length (%) length of the bearing radial clearance fractal dimension equivalent modulus of elasticity eccentricity journal load asperity load hydrodyna~c load coefficient of friction probability density function of R spatial frequency power spectral density
effective film thickness Vickers surface hardness of bush and journal film thickness at any angular position 0 fractal scale factor specific wear rate mean specific wear rate of bush for the ith experiment trace length number of measuring units overall mean value of signal-to-noise ratio combined number of asperities operating speed of journal load per unit projected area combined surface profile height of bush and journal (profile sum) profile height variables of bush and journal half the range of the profile sum variable
sb,
sj
sbb
Sjl
Sbu,
sju
T t t.7
ai
2
centre line average value polar co-ordinates radii of bush and journal bearing characteristic number standard deviation of profile sum R standard deviation 95% lower confidence limit of standard deviation 95% upper confidence limit of standard deviation test duration time interval between successive starts surface velocity of journal observed signal-to-noise ratio of ith experiment sampling interval of digitized profile data eccentricity ratio lubricant viscosity (constant) combined mean asperity radius of curvature mean asperity radii of curvature angular velocity of journal clearance ratio