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The interpretation of data from wear debris analysis, with particular reference to ferrography
Wear, 70 (1981) 335 - 345 0 Elsevier Sequoia S.A., Lausanne
335 - Printed
in The Netherlands
THE INTERPRETATION OF DATA FROM WEAR DEBRIS WITH PARTICULAR REFERENCE TO FERROGRAPHY
ANALYSIS,
L. G. HAMPSON National Centre of Tribology, Risley Nuclear Power Development Laboratories, U.K. Atomic Energy Authority, Risley, Warrington WA3 6AT (Gt. Britain) (Received
December
20, 1980)
Summary A theoretical model of an oil lubrication system is presented. Wear particle generation and loss and lubricant usage are taken into account. The model can be used to reveal changes in the instantaneous wear rate from measurements of the wear debris concentration. The example of a diesel engine run-in is given. The model is also used to highlight the differences between oil analysis techniques which result from their differing sensitivities to particle sizes.
1. Introduction The primary reason for measuring the quantity of wear debris in used lubricants is usually to determine the wear rates of various components of a machine and in the course of time to measure changes in these parameters. However, an oil sample contains particles which have been produced at various times and it is not obvious how the instantaneous wear rate can be determined or whether it is necessary to determine the instantaneous wear rate. Various models of lubrication systems (e.g. those of Lotan [l] and of Bendiksen [2] ) have been used in the monitoring of aeroplane engines using spectrometric oil analysis. Essentially these models take into account the loss of wear particles with oil usage or by the drainage and replacement of oil. These factors are of particular importance because of the high rate of oil use in aircraft and the small particle size; this is the size to which spectrometers are most sensitive. An alternative method is necessary for larger particle sizes and Anderson and Driver [3] have suggested an oil system model for ferrography which takes into account particle loss by filtration and settling. The purpose of this paper is to present an oil system model developed at the National Centre of Tribology primarily for use with ferrography. It is of use in assessing instantaneous wear rates and in the comparison of debris analysis techniques.
336
2. Particle removal mechanisms Particles are lost from an oil supply by oil use (leakage or combustion), by settling out and by filtration. Particles may also be removed from the size range of interest by being broken up. The larger the particles are, the more effective are these removal mechanisms. The settling velocity in a static fluid can be estimated using Stokes’ law for spherical particles, although wear debris usually has one reduced dimension. In a typical lubricant (SAE 30 at 100 “C) the settling velocities of iron particles would be about 10 mm h-l for particles 10 pm in size and about 0.1 mm h-l for particles 1 pm in size. Brownian motion affects only very small particles and in a static fluid most particles would eventually settle out. However, in a machine, fluid motion due to input, output, agitation and convection currents would tend to keep particles suspended and it is likely that most particles up to at least 1 pm in size never settle. The debris which does settle collects as a sludge in sumps and passageways. Under some circumstances settled debris can be released again into an oil supply: for example, in one project at the National Centre of Tribology an increase in debris level in a large marine gearbox was eventually attributed to passage through heavy seas rather than to an increase in the wear rate. There is a tendency for very small particles to coagulate because this results in a decrease in surface energy. Lubricant additives can be used to restrict this effect. In a time scale of 5 - 10 h particles below 0.2 pm in size could be affected by this mechanism but the effect on larger particles can be ignored. Many lubrication systems incorporate a filtration system. The filter can be centrifugal, magnetic or based on small pores in paper, felt or wire mesh. It is usual to think of filters in terms of the largest particle size which will pass through and to relate this size to critical clearances in the machine. In reality there is no absolute size cut-off but a variation in collection efficiency with size. Machine designers are often unaware of the actual filter performance, which changes with the filter loading, but will specify a nominal rating typically of 20 - 100 pm. 3. Oil analysis methods It is useful to classify methods of wear debris analysis in terms of their size response because this feature controls many of the practically important characteristics. Spectrometry, ferrography and magnetic chip detection are three techniques which together cover the submicron to millimetre size range. Oil analysis by emission spectrometry primarily responds to small particles (less than 1 pm in size) although sizes up to about 5 pm may be at least partially accounted for. Therefore the results of this type of analysis are little affected by filtration or settling and because the background level
337
is being monitored a fairly smooth variation with time is usually observed. However, this is not necessarily advantageous in predicting failure and several missed failures have been noted (e.g. by Jones and Loewenthal [ 41). The examination of wear debris reveals that most debris is generated as particles of typically from 2 to 100 I.tm or more in size, depending on the severity of the surface contacts. This observation is in accordance with the delamination explanation of wear [ 51, and it suggests that spectrometric analysis must respond to secondary effects, such as the breaking-up of debris, and that this technique may not be adequate for the detection of some failure modes. The detection of increasing wear of ferrous components using ferrography is based on the determination of changes in the quantity of larger wear particles (greater than 5 - 10 pm in size) in relation to the quantity of smaller particles of about 2 pm in size. The additional ability of the technique to display debris for examination is largely irrelevant to failure detection but may be of value for subsequent analysis. It is apparent that ferrography results will be appreciably affected by filtration; this has been demonstrated by Westcott and Seifert [6]. With any method of lubricant analysis which depends on sampling there is a practical difficulty in ensuring that the sample is representative of the system. There is inevitably some scatter introduced into the analysis results because of the statistical effects of sampling in addition to the scatter due to poor procedures. Typical practice is to extract a sample from a lubricant tank or flow pipe; this sample is later subdivided for analysis. Bendiksen [2] determined the minimum scatter introduced for various particle sizes and concentrations; this is shown in Fig. 1. It is apparent that ferrographic results could be affected significantly at low concentrations but that the effects on spectrometric analysis would be small. There is also some scatter introduced by the measurement process and this again tends to increase with particle size. Ferrographic results have been found to vary typically by +20% because of these factors and other factors such as the presence of random amounts of silica and other contaminants. Magnetic chip detectors, which are essentially magnetic plugs introduced into a circulating oil system in front of the filters, have proved succesful in monitoring gas turbine engines. They collect the large ferrous particles 50 pm or more in size which are produced when failure is imminent. High collection efficiencies are achievable for large particle sizes. Because of their differing size sensitivities the various techniques produce results which are not directly comparable. It is especially noticeable that the results from techniques sensitive to larger particle sizes show significant background scatter. However, the important point is whether the technique responds rapidly to increasing severity of wear by giving a signal which is noticeable above the background signal.
20
60
LO Size
of
iron
particles
80
100
120
Imicronsi
The scatter ~n~r~d~~~dby sampfing a lubrication system. {From Bendiksen
I21.1
4. The oil system madei A general oil system model needs to take into account the removal of particles by all the mechanisms which have been described. However, because it is impossible to evaluate these in detail it is reasonable to lump them together and to try to assess the total effect. The modd to be described is based on the diagram of a typical oil system shown in Fig. 2. A removal factor f represents the proportion of debris in the size band being considered which is removed by all the mechanisms. It is assumed that particles injected into the system are mixed instantaneously and that the oil lost takes with it a proportionate amount of debris. The number of particles at time t is given by the product su of the oil volume and the particle ~oncent~ti~~. At time t + dL the number of particles changes to su + mdt -_sfpdt qsdt as particles are generated and lost and the lubricant is used. The number of particles must also be given by (s + ds)(u - qdt), the product of the volume and the concentration at time t + dt. The changing west: rate and lubricant volume are represented by m = mo+rxtandu=uo - qt respectively, Both orand q may vary over the life of a machine. ~ub~it~t~g for M and u and ignoring second-order terms gives P%
--sfp + cut)dt = (ua - qt)ds
339 p sf
particles
PARTICLE
removed/unit
time
REMOVAL
I
1 no of particles particle
=C m particles generated/unit
concentration
Residence
vv E A
time
R
time
L
A
Volume
q lost /untt
return lme sampling point
time
Fig. 2. The model of the lubrication system.
This general equation; which represents the behaviour of the system, is difficult to deal with but several special cases of practical significance can be solved. 4.1. Case a: no oil loss There are many practical situations, e.g. gearboxes, in which it is reasonable to assume that there is no oil lost. Because q = 0 the equation becomes d2s
(Y
s=--
fP -- ds u.
00
dt
which has a general solution s = A exp(-fpt/uo) s=s
0
at
t=O
+ B + OL t/fp. By putting
and
we obtain
(1)
340
This equation indicates that if LY= 0 (i.e. the wear rate is constant with time) there will eventually be an equilibrium between the particles being generated and the particles being removed. The equation becomes
which is an exponential rise to an equilibrium value sWti = uomo/fp at t = 00. However, 90% of the equilibrium value will be reached after time t = 2.3uJpf and hence the measured particle concentration is then a good measure of thegeneration rate. The greater the efficiency of the particle loss mechanisms is (i.e. the larger the particle size being detected), the shorter the time to reach equilibrium becomes. The two normal alternative sampling points are the lubricant supply tank and the return line from the wearing components. As shown above, a step change in the wear rate eventually leads to a new equilibrium debris concentration in the sump. However, the debris concentration in the return line (Fig. 2, point A) will show an immediate step change and then an increase to a new equilibrium value. The debris concentration at point A is given by SA
=
;
+s(1-f)
Hence the more efficient the filtration is, the greater will be the relative importance of the instantaneous particle generation rate m in the measured concentration at A. It can also be concluded that it is more satisfactory to sample the return line rather than the supply tank if the sampling time is short compared with the response time of the system. For spectrometric analysis f -f 0 because a significant fraction of the reading is caused by compounds in solution or small particles in suspension which are not affected by filtration or by settling out. Hence this technique is less responsive to step changes in the particle generation rate than, for example, ferrography is and the time to reach equilibrium in the supply tank will be long. In using these equations in the interpretation of data the intention is to derive variations in the particle generation rate m from the measure values of s. sir -a2etc. will be measured at tl, t2 etc. respectively and m has been assumed to vary linearly between successive samples. For sampling from position A, eqn. (2) gives (sA )2 = 4lW2, s2, UO, f), eqn. (1) givess2 = @2(%,a,
UO,P,
f, t, ml) andeqn.(2) gives@A)1 = Gl(ml, ~1,UO, f) andt= tz -tl,
ml + at. One more equation is required because there are five unknowns (sz, sl, ml, m2, a). This equation has to be based on knowledge of the particular system or on an assumption about its behaviour. The example given in Section 4.4 illustrates a method of deriving the additional data and solving the equations to indicate trends in the actual wear rate. In general the particular removal factor f has to be inferred from the behaviour of the system. m2
=
341
4.2. Case b: constant oil loss rate and constant wear rate
To be of value in many practical situations the model must be able to deal with oil losses. This introduces an additional difficulty into the solution of the general equation and so it is useful to assume a constant wear rate between samples, The general equation for the system becomes ds
dt -= % -qt
m
--sfP
when (11= 0 which gives - qt) = 4- In(m
lntv0
fP
-sfp) +k
Putting s = so at t = 0 gives k = In v. - (q/fp) In (m - sofp) and m= pxp i _ 1 (sofpexp P - s1 fp)
(3)
.d
in the interval t between so and sl, where
-uo-qt
p _fP,,
--
Q
Equation s1
i
UO
1
(3) can be rewritten
=sOexpPfp
E
(1
as
-expp)
as q tends to zero this relation as in case a.
gives an equilibrium
value of s equal to mf/p
4.3. &se c: periodic oil refilling Oil replenishment or partial replacement with clean oil reduces the concentration of particles in the lubrication system. If the concentration so before refilling with volume AVand so1 afterwards then
where t is now the time between refills. The variation in the particle concentration between replenishments is shown in Fig. 3. From eqn. (3) f?@+?
Pf
f1
-expP)
is
342
I time
Fig. 3. The change
in particle
concentration
caused by lubricant
replacement.
For n periods involving n replenishments at uniform time intervals, with m constant between samples, a series can be produced which is summed as follows: s,
=
C”-1
SOAn
+mB
l-(cA)” l-CA
where ,=,_;;
A=C!expfl
B= 1 -expfl fP
Hence m = (s, -s~A,$~-~) B{l-(AC)“}
(1 -AC)
(4)
This equation allows the actual particle generation rate to be determined from samples taken from a system which is being replenished with lubricant at intervals equal to or less than the sampling interval. For example, an aircraft engine loses a significant proportion of its oil supply during a long flight and hence this is frequently topped up. The lubricant could be sampled for analysis at each replenishment or on the return of the aircraft to the home base; eqn. (4) would be relevant in either case. It can be shown that, as n becomes large, eqn. (4) indicates that s, approaches the equilibrium value of the concentration predicted in case a. Hence it is only worth taking oil replenishment into account if the sampling time is much less than the equilibrium time constant of the system. The time constant will be much larger for small particle sizes because of the inefficiency of the removal mechanism. It can therefore be concluded that it is less
343
important to take account of oil loss and replenishment when using ferrography than when using spectrometric analysis. 4.4. Example The results shown in Fig. 4 are from the ferrographic analysis of samples taken from a diesel engine which was running in after initial assembly. Samples were taken from the return line to the sump,
200
600
400 Minutes
of
Fig. 4. The results of ferrographic (s, optical density of the particles
800
1000.
operotlon
analysis of diesel engine lubricant during running-in at the entry point of the ferrograms).
It will be assumed that the engine was perfectly clean on start-up (C, = 0) and that no oil was lost. The oil sump held 100 1 and this quantity circulated in 15 min. The equation derived for case a will be used to relate the situation at a particular sample to that at the previous sample. From eqn. (2) f32A
=
m2T
-
V
+
G p--f)
From eqn. (1) cs =$
(uT2 = c*+--f2 (
-fml)
exp(-g)+;m,-$
+$
and m2
=ml+cllt
where subscripts 1 and 2 denote successive samples. By extrapolating from Fig. 4 so = 68; this gives m. = sV/T = 432 in arbitrary units. It is known that T = 15 and V = 100. The value off is estimated to be 0.1 by considering the
344
time after the oil change for the measured values of the particle concentration to return to the equilibrium value of about 33. Then using the equations above it is possible to calculate m and c successively from the values of s starting from the known initial values. The oil change can be taken into account by assuming that a certain proportion of the particles are removed; this proportion can be determined from the change in s before and after the oil change. Figure 5 shows the metal generation rate as calculated by this procedure. It can be seen that running-in is essentially over in about 5 h and that the initial rate of wear is much greater than that at equilibrium. The reduction in wear rate would have been less if the presence of any built-in debris had been taken into account.
Minutes
of
operation
Fig. 5. Calculated metal wear rate from Fig. 4 (m is in arbitrary units).
5. Conclusions The model of oil systems with particulate contamination which has been developed allows data from debris analysis to be interpreted in terms of the trends in the actual wear rate. The effectiveness of particulate removal mechanisms, which are lumped together, has to be determined from the system characteristics. If particle removal mechanisms are effective then an equilibrium concentration of debris will be reached in a system which does not lose oil or in which oil is periodically replenished. The time to reach equilibrium depends on the efficiency of particle removal and hence is inversely dependent on particle size.
345
Once equilibrium has been reached, the measured particle concentration is a good measure of the generation rate. If the sampling time is short compared with the response time of the system it is more satisfactory to sample from a return line after wearing components than from the sump. The larger the particle size to which the analysis technique responds, the less important it is to take lubricant loss and replenisment into account.
References 1 D. Lotan, Spectrometric oil analysis - use and interpretation of data, SAE Paper 72030, 1972 (Society of Automotive Engineers). 2 0. 0. Bendiksen, Improved failure detection techniques based on spectrometric oil analysis data, SAE Paper 730344, 1973 (Society of Automotive Engineers). 3 D. P. Anderson and R. D. Driver, Equilibrium particle concentration in engine oil, Wear, 56 (1979) 415. 4 W. R. Jones and S. H. Loewenthal, Ferrographic analysis of wear debris from full scale bearing fatigue tests, NASA Tech. Paper 1511, 1979. 5 N. P. Suh and coworkers, The Delamination Theory of Wear, Elsevier, Lausanne, 1977; Wear, 44 (1977) 1 - 162. 6 V. C. Westcott and W. W. Seifert, Investigation of iron content of lubricating oil using a ferrograph and an emission spectrometer, Wear, 23 (1973) 239.
335 - Printed
in The Netherlands
THE INTERPRETATION OF DATA FROM WEAR DEBRIS WITH PARTICULAR REFERENCE TO FERROGRAPHY
ANALYSIS,
L. G. HAMPSON National Centre of Tribology, Risley Nuclear Power Development Laboratories, U.K. Atomic Energy Authority, Risley, Warrington WA3 6AT (Gt. Britain) (Received
December
20, 1980)
Summary A theoretical model of an oil lubrication system is presented. Wear particle generation and loss and lubricant usage are taken into account. The model can be used to reveal changes in the instantaneous wear rate from measurements of the wear debris concentration. The example of a diesel engine run-in is given. The model is also used to highlight the differences between oil analysis techniques which result from their differing sensitivities to particle sizes.
1. Introduction The primary reason for measuring the quantity of wear debris in used lubricants is usually to determine the wear rates of various components of a machine and in the course of time to measure changes in these parameters. However, an oil sample contains particles which have been produced at various times and it is not obvious how the instantaneous wear rate can be determined or whether it is necessary to determine the instantaneous wear rate. Various models of lubrication systems (e.g. those of Lotan [l] and of Bendiksen [2] ) have been used in the monitoring of aeroplane engines using spectrometric oil analysis. Essentially these models take into account the loss of wear particles with oil usage or by the drainage and replacement of oil. These factors are of particular importance because of the high rate of oil use in aircraft and the small particle size; this is the size to which spectrometers are most sensitive. An alternative method is necessary for larger particle sizes and Anderson and Driver [3] have suggested an oil system model for ferrography which takes into account particle loss by filtration and settling. The purpose of this paper is to present an oil system model developed at the National Centre of Tribology primarily for use with ferrography. It is of use in assessing instantaneous wear rates and in the comparison of debris analysis techniques.
336
2. Particle removal mechanisms Particles are lost from an oil supply by oil use (leakage or combustion), by settling out and by filtration. Particles may also be removed from the size range of interest by being broken up. The larger the particles are, the more effective are these removal mechanisms. The settling velocity in a static fluid can be estimated using Stokes’ law for spherical particles, although wear debris usually has one reduced dimension. In a typical lubricant (SAE 30 at 100 “C) the settling velocities of iron particles would be about 10 mm h-l for particles 10 pm in size and about 0.1 mm h-l for particles 1 pm in size. Brownian motion affects only very small particles and in a static fluid most particles would eventually settle out. However, in a machine, fluid motion due to input, output, agitation and convection currents would tend to keep particles suspended and it is likely that most particles up to at least 1 pm in size never settle. The debris which does settle collects as a sludge in sumps and passageways. Under some circumstances settled debris can be released again into an oil supply: for example, in one project at the National Centre of Tribology an increase in debris level in a large marine gearbox was eventually attributed to passage through heavy seas rather than to an increase in the wear rate. There is a tendency for very small particles to coagulate because this results in a decrease in surface energy. Lubricant additives can be used to restrict this effect. In a time scale of 5 - 10 h particles below 0.2 pm in size could be affected by this mechanism but the effect on larger particles can be ignored. Many lubrication systems incorporate a filtration system. The filter can be centrifugal, magnetic or based on small pores in paper, felt or wire mesh. It is usual to think of filters in terms of the largest particle size which will pass through and to relate this size to critical clearances in the machine. In reality there is no absolute size cut-off but a variation in collection efficiency with size. Machine designers are often unaware of the actual filter performance, which changes with the filter loading, but will specify a nominal rating typically of 20 - 100 pm. 3. Oil analysis methods It is useful to classify methods of wear debris analysis in terms of their size response because this feature controls many of the practically important characteristics. Spectrometry, ferrography and magnetic chip detection are three techniques which together cover the submicron to millimetre size range. Oil analysis by emission spectrometry primarily responds to small particles (less than 1 pm in size) although sizes up to about 5 pm may be at least partially accounted for. Therefore the results of this type of analysis are little affected by filtration or settling and because the background level
337
is being monitored a fairly smooth variation with time is usually observed. However, this is not necessarily advantageous in predicting failure and several missed failures have been noted (e.g. by Jones and Loewenthal [ 41). The examination of wear debris reveals that most debris is generated as particles of typically from 2 to 100 I.tm or more in size, depending on the severity of the surface contacts. This observation is in accordance with the delamination explanation of wear [ 51, and it suggests that spectrometric analysis must respond to secondary effects, such as the breaking-up of debris, and that this technique may not be adequate for the detection of some failure modes. The detection of increasing wear of ferrous components using ferrography is based on the determination of changes in the quantity of larger wear particles (greater than 5 - 10 pm in size) in relation to the quantity of smaller particles of about 2 pm in size. The additional ability of the technique to display debris for examination is largely irrelevant to failure detection but may be of value for subsequent analysis. It is apparent that ferrography results will be appreciably affected by filtration; this has been demonstrated by Westcott and Seifert [6]. With any method of lubricant analysis which depends on sampling there is a practical difficulty in ensuring that the sample is representative of the system. There is inevitably some scatter introduced into the analysis results because of the statistical effects of sampling in addition to the scatter due to poor procedures. Typical practice is to extract a sample from a lubricant tank or flow pipe; this sample is later subdivided for analysis. Bendiksen [2] determined the minimum scatter introduced for various particle sizes and concentrations; this is shown in Fig. 1. It is apparent that ferrographic results could be affected significantly at low concentrations but that the effects on spectrometric analysis would be small. There is also some scatter introduced by the measurement process and this again tends to increase with particle size. Ferrographic results have been found to vary typically by +20% because of these factors and other factors such as the presence of random amounts of silica and other contaminants. Magnetic chip detectors, which are essentially magnetic plugs introduced into a circulating oil system in front of the filters, have proved succesful in monitoring gas turbine engines. They collect the large ferrous particles 50 pm or more in size which are produced when failure is imminent. High collection efficiencies are achievable for large particle sizes. Because of their differing size sensitivities the various techniques produce results which are not directly comparable. It is especially noticeable that the results from techniques sensitive to larger particle sizes show significant background scatter. However, the important point is whether the technique responds rapidly to increasing severity of wear by giving a signal which is noticeable above the background signal.
20
60
LO Size
of
iron
particles
80
100
120
Imicronsi
The scatter ~n~r~d~~~dby sampfing a lubrication system. {From Bendiksen
I21.1
4. The oil system madei A general oil system model needs to take into account the removal of particles by all the mechanisms which have been described. However, because it is impossible to evaluate these in detail it is reasonable to lump them together and to try to assess the total effect. The modd to be described is based on the diagram of a typical oil system shown in Fig. 2. A removal factor f represents the proportion of debris in the size band being considered which is removed by all the mechanisms. It is assumed that particles injected into the system are mixed instantaneously and that the oil lost takes with it a proportionate amount of debris. The number of particles at time t is given by the product su of the oil volume and the particle ~oncent~ti~~. At time t + dL the number of particles changes to su + mdt -_sfpdt qsdt as particles are generated and lost and the lubricant is used. The number of particles must also be given by (s + ds)(u - qdt), the product of the volume and the concentration at time t + dt. The changing west: rate and lubricant volume are represented by m = mo+rxtandu=uo - qt respectively, Both orand q may vary over the life of a machine. ~ub~it~t~g for M and u and ignoring second-order terms gives P%
--sfp + cut)dt = (ua - qt)ds
339 p sf
particles
PARTICLE
removed/unit
time
REMOVAL
I
1 no of particles particle
=C m particles generated/unit
concentration
Residence
vv E A
time
R
time
L
A
Volume
q lost /untt
return lme sampling point
time
Fig. 2. The model of the lubrication system.
This general equation; which represents the behaviour of the system, is difficult to deal with but several special cases of practical significance can be solved. 4.1. Case a: no oil loss There are many practical situations, e.g. gearboxes, in which it is reasonable to assume that there is no oil lost. Because q = 0 the equation becomes d2s
(Y
s=--
fP -- ds u.
00
dt
which has a general solution s = A exp(-fpt/uo) s=s
0
at
t=O
+ B + OL t/fp. By putting
and
we obtain
(1)
340
This equation indicates that if LY= 0 (i.e. the wear rate is constant with time) there will eventually be an equilibrium between the particles being generated and the particles being removed. The equation becomes
which is an exponential rise to an equilibrium value sWti = uomo/fp at t = 00. However, 90% of the equilibrium value will be reached after time t = 2.3uJpf and hence the measured particle concentration is then a good measure of thegeneration rate. The greater the efficiency of the particle loss mechanisms is (i.e. the larger the particle size being detected), the shorter the time to reach equilibrium becomes. The two normal alternative sampling points are the lubricant supply tank and the return line from the wearing components. As shown above, a step change in the wear rate eventually leads to a new equilibrium debris concentration in the sump. However, the debris concentration in the return line (Fig. 2, point A) will show an immediate step change and then an increase to a new equilibrium value. The debris concentration at point A is given by SA
=
;
+s(1-f)
Hence the more efficient the filtration is, the greater will be the relative importance of the instantaneous particle generation rate m in the measured concentration at A. It can also be concluded that it is more satisfactory to sample the return line rather than the supply tank if the sampling time is short compared with the response time of the system. For spectrometric analysis f -f 0 because a significant fraction of the reading is caused by compounds in solution or small particles in suspension which are not affected by filtration or by settling out. Hence this technique is less responsive to step changes in the particle generation rate than, for example, ferrography is and the time to reach equilibrium in the supply tank will be long. In using these equations in the interpretation of data the intention is to derive variations in the particle generation rate m from the measure values of s. sir -a2etc. will be measured at tl, t2 etc. respectively and m has been assumed to vary linearly between successive samples. For sampling from position A, eqn. (2) gives (sA )2 = 4lW2, s2, UO, f), eqn. (1) givess2 = @2(%,a,
UO,P,
f, t, ml) andeqn.(2) gives@A)1 = Gl(ml, ~1,UO, f) andt= tz -tl,
ml + at. One more equation is required because there are five unknowns (sz, sl, ml, m2, a). This equation has to be based on knowledge of the particular system or on an assumption about its behaviour. The example given in Section 4.4 illustrates a method of deriving the additional data and solving the equations to indicate trends in the actual wear rate. In general the particular removal factor f has to be inferred from the behaviour of the system. m2
=
341
4.2. Case b: constant oil loss rate and constant wear rate
To be of value in many practical situations the model must be able to deal with oil losses. This introduces an additional difficulty into the solution of the general equation and so it is useful to assume a constant wear rate between samples, The general equation for the system becomes ds
dt -= % -qt
m
--sfP
when (11= 0 which gives - qt) = 4- In(m
lntv0
fP
-sfp) +k
Putting s = so at t = 0 gives k = In v. - (q/fp) In (m - sofp) and m= pxp i _ 1 (sofpexp P - s1 fp)
(3)
.d
in the interval t between so and sl, where
-uo-qt
p _fP,,
--
Q
Equation s1
i
UO
1
(3) can be rewritten
=sOexpPfp
E
(1
as
-expp)
as q tends to zero this relation as in case a.
gives an equilibrium
value of s equal to mf/p
4.3. &se c: periodic oil refilling Oil replenishment or partial replacement with clean oil reduces the concentration of particles in the lubrication system. If the concentration so before refilling with volume AVand so1 afterwards then
where t is now the time between refills. The variation in the particle concentration between replenishments is shown in Fig. 3. From eqn. (3) f?@+?
Pf
f1
-expP)
is
342
I time
Fig. 3. The change
in particle
concentration
caused by lubricant
replacement.
For n periods involving n replenishments at uniform time intervals, with m constant between samples, a series can be produced which is summed as follows: s,
=
C”-1
SOAn
+mB
l-(cA)” l-CA
where ,=,_;;
A=C!expfl
B= 1 -expfl fP
Hence m = (s, -s~A,$~-~) B{l-(AC)“}
(1 -AC)
(4)
This equation allows the actual particle generation rate to be determined from samples taken from a system which is being replenished with lubricant at intervals equal to or less than the sampling interval. For example, an aircraft engine loses a significant proportion of its oil supply during a long flight and hence this is frequently topped up. The lubricant could be sampled for analysis at each replenishment or on the return of the aircraft to the home base; eqn. (4) would be relevant in either case. It can be shown that, as n becomes large, eqn. (4) indicates that s, approaches the equilibrium value of the concentration predicted in case a. Hence it is only worth taking oil replenishment into account if the sampling time is much less than the equilibrium time constant of the system. The time constant will be much larger for small particle sizes because of the inefficiency of the removal mechanism. It can therefore be concluded that it is less
343
important to take account of oil loss and replenishment when using ferrography than when using spectrometric analysis. 4.4. Example The results shown in Fig. 4 are from the ferrographic analysis of samples taken from a diesel engine which was running in after initial assembly. Samples were taken from the return line to the sump,
200
600
400 Minutes
of
Fig. 4. The results of ferrographic (s, optical density of the particles
800
1000.
operotlon
analysis of diesel engine lubricant during running-in at the entry point of the ferrograms).
It will be assumed that the engine was perfectly clean on start-up (C, = 0) and that no oil was lost. The oil sump held 100 1 and this quantity circulated in 15 min. The equation derived for case a will be used to relate the situation at a particular sample to that at the previous sample. From eqn. (2) f32A
=
m2T
-
V
+
G p--f)
From eqn. (1) cs =$
(uT2 = c*+--f2 (
-fml)
exp(-g)+;m,-$
+$
and m2
=ml+cllt
where subscripts 1 and 2 denote successive samples. By extrapolating from Fig. 4 so = 68; this gives m. = sV/T = 432 in arbitrary units. It is known that T = 15 and V = 100. The value off is estimated to be 0.1 by considering the
344
time after the oil change for the measured values of the particle concentration to return to the equilibrium value of about 33. Then using the equations above it is possible to calculate m and c successively from the values of s starting from the known initial values. The oil change can be taken into account by assuming that a certain proportion of the particles are removed; this proportion can be determined from the change in s before and after the oil change. Figure 5 shows the metal generation rate as calculated by this procedure. It can be seen that running-in is essentially over in about 5 h and that the initial rate of wear is much greater than that at equilibrium. The reduction in wear rate would have been less if the presence of any built-in debris had been taken into account.
Minutes
of
operation
Fig. 5. Calculated metal wear rate from Fig. 4 (m is in arbitrary units).
5. Conclusions The model of oil systems with particulate contamination which has been developed allows data from debris analysis to be interpreted in terms of the trends in the actual wear rate. The effectiveness of particulate removal mechanisms, which are lumped together, has to be determined from the system characteristics. If particle removal mechanisms are effective then an equilibrium concentration of debris will be reached in a system which does not lose oil or in which oil is periodically replenished. The time to reach equilibrium depends on the efficiency of particle removal and hence is inversely dependent on particle size.
345
Once equilibrium has been reached, the measured particle concentration is a good measure of the generation rate. If the sampling time is short compared with the response time of the system it is more satisfactory to sample from a return line after wearing components than from the sump. The larger the particle size to which the analysis technique responds, the less important it is to take lubricant loss and replenisment into account.
References 1 D. Lotan, Spectrometric oil analysis - use and interpretation of data, SAE Paper 72030, 1972 (Society of Automotive Engineers). 2 0. 0. Bendiksen, Improved failure detection techniques based on spectrometric oil analysis data, SAE Paper 730344, 1973 (Society of Automotive Engineers). 3 D. P. Anderson and R. D. Driver, Equilibrium particle concentration in engine oil, Wear, 56 (1979) 415. 4 W. R. Jones and S. H. Loewenthal, Ferrographic analysis of wear debris from full scale bearing fatigue tests, NASA Tech. Paper 1511, 1979. 5 N. P. Suh and coworkers, The Delamination Theory of Wear, Elsevier, Lausanne, 1977; Wear, 44 (1977) 1 - 162. 6 V. C. Westcott and W. W. Seifert, Investigation of iron content of lubricating oil using a ferrograph and an emission spectrometer, Wear, 23 (1973) 239.