ANDRZEJ KULCZYCKI
Institute of Petroleum Processing, Aleja Zwirki i Wigury 31, 02-091 Warsaw (Poland)

*THE CORRELATION BETWEEN RESULTS OF DIFFERENT MODEL FRICTION TESTS IN TERMS OF AN ENERGY ANALYSIS OF FRICTION AND LUBRICATION

*Wear, 103 (1985) 67 - 75
(Received June 18, 1984; accepted March 20, 1985)

Summary

A general method for anticipating results of highly complex tests on the basis of simple measurements has not yet been worked out. An energy-based method for determining antiwear and extreme pressure (EP) properties of oils containing additives is described in the present paper. The method allows the parameters characterizing the ability of additive-containing oils to form boundary layers in the antiwear (aAW) and EP (aEP) regions to be determined.
The parameters aAW and aEP make it possible to correlate the results of different friction tests. The correlation between seizure load Pt, welding load Pz, wear load index Ih, four-ball wear test results d40 and results of the FZG tests is presented in this paper.

1. Introduction

The selection of lubricants for various applications, such as in engines or gears, is connected with the methods of oil quality evaluation. Lubricated elements of machines form complex systems in which it is very difficult to determine the quality of oils. This is why various model tests have been devised to determine oil properties in simpler systems. Results obtained in model tests will be useful if they tell us whether the oils tested can be used in a machine. No method has so far been found to transpose the results of model tests to apply to more complex machines. This refers also to the examination of lubricating properties of oils.
Many model friction machines have been constructed but few have been put to universal use, and assessment of the lubricating properties of oils in them yields only approximate knowledge of the efficiency of lubrication of the machine by the oil tested.
Hence oils have been studied in testing machines that are gradually becoming more and more complex. Until now no method has been found which would allow the results obtained in simple and in more complex tests to be correlated. The main problems in the correlation of results of various model tests have been discussed in refs. 1-3. The potential utility of these researches is why many workers try to solve this problem.

2. Analysis of tribological processes

The problem of lubrication can be considered in two ways [4]. One way is an analysis of the structure of lubricant layers formed on the surface of lubricated elements. The other way is examination of the effect of various mechanical factors, such as sliding speed, load and temperature, on the durability of lubricant layers.
Although a combination of both of these ways makes it possible to obtain more information about lubrication, it is still difficult to study lubrication in a direct way. The first of the above methods is the analysis of physical and chemical processes, the second dealing with the mechanical quantities. The physicochemical and mechanical studies can be carried out on the basis of an energy analysis of the processes which take place during lubrication.
Examination of various forms of energy flowing through the tribological system can be treated as the base for connecting the physicochemical and mechanical effects and consequently formulating the equation describing quantitatively the formation of the lubricating layer.

3. Energy analysis of processes of friction and lubrication

Energy considerations can be treated as the balance of energy which flows through the tribological system [5]. This was described in ref. 6, where it was confirmed that a portion of the energy put into the system (friction node) is absorbed by endoenergetic changes which take place at the friction node during friction, while the remainder is dissipated as heat and frictional work. The balance of energy can be written as follows:

E = Du + A + q(1)

where E is the energy input into the friction node, Du is the change in internal energy, A is the frictional work and q is the heat dissipated.

Equation (1) represents the flow of energy through the friction node, without account being taken of the distribution of that energy to each of the elements of the node, since the amount of energy going through the different constituents of the friction node may often vary.
What seems most interesting from the point of view of assessment of the oil's lubricating properties is the impact of the energy E put into the friction node on the ensuing changes Au in internal energy. Energy builds up in the system as a result of physicochemical transformations that take place simultaneously both at contacting surfaces and between microregions within each surface.
An energy analysis which treats the entire friction node as one system cannot take into account the flows of energy between individual constituents of this system, which would be useful in formulating general rules for the process of boundary layer formation.
The durability of the lubricant layer can be assessed in terms of the amount of energy put into the friction node, and flowing through the system, without destroying it. Changes in the durability of the lubricant layer can be caused by changes in the ability to accumulate energy. Examination of various factors modifying the amount of energy accumulated can be a source of much information concerning the ability of an oil to form boundary layers with lubricating additives. It has been confirmed [6] that the amount of energy put into the friction node which can be accumulated by the system depends on its initial state. Observation of changes in the initial state, which affect the durability of the boundary layer, can lead to the determination of the quality of oil with lubricating additives.

4. The method of determining the ability of oils to produce a boundary layer

An energy analysis of the lubricating process resulted in the formulation of an experimental method for determining the ability of oils with lubricating additives to form a boundary layer. It allows the durability of the boundary layer in antiwear and extreme pressure (EP) regions to be determined.
Individual microregions of the interacting surface work under changing pressures caused, under stable macroscopic pressures, by surface roughness. The changing microregion pressures bring about the so-called "flash temperatures", at the points of generation of which there may occur breakthroughs in the boundary layer and a resultant seizure. If a boundary layer is to be durable in the macroscopic sense, it must be durable also under flash temperatures. An oil with lubricating additives must then respond early enough to a change in conditions in a given microregion, i.e. it must form a boundary layer whose structure will be appropriate for given conditions [7].
The response must take place within an appropriate length of time. The speed of this response in a flash temperature area depends on the degree of change in the input and on the conditions prevailing in the given microregion before the occurrence of flash temperatures there, i.e. on P, V and T, which is to say the amount of energy accumulated at the given microregion before extreme conditions arose.
The test allows the effect of the amount of energy put into the friction node before the emergence of extreme conditions in it on the durability of the boundary layer under growing pressure to be observed.
It is carried out with the use of a four-ball apparatus whose structure allows measurements under constant or uniformly rising pressures. The rate of increase V in the load is 45 N s -1; the rotational speed V1, of the upper ball is 470 ± 20 rev min -1. The load may increase from any point until a seizure signalled by a tensometric system which is used for measuring the friction moment (Fig. 1).
The test is characterized by the start of the friction process under a load P0 = 900 N at which the friction takes place within a time t0, and the system is fed with energy E0 :
E0 = µP0t0Vs(2)

where Vs is the sliding speed. After t0, the test is continued under increasing load. The change in t0, and consequently E0, induces the change in the initial state of the system under increasing load, leading to the dependence Pt = f(t0) (Fig. 2).

The friction process under P0 = 900 N and within time t0 reflects the conditions in the given microregion before the occurrence of extreme conditions. What is observed next is the effect of the amount of accumulated energy and the effect of the time span t0 on E0; in other words, the effect of quantitative changes within the structure of the boundary layer, formed before extreme conditions arise, on the oil's ability to respond to growing pressure.
The dependence shown in Fig. 2 allows the total energy Et flowing through the friction node until the moment when boundary layer is destroyed to be calculated:

Et = µP0t0Vs + 0.5µ(Pt2 - P02)V -1Vs(3)

The changes in Et, calculated for successive values of t0, connected with similar changes obtained for base oil made it possible to determine :

(4)

where Et0 is the value of Et calculated for t0 and Et0+1 is the energy Et calculated for the succeeding value of t0; the subscript ol indicates the Et calculation for oil with additives and the subscript b that for the base oil.
Fig. 1. Friction moment changes caused by changes in the load: MT = f(P).
Fig. 2. The dependence Pt = f(t0) for additives containing oils and base oil.

The application of changes in Et (as calculated for oils with lubricating additives) to similar changes for base oils allows energy changes connected with the activity of the additives to be observed.
The values of represent the changes in energy accumulated within the system as a result of modification of the initial state of the friction node. On the basis of this eqn. (4) was obtained and it was confirmed (on the basis of the mechanism of boundary layer formation; see for example refs. 6 and 7) that the values of < 0 were representative of the structure of boundary layers characteristic of the antiwear region and the values of > 0 were similarly representative for the EP region.
The standard for the effect of initial conditions on an oil's ability to respond to a change in the input is the value of the ratio

under various values of t0. To be an effective standard, the ratio needs a point of reference, which could be provided by the difference in the effects of energy related to changes in additives caused by the consumption of the initial energy. Their different rates of change are responsible for changes Pt.

Thus parameters aAW and aAW are obtained as the tangent of the angle of the following line:
(5)

where (Pt)t0 is the value of Pt that corresponds to the energy Et0 and (Pt) t0+1 corresponds to the energy Et0+1; this equation gives the change in the durability of the boundary layer (its ability to respond to changing inputs) corresponding to a given change in the effect of energy caused by changes in the additives.

The parameter | aAW | indicates the ability to form boundary layers in the antiwear region, | aEP | corresponds to the EP structure of boundary layers. The parameters | aAW | and | aEP | have a general character, so they can be useful for determining the oil's ability to form a boundary layer in different machines.
The comparison of the different ai values of the oils, with respect to the durability of the boundary layer they form at various friction nodes, is equivalent to the juxtaposition of the effect of these oils with the ideal intensity of the durability change of the boundary layer best adapted to a given friction node and caused by changes in the initial energy. It turns out that for some machines the ideal oil has a higher a; value than that found in real oils, and then the higher the value of a, for an oil, the better it works in a machine. For other machines, the lower the value of a,, the better the lubrication.
It also turns out that, in some cases, what determines whether the intensity of durability changes in the boundary layer caused by changes in the initial energy should be greater or lower than the ideal intensity for a given friction node is the oil's viscosity.

5. The relationship between | aAW | and Pt

The values of the parameters | aAW | and | aEP | were determined for 20 oils (engine oils, gear oils and hydraulic oils) by the method described above. The values of the seizure load Pt were measured with a four-ball apparatus: the rotational speed of the upper ball was 470 ± 20 rev min -1 and the rate of increase V in the load with speed was 45 N s -1 from P0 = 0 N to the seizure load Pt [8]. It appeared that there was a correlation between | aAW | (i.e. the absolute value of aAW) and EPt for oils of the same viscosity:

EPt = 0.5 µPt2V -1Vs(6)

The dependence | aAW | = f(EPt) is shown in Fig. 3. It was confirmed that the slopes of the straight lines | aAW | = f(EPt) were a function of the oil's viscosity. It turned out that the values of the slopes of the straight lines depended on the kinematic viscosity n40 measured at 40 °C, which led to the formulation of the following equation:

| aAW | = 0.000 086 n40 EPt + 0.2 - 0.000 73 n40(7)

Equation (7) shows that the lubricants having a viscosity n40 of nearly 100 mm2 s -1 form an antiwear layer whose durability depends on a mechanism other than that of the remaining oils.

It was confirmed that eqn. (7) can be used to calculate the values of | aAW | instead of measuring them experimentally.
Fig. 3. The dependence | aAW | = f(EPt)

6. Correlation between | aEP | the welding load Pz

The welding load is a typical parameter used in the evaluation of oils [8,9] (Fig. 4). An example is the welding load determined on a four-ball apparatus with Vr = 1450 ± 50 rev min -1 and under stepwise rising load. The welding load Pz was measured for 30 oils (engine oils, gear oils and hydraulic oils) and was related to appropriate values of aEP. As shown in Fig. 4, the dependence | aEP | = f(EPz) could be used to determine the values of | aEP |.
Fig. 4. The dependence | aEP | = f(EPz)
Fig. 5. The dependence Ih = f( | aAW | + | aEP |).

7. Correlation between | aAW |, | aEP | and the load-wear index Ih

One of the fundamental parameters in the evaluation of lubricating oils is the load-wear index [8, 9]. This connects the antiwear and EP properties of evaluated oils. This was why the correlation between | aAW |, | aEP | and Ih was established (Fig. 5). It will thus be possible to calculate Ih if the values of Pt, n40 and Pz are known.

8. The correlation between | aAW |, | aEP | four-ball wear tests results d40

A lot of specifications for gear and hydraulic oils contain the four-ball wear test which consists in measuring the wear diameter d40 after 1 h of work [10]. The load applied is 400 N and the rotational speed is 1470 ± 50 rev min -1. It was found that the values of d40 correlated with 0.6| aAW | + 0.4 | aEP |. It follows that the wear scar diameter depends on the antiwear properties of an oil to an extent of 60% and on the EP properties to an extent of 40%.
As shown in Fig. 6, some of the oils tested yield a different dependence between 0.6| aAW | + 0.4 | aEP | and d40. These oils are characterized by a very low value of aAW and usually produce relatively high wear scar diameters.
Fig. 6. The dependence d40 = f(0.6|aAW| + 0.4 |aEP|)

9. Correlations between | aAW |, | aEP | and the results of FZG tests

The FZG machine, as a model rig, is a more complex system than the four-ball apparatus [11,12]. As was described above, aAW and aEP were general parameters for predicting the results of FZG tests (Figs. 7 and 8). It turned out that the results of FZG tests depended on the function 0.75| aAW | +0.25 | aAW |, a dependence observed under differing conditions in the FZG test, i.e. initial temperature and tangential velocity. It was observed that different initial temperatures between 90 and 110 °C had no significant effect on the results of the FZG test. It was confirmed that different tangential velocities caused changes in the slope of the correlation line.
Thus it is possible to predict the FZG test results on the basis of values Pt,Pz,. and n40. Fig. 7. The relationship between pass stage and 0.75| aAW | +0.25 | aAW | for FZG test; under the following conditions: gear, FZG-A; width of tooth, 20 mm; tangential velocity 8.3 m s -1; test time, 15 min.
Fig. 8. The relationship between pass stage and 0.75| aAW | +0.25 | aAW | for FZG test; under the following conditions: gear, FZG-A; width of tooth, 20 mm; tangential velocity 16.6 m s -1; test time, 15 min.

10. Conclusions

The results of the investigations described above testify to the usefulness of the energy method in determining the lubricating properties of oils with additives. The method permits the results of highly complex tests to be anticipated on the basis of simple measurements.
The correlation between the parameters |aAW and |aEP| and the results of the various tests, described in this paper, marks the beginning of research aimed at formulating the principles of lubricant selection for various purposes, thus continuing the studies of correlations between the parameters |aAW| and |aEP| and the results of other friction tests.
A problem still unexplained is the determination of the role of antiwear and EP structures in boundary layers formed at different friction nodes.
An analysis of the correlation between |aAW| and |aEP| and the results of various friction tests can contribute to the investigation of the boundary layer structure and the influence of additives on its durability.

References

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