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Chapter 1 Introduction to the book
Chapter 1 Introduction to the book 1.1
The structure of the book
The structure of this book follows three different, but parallel, lines. The first, and most obvious, is the logical/chronological order. The book starts with the history of rheology and ends with the most recent research results regarding the influence of microscopically small highly stressed areas in lubricated machine elements. In between it deals with methods to measure rheological properties of the lubricant, both Newtonian and non-Newtonian and the limits of Newtonian behaviour caused by both high stresses and by elasticity at low stresses. The knowledge gained about these non-Newtonian types of behaviour is then collected in rheological models 'for the lubricants. At about the same time as powerful computers started to become available in the early 1 9 6 0 ' ~ ~ it became clear that a simple liquid model for the lubricant could not describe both the filmbuilding ability, mainly governed by the viscosity and the viscosity-pressure coefficient of the lubricant, and the traction properties of a heavily loaded, lubricated contact. It became necessary to take into consideration the solid type behaviour of the lubricant in the high pressure part of the lubricated contact. This was done in the solidification theory. The remaining problem was that the solid type, or rather the high pressure type, properties of lubricants were not known so high pressure equipment had to be built for the measurement of both solidification pressure and the increase of shear strength of the lubricant for an increase in pressure, as well as the compressibility and bulk modulus of the lubricant in the liquid and solid states. These lubricant properties were then used to calculate the oil film thickness numerically, which calculation could then be compared to experimental measurements using interferometry. The interferometry experiments also showed that the sliding component of the entrainment velocity had an influence on the oil film thickness in the high pressure part of the lubricated contact. High-speed photography experiments also showed that a small transverse vibration completely changed the appearance of the oil film, making it look like a flight of stairs instead of the normal horse-shoe form. This showed that the oil was already behaving in a non-Newtonian manner in the inlet of the Hertzian contact. To measure the non-Newtonian properties of the lubricant at the same pressure level and the same compression time as in a real EHL contact, various types of jumping ball apparatus were built and used to acquire input data for the computer calculations of oil film thickness and traction curves. By studying the numerical results it was possible to see the influence of 1
2
CHAPTER 1. INTRODUCTION T O T H E BOOK
different parameters on the behaviour of the lubricated contact. It also gave some insight into the phenomena of surface distress and mixed lubrication. The endurance life of lubricated machine elements is a function of the local stress compared to the local strength of the material. Both when the oil film thickness is very thin and when contaminants are present in the lubricant, the local stresses close to the surface become very large and the endurance life of the machine element short. The most recent part of the present research includes the influence that local stresses and static stresses have on the endurance strength of the bearing material. The second line follows the development from simple basic properties of continuous media to more and more complicated models of solid and liquid media and the influence of their properties on the behaviour of the system. The starting point is the measurement of viscosity, the ratio between shear stress and shear strain rate. Then the viscosity is studied as a function of pressure and temperature. Non-Newtonian liquids are described using curve fitting techniques and the stress in the liquid is given, for instance, by a power-law relationship. In high pressure lubricated contacts where the lubricant is compressed into the glassy state, not only the variation of viscosity with pressure and temperature has to be taken into account, but also the solid type properties of the lubricant, like shear strength, its variation with pressure and temperature as well as the bulk modulus for the solid state. These lubricant parameters can be included in theoretical calculations of different complexity, like pure rolling or combined rolling and sliding, like line contacts and point contacts and so on. A further increase in complexity comes from the consideration of surface roughness and the influence it has on the squeeze term in the pressure equation as well as on the collapse of the oil film and the direct contact between colliding asperities. The third, and maybe least obvious, line is the development of my own research and understanding of heavily loaded lubricated machine elements over the past twenty-five years. As the three lines are parallel and almost consecutively followed throughout the book, I will describe them together. To be able to guide the reader into the micro-world of tribology, it is necessary to describe how the different elements in a lubricated contact work together. This description starts with the history of rheology and Newton.
1.2
History of rheology and Newton
In chapter 2 a short overview of how people looked upon liquid lubricants and their properties is given. We know that lubricants have actively been used for more than 4500 years, at least to decrease friction but probably also to increase the wear resistance of machine elements in relative motion. It is therefore very surprising that no analysis of why and how lubricants functioned seems to have been performed for more than four thousand years. When Newton postulated the linear relationship between shear rate and shear stress in liquids, he tried to explain the motion of the planets and not the behaviour of a lubricant in a bearing. Up until two hundred years ago, lubricants were still often chosen according to old rules and according to experience of what had worked before, often with the density as the determining factor. One hundred years ago viscometers were still being used just to make a comparison between the old and well-known animal and vegetable oils and the new and not yet trustworthy mineral oils. Not until Osborne Reynolds analysed the lubrication of bearings, and described the connec-
1.3. DIFFERENT VISCOMETERS
3
tion between bearing geometry, load and motion with the viscosity of the lubricant, was the importance of lubricant viscosity understood.
1.3
Different viscometers
In order to be able to use Reynolds’ equation to predict the behaviour of a bearing, it is necessary to know the viscosity of the lubricant. A number of early viscometers compared the viscosity of an unknown liquid with the viscosity of a well-known liquid like water, but later, absolute measurements of the viscosity were performed. The early viscometers often had such high flow velocities that inertia forces were important. Even later types of viscometers, using lower flow velocities, were normally calibrated using standard viscosity liquids. Even today most viscometers are calibrated using standard viscosity liquids because small errors in the geometry often give rather large errors in the measured viscosity value. This type of calibration is only possible as long as the liquid behaves in a Newtonian fashion.
1.4
Limits of Newtonian behaviour
The definition of Newtonian behaviour is that the shear stress in a liquid increases linearly with the shear rate. The ratio between the shear stress and the shear rate is called the viscosity of the liquid. For a Newtonian liquid the viscosity is not a function of the shear rate but can be a function of pressure and temperature. If a liquid is sheared between two parallel surfaces, where one surface is sliding with a velocity v along the other surface, the shear stress in the liquid increases linearly with the velocity for small sliding velocities v. When the velocity is increased to a certain value, the stress in the liquid reaches the limit of Newtonian behaviour and the shear stress increases at a lower rate. If the velocity is increased further the shear strength of the liquid will be reached and no further increase of shear stress is possible. This is one limit of the Newtonian behaviour.
1.5
Rheological models for non-Newtonian fluids
When the liquids are non-Newtonian the whole volume of the tested liquid has to be equally stressed, otherwise the measured value will be some kind of mean value over the stress range in the viscometer. This makes it impossible to analyse shear stress - shear strain rate relationships using viscometers which build on some kind of integration over a flow field, as for example, capillary tube viscometers and falling body viscometers, where assumptions have to be made about the flow velocity distribution in the liquid. The rheological models used for non-Newtonian liquids are based on curve fitting techniques where experimental measurements of shear stress - shear strain rate relationships are approximated by mathematical expressions. To be able to measure these non-Newtonian parameters it is necessary to construct rheometers giving a constant shear rate throughout the entire volume of the liquid being tested.
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1.6
CHAPTER 1 . INTRODUCTION T O THE BOOK
Rheometers for the nowNewtonian range
To get a constant shear rate and a constant shear stress in the entire liquid volume under test, the viscosity and thereby the temperature of the liquid has to be constant throughout the volume. To enable easy control of the temperature, viscometers are designed with surface areas large compared to the volume being tested. The fundamental geometry for measurement of shear stress - shear strain rate relationships is two infinite parallel plates having the space between them filled with the liquid to be tested. In practice this is translated to a cylindrical geometry with two concentric cylinders where one cylinder rotates relative to the other. Another possible geometry is a conical one where one of the cones can eventually degenerate to a flat surface which the top of the cone is touching. These types of rheometers can be used as long as there is some relationship between shear stress and shear strain rate. If the pressure in a lubricant is increased high enough the lubricant will convert from a liquid to a solid, and in engineering terms it is no longer applicable to describe the lubricant as a liquid. The viscosity has lost its importance because the stresses and flows in the lubricant are determined by its solid-type properties.
1.7
Solidification theory
If the lubricant converts from liquid to solid behaviour at high pressures this can be used to develop a calculational model for the pressure build-up and the lubricant film thickness in heavily loaded lubricated rolling contacts. At low pressures the lubricant behaves like a normal liquid and the same type of properties as for liquid lubricants can be used to analyze the pressure build-up, oil film thickness and elastic deformations of the bearing surfaces. At high pressures, where the lubricant is solidified, the pressure build-up is governed by the shear strength and the compressibility of the solidified oil and the elastic properties of the bearing surfaces. Depending on the pressure gradients in the lubricant film, two different types of behaviour of the solidified oil are conceivable. Either the oil sticks to the rolling surfaces and moves with the same velocity and in the same direction as the surfaces, or the solid oil slides along the bearing surfaces in the direction of the local pressure gradient. Which of these two possible scenarios actually takes place depends on the shear stress at the oil-bearing interface. If the shear stress is less than the local shear strength of the interface or the solidified oil, the oil will stick to the surfaces and move like a solid layer without slip between the bearing surfaces. When the stress reaches the shear strength, slip will take place in the direction of maximum stress. To be able to calculate the total pressure build-up in the different regions of the lubricated contact, continuity of mass flow must be guaranteed at all boundaries between the regions with different lubricant behaviour: This means that continuity of mass flow must be maintained at the boundary between liquid and solidified oil, at the boundary between solidified oil sticking to the bearing surfaces and solidified oil sliding along the surfaces in the direction of the maximum pressure gradient, and last but not least the continuity of mass flow must be maintained at the boundary between liquid oil and the cavitated region. To be able to solve this lubrication problem numerically, the lubricant properties in the solidified state have to be determined experimentally.
1.8. LUND HIGH PRESSURE CHAMBER
1.8
5
Lund high pressure chamber
The lubricant behaviour in the solidified state was first investigated using a high pressure chamber built at Lund Technical University. This high pressure chamber was designed to measure both the pressure when the oil converted to a solid, and the shear strength of the oil at slightly higher pressures. The pressure was transmitted to the tested oil using a liquid with a high solidification pressure. This pressure transmission fluid surrounded the test piston and was separated from the test fluid by means of three O-ring seals. The internal flow in the test piston, where the oil to be tested had to flow to compensate for the volume decrease in the shear strength measurement area, took place through four small holes connecting the test fluid container with the measurement area. The flow of solidified oil through these small holes during the compression of the oil induced a rather large and uncontrollable pressure drop when the oil was solidified. It was therefore difficult to measure the increase in shear strength caused by an increase in pressure. To be able to do these measurements a new high pressure chamber was developed and built.
1.9
Luled high pressure chamber
In this high pressure chamber, which took 10 years to develop and build, it was not only possible to measure the pressure, the shear strength of the solidified oil and the increase in shear strength of the oil for an increase in the pressure, but also to measure the compression of the oil with very high precision. The main high pressure parts in this high pressure chamber were made of cemented carbide, having 89 weight per cent tungsten carbide and 11 weight per cent cobalt. This type of cemented carbide has a compressive strength of 4.6 GPa (4 600 000 000 N/m2) and therefore it was possible to take the pressure increase from ambient to the 2.2 GPa present in the high pressure chamber in one step. To ensure that the compressed lubricant did not leak past the compression plungers, “soft seals” made of hardened tool steel were placed at the top of the plungers. Less strong steels were also tested as seal material, but these were extruded out from the high pressure volume along the plungers and caused the plungers to stick and the tested lubricant to leak out. The shear strength measurements were performed at different temperatures from room temperature to 200 “C, and the pressure needed to compress the lubricant into the solid state increased strongly with increasing temperature. For most of the lubricants the shear strength increase for a pressure increase in the solid state gave similar values at the different temperatures. This was not true for the traction fluid which lost a large part of the traction at high temperatures. The behaviour of the lubricants at high temperatures showed that the increase in solidification pressure caused by an increase in temperature was governed by the thermal expansion of the oil and the extra pressure needed to compress the oil back to the same solidification density it had at a lower temperature.
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1.10
CHAPTER 1. INTRODUCTION TO THE BOOK
Lubricant compressibility
At low pressures the compressibility of lubricating oils is very high. If the same bulk modulus (the inverse of the compressibility) as at ambient pressure was maintained at high pressures, normal elastohydrodynamic pressures in rolling element bearings should compress the lubricant down to zero volume. In reality the bulk modulus of a lubricant increases steeply with increasing compression, so that at pressures above the solidification pressure the bulk modulus is about ten times larger than at ambient pressure. The total compression of normal lubricating oils at elastohydrodynamic pressures is in the order of 20 to 35 per cent. When a lubricating oil is compressed by a hard elastohydrodynamic contact, the viscosity increases strongly, and when the lubricant is compressed above the glass transition pressure an amorphous structure is frozen into the oil and the oil molecules can no longer move freely. The transition from liquid to solid behaviour at different temperatures seems to be a simple function of the compression and the thermal expansion, as stated earlier. The solidification pressure and the compressibility of the lubricant are needed as input data if the oil film thickness and pressure distribution are going to be calculated using the solidification theory. To be able to verify the calculated values experimentally, direct measurements of the oil film thickness are needed.
1.11
Interferometry film thickness measurement
There are a number of different ways to measure oil film thicknesses in elastohydrodynamically lubricated contacts, but by far the most elegant is to use interferometry. The first interferometry measurements of oil film thicknesses in elastohydrodynamic lubrication were published by Cameron and Gohar in the mid-l960’s, and the method has been used extensively since then by many authors of technical papers. The first experiments were performed using a glass disc as the transparent medium. This made it possible t o investigate contacts with maximum Hertzian pressures up to about 0.7 GPa. At higher pressures thin chips started to flake off from the surface of the hardened glass disc and the surface finish was destroyed. Later, both Cameron and other authors used sapphire (AlzOs) discs to reach higher contact pressures, up to about 2 GPa. At these high pressures and loads the elastic energy stored in the sapphire is considerable. This leads to a catastrophic type of failure, where the sapphire surface does not flake off when the load is too high but the whole sapphire explodes into small sharp splinters. This happened a couple of times in the Lulel laboratory. A number of different bearing arrangements for the lubricated ball were used in different laboratories. Cameron used V-shaped rollers under the ball, while the author used the ball in a tube geometry. The ball was placed in a tube, having a diametral clearance of 25 pm, and the lubricating oil was pumped in under the ball giving both the load and the bearing arrangement for the ball. During these experiments the paradox of the ball in the tube was discovered. It was found that the hydrodynamic forces acting on the ball in the tube were strongly influenced by rather small variations of the location of the cavitation boundary formed between the ball and the tube. These small variations made the ball-tube-lubricant system work as a spring, driving the ball backwards when it was suddenly stopped during rotation. This backwards spring action lasted for about a quarter of a rotation of the ball until the cavitation boundary around the ball had redistributed evenly around it. Then the ball moved to a position in the
1.12. FILM THICKNESS AT COMBINED ROLLING AND SLlDING
7
centre of the tube and the rotation was stopped. In the interferometry experiments, having the ball-tube geometry, the ball was driven by the traction forces in the oil film. This limited the test apparatus to pure rolling. To be able to study traction and the influence of sliding speeds on the oil film build-up the two lubricated surfaces had to be driven separately.
1.12
Film thickness at combined rolling and sliding
One of the sapphire disc apparatuses built at LuleH Technical University had another bearing arrangement for the ball, which made it possible to drive each one of the surfaces separately. This made it possible to study the oil film build-up at pure rolling, pure sliding or any combination in between. These experiments showed that the simple Reynolds equation, where only the sum of the surface velocities is included in the analysis, does not completely describe the oil film thickness build-up in heavily loaded elastohydrodynamic contacts. The oil film thickness in the most heavily loaded central part of the contact decreased strongly compared to the film thickness in the side lobes, giving a much more even oil film thickness across the contact than for pure rolling. The same phenomenon also has a big influence on the lubricant film if a transverse vibration induces sideways sliding in the contact.
1.13
Transverse sliding
By adding an arrangement with a hammer to the ball-in-the-tube system, it was possible to induce high frequency sideways vibrations perpendicular to the rolling velocity. These sliding motions were very small, only a fraction of the size of the Hertzian contact. If the oil had been Newtonian in the high pressure contact, this small sideways motion would not have had any influence on the oil film thickness and pressure build-up. By using two different optical techniques it was possible to show that the oil film pressure build-up at the inlet of the contact was more or less destroyed by the sideways sliding. Both the interferometry measurements and the shadowgraph technique used a high speed flash unit with a flash duration down to 18 ns. This very short flash duration made it possible to take sharp pictures of the highly dynamic events, even through a large amplification microscope. During the time a normal photo flash is lit (0.001 s) the light travels 300 km, but it has only time to go 5 m during the flash time of 18 ns (0.000 000 018 s). The influence of slight sideways sliding shows that the non-Newtonian behaviour has a big influence on the oil film build-up when the pressure gradients, and thereby the shear stresses induced by the pressure distribution, are large. This is the main reason why surface roughness asperities cannot be lubricated using micro-EHL if the surface slopes and the asperity heights are too large. The local pressure spikes caused by the surface roughness give high local pressure gradients and thereby high shear stresses in the oil at the same time as the local asperity pressure is high enough to compress the oil into the solid state. This means that a sliding distance of only a fraction of the surface roughness wavelength during the contact time is enough to stop the micro-EHL mechanism from working. The oil film built up by the main
8
CHAPTER 1. INTRODUCTION TO THE BOOK
contact must then be so thick that the full height asperities cannot reach each other through the oil film and cause damage. This type of non-Newtonian behaviour is only present in lubricants when the shear stress is large compared to the local shear strength of the lubricant. For soft elastohydrodynamic contacts, like rubber on steel, mineral oils seem to behave like Newtonian liquids. Due to the much softer surfaces the shear stress in the lubricant is low and the oil film thickness built up is therefore much larger than for a hard EHL contact. This, combined with the fact that soft rubber materials do not reflect light very well, makes it very difficult to use interferometry techniques to measure the lubricant film thickness in soft lubricated contacts. One way to measure the film thickness, though, is to use laser induced fluorescence.
1.14
The blue laser technique
Many lubricant molecules show fluorescence. When they are hit by light of a certain wavelength, the light is absorbed and light of another frequency (colour) is emitted. For mineral oils one possible light source to use is an He-Cd laser which has a blue light. When this light is absorbed by an oil molecule, the emitted light is green. The intensity of the emitted light is proportional to the amount of oil and a function of the intensity of the incoming light beam. This can be utilized as a measurement signal for the amount of oil present. The method has been used for tracing oil spills on water, but the first time it was used for quantitative measurements was when hydraulic rubber seals were studied. The different oil film thickness measurement techniques described so far gave accurate information about the oil film. The time scales of the experiments were similar to the time scales in real lubrication applications, i.e., the lubricant was stressed to the same stress level within the same compression time as in real applications. For the high pressure chamber experiments this was not true. The compression time there was lo4 to 10' times longer than in a typical EHL contact, where the lubricant is compressed and decompressed during overrolling within to seconds. To see if the compression time had any significant influence on the solidification and shear strength of the solidified lubricant, dynamic experiments were performed.
1.15
The jumping ball apparatus
The idea behind the jumping ball apparatus was to obtain a tool to measure the behaviour of lubricants under pressure, when the compression time was of the same order as in a normal elastohydrodynamic contact and the pressure at least as high as in a Hertzian contact of a rolling element bearing. To make sure that the properties measured using the test apparatus were the properties of the lubricated system and not a function of any dry friction in the system, the measurement surfaces had to be completely separated by the tested lubricant. The simplest and most obvious way to do this was to compress the oil using a squeeze film motion between two nonconforming surfaces. The shear strength of the oil had to be measured during the very short compression time. The experiments in the Lulet high pressure chamber had shown that the shear strength of solidified oils increased linearly with pressure. It was also well known that
1.16. COMPUTERIZED JUMPING BALL APPARATUS
9
the flow properties of liquids became more like the flow properties of solids when the stress time decreased below the relaxation time of the liquid. All this made it natural to choose the geometry of a ball impacting a smooth flat lubricated surface. By not having a perpendicular impact between the ball and the flat surface, the shear force in the oil film and at the surface of the ball could be analysed by studying the rotational acceleration of the ball. In the first jumping ball apparatus, the time integral of the rotational acceleration, the rotational speed, was analysed by mechanical means, using a small cart as landing place for the ball after the impact had made it bounce up into the air and rotate. Later a fully computerized version of the jumping ball apparatus was built.
1.16
Computerized jumping ball apparatus
Instead of using the mechanical cart for the analysis of the motion of the ball, a computeraided picture analysis system and a high speed video camera were used. The principle of the lubricated impact was also changed. In the mechanical cart apparatus the sliding speed between the ball and the impacted surface decreased to zero at the end of the impact. In the picture analysis apparatus it was arranged to have sliding speed left at the end of the impact to ensure that the shear stress in the oil was equal to the shear strength. The main advantages of the computerized jumping ball apparatus compared to the mechanical jumping ball apparatus was the repeatability and the shorter testing time. To analyse one oil at one temperature using the mechanical jumping ball apparatus took typically one working day. The computerized apparatus gives a measured 'value within a few seconds and could analyse a lubricant at different temperatures to give statistically valid results in a matter of hours. These lubricant parameters can now be used in elastohydrodynamic calculations both to determine the limit of Newtonian lubrication and to see what happens to the lubrication when sliding speeds are increased above the limit of Newtonian behaviour.
1.17
The Newtonian elastohydrodynamic problem
If the increase in viscosity and the compressibility of the lubricant at high pressures are taken into account, as well as the elastic deformation of the bearing surfaces, the EHL problem can be solved. If unlimited shear stresses are allowed in the oil film, the Newtonian behaviour of the oil will give pressure distributions and oil film thicknesses which are independent of the sliding speed, and only dependent on the entrainment velocity (the sum of the surface velocities). A major problem in the numerical solution of the Newtonian elastohydrodynamic calculations is the numerical instability. The EHL problem is very ill conditioned. For heavy loads and low oil film thicknesses, the elastic deformation of the surfaces can be many hundred times larger than the oil film thickness. This means that an error in the pressure distribution of one per cent gives an error in the deformation af about one per cent, and hence an error in the oil film thickness as large as the whole oil film thickness. If this estimate of the oil film thickness is then used to calculate the local pressure in an iterative solution scheme, the errors can grow without bounds and the calculations fail to converge. Similar type instabilities are also seen in non-Newtonian calculations.
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1.18
CHAPTER 1. INTRODUCTION TO T H E BOOK
Non-Newtonian fluid model
If the shear stress in the oil exceeds the shear strength of the oil or of the oil-bearing-interface, slip will occur. For isothermal conditions the slip will always take place at the metal surface, because the shear stress is highest there. In more lightly loaded high speed sliding contacts, the temperature increase in the middle of the oil film will locally reduce the shear strength of the oil or transform it into liquid behaviour, giving a local slip surface somewhere in the middle of the oil film. In the analysis in chapter 18 the lubrication is assumed to be isothermal, so the slip planes will always be located at one of the bearing surfaces, but if other assumptions are made about the lubricant parameters, other pressure and shear stress distributions will result from the calculations.
1.19
Pitting and micropitting
If the shear stresses acting on the lubricated surface are large enough, the maximum stress according to all stress criteria will be present very close to and just under the surface. The same is also true if local micro-contacts or indentations from particles are carrying part of the load. The local micro-Hertzian pressure fields have their maximum shear stress close to the surface, in proportion to the size of the asperity compared to the size of the Hertzian contact. These high stresses close to the surface have a detrimental influence on the bearing life and cause small pieces of bearing material to break loose from the surfaces. Just as overrolling of contaminant particles causes the surface quality to deteriorate, so does micropitting destroy the surfaces and prevent them from being separated by a continuous oil film.
1.20
Mixed lubrication
If a Newtonian model is used to describe the lubricant behaviour, breakdown of the lubricant film can never be explained. If the lubricant film becomes too thin at any point Reynolds’ equation will predict very high pressures which then elastically deform the surface in such a way that the surfaces never touch each other. This is obviously not true for hard elastohydrodynamic contacts. What happens is that the shear stresses in the lubricant reach the shear strength, and the oil is no longer dragged along the surfaces straight into the contact. The oil loses its grip on the surface and slides down into the valleys between surface asperities. This makes it possible for the tops of the surface asperities to break through the oil film and make contact with the opposite surface. This non-Newtonian behaviour of the lubricant is influenced by a number of properties of the elastohydrodynamic contact. It is strongly influenced by the surface roughness, and seems to be especially sensitive to the surface slopes and to the wavelength of the surface asperities. It is strongly dependent on the local oil film pressure and the solidification properties of the lubricant. It is also strongly dependent on the elastic properties of the contacting surfaces. The analysis so far, except for a few words in 1.19, has covered clean lubricants. Filters for oil circulation systems, if they are used at all, normally allow much larger particles to pass than can be accommodated in the oil film without damaging the lubricated surfaces.
1.21. LUBRICANT CONTAMINATION
11
1.21 Lubricant contamination Recent research has shown that particulate contamination damages lubricated surfaces if the particle size is larger than the oil film thickness and the particles are hard. Depending on the relative hardness and toughness of the contaminant particles, different sizes can be accommodated in the oil film without resulting in plastic deformation of the lubricated surfaces. Very hard and tough particles, like aluminium oxide, as small in size as the calculated oil film thickness may cause wear damage of the surfaces. On the other hand, very soft particles like plastic can cause permanent indentation of the bearing surfaces if the particles are larger than 50-100 pm. In both cases the bearing life will be reduced considerably. The most difficult part of this research is that people are so used to having very dirty lubrication systems that they are not aware of the detrimental effects. They think it is natural for a machine to wear out and equally natural for the lubricant to contain all the wear particles. For bearing applications run in clean lubricants, the load can be kept just under the threshold for gross plastic flow and still the bearings will not fail. The improvement in life for a clean system compared to a heavily contaminated system can be more than a factor of 500 for lightly loaded applications. In the clean system all material stresses are well within the elastic limit, but in the contaminated system new indentations are formed by the overrolled particles for every revolution of the machine. This inevitably leads to premature failure. Even if the damage created by the overrolled paricles is not allowed to accumulate over time because the particles are removed either by changing the oil or by installing a fine filter, the life of the damaged surfaces will be short.
1.22
Influence of residual and static stresses
Experimental investigations of the influence of superimposed tensile stresses on the endurance stress limit show that the endurance stress limit decreases by about 30 per cent of the hydrostatic tensile stress in the material. This means that hoop stresses in inner rings of bearings and residual stresses caused by plastic flow around particle indentations not only increase the local stress, but at the same time decrease the endurance stress limit of the bearing steel. This can give an extremely large reduction in life of the bearings, but knowledge about the guiding mechanism can teach us how to circumvent the problem. One possible way is to build compressive stresses into the material influenced by the Hertzian stress field.
1.23
Overview of the different parameters
From knowledge of the main elastohydrodynamic parameters and their numerical values it is possible to predict the overall behaviour of EHL contacts. The viscosity at ambient pressure multiplied by the viscosity-pressure coefficient gives a good indication of the entrainment speed needed to obtain a certain oil film thickness. Both the viscosity and the viscosity-pressure coefficient have to be of a reasonably large size to make it possible to separate the stressed machine elements from each other with a lubricant film. A typical case when this is not possible is lubrication using water-based hydraulic fluids. Even if the fluids are thickened to have high viscosities at atmospheric pressure, the very low viscosity increase for a pressure increase gives a very thin lubricant film. The product viscosity times
12
CHAPTER 1 . INTRODUCTION TO THE BOOK
the viscosity-pressure coefficient has to be of a certain size to make hard elastohydrodynamic lubrication possible. For soft elastohydrodynamic lubrication it is only necessary to have a certain viscosity because there the pressures are so low that no important viscosity increase takes place. To obtain information about the traction properties of an elastohydrodynamic contact, the viscosity-pressure coefficient multiplied by the maximum Hertzian pressure in the contact can be used. If this product is larger than about 12-15 the sliding velocity needed to reach nonNewtonian behaviour is low, and the local shear strength of the lubricant has to be taken into account. The shear strength of the lubricant is a function of the molecular structure, but only weakly dependent on molecule size. Elastic molecules, having a large free volume, need higher pressures for a given temperature to solidify compared to stiff compact molecules. At the same time it seems as if the compact molecules, when they are solidified by the pressure, increase their shear strength faster with a pressure increase than the more elastic molecules. This leads to high friction for contacts lubricated with oils like naphthenic extracts which have these stiff molecules. The viscosity-pressure coefficient, a,by itself has a large influence on the theoretically predicted pressure spike at the outlet of the elastohydrodynamic contact. High a-values give a high pressure spike and thereby induce high stresses in the bearing just below the surface. If these local stresses become large enough, either because of the properties of the lubricant or overrolling of contaminant particles or surface asperities, micropitting can occur. Besides the properties of the oil, the properties of the surfaces are also important. Surface roughness slopes, wavelengths, heights, radii of curvature and direction of patterns all contribute to the behaviour of lubrication, the ability to run in and the endurance life of the surfaces. The size of the Hertzian contact compared to the size of grinding and honing marks, that is, the number of asperities within the contact also influences the asperity collapse.
The structure of the book
The structure of this book follows three different, but parallel, lines. The first, and most obvious, is the logical/chronological order. The book starts with the history of rheology and ends with the most recent research results regarding the influence of microscopically small highly stressed areas in lubricated machine elements. In between it deals with methods to measure rheological properties of the lubricant, both Newtonian and non-Newtonian and the limits of Newtonian behaviour caused by both high stresses and by elasticity at low stresses. The knowledge gained about these non-Newtonian types of behaviour is then collected in rheological models 'for the lubricants. At about the same time as powerful computers started to become available in the early 1 9 6 0 ' ~ ~ it became clear that a simple liquid model for the lubricant could not describe both the filmbuilding ability, mainly governed by the viscosity and the viscosity-pressure coefficient of the lubricant, and the traction properties of a heavily loaded, lubricated contact. It became necessary to take into consideration the solid type behaviour of the lubricant in the high pressure part of the lubricated contact. This was done in the solidification theory. The remaining problem was that the solid type, or rather the high pressure type, properties of lubricants were not known so high pressure equipment had to be built for the measurement of both solidification pressure and the increase of shear strength of the lubricant for an increase in pressure, as well as the compressibility and bulk modulus of the lubricant in the liquid and solid states. These lubricant properties were then used to calculate the oil film thickness numerically, which calculation could then be compared to experimental measurements using interferometry. The interferometry experiments also showed that the sliding component of the entrainment velocity had an influence on the oil film thickness in the high pressure part of the lubricated contact. High-speed photography experiments also showed that a small transverse vibration completely changed the appearance of the oil film, making it look like a flight of stairs instead of the normal horse-shoe form. This showed that the oil was already behaving in a non-Newtonian manner in the inlet of the Hertzian contact. To measure the non-Newtonian properties of the lubricant at the same pressure level and the same compression time as in a real EHL contact, various types of jumping ball apparatus were built and used to acquire input data for the computer calculations of oil film thickness and traction curves. By studying the numerical results it was possible to see the influence of 1
2
CHAPTER 1. INTRODUCTION T O T H E BOOK
different parameters on the behaviour of the lubricated contact. It also gave some insight into the phenomena of surface distress and mixed lubrication. The endurance life of lubricated machine elements is a function of the local stress compared to the local strength of the material. Both when the oil film thickness is very thin and when contaminants are present in the lubricant, the local stresses close to the surface become very large and the endurance life of the machine element short. The most recent part of the present research includes the influence that local stresses and static stresses have on the endurance strength of the bearing material. The second line follows the development from simple basic properties of continuous media to more and more complicated models of solid and liquid media and the influence of their properties on the behaviour of the system. The starting point is the measurement of viscosity, the ratio between shear stress and shear strain rate. Then the viscosity is studied as a function of pressure and temperature. Non-Newtonian liquids are described using curve fitting techniques and the stress in the liquid is given, for instance, by a power-law relationship. In high pressure lubricated contacts where the lubricant is compressed into the glassy state, not only the variation of viscosity with pressure and temperature has to be taken into account, but also the solid type properties of the lubricant, like shear strength, its variation with pressure and temperature as well as the bulk modulus for the solid state. These lubricant parameters can be included in theoretical calculations of different complexity, like pure rolling or combined rolling and sliding, like line contacts and point contacts and so on. A further increase in complexity comes from the consideration of surface roughness and the influence it has on the squeeze term in the pressure equation as well as on the collapse of the oil film and the direct contact between colliding asperities. The third, and maybe least obvious, line is the development of my own research and understanding of heavily loaded lubricated machine elements over the past twenty-five years. As the three lines are parallel and almost consecutively followed throughout the book, I will describe them together. To be able to guide the reader into the micro-world of tribology, it is necessary to describe how the different elements in a lubricated contact work together. This description starts with the history of rheology and Newton.
1.2
History of rheology and Newton
In chapter 2 a short overview of how people looked upon liquid lubricants and their properties is given. We know that lubricants have actively been used for more than 4500 years, at least to decrease friction but probably also to increase the wear resistance of machine elements in relative motion. It is therefore very surprising that no analysis of why and how lubricants functioned seems to have been performed for more than four thousand years. When Newton postulated the linear relationship between shear rate and shear stress in liquids, he tried to explain the motion of the planets and not the behaviour of a lubricant in a bearing. Up until two hundred years ago, lubricants were still often chosen according to old rules and according to experience of what had worked before, often with the density as the determining factor. One hundred years ago viscometers were still being used just to make a comparison between the old and well-known animal and vegetable oils and the new and not yet trustworthy mineral oils. Not until Osborne Reynolds analysed the lubrication of bearings, and described the connec-
1.3. DIFFERENT VISCOMETERS
3
tion between bearing geometry, load and motion with the viscosity of the lubricant, was the importance of lubricant viscosity understood.
1.3
Different viscometers
In order to be able to use Reynolds’ equation to predict the behaviour of a bearing, it is necessary to know the viscosity of the lubricant. A number of early viscometers compared the viscosity of an unknown liquid with the viscosity of a well-known liquid like water, but later, absolute measurements of the viscosity were performed. The early viscometers often had such high flow velocities that inertia forces were important. Even later types of viscometers, using lower flow velocities, were normally calibrated using standard viscosity liquids. Even today most viscometers are calibrated using standard viscosity liquids because small errors in the geometry often give rather large errors in the measured viscosity value. This type of calibration is only possible as long as the liquid behaves in a Newtonian fashion.
1.4
Limits of Newtonian behaviour
The definition of Newtonian behaviour is that the shear stress in a liquid increases linearly with the shear rate. The ratio between the shear stress and the shear rate is called the viscosity of the liquid. For a Newtonian liquid the viscosity is not a function of the shear rate but can be a function of pressure and temperature. If a liquid is sheared between two parallel surfaces, where one surface is sliding with a velocity v along the other surface, the shear stress in the liquid increases linearly with the velocity for small sliding velocities v. When the velocity is increased to a certain value, the stress in the liquid reaches the limit of Newtonian behaviour and the shear stress increases at a lower rate. If the velocity is increased further the shear strength of the liquid will be reached and no further increase of shear stress is possible. This is one limit of the Newtonian behaviour.
1.5
Rheological models for non-Newtonian fluids
When the liquids are non-Newtonian the whole volume of the tested liquid has to be equally stressed, otherwise the measured value will be some kind of mean value over the stress range in the viscometer. This makes it impossible to analyse shear stress - shear strain rate relationships using viscometers which build on some kind of integration over a flow field, as for example, capillary tube viscometers and falling body viscometers, where assumptions have to be made about the flow velocity distribution in the liquid. The rheological models used for non-Newtonian liquids are based on curve fitting techniques where experimental measurements of shear stress - shear strain rate relationships are approximated by mathematical expressions. To be able to measure these non-Newtonian parameters it is necessary to construct rheometers giving a constant shear rate throughout the entire volume of the liquid being tested.
4
1.6
CHAPTER 1 . INTRODUCTION T O THE BOOK
Rheometers for the nowNewtonian range
To get a constant shear rate and a constant shear stress in the entire liquid volume under test, the viscosity and thereby the temperature of the liquid has to be constant throughout the volume. To enable easy control of the temperature, viscometers are designed with surface areas large compared to the volume being tested. The fundamental geometry for measurement of shear stress - shear strain rate relationships is two infinite parallel plates having the space between them filled with the liquid to be tested. In practice this is translated to a cylindrical geometry with two concentric cylinders where one cylinder rotates relative to the other. Another possible geometry is a conical one where one of the cones can eventually degenerate to a flat surface which the top of the cone is touching. These types of rheometers can be used as long as there is some relationship between shear stress and shear strain rate. If the pressure in a lubricant is increased high enough the lubricant will convert from a liquid to a solid, and in engineering terms it is no longer applicable to describe the lubricant as a liquid. The viscosity has lost its importance because the stresses and flows in the lubricant are determined by its solid-type properties.
1.7
Solidification theory
If the lubricant converts from liquid to solid behaviour at high pressures this can be used to develop a calculational model for the pressure build-up and the lubricant film thickness in heavily loaded lubricated rolling contacts. At low pressures the lubricant behaves like a normal liquid and the same type of properties as for liquid lubricants can be used to analyze the pressure build-up, oil film thickness and elastic deformations of the bearing surfaces. At high pressures, where the lubricant is solidified, the pressure build-up is governed by the shear strength and the compressibility of the solidified oil and the elastic properties of the bearing surfaces. Depending on the pressure gradients in the lubricant film, two different types of behaviour of the solidified oil are conceivable. Either the oil sticks to the rolling surfaces and moves with the same velocity and in the same direction as the surfaces, or the solid oil slides along the bearing surfaces in the direction of the local pressure gradient. Which of these two possible scenarios actually takes place depends on the shear stress at the oil-bearing interface. If the shear stress is less than the local shear strength of the interface or the solidified oil, the oil will stick to the surfaces and move like a solid layer without slip between the bearing surfaces. When the stress reaches the shear strength, slip will take place in the direction of maximum stress. To be able to calculate the total pressure build-up in the different regions of the lubricated contact, continuity of mass flow must be guaranteed at all boundaries between the regions with different lubricant behaviour: This means that continuity of mass flow must be maintained at the boundary between liquid and solidified oil, at the boundary between solidified oil sticking to the bearing surfaces and solidified oil sliding along the surfaces in the direction of the maximum pressure gradient, and last but not least the continuity of mass flow must be maintained at the boundary between liquid oil and the cavitated region. To be able to solve this lubrication problem numerically, the lubricant properties in the solidified state have to be determined experimentally.
1.8. LUND HIGH PRESSURE CHAMBER
1.8
5
Lund high pressure chamber
The lubricant behaviour in the solidified state was first investigated using a high pressure chamber built at Lund Technical University. This high pressure chamber was designed to measure both the pressure when the oil converted to a solid, and the shear strength of the oil at slightly higher pressures. The pressure was transmitted to the tested oil using a liquid with a high solidification pressure. This pressure transmission fluid surrounded the test piston and was separated from the test fluid by means of three O-ring seals. The internal flow in the test piston, where the oil to be tested had to flow to compensate for the volume decrease in the shear strength measurement area, took place through four small holes connecting the test fluid container with the measurement area. The flow of solidified oil through these small holes during the compression of the oil induced a rather large and uncontrollable pressure drop when the oil was solidified. It was therefore difficult to measure the increase in shear strength caused by an increase in pressure. To be able to do these measurements a new high pressure chamber was developed and built.
1.9
Luled high pressure chamber
In this high pressure chamber, which took 10 years to develop and build, it was not only possible to measure the pressure, the shear strength of the solidified oil and the increase in shear strength of the oil for an increase in the pressure, but also to measure the compression of the oil with very high precision. The main high pressure parts in this high pressure chamber were made of cemented carbide, having 89 weight per cent tungsten carbide and 11 weight per cent cobalt. This type of cemented carbide has a compressive strength of 4.6 GPa (4 600 000 000 N/m2) and therefore it was possible to take the pressure increase from ambient to the 2.2 GPa present in the high pressure chamber in one step. To ensure that the compressed lubricant did not leak past the compression plungers, “soft seals” made of hardened tool steel were placed at the top of the plungers. Less strong steels were also tested as seal material, but these were extruded out from the high pressure volume along the plungers and caused the plungers to stick and the tested lubricant to leak out. The shear strength measurements were performed at different temperatures from room temperature to 200 “C, and the pressure needed to compress the lubricant into the solid state increased strongly with increasing temperature. For most of the lubricants the shear strength increase for a pressure increase in the solid state gave similar values at the different temperatures. This was not true for the traction fluid which lost a large part of the traction at high temperatures. The behaviour of the lubricants at high temperatures showed that the increase in solidification pressure caused by an increase in temperature was governed by the thermal expansion of the oil and the extra pressure needed to compress the oil back to the same solidification density it had at a lower temperature.
6
1.10
CHAPTER 1. INTRODUCTION TO THE BOOK
Lubricant compressibility
At low pressures the compressibility of lubricating oils is very high. If the same bulk modulus (the inverse of the compressibility) as at ambient pressure was maintained at high pressures, normal elastohydrodynamic pressures in rolling element bearings should compress the lubricant down to zero volume. In reality the bulk modulus of a lubricant increases steeply with increasing compression, so that at pressures above the solidification pressure the bulk modulus is about ten times larger than at ambient pressure. The total compression of normal lubricating oils at elastohydrodynamic pressures is in the order of 20 to 35 per cent. When a lubricating oil is compressed by a hard elastohydrodynamic contact, the viscosity increases strongly, and when the lubricant is compressed above the glass transition pressure an amorphous structure is frozen into the oil and the oil molecules can no longer move freely. The transition from liquid to solid behaviour at different temperatures seems to be a simple function of the compression and the thermal expansion, as stated earlier. The solidification pressure and the compressibility of the lubricant are needed as input data if the oil film thickness and pressure distribution are going to be calculated using the solidification theory. To be able to verify the calculated values experimentally, direct measurements of the oil film thickness are needed.
1.11
Interferometry film thickness measurement
There are a number of different ways to measure oil film thicknesses in elastohydrodynamically lubricated contacts, but by far the most elegant is to use interferometry. The first interferometry measurements of oil film thicknesses in elastohydrodynamic lubrication were published by Cameron and Gohar in the mid-l960’s, and the method has been used extensively since then by many authors of technical papers. The first experiments were performed using a glass disc as the transparent medium. This made it possible t o investigate contacts with maximum Hertzian pressures up to about 0.7 GPa. At higher pressures thin chips started to flake off from the surface of the hardened glass disc and the surface finish was destroyed. Later, both Cameron and other authors used sapphire (AlzOs) discs to reach higher contact pressures, up to about 2 GPa. At these high pressures and loads the elastic energy stored in the sapphire is considerable. This leads to a catastrophic type of failure, where the sapphire surface does not flake off when the load is too high but the whole sapphire explodes into small sharp splinters. This happened a couple of times in the Lulel laboratory. A number of different bearing arrangements for the lubricated ball were used in different laboratories. Cameron used V-shaped rollers under the ball, while the author used the ball in a tube geometry. The ball was placed in a tube, having a diametral clearance of 25 pm, and the lubricating oil was pumped in under the ball giving both the load and the bearing arrangement for the ball. During these experiments the paradox of the ball in the tube was discovered. It was found that the hydrodynamic forces acting on the ball in the tube were strongly influenced by rather small variations of the location of the cavitation boundary formed between the ball and the tube. These small variations made the ball-tube-lubricant system work as a spring, driving the ball backwards when it was suddenly stopped during rotation. This backwards spring action lasted for about a quarter of a rotation of the ball until the cavitation boundary around the ball had redistributed evenly around it. Then the ball moved to a position in the
1.12. FILM THICKNESS AT COMBINED ROLLING AND SLlDING
7
centre of the tube and the rotation was stopped. In the interferometry experiments, having the ball-tube geometry, the ball was driven by the traction forces in the oil film. This limited the test apparatus to pure rolling. To be able to study traction and the influence of sliding speeds on the oil film build-up the two lubricated surfaces had to be driven separately.
1.12
Film thickness at combined rolling and sliding
One of the sapphire disc apparatuses built at LuleH Technical University had another bearing arrangement for the ball, which made it possible to drive each one of the surfaces separately. This made it possible to study the oil film build-up at pure rolling, pure sliding or any combination in between. These experiments showed that the simple Reynolds equation, where only the sum of the surface velocities is included in the analysis, does not completely describe the oil film thickness build-up in heavily loaded elastohydrodynamic contacts. The oil film thickness in the most heavily loaded central part of the contact decreased strongly compared to the film thickness in the side lobes, giving a much more even oil film thickness across the contact than for pure rolling. The same phenomenon also has a big influence on the lubricant film if a transverse vibration induces sideways sliding in the contact.
1.13
Transverse sliding
By adding an arrangement with a hammer to the ball-in-the-tube system, it was possible to induce high frequency sideways vibrations perpendicular to the rolling velocity. These sliding motions were very small, only a fraction of the size of the Hertzian contact. If the oil had been Newtonian in the high pressure contact, this small sideways motion would not have had any influence on the oil film thickness and pressure build-up. By using two different optical techniques it was possible to show that the oil film pressure build-up at the inlet of the contact was more or less destroyed by the sideways sliding. Both the interferometry measurements and the shadowgraph technique used a high speed flash unit with a flash duration down to 18 ns. This very short flash duration made it possible to take sharp pictures of the highly dynamic events, even through a large amplification microscope. During the time a normal photo flash is lit (0.001 s) the light travels 300 km, but it has only time to go 5 m during the flash time of 18 ns (0.000 000 018 s). The influence of slight sideways sliding shows that the non-Newtonian behaviour has a big influence on the oil film build-up when the pressure gradients, and thereby the shear stresses induced by the pressure distribution, are large. This is the main reason why surface roughness asperities cannot be lubricated using micro-EHL if the surface slopes and the asperity heights are too large. The local pressure spikes caused by the surface roughness give high local pressure gradients and thereby high shear stresses in the oil at the same time as the local asperity pressure is high enough to compress the oil into the solid state. This means that a sliding distance of only a fraction of the surface roughness wavelength during the contact time is enough to stop the micro-EHL mechanism from working. The oil film built up by the main
8
CHAPTER 1. INTRODUCTION TO THE BOOK
contact must then be so thick that the full height asperities cannot reach each other through the oil film and cause damage. This type of non-Newtonian behaviour is only present in lubricants when the shear stress is large compared to the local shear strength of the lubricant. For soft elastohydrodynamic contacts, like rubber on steel, mineral oils seem to behave like Newtonian liquids. Due to the much softer surfaces the shear stress in the lubricant is low and the oil film thickness built up is therefore much larger than for a hard EHL contact. This, combined with the fact that soft rubber materials do not reflect light very well, makes it very difficult to use interferometry techniques to measure the lubricant film thickness in soft lubricated contacts. One way to measure the film thickness, though, is to use laser induced fluorescence.
1.14
The blue laser technique
Many lubricant molecules show fluorescence. When they are hit by light of a certain wavelength, the light is absorbed and light of another frequency (colour) is emitted. For mineral oils one possible light source to use is an He-Cd laser which has a blue light. When this light is absorbed by an oil molecule, the emitted light is green. The intensity of the emitted light is proportional to the amount of oil and a function of the intensity of the incoming light beam. This can be utilized as a measurement signal for the amount of oil present. The method has been used for tracing oil spills on water, but the first time it was used for quantitative measurements was when hydraulic rubber seals were studied. The different oil film thickness measurement techniques described so far gave accurate information about the oil film. The time scales of the experiments were similar to the time scales in real lubrication applications, i.e., the lubricant was stressed to the same stress level within the same compression time as in real applications. For the high pressure chamber experiments this was not true. The compression time there was lo4 to 10' times longer than in a typical EHL contact, where the lubricant is compressed and decompressed during overrolling within to seconds. To see if the compression time had any significant influence on the solidification and shear strength of the solidified lubricant, dynamic experiments were performed.
1.15
The jumping ball apparatus
The idea behind the jumping ball apparatus was to obtain a tool to measure the behaviour of lubricants under pressure, when the compression time was of the same order as in a normal elastohydrodynamic contact and the pressure at least as high as in a Hertzian contact of a rolling element bearing. To make sure that the properties measured using the test apparatus were the properties of the lubricated system and not a function of any dry friction in the system, the measurement surfaces had to be completely separated by the tested lubricant. The simplest and most obvious way to do this was to compress the oil using a squeeze film motion between two nonconforming surfaces. The shear strength of the oil had to be measured during the very short compression time. The experiments in the Lulet high pressure chamber had shown that the shear strength of solidified oils increased linearly with pressure. It was also well known that
1.16. COMPUTERIZED JUMPING BALL APPARATUS
9
the flow properties of liquids became more like the flow properties of solids when the stress time decreased below the relaxation time of the liquid. All this made it natural to choose the geometry of a ball impacting a smooth flat lubricated surface. By not having a perpendicular impact between the ball and the flat surface, the shear force in the oil film and at the surface of the ball could be analysed by studying the rotational acceleration of the ball. In the first jumping ball apparatus, the time integral of the rotational acceleration, the rotational speed, was analysed by mechanical means, using a small cart as landing place for the ball after the impact had made it bounce up into the air and rotate. Later a fully computerized version of the jumping ball apparatus was built.
1.16
Computerized jumping ball apparatus
Instead of using the mechanical cart for the analysis of the motion of the ball, a computeraided picture analysis system and a high speed video camera were used. The principle of the lubricated impact was also changed. In the mechanical cart apparatus the sliding speed between the ball and the impacted surface decreased to zero at the end of the impact. In the picture analysis apparatus it was arranged to have sliding speed left at the end of the impact to ensure that the shear stress in the oil was equal to the shear strength. The main advantages of the computerized jumping ball apparatus compared to the mechanical jumping ball apparatus was the repeatability and the shorter testing time. To analyse one oil at one temperature using the mechanical jumping ball apparatus took typically one working day. The computerized apparatus gives a measured 'value within a few seconds and could analyse a lubricant at different temperatures to give statistically valid results in a matter of hours. These lubricant parameters can now be used in elastohydrodynamic calculations both to determine the limit of Newtonian lubrication and to see what happens to the lubrication when sliding speeds are increased above the limit of Newtonian behaviour.
1.17
The Newtonian elastohydrodynamic problem
If the increase in viscosity and the compressibility of the lubricant at high pressures are taken into account, as well as the elastic deformation of the bearing surfaces, the EHL problem can be solved. If unlimited shear stresses are allowed in the oil film, the Newtonian behaviour of the oil will give pressure distributions and oil film thicknesses which are independent of the sliding speed, and only dependent on the entrainment velocity (the sum of the surface velocities). A major problem in the numerical solution of the Newtonian elastohydrodynamic calculations is the numerical instability. The EHL problem is very ill conditioned. For heavy loads and low oil film thicknesses, the elastic deformation of the surfaces can be many hundred times larger than the oil film thickness. This means that an error in the pressure distribution of one per cent gives an error in the deformation af about one per cent, and hence an error in the oil film thickness as large as the whole oil film thickness. If this estimate of the oil film thickness is then used to calculate the local pressure in an iterative solution scheme, the errors can grow without bounds and the calculations fail to converge. Similar type instabilities are also seen in non-Newtonian calculations.
10
1.18
CHAPTER 1. INTRODUCTION TO T H E BOOK
Non-Newtonian fluid model
If the shear stress in the oil exceeds the shear strength of the oil or of the oil-bearing-interface, slip will occur. For isothermal conditions the slip will always take place at the metal surface, because the shear stress is highest there. In more lightly loaded high speed sliding contacts, the temperature increase in the middle of the oil film will locally reduce the shear strength of the oil or transform it into liquid behaviour, giving a local slip surface somewhere in the middle of the oil film. In the analysis in chapter 18 the lubrication is assumed to be isothermal, so the slip planes will always be located at one of the bearing surfaces, but if other assumptions are made about the lubricant parameters, other pressure and shear stress distributions will result from the calculations.
1.19
Pitting and micropitting
If the shear stresses acting on the lubricated surface are large enough, the maximum stress according to all stress criteria will be present very close to and just under the surface. The same is also true if local micro-contacts or indentations from particles are carrying part of the load. The local micro-Hertzian pressure fields have their maximum shear stress close to the surface, in proportion to the size of the asperity compared to the size of the Hertzian contact. These high stresses close to the surface have a detrimental influence on the bearing life and cause small pieces of bearing material to break loose from the surfaces. Just as overrolling of contaminant particles causes the surface quality to deteriorate, so does micropitting destroy the surfaces and prevent them from being separated by a continuous oil film.
1.20
Mixed lubrication
If a Newtonian model is used to describe the lubricant behaviour, breakdown of the lubricant film can never be explained. If the lubricant film becomes too thin at any point Reynolds’ equation will predict very high pressures which then elastically deform the surface in such a way that the surfaces never touch each other. This is obviously not true for hard elastohydrodynamic contacts. What happens is that the shear stresses in the lubricant reach the shear strength, and the oil is no longer dragged along the surfaces straight into the contact. The oil loses its grip on the surface and slides down into the valleys between surface asperities. This makes it possible for the tops of the surface asperities to break through the oil film and make contact with the opposite surface. This non-Newtonian behaviour of the lubricant is influenced by a number of properties of the elastohydrodynamic contact. It is strongly influenced by the surface roughness, and seems to be especially sensitive to the surface slopes and to the wavelength of the surface asperities. It is strongly dependent on the local oil film pressure and the solidification properties of the lubricant. It is also strongly dependent on the elastic properties of the contacting surfaces. The analysis so far, except for a few words in 1.19, has covered clean lubricants. Filters for oil circulation systems, if they are used at all, normally allow much larger particles to pass than can be accommodated in the oil film without damaging the lubricated surfaces.
1.21. LUBRICANT CONTAMINATION
11
1.21 Lubricant contamination Recent research has shown that particulate contamination damages lubricated surfaces if the particle size is larger than the oil film thickness and the particles are hard. Depending on the relative hardness and toughness of the contaminant particles, different sizes can be accommodated in the oil film without resulting in plastic deformation of the lubricated surfaces. Very hard and tough particles, like aluminium oxide, as small in size as the calculated oil film thickness may cause wear damage of the surfaces. On the other hand, very soft particles like plastic can cause permanent indentation of the bearing surfaces if the particles are larger than 50-100 pm. In both cases the bearing life will be reduced considerably. The most difficult part of this research is that people are so used to having very dirty lubrication systems that they are not aware of the detrimental effects. They think it is natural for a machine to wear out and equally natural for the lubricant to contain all the wear particles. For bearing applications run in clean lubricants, the load can be kept just under the threshold for gross plastic flow and still the bearings will not fail. The improvement in life for a clean system compared to a heavily contaminated system can be more than a factor of 500 for lightly loaded applications. In the clean system all material stresses are well within the elastic limit, but in the contaminated system new indentations are formed by the overrolled particles for every revolution of the machine. This inevitably leads to premature failure. Even if the damage created by the overrolled paricles is not allowed to accumulate over time because the particles are removed either by changing the oil or by installing a fine filter, the life of the damaged surfaces will be short.
1.22
Influence of residual and static stresses
Experimental investigations of the influence of superimposed tensile stresses on the endurance stress limit show that the endurance stress limit decreases by about 30 per cent of the hydrostatic tensile stress in the material. This means that hoop stresses in inner rings of bearings and residual stresses caused by plastic flow around particle indentations not only increase the local stress, but at the same time decrease the endurance stress limit of the bearing steel. This can give an extremely large reduction in life of the bearings, but knowledge about the guiding mechanism can teach us how to circumvent the problem. One possible way is to build compressive stresses into the material influenced by the Hertzian stress field.
1.23
Overview of the different parameters
From knowledge of the main elastohydrodynamic parameters and their numerical values it is possible to predict the overall behaviour of EHL contacts. The viscosity at ambient pressure multiplied by the viscosity-pressure coefficient gives a good indication of the entrainment speed needed to obtain a certain oil film thickness. Both the viscosity and the viscosity-pressure coefficient have to be of a reasonably large size to make it possible to separate the stressed machine elements from each other with a lubricant film. A typical case when this is not possible is lubrication using water-based hydraulic fluids. Even if the fluids are thickened to have high viscosities at atmospheric pressure, the very low viscosity increase for a pressure increase gives a very thin lubricant film. The product viscosity times
12
CHAPTER 1 . INTRODUCTION TO THE BOOK
the viscosity-pressure coefficient has to be of a certain size to make hard elastohydrodynamic lubrication possible. For soft elastohydrodynamic lubrication it is only necessary to have a certain viscosity because there the pressures are so low that no important viscosity increase takes place. To obtain information about the traction properties of an elastohydrodynamic contact, the viscosity-pressure coefficient multiplied by the maximum Hertzian pressure in the contact can be used. If this product is larger than about 12-15 the sliding velocity needed to reach nonNewtonian behaviour is low, and the local shear strength of the lubricant has to be taken into account. The shear strength of the lubricant is a function of the molecular structure, but only weakly dependent on molecule size. Elastic molecules, having a large free volume, need higher pressures for a given temperature to solidify compared to stiff compact molecules. At the same time it seems as if the compact molecules, when they are solidified by the pressure, increase their shear strength faster with a pressure increase than the more elastic molecules. This leads to high friction for contacts lubricated with oils like naphthenic extracts which have these stiff molecules. The viscosity-pressure coefficient, a,by itself has a large influence on the theoretically predicted pressure spike at the outlet of the elastohydrodynamic contact. High a-values give a high pressure spike and thereby induce high stresses in the bearing just below the surface. If these local stresses become large enough, either because of the properties of the lubricant or overrolling of contaminant particles or surface asperities, micropitting can occur. Besides the properties of the oil, the properties of the surfaces are also important. Surface roughness slopes, wavelengths, heights, radii of curvature and direction of patterns all contribute to the behaviour of lubrication, the ability to run in and the endurance life of the surfaces. The size of the Hertzian contact compared to the size of grinding and honing marks, that is, the number of asperities within the contact also influences the asperity collapse.