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**Surface roughness and its effects in tribology**

1st BioTiNet Workshop Surface roughness and its effects in tribology Mitjan Kalin, Janez Kogovšek University of Ljubljana, Faculty of Mechanical Engineering Centre for Tribology and Technical Diagnostics October 25, 2011

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**Tribological surfaces**

Surfaces and surface roughness (engineering perspective): meaning, measuring surface roughness, characterization of surfaces roughness, real contact area, plasticity index. Friction: basic concepts, dependence on surface properties. In this couple of days you are able to hear a lot about the importance of interactions between interfaces and about properties and characterization of materials, a lot of it from perhaps a little more chemical aspects. In this presentation, I will talk about surfaces and surface rougnes from the mechanical or engineering perspective. I will explain what surface roughness is, how it is measured and how the acquired data is processed in order to characterize the surfaces with different parameters. I will explain how that correlates to contact area and plasticity index, which are both important for the behaviour of material pair in contact. Then, I will present some basic concepts behind friction and how it depends on the interaction between the surfaces and their properties. 2

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**Form (ideal geometrical shape)**

Surface properties Engineering surfaces never have an ideal geometrical shape, but instead include different deviations. With regards to the level of approximation they can be considered: • smooth and even, • smooth and wavy, • rough and even, • rough and wavy. Roughness Waviness Form (ideal geometrical shape) If we take a surface of any object that we encounter in everyday life and look at it in detail, we can observe that this surface never has an ideal geometrical shape. Instead, it includes different deviations from that ideal shape. And depending on what we want to do with that object or surface, we can make a different degree of simplifications but in reality instead of being smooth and even, surfaces are actually rough and wavy. And all that is a part of the surface topography. Waviness can be considered as relatively large deviation from the ideal shape, for example due to inaccuracy of the manufacturing process, and roughness is a consequence of deviations on a smaller scale, for example because of the nature of the machining process, such as grinding or polishing – obviously, they are ensuring more or less rough surfaces. Surface topography 3

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**Errors of form What is „rough“? An objective “measure” is required.**

Micro-geometrical deviations – roughness (important for interaction of surfaces) Macro-geometrical deviations – waviness What is „rough“? Tolerances Height of a realistic surface Diameter of a point contatc EHD film thickness Single-layer fatty acids Natural oxide thickness Oxygen molecule diameter Engineering components Surface roughness So roughness and waviness can be considered as micro- and macro-geometrical errors of form. The roughenss is the one, that has a greater importance when it comes to interactions between surfaces. But how rough exactly is rough? What are the dimensions we are referring to? On this lenght scale dimensions of some important engineering phenomena are presented. And surface roughness, at least the one that is important in engineering surfaces, ranges between 10 nanometres and 100 micrometres. That are the dimensions that correspond to several phenomena that are more or less directly connected to surface roughness. However, that does not tell us, what is, so to say, “rough”. For that, we need some objective measures. An objective “measure” is required. 4

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**Surface roughness measurement methods**

1. Stylus instruments Electromotor Amplifier A/D converter PC Chart recorder LVDT Sample Stylus tip And to get these objective measures, we first need to be able to characterize the surface – we need to measure the surface rougness with specific methods and tools. One of the most commonly used tools for that task are stylus instruments. That are so called profilometers, which are based on a principle with which we drag a sharp stylus or a tip, if you like, over the surface. 5

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**Stylus with greater sensitivity**

1. Profilometer 2D The resolution depends on the stylus tip and the velocity of scanning. Z = 10 nm X = f (v, f) This is shown here. We get a profile of a single line scan of the surface, so the method actually gives us two-dimensional data, however, several profiles can also be measured or scanned next to each other to give us a basic idea of the actual surface topography. The benefits of this method are that it is cheap and relatively robust, but on the other hand, the resolution is not the best. For the most part it depends on the stylus tip – meaning the sharper the tip, the better the resolution or accuracy – and it also depends on the velocity of scanning. Standard stylus Stylus with greater sensitivity 6

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**Output for the microprocessor**

2. Optical interferometer Surface Aperture stop Reference surface Microscope objective Eye Output for the microprocessor Detector (photodiode) Light source Spectral filter Beam splitter 3D The resolution depends on optics and light wavelength. Z < 1 nm Y = f (λ; nm) Another method for measuring surface rougness is by optical inferometery that is increasingly gaining on popularity. It uses the wave nature of the light by observing interference between a measuring light beam and a reference light beam. In general it enables you to get an actual 3-dimensional image with a better resolution. The resolution of course depends on the optics of the device and on the wavelength of light – lights with different wavelengths and even combination of lights can be used. 7

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**3. Atomic Force Microscope (AFM, 1986)**

Cantilever (spring) Laser diode Position sensitive light detector Laser beam Tip Sample Another recently developed tool for surface characterization is an atomic force microscope. It’s similar to stylus measuring techniques, only on a smaller scale. It uses a very sharp tip to scan over the surface and detect very small forces. That’s where the name is coming from. The movement of the tip is then detected through the deflections of the cantilever which are monitored by an optical lever. The atomic force microscope can be operated in different modes to characterize mechanical, frictional, chemical, or electrical properties of the surfaces. It is a high-resolution measurement tool and its resolution depends on the tip sharpness, optical and electro-mechanical components and also on the scanning or measuring parameters. Nanotubes 3D The resolution depends on the laser, scanner, feedback loop, software, probe (tip)… Z < 0,007 nm, XY = 0,1 nm 8

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**Analysis of the measured surface roughness parameters**

(LT = LV + LM = LV + 5 x LV) Basic element: surface profile. Traversing length is denoted with LT and represents the distance that is traversed across the surface by the stylus when characterizing the surface, i.e. measurement length. Planing (wood): 2,5-25 mm Milling, drilling: 0,8-8 mm Turning: 0,8-2,5 mm Grinding: 0,25-2,5 mm Honing, lapping: 0,25 mm Assessment length LM is the length over which surface data is acquired and assessed. So to get the desired objective measures once the data has been aquired we need to analyse it – that means we need to transalte that data to surface roughness parameters. The basic element for the analysis is a profile of the surface. For the measurements and analysis three lengths of that profile are important. The first one is a mesurement or traversing length – that is the length that a stylus or a tip has scanned over. Because of the border-line conditions the assessment length over which the data is then actually analysed is a bit shorter. This assesment length is then commonly divided into smaller sections, of equal length – that is a sampling or reference length. The analysis procedure is standardized so that also all of this lengths have to be chosen appropriately by which macro-geometrical deviations should be excluded from the measurement. Sampling length (reference length) is denoted by LV. It is a length of a section inside the assessment length and it is equivalent to wavelength of the filter, λC (it distinguishes the roughness from the waviness). Standardized: important to choose the correct reference length and assessment length, so that the macro-geometrical deviations are excluded from the measurement. 9

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**Mean line of the profile, m**

Mean line of the profile is denoted by m. It is a line with a shape of geometrical profile (perfect geometric line) and it runs parallel to that profile. The mean line of the profile is determined so that the sum of squared deviations from this line is the smallest. ...or otherwise: Surface area above and below the mean line of the profile is the same! z x Mean line . We then start the analysis by determining the mean line of the profile. It has an ideal geometrical shape – for example it’s perfectly straight or ideally circular. And it is determined so, that the sum of squared deviations from this line is the smallest – it is the arithmetic mean of the profile. That basically means that if we draw the mean line on the profile, the surface areas below and above this line are the same. The mean line is a starting point for further examination. L = LV Mean line z x 10

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**Arithmetical mean deviation, Ra**

The most widely recognized and used parameter for surface rougness characterization. Ra is arithmetical mean deviation of all the measured values in the assesed profile (LM) from the mean line of that profile. m LM = L Mean line The arithmetical mean deviation, denoted by R-a is the most widely recognized and the most commonly used parameter for surface roughness characterization. It is an arithmetical mean deviation of all of the measured values from the mean line within the assessed length of the profile. So the R-a paramater tells us what is the average value of the absolute deviation from the mean line. 11

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**Arithmetical mean deviation of the assessed profile, Ra**

Averaging of data: Ra does not differentiate between profile peaks and valleys !! Ra or any other parameter by itself: not sufficient. Additional parameters necessary: more sensitive & able to distinguish between surfaces with different shapes and/or ratios of peaks and valleys. But because it is based on averaging of data, the R-a parameter does not differentiate between profile peaks and valleys. This is why R-a or any other parameter by itself is not sufficient for surface roughness characterization. We can see from the picture on the right that surfaces can be very differently structured but still have very similar if not the same R-a value. From this position, it is necessary to introduce additional parameters, which will be more sensitive and will be able to distinguish between surfaces with different shapes and ratios of peaks and valleys. 12

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**Root mean square deviation of the assessed roughness profile, s = Rq (m=0)**

In statistics: standard deviation, s - not only for surfaces Good bearing surface Mean line Bad bearing surface Another popular surface parameter is a root mean square deviation of the assessed roughness profile and it is denoted by R-q. It is a standard deviation of the profile from the mean line. We can see that the surfaces in the picture have the same R-a value, but different value of the R-q parameter. So, the R-q parameter is more sensitive to different shapes and distributions of valleys and peaks, but it still doesn‘t distinguish one from another, because it is still based on averaging of values. Rq: - more sensitive to different shapes and distributions of valleys and peaks, - it still does not distinguish one from another, - also based on averaging of values. In general, parameter Rq has a slightly higher value than parameter Ra (10-25 %). 13

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**Amplitude density function p(z)**

Amplitude density function (= probability distribution of surface heights) is denoted by p(z); Its value is proportional to probability, that a point of the surface profile exists at a certain height – z. (proportion of individual heights of the profile) A “tool” for further mathematical evaluation of surface roughness. The next important property is the amplitude density function. That is a probability distribution of surface heights. So it doesn’t tell us how surface peaks are spatially distributed but it tells us what is the proportion of individual heights of the profile. The amplitude density function gives us a tool for further mathematical evaluation of surface roughness. 14

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**Skewness, Sk – measure of asymmetry of p(z)**

Peaks and valleys are distributed symmetrically in relation to mean line: => p(z) is symmetrical in relation to m. Peaks and valleys are distributed asymmetrically in relation to mean line: => p(z) is asymmetrical in relation to m – it is shifted “higer” or “lower”. Surfaces with the same Ra and Rq can have a different Sk. Z = positive (Sk = negative) +z -z p(z) profile One of the parameters that can be derived from the amplitude density function is a Skewness parameter. It tells us how symetrically the peaks and valleys are distributed in relation to the mean line. If they are distributed symetrically, like for Gaussian distribution for example, the value of Skewness parameter is zero. If there are more peaks than valleys, the Skewness is negative, and vice versa – if there are more valleys, Skewness is positive. Accordingly, this parameter already gives us some idea of the shape of the surface. For Gaussian distribution: Sk = 0. 15

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**Kurtosis K – measure of flatness of p(z)**

Kurtosis K – tells us how high or how flat the p(z) is. p(z) z A paramater called Kurtosis tells us how flat the amplitude densitiy function is. For Gaussian distribution the value of Kurtosis is 3. If we have flat peaks and valleys, the amplitude density function is flat and the Kurtosis is lower than 3. And if we have very sharp, pointy peaks and valleys, the Kurtosis is higher than 3. For Gaussian distribution: Kurtosis = 3. Flat peaks and valleys: K < 3. Sharp peaks and valleys: K > 3. 16

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**Portion of the surface that will carry the load at certain height.**

Which of the two surfaces has a greater load-bearing capacity? cumulative distribution function 100 [%] z Portion of the surface that will carry the load at certain height. This is important in determining which surface has a greater load-bearing capacity. We can see that the left surface has a lot sharper peaks and they will probably be broken. So the right, flatter surface will be able to carry the load more effectively with less deformation. 17

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**Measurement scale and slope of the peaks**

Measurement scale of a profile, e.g. acquired with a stylus profilometer: M 50:1 Inclination of peaks and valleys: At this point I have to explain about the scale of the profiles. The 2-dimensional profiles, that you see as a result of profile measurements, have a highly magnified height or z-axis, so that the measurement scale is around 50-to-1. This is because we need to be able to draw a profile graph on a limited space with a high enough resolution to, so to say, actually see the roughness. But in reality, the peaks and valleys aren’t nearly as sharp as presented in these diagrams. If we would draw a profile line in 1-to-1 ratio, like on the bottom image, we would be able to see, that the inclination of the peaks is only around 5 to 20 degrees. 5 o – 20 o 18

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Real contact area Atomic level Macro-scale Micro-scale This, however, does not change the fact that when two surfaces come into contact, the contact area is not what it seems. If we looked at the contact between a block and a surface on a microscopic level we could see that only several peaks of the surfaces are in contact. On an even smaller scale the contact area is even further decreased. The real contact area is therefore a sum of these discrete contacts. The question is, what proportion of the nominal contact area is then actually included in the real contact area. What proportion of the nominal contact area is actually included in the real contact area? 19

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**1% A nom Real contact area pr = F/Ar**

the real contact pressure is significantly larger than the nominal contact pressure conditions on the contact peaks are completely different from our „anticipations“. In example such as this, the real contact area can be as small as 1 % of the apparent contact area. In general, the real contact area is estimated to 1 to 10 % (or sometimes to maximum of 30 %) of the nominal contact area in the most typical engineering cases. That is why also the real contact pressure is significantly larger than the nominal contact pressure. And consequently, also the conditions on the contact peaks are completely different and more severe than we would anticipate. A real = 1-10 % (20, 30 %) of the nominal contact area – in the most typical engineering cases. Diameter of a single peak contact: d = 1-50 µm. 20

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**Determination of the real contact area**

Difficult to determine – for usage in “models”. (Sometimes the value is measured/determined but is not valid in general...) Calculations – assumptions! - Asperities are randomly distributed, are of different sizes (height, width), asperities in interactions with each other get changed in very short time intervals (position), asperities are constantly modified by wear, wear particles influence the real contact area. Mesurement methods: - static (replica...); are not valid for dynamic contacts, contact resistance, pressure sensor (materials with a known phase transformation), contacts cannot be seen (closed); visible contacts (sapphire) are not valid in general. To know the size of the real contact area would be very useful – for example in simulations, calculations and general understanding about the conditions in the contatc. But the real contact area is very difficult to determine and can usually only be estimated… at least to some degree. Calculations of the real contact area are often based on several assumptions that might not correspond to the actual conditions, which are constantly changing in a dynamic contact. There are also some measurement methods, however, they too ofer only limited accuracy. 21

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**Plasticity index Determination of plastic deformation of asperities:**

E*… Young‘s modulus, H... hardness of the softer material, r… radius of asperities, s = SD = RMS = Rq. ... plasticity index. ψ < 0, – most of the asperities are deformed elastically; plastic deformation occurs only under high contact pressures, ψ > 1, – most of the asperities will be plastically deformed already under low contact pressures, 0,6 < ψ < 1 – intermediate area. One of the reasons, why the real contact area is difficult to determine is also because different surfaces and materials deform in different ways. Plasticity index is a parameter that helps us understand when asperities are plastically and when elastically deformed. With low plasticity index, the asperities will mostly experience elastic deformations and with high plasticity index the asperities will for the most part get plastically deformed. The plasticity index itself is related to the mechanical properties of the material, like Young‘s modulus and hardness, but it is also inseparably related to surface roughnes. Deformation mode of the contact is inseparably related to the surface roughness and material properties (hardness)! 22

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**Relation between plasticity index and surface roughness**

Contact pressure Surface roughness Plasticity index finely polished coarsely polished average metallurgically polished finely grinded coarsely grinded elastic area plastic area This example chart applies to metals. We can see from this graph that when we have a high Young’s modulus to hardness ratio, like with steel, we will have a high plasticity index and we will have to lower either the surface roughness – make surfaces smoother – or lower the contact pressure, to stay within the area of elastic deformations. But just lowering the contatc pressure is still not sufficient if we have very rough surfaces, so we can say, that only finely polished surfaces will remain in the elastic area. If the ratio of Young’s modulus to hardness is low, as is the case with ceramics, then the majority of contatcs will be deformed elastically even at a slightly higher surface roughness. High E*/H ratio (e.g. for steel) – high plasticity index: If we want to be in the elastic area, we have to lower either surface roughness – or contact pressure (at significantly higher surface roughness it is not sufficient!). Only finely polished surfaces will remain in the elastic area (all other surfaces will be in the plastic area). Low E*/H ratio (e.g. ceramics): In this case the majority of the contacts will be elastic even at slightly higher surface roughness. 23

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**Surface roughness & friction?**

All that also has an influence on friction… and we will take a look at some basic concepts related to this phenomena. 24

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What is friction? Friction force or friction: a resisting force encountered by one body moving over another = resistance to movement in tangential direction of the contact. Work to overcome friction = energy „loss“: transferred to the surroundings as heat, friction forces in a tribological contact: desired minimal; e. g. modern internal combustion engine: ~15-20 % of the energy is lost (useless heating of components). Exceptions (friction of key importance): tires on the road, brakes, clutches… In long-term: the influence of friction even more detrimental: wear of components: higher friction – greater wear (but not always!), increased contact temperature; effects on material properties, direct mechanical influences (replacement of worn-out components, costs of delays, repairing, maintenance and replacement of machinery). Friction force Friction force or friction is a resisting force which is encountered by one body moving over another. It is a resistance to movement in the tangential direction in the contact. The work required to overcome friction is considered as energy „loss“ and it is for the most part transferred to the surroundings as heat. For this reason it is desired for the friction forces in a tribological contact to be minimal. In a modern internal combustion engine, for example, approximately % of the energy is lost due to useless heating of components. There are, however, several exceptions, where friction is of key importance for the functioning of a mechanical system, for example with tires on the road, brakes, clutches… and not last, with walking… In addition to these direct effects the influence of friction can be even more detrimental when we are looking at the system in a long-term, since it is very often accompanied by wear of components. Higher friction is almost always related to greater wear, both due to accompanying increased temperature and consequent effects on material properties, as well as due to direct mechanical influences (=> worn-out components need to be replaced, there are costs related to delays, repairing, maintenance and replacement of machinery). 25

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**First “rules” – laws of friction**

(1) 1st Amonton‘s law: friction force F between a pair of surfaces is directly proportional to the normal load W (Figure a, b). The constant that gives the proportionality between the normal and tangential force, is generally known as coefficient of friction . (2) 2nd Amonton‘s law: friction force F is independent of the nominal (apparent) contact area (Figure a, c). This arises from the fact that the real contact area, Ar, is proportional to the normal load W and independent of the nominal contact area! (3) Coulomb‘s law of friction: coefficient of friction is independent of sliding velocity once the movement is established. Once the contact temperatures must be accounted for, it becomes increasingly less accurate (tribofilms, reactions…). You are all probably familiar with the basic laws of friction. The first Amonton’s law of friction states that a friction force between a pair of surfaces that are sliding against each other under a certain load, is directly proportional to that normal load. The second Amonton‘s law states that a friction force between a pair of surfaces that are sliding against each other is independent of the nominal or apparent contact area. It therefore makes no difference whether we are sliding a block, for example, on its smaller or larger side – the same pulling force will be required in both cases (Figure a, c). This is because the real contact area is only proportional to the normal load and independent of the nominal contact area! And a third law is also commonly added to the previous two: the Coulomb’s law of friction states that the coefficient of friction is independent of sliding velocity once the movement has been established. 26

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**Understanding friction**

depends on physical (chemical) properties of shearing of surfaces: formation and type of bonds between surfaces and on the manner these bonds are broken. depends on mechanical properties of the contact surface: on the deformation – it depends on roughness, hardness, elasticity, toughness, collapse mode of material. But the phenomenon of friction is actually not as simple as that. Here is the general equation to calculate the friction coefficient as the ratio between the tangential force and the normal load. The tangential force further depends on the shear strength of the material, which depends on physical and chemical properties. And the tangential force also depends on the real contact area, which is further related to the mechanical properties of the contact surface, among others also to the surface roughness! The value of friction coefficient is therefore not only related to the material pair in contact, but also to the physical conditions of sliding! So we can say that an universal model for friction, which is obviously not constant, doesn‘t exist! The value of friction coefficient: related to the material pair in contact (supposedly constant for each material pair), but also to the physical conditions of sliding! Universal model for friction (not constant) does not exist! 27

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**Mechanisms (causes) of friction**

I. Proportion of friction due to adhesion Finite number of contact points (real contact area), contact stress significantly larger than the nominal value of the contact pressure, atoms of one surface may come very close to the atoms of the other surface, strong bonds can be formed (electron exchange). Adhesion cannot take place because the bodies are too far away from each other. Now, let’s look at what are the mechanisms or causes of friction. The first proportion that contributes to friction is adhesion. Namely, because of a final number of contact points, the contact stress in the asperities is significantly larger than the nominal value. Because of that, the atoms of the surfaces can come close enough to form strong bonds that need to be sheared if we want to have any tangential movement. So, if we want to separate the adhered surfaces, we have to pull or tear them apart with large enough force. This is very pronounced with ductile and soft materials like copper or with noble metals that don’t form stable oxide layers. An additional explanation lies in a theory called Junction growth. Shearing of these connections to get tangential motion (tearing/pulling bodies apart), pronounced with ductile and soft materials (copper) or noble metals (don’t form stable oxide layers) Additional explanation: Junction growth. 28

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**contact increase due to action**

Junction growth Single asperity contacts: in a region of plastic deformation (high contact pressure), easily additionally deformed (tangential force due to sliding), material flows – it „fills“ all the valleys and peaks, increase in the real contact area, larger adhesive connections, greater tangential force required to break these connections, higher coefficient of friction. asperity length of contact shear forces contact increase due to action of shear forces In this theory, we have single asperity contacts that are already in a region of plastic deformation due to high contact pressure. Such asperities can be easily additionally deformed under the influence of tangential force so that the material flows. That means that the real contact area can be significantly increased because the material „fills“ all the surface valleys and peaks. And because the contact area increases, there is an increased area or possibility for the adhesive connections to form. In consequece, that means that a greater tangential force must be applied to the material before the adhesive connections are broken – this is of course evident in a higher COF. The tangential force and the real contact area in this case will be increasing as long as the maximum shear strength of the material isn’t reached. Tangential force and real contact area will be increasing as long as the maximum shear strength of material is not reached. 29

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**II. Proportion of friction due to abrasion**

Surfaces after sliding interaction: abrasion scars, (direction of the scars indicates sliding direction). Result of „scratching“of harder particle; energy losses contibute to the total friction loss. The second contribution to friction is due to abrasion. When we are observing two surfaces after sliding, we can almost always notice abrasion scars on at least one of the surfaces – the direction of the scars also indicates the sliding direction. This plastic deformation is a result of „scratching“ of a harder particle, which keeps moving despite any „obsticles”, like softer material, in its way. The energy losses, which result in this process, are contibuting to the total friction loss. The actual particles or asperities included in this process usually have a complex shape. However, to understand their influences on friction, the geometry of the particles can be simplified, so that only two border-line cases can be considered: very sharp conical particles and perfectly spherical particles. Particles or asperities have a complex shape: the geometry of the particles can be simplified, two extreme cases: sharp conical particles and spherical particles. 30

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**II. Proportion of friction due to abrasion**

Sharp, conical particles: COF only depends on slope (not height), surface asperities, slope is small (≈ 10 °), => COF is small (< 0.1). Spherical particles: COF depends on radius and penetration depth, contribution to COF can be high (> 0.2), correlated to wear particles, particles from surroundings, filtering to eliminate them. For sharp conical particles the coefficient of friction only depends on the slope of the particle and not on its height. These conical particles are usually connected with the surface asperities. Therefore, the slope of these particles is rather small, around 10 ° and their contribution to friction is also small – usually below 0.1. With spherical particles, the friction coefficient depends on their radius and how deep they are pressed into the surface. In this case the contribution to friction can be quite high, often above 0.2. These spherical particles are correlated to wear particles and particles that enter into the contact from the surroudings. So to avoid the additional friction, caused by these particles, we try to exclude them from the system by using a filter. 31

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**III. Proportion of friction due to deformation of asperities**

Coefficient of friction depends on: slope of asperities, engagement angle of asperities, angle of deformation of material. a = q slope of asperities attack angle of asperities Coefficient of friction due to deformation of asperities is indicated to be very high ( )! High COF values similar to static friction! it is likely that most deformations occur before the beginning of sliding. The third main contribution to friction is a proportion of friction due to deformation of asperities. Investigations showed that in this case the contribution to friction depends on the slope of asperities, the angle at which asperities are engaged in the contact and also on the angle at which the material finally deforms. The contribution to friction by this mechanism can be very high, easily over 0.4 or even more depending on the conditions. This high values of coefficient of friction are very similar to the values of static friction. So it is likely, that most of these deformations occur before the beginning of sliding. 32

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**Thank you for attention!**

Summary Surface topography includes roughness, wavines and form. Surface roughness is measured by profilometry, optical interferometry, AFM. Some of the main parameters for characterization are: Ra, Rq, Rz, Sk, K, tp. Surface roughness has influence on the real contact area and type of surface deformation (elastic/plastic – plasticity index). Surface roughness influences all of the main causes of friction: adhesion, abrasion, deformation of asperities. There are also some other contribution to friction but we can see, that all three of the main causes of friction are more or less directly connected to the shape of the surface features and therefore to the surface roughness. I hope, I have explained in this presentation how the surface roughness is measured, how it is characterized and how it correlates to friction mechanisms. If not, I can answer some questions and at the end, I would like to thank you for your attention. Thank you for attention! 33

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