KINETIC FRICTION TROUGH SURFACE MICRO ANALYSIS

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International Journal of Metallurgical & Materials Science and Engineering (IJMMSE) ISSN 2278-2516 Vol. 3, Issue 1, Mar 2013, 31-36 TJPRC Pvt. Ltd.

1 International Journal of Metallurgical & Materials Science and Engineering (IJMMSE) ISSN Vol. 3, Issue 1, Mar 2013, TJPRC Pvt. Ltd. KINETIC FRICTION TROUGH SURFACE MICRO ANALYSIS NIKOLA AVRAMOV & PETAR SIMONOVSKI Ss. Cyril and Methodius University, Faculty of Mechanical Engineering, Skopje, Macedonia ABSTRACT This paper gives an in-depth study of a kinetic friction trough micro analysis of a surface topography. Both of the surfaces are identical or taken as samples from same part, with no difference in the grain structure or in the material properties and with same surface structure. For overcoming the influence that can arise as a result of the different topography this factor is neglected by using two identical surfaces. In this paper are elaborated different conditions that have influence on the magnitude of the frictional force created between the examined surfaces. The situations that are examined are metal-metal and metal-rubber-metal type of contact and the ratio of the sliding energy absorbed by changing the surface roughness. Considering the diversity in the surface topography and no existing pattern that can be used for the same group of surfaces, the one used is micro segment of randomly used metal surface. One of the approaches for examining area with high irregularities is dividing the length of the surface to infinite small portions and approximation that the asperities contour is even by this portion width. The size of the section observed is 100 micrometers length, 3 micrometers width and changing the height of the surface asperities. For the analysis no additional normal load is applied as a clamping force between the surfaces. KEYWORDS: Surface Topography, Asperities, Roughness, Sliding Energy, Friction Force INTRODUCTION When two surfaces come into contact, in this case one is stable or stands still and the other is the closing part. Both of the surfaces behaviour is investigated trough infinite small segment of the part surface area, or surface patch. Portion of the kinetic energy is transferred in surface friction or temperature increase and asperity deformation and the energy of the closing will be absorbed only by this patch of the stable part. The total kinetic energy carried by the moving part is represented by the examined part segment as well. The asperities deformation and temperature increase will lower the total energy carried by the part. Figure 1: Different Surface Topographies [1]

2 32 Nikola Avramov & Petar Simonovski INFLUENCE OF THE TYPE OF CONTACT BETWEEN THE SURFACES Metal-Metal Contact This kind of contact is the contact between two metal parts. The model consists of two micro-surfaces and is modelled in the finite element code LS-DYNA using 8-node solid elements. The brick elements are fully integrated. The bottom surface corresponds to the base or floor and it is constrained in all directions. The material characteristics used for both the surfaces in contact are steel designated as S355JR (according to EN steel designation). The parameter that we are interested in and the main objective of this manuscript is the contact force generated between the surfaces or the sliding energy. There is no clear representation about the kinetic friction and its change in time duration contrary to the static friction for which we now that is steady-state or time independent and equals Metal-Rubber-Metal F µ = µ This contact type is for example rubber seal between metal flange to flange contacts. Non-linear elasticity exists in many models describing the hyper elastic behaviour of materials like rubber. These models are available in many commercial finite element codes like LS-Dyna. The explicit method requires small time increment to produce accurate results. This is due to the fact that the responses vary with time and the durations are very small. [2] Fn Figure 2: Rubber Seal without and with Normal Load Applied It is then assumed that static friction occurs between a rubber solid and a counter surface when there is no relative motion. To accelerate the rubber solid, the static friction needs to be overcome and when the two solids are in relative motion to each other, the kinetic friction prevails. It is usually assumed that µ static > µ dynamic. The different energy dissipation mechanisms discussed below require information about the area of real contact, the size of the contact spots and the elastic deformations. Measuring the friction of rubber-like materials, it is observed that the coefficient of friction increases with the sliding velocity until a maximum is reached, after which it decreases again. Generally, friction is a function of the sliding velocity. There are at least four different contributions to rubber friction: adhesion, hysteresis, viscous damping and cohesion. [3] RESULTS AND DISCUSSIONS Stress Relationship Trough micro analysis opposing surface asperities come in contact with each other and the contact patch is explained as the sum of the closing areas of those asperities. By introducing normal force on the moving surface, the contact patch increases as a result of the asperity deformation. Because of the difficulty to measure the asperity in contact or the real contact, in most of the analysis the contact patch is presented as the surface area, this is the case of total asperity deformation by the normal force and the ideal alignment of the surfaces. In our model there is no initial contact between the surfaces because of the initial penetration that can occur but for the time duration the offending asperities come in contact. On Figure 3. and Figure 4. are presented colour plots of the stress conditions.

3 Kinetic Friction Trough Surface Micro Analysis 33 From the fringe levels on the figures presented we can see that higher stress dissipation have the surfaces from the metal-metal contact. This state arises because of the contact between two stiff surfaces and each deformation means higher force generation. The asperities deformation is plastic shown as reached yield stress or the highest fringe level. At the metal-rubber-metal contact the rubber elasticity damps the kinetic energy carried by the moving surface, trough elastic deformation of the rubber seal. On the fringe plot we can see that the yield stress is reached but only by particular asperities. Figure 4. presents the metal to rubber sliding contact together with the stress levels and the position of the most stressed points. We can see that at the same time state the metal to metal surfaces are far more subjected to frictional forces than metal to rubber contacts. The presented low stresses at the second plot come from the elasticity of the rubber seal. The kinetic energy is dissipated trough elastic deformation of the rubber and less of the energy remains for the sliding friction between the surfaces. Figure 3: Stress Distribution of a Metal-Metal Contact Figure 4: Stress Distribution of a Metal-Rubber-Metal Contact INFLUENCE OF THE SURFACE ROUGHNESS Surface Asperity Normal Distribution Each asperity peak can be seen as a randomly distributed point around a mean line. In this paper statistical analysis are preformed on the points coordinates defining the height of the surfaces asperities. These points are then numerically evaluated and a Gaussian curve or a normal distribution curve is presented.

4 34 Nikola Avramov & Petar Simonovski 2 1 x µ σ f ( x, µ, σ ) = e (1) σ 2π From eq. (1) can be seen that the normal distribution function is dependant of the asperity height, denoted as x in the equation, mean value and the standard deviation around the mean value. The standard deviation further away from the mean line means that the asperities are higher or the distance from the mean line is greater. That is the case of a surface with higher roughness. One of the today s approaches for evaluating surface roughness is using the amplitude height of its asperities. The only reason for that approach is the fact that there is no existing particular pattern of a surface topography. For in-depth studies this is mistaken because the surface edge is not sinusoidal and not only peaks with the stated amplitude are involved in the contact between the surfaces. In this paper are presented different surface roughness trough normal distribution and two parameters, one is the mean value and the other is the standard deviation around the mean. The main reason for analyzing surface roughness trough normal distribution instead of using amplitude height of the asperities is for bringing closer the surface topography. The standard deviation can be the one used in the further calculations considering the surface roughness not only for this example but in general as well. Figure 5: Gaussian Curve for Different Surface Roughness Three Gaussian curves are plotted for different surface topographies, varying the height of the surface asperities buy the factor of k=2 for the same surface patch. The referenced is named median, one with twice the size of the median is coarse, and the one with lower asperity is named fine. The calculation of the standard deviation is the result of the squared root of average of the sum of the differences between the peak asperities and the mean powered by two, shown at eq.(2). Standard deviation is directly proportional to the differences between the peak asperities and the mean. This difference is larger for course surfaces compared to the others, seen at the wider area below the curve line. 1 N 2 σ = ( x i µ ) (2) N i= 1

Kinetic Friction Trough Surface Micro Analysis 35 The surface topography is drawn using commercialized CAD software and it is divided by a number of points.

5 Kinetic Friction Trough Surface Micro Analysis 35 The surface topography is drawn using commercialized CAD software and it is divided by a number of points. These points are then imported in MATLAB and the statistical analysis is preformed. For calculating the Gaussian curves the functions used are: load surface.txt; y=surface(:,2); mean=sum(y)/length(y); sigma=std(y); fy=1/(sigma*sqrt(2*pi))*exp((-1/2)*((y-mean)/sigma).^2) plot(y,fy); Sliding Energy for Different Surface Roughness After understanding the surface topography trough analysis of the asperity points normal distribution, the influence of the surface topography is studied by increasing and decreasing the asperity height by the factor of k=2. The surface edge sample is the same for all of the examined cases but properly scaled maintaining the same surface length. The influence of the roughness is presented by the amount of sliding energy dissipated between the surfaces. Figure 6: Model of a Fine, Median and Coarse Surface Roughness Figure 7: Sliding Energy for Different Surface Roughness From Figure 7. we can see the change in the sliding energy between surface samples in contact for different surface roughness. The sliding energy is represented as the contact energy between the surfaces and is proportional to the frictional force and the distance past. The highest sliding energy occurs between the surfaces with coarse roughness, which comes by knowing that more energy is needed for deformation of higher asperities than the rest. The refraction of the

6 36 Nikola Avramov & Petar Simonovski sliding energy lines show the time spent between the next asperities to come into contact with the previous one. The smoothness of the line corresponding to the fine surface roughness shows that the time between two adjacent asperities to come into contact is small so there is low time increment between the next asperities to make a contact with the previous ones. The interesting fact to note is that surface designated as fine has higher sliding energy compared to the median one. One of the possible explanations can be the length of the asperities in contact. Two main factors to consider when analyzing the friction force between surfaces are the surface asperities height and the asperities in contact or new variable is introduced loc (length of contact). These parameters are subject for future evaluation. CONCLUSIONS This paper focused on developing methods for surface contact assessment trough microanalysis of a surface topography. The evaluation at first consisted of examining different types of materials in contact like metal-to-metal and metal-rubber-metal. After knowing the type of contact affect, the surface roughness influence on the sliding energy was also analysed. From the presented we can say that: The stress levels arising at the surfaces from metal contacts are much higher compared to those with the rubber between. The condition happens because of the surface asperities being directly subjected to impact from the closing asperities. The kinetic energy from the moving part is being absorbed by the elasticity of the rubber element if present between, and less remains for asperity deformation. Considering static friction, better situation is having supplementary element in between for increasing the friction coefficient with constant normal force. For dynamic friction with same friction coefficient the contact forces will be lower for metal-rubber contact. By using rubber element between surfaces we have influence on increasing only the frictional coefficient but not the frictional forces, this statement can be better understood by using same coefficient with and without rubber element between, like the one explained in this paper. Instead of considering the surface edge as a sinusoidal function and using the amplitude of that function for further calculation, normal distribution of the surface points around a mean line can be utilized for evaluation of the surface roughness or the standard deviation as a substitute for the amplitude value. From the surface roughness evaluation can be seen that the sliding energy is highest for coarse surfaces, which is due to the surface deformation. Interesting to note is that fine surfaces have higher contact force than median one, which happens because of the bigger amount of the asperities in contact. REFERENCES 1. H. Ramasawmy, L. Blunt (2002), 3D surface topography assessment of the effect of different electrolytes during electrochemical polishing of EDM surfaces 2. Oscar J., Centeno G. (2009), Finite element modeling of rubber bushing for crash simulation, Experimental tests and validation 3. Valentin L. Popov (2010), Contact Mechanics and Friction, Physical Principles and Applications 4. Boris Lorenz (2012), Contact Mechanics and Friction of Elastic Solids on Hard and Rough Substrates 5. ASM Handbook (1992), Friction, lubrication and wear technology, Volume 18

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