Friction, coefficient of

The coefficient of friction of the bulk material is another very important property. One can distinguish both internal and external coefficient of friction. The internal coefficient of friction is a measure of the resistance present when one layer of particles slides over another layer of particles of the same material. The external coefH-cient of friction is a measure of the resistance present at an interface between the polymeric particles and a wall of a different material of construction. The coefficient of friction is simply the ratio of the shear stress at the interface to the normal stress at the interface. Friction itself is the tangential resistance offered to the sliding of one solid over another. 

In discussing the coefficient of friction, one has to specify whether it is a static or dynamic coefficient of friction. The static coefficient of friction, f, is determined by 

Measurement of the external coefficient of friction of particulate polymers is very difficult because of the very large number of variables that influence the coefficient of friction. Many investigators have made elaborate measurements on the external coefficient of friction [24-32]. The result of this work is that many variables have been identified that affect the frictional behavior however, most measurement techniques do not yield accurate and reproducible results that can be used in the analysis of the extrusion process. The most elaborate measurements and the most meaningful results have probably been obtained at the DKl in Darmstadt, Germany [95]. It is possible to obtain reproducible results by very careful experimental techniques and special surface preparation of the metal wall. However, the frictional coefficients determined in this fashion are hardly representative of the frictional process conditions occurring in an extruder. 

Some of the variables that affect the coefficient of friction are temperature, sliding speed, contact pressure, metal surface conditions, particle size of polymer, degree of compaction, time, relative humidity, polymer hardness, etc. 

The coefficient of friction is very sensitive to the condition of the metal surface. The coefficient of friction of a polymer against an entirely clean metal surface is very low initially, as low as 0.05 or less. However, after the polymer has been sliding on the surface for some time, the coefficient of friction will increase substantially and may stabilize at a value about an order of magnitude higher than the initial value. This behavior was described in detail by Schneider [24, 25] for a variety of polymers. This effect is attributed to the transfer of polymer to the metal surface. Instead of 

The coefficient of friction of polyurethanes has been found to be similar to that of rubbers. The coefficient is the resistance to sliding or rolling of the surfaces of two bodies in contact with each other. It has been found that the softer the material, the higher the coefficient of friction. The values vary from 0.2 for the harder grades to approximately 3 for the softer grades. This is thought to be due to the higher actual area of contact between the elastomer and the second surface. A hard material under moderate loads will not deform and follow the surface profile of the second material. The coefficient of friction reaches a maximum at approximately 60°C. 

Laboratory tests must be taken only as a general guide. In practice, surface cleanliness and lubrication by dust, moisture and oil traces will greatly affect the actual friction properties. 

The speed of friction will increase the coefficient slightly as it increases. The coefficient of friction will reduce over the course of time when the material is under load. It is thought that this may be due to the development of abrasive debris. 

As the coefficient of friction can be reduced by the use of a lubricant, it is generally beneficial to use a suitable oil or grease when required. The addition of a modifier to the prepolymer itself must be done with care, as the material will reduce the overall properties including aging and may influence the bond ability of the material. Additives that have been employed in this application include molybdenum disulfide, graphite, and silicone oil. They must be used at the lowest level possible. 

This is an assessment of the coefficient of friction of material in terms of dynamic (sliding) friction against steel. It should be remembered that friction is influenced by temperature, surface contamination and most importantly by the two material surfaces. An excellent rating indicates a low coefficient of friction (see Table 5.1). A very poor rating indicates a high coefficient of friction. 

Miyata and Yamaoka [26] used scanning probe microscopy (SPM) to determine the micro-scale friction force of a silicone-treated polymer film surface. PU acrylates cured by an electron beam were used as the polymer films. The micro-scale friction force obtained by SPM was compared with macro-scale data, such as surface free energy determined by the Owens-Wendt method and the macro-scale friction coefficient determined by the ASTM D1894 method [27]. These comparisons showed that a good linear relationship existed between the surface free energy and the friction force, which was insensitive to the nature of the polymer specimens or to the silicone 

Zsidai and co-workers [29] reported results of a series of test carried out to determine the friction properties of engineering plastics by the measurement of small and large test specimens on a steel and diamond-like carbon coating surface. The objective was to compare the friction properties of a surface provided with a diamond-like carbon coating with measurements obtained on a steel surface as a function of the engineering plastic used, and to examine the practical possibilities of the diamond-like coating. The plastics tested included PA, polyacetals and PET/PTFE. 

Taylor and Pollet [30] reported the results of a study of friction between fabrics used for clothes, including cotton, wool, polyester fibre and acrylic fibre, and aluminium, Formica and rubber under zero or low applied normal forces. The effects of various factors, such as surface roughness, directionality, nature of table surface, pressure and velocity, on frictional force are discussed and an empirical law proposed to model the dependence of friction on velocity. 

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The coefficient of friction /x between two solids is defined as F/W, where F denotes the frictional force and W is the load or force normal to the surfaces, as illustrated in Fig. XII-1. There is a very simple law concerning the coefficient of friction /x, which is amazingly well obeyed. This law, known as Amontons law, states that /x is independent of the apparent area of contact it means that, as shown in the figure, with the same load W the frictional forces will be the same for a small sliding block as for a laige one. A corollary is that /x is independent of load. Thus if IVi = W2, then Fi = F2. 

The basic law of friction has been known for some time. Amontons was, in fact, preceded by Leonardo da Vinci, whose notebook illustrates with sketches that the coefficient of friction is independent of the apparent area of contact (see Refs. 2 and 3). It is only relatively recently, however, that the probably correct explanation has become generally accepted. 

Another point in connection with Eq. XII-5 is that both the yielding and the shear will involve mainly the softer material, so that li is given by a ratio of properties of the same substance. This ratio should be nearly independent of the nature of the metal itself since s and P tend to vary together in agreement with the observation that for most frictional situations, the coefficient of friction lies between about O.S and 1.0. Also, temperature should not have much effect on n, as is observed. 

The coefficient of friction may also depend on the relative velocity of the two surfaces. This will, for example, affect the local temperature, the extent... 

In the absence of skidding, the coefficient of static friction applies at each instant, the portion of the tire that is in contact with the pavement has zero velocity. Rolling tire friction is more of the type discussed in Section XII-2E. If, however, skidding occurs, then since rubber is the softer material, the coefficient of friction as given by Eq. XII-5 is determined mainly by the properties of the rubber used and will be nearly the same for various types of pavement. Actual values of p, turn out to be about unity. 

Thus if Amontons law is obeyed, the initial velocity is determined entirely by the coefficient of friction and the length of the skid marks. The mass of the vehicle is not involved, neither is the size or width of the tire treads, nor how hard the brakes were applied, so long as the application is sufficient to maintain skidding. 

The situation is complicated, however, because some of the drag on a skidding tire is due to the elastic hysteresis effect discussed in Section XII-2E. That is, asperities in the road surface produce a traveling depression in the tire with energy loss due to imperfect elasticity of the tire material. In fact, tires made of high-elastic hysteresis material will tend to show superior skid resistance and coefficient of friction. 

As might be expected, this simple picture does not hold perfectly. The coefficient of friction tends to increase with increasing velocity and also is smaller if the pavement is wet [14]. On a wet road, /x may be as small as 0.2, and, in fact, one of the principal reasons for patterning the tread and sides of the tire is to prevent the confinement of a water layer between the tire and the road surface. Similarly, the texture of the road surface is important to the wet friction behavior. Properly applied, however, measurements of skid length provide a conservative estimate of the speed of the vehicle when the brakes are first applied, and it has become a routine matter for data of this kind to be obtained at the scene of a serious accident. 

The coefficient of friction between two unlubricated solids is generally in the range of 0.5-1.0, and it has therefore been a matter of considerable interest that very low values, around 0.03, pertain to objects sliding on ice or snow. The first explanation, proposed by Reynolds in 1901, was that the local pressure caused melting, so that a thin film of water was present. Qualitatively, this explanation is supported by the observation that the coefficient of friction rises rapidly as the remperarure falls, especially below about -10°C, if the sliding speed is small. Moreover, there is little doubt that formation of a water film is actually involved [3,4]. 

Another indication of the probable incorrectness of the pressure melting explanation is that the variation of the coefficient of friction with temperature for ice is much the same for other solids, such as solid krypton and carbon dioxide [16] and benzophenone and nitrobenzene [4]. In these cases the density of the solid is greater than that of the liquid, so the drop in as the melting point is approached cannot be due to pressure melting. 

A number of substances such as graphite, talc, and molybdenum disulfide have sheetlike crystal structures, and it might be supposed that the shear strength along such layers would be small and hence the coefficient of friction. It is true... 

The structurally similar molybdenum disulfide also has a low coefficient of friction, but now not increased in vacuum [2,30]. The interlayer forces are, however, much weaker than for graphite, and the mechanism of friction may be different. With molecularly smooth mica surfaces, the coefficient of friction is very dependent on load and may rise to extremely high values at small loads [4] at normal loads and in the presence of air, n drops to a near normal level. 

A number of friction studies have been carried out on organic polymers in recent years. Coefficients of friction are for the most part in the normal range, with values about as expected from Eq. XII-5. The detailed results show some serious complications, however. First, n is very dependent on load, as illustrated in Fig. XlI-5, for a copolymer of hexafluoroethylene and hexafluoropropylene [31], and evidently the area of contact is determined more by elastic than by plastic deformation. The difference between static and kinetic coefficients of friction was attributed to transfer of an oriented film of polymer to the steel rider during sliding and to low adhesion between this film and the polymer surface. Tetrafluoroethylene (Telfon) has a low coefficient of friction, around 0.1, and in a detailed study, this lower coefficient and other differences were attributed to the rather smooth molecular profile of the Teflon molecule [32]. 

Fig. XIl-5. Coefficient of friction of steel sliding on hexafluoropropylene as a function of load (first traverse). Velocity 0.01 cm/sec 25°C. (From Ref. 31.)...

Finally, if the sliding surfaces are in contact with an electrolyte solution, an analysis indicates that the coefficient of friction should depend on the applied potential [41]. 

TWo limiting conditions exist where lubrication is used. In the first case, the oil film is thick enough so that the surface regions are essentially independent of each other, and the coefficient of friction depends on the hydrodynamic properties, especially the viscosity, of the oil. Amontons law is not involved in this situation, nor is the specific nature of the solid surfaces. 

As load is increased and relative speed is decreased, the film between the two surfaces becomes thinner, and increasing contact occurs between the surface regions. The coefficient of friction rises from the very low values possible for fluid friction to some value that usually is less than that for unlubricated surfaces. This type of lubrication, that is, where the nature of the surface region is... 

The lubricating properties of tears are an important feature in normal blinking. Kalachandra and Shah measured the coefficient of friction of ophthalmic solutions (artificial tears) on polymer surfaces and found no correlation with viscosity, surface tension or contact angle [58]. The coefficient of friction appears to depend on the structure of the polymer surfaces and decreases with increasing load and sliding speed. 

Hardy s explanation that the small coefficients of friction observed under boundary lubrication conditions were due to the reduction in the force fields between the surfaces as a result of adsorbed films is undoubtedly correct in a general way. The explanation leaves much to be desired, however, and it is of interest to consider more detailed proposals as to the mechanism of boundary lubrication. 

The coefficient of friction for copper on copper is about 0.9. Assuming that asperities or junctions can be represented by cones of base and height each about 5 x 10" cm, and taking the yield pressure of copper to be 30 kg/mm, calculate the local temperature that should be produced. Suppose the frictional heat to be confined to the asperity, and take the sliding speed to be 10 cm/sec and the load to be 20 kg. 

Calculate the angle of repose for a solid block on an inclined plane if the coefficient of friction is 0.52. 

The reported apparent viscosity is 200 poise. Estimate the coefficient of friction that corresponds to these data. Discuss any assumptions and approximations. 

Thus, under conditions of plastic defonnation the real area of contact is proportional to the nonnal force. If the shear force during sliding is proportional to that area, one has the condition that the shear force is proportional to the nonnal force, thus leading to the definition of a coefficient of friction. 

Tetralluoroethylene polymer has the lowest coefficient of friction of any solid. It has remarkable chemical resistance and a very low brittleness temperature ( — 100°C). Its dielectric constant and loss factor are low and stable across a broad temperature and frequency range. Its impact strength is high. 

It resembles polytetrafiuoroethylene and fiuorinated ethylene propylene in its chemical resistance, electrical properties, and coefficient of friction. Its strength, hardness, and wear resistance are about equal to the former plastic and superior to that of the latter at temperatures above 150°C. 

Dry Lubricant. The static and dynamic coefficients of friction for the parylenes are low and virtually the same. This feature is an advantage in the use of a parylene coating as a dry lubricant on the bearing surfaces of miniature stepping motors. Coating a threaded ferrite core significantly reduces the abrasion to coil forms (82). 

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