External coefficient of friction

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. 

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. 

A typical plot of external coefficient of friction versus temperature at various pressures is shown in Fig. 6.4(a). 

If the transport of particulate polymer occurs by plug flow, then the only frictional coefficient of importance is the external coefficient of friction. This condition is usu-... 

The particle shape can generally be established by simple visual observation or by using a microscope. The transport characteristics of particulate solids are quite sensitive to the particle shape. Both the internal and external coefficient of friction can change substantially with variations in particle shape even if the major particle dimensions remain unchanged. Small differences in the pelletizing process can cause major problems in a downstream extrusion process. Variations in the ratio of regrind to virgin polymer can cause variations in the extrusion process. 

Important bulk properties are bulk density, compressibility, internal coefficient of friction, external coefficient of friction, particle size and particle size distribution, and particle shape and particle shape distribution. 

The internal coefficient of friction is the friction between the plastic particles themselves. The external coefficient of friction is the friction between the plastic particles and another surface, such as the barrel surface. For efficient conveying in the feed hopper, it is required that both the internal and external frictions should be low. For efficient conve5ung along the extruder screw, it is required that the barrel friction to be high and the screw friction should be low this is discussed later. 

The first recorded systematic studies on static friction have been carried out by Leonardo da Vinci.1 He had already stated that friction does not depend on the contact area and that doubling the weight doubles the friction. The most important empirical law found for describing friction was published in 1699 by Guillaume Amontons.2 Like da Vinci he measured the force Ff required to slide a body over a solid surface at a given load Fp (Fig. 11.1). The load is usually the weight of the body but it can also contain an additional external force pushing the body down. Amonton found that the frictional force is proportional to the load and does not depend on the contact area. For example, in Fig. 11.1 the loads F[ = Fp are equal, then the frictional forces are also equal Fp = Fp. In other words the coefficient of friction p defined by... 

Macroemulsions remain on the external surface of fabrics. They achieve an excellent lubrication through the decrease of the dynamic coefficient of friction (see below). An excellent softness results. 

Polymer emulsions (150 to 250 nm) deposit on the external surface of fabrics and on fibers. They improve the softness and the ease of ironing since they reduce both static and dynamic coefficients of friction. 

Processing aids to assist material flow during extrusion or injection molding. The internal and external lubricants are recognized. Internally lubricated resins use oils. Teflon , M0S2, or other materials to give the molded part a lower coefficient of friction. The external lubricant can be a sohd, such as sodium or zinc stearate, a fluoropolymer, or silicone resin or liquid. 

If the detaching force is directed perpendicular to the surface, 3 = 1 and Fdet ad the force is directed tangential to the surface, /3 = 0 and F et Fff. The friction of adherent particles in the absence of any external load is caused by adhesion Fg. = /xFgd (where [x is the coefficient of friction). Then, with p = 0,we find that F et Fad -... 

The frictional behaviour of polymers differs somewhat from that of perhaps more familiar materials. The frictional force tends to be proportional not to load (as in the classical case) but to speed. The coefficient of friction is very dependent on the nature of the two surfaces in contact, but is generally low, when suitable pairs are selected. This means that plastics gears can usually be run without external lubricants. Often the static friction coefficient is lower than the dynamic, which helps to explain the absence of slip-stick phenomenon exhibited by some plastics systems in motion this is especially marked with PTFE, which has an exceptionally low coefficient (around 0.02). The non-classical response of plastics materials results from their much lower modulus. Their frictional response is characterized by adhesion and deformation. 

Equation 7.85 allows the calculation of the optimum barrel helix angle if the screw geometry is known and if the various coefficients of friction, internal and external, are known as well. The solution for the optimum helix angle is not completely analytical because Aj contains a term that is dependent on the barrel helix angle. This can be solved by initially guessing a value of Wb, then calculating cpj according to Eq. 7.85. The Wb can be calculated with ... 

The performance of an extruder is determined as much by the characteristics of the feedstock as it is by the machine. Feedstock properties that affect the extrusion process inciude buik properties, meit flow properties, and thermal properties. Important buik flow properties are the buik density, compressibility, particle size, particle shape, external and internal coefficient of friction, and agglomeration tendency. Important melt flow properties are the shear and eiongational viscosity as a function of strain rate and temperature. The commonly used melt indexer provides only limited information on the meit viscosity. Important thermal properties include the specific heat, the glass transition temperature, the crystalline melting point, the latent heat of fusion, the thermal conductivity, the density, the degradation temperature, and the induction time as a function of temperature. 

Be Strain measured (by a strain gage) on the external surface of the hub in the tangential direction fJ-A Axial static coefficient of friction... 

With these complications in mind, research in this area has blossomed rapidly. Two main foci of research in this area are on (1) how external conditions (such as levels of loadings, the use of different indenters, and scratch rate) and (2) intrinsic materials properties (such as modulus and crystallinity) affect the tribological behaviors of the polymers. Apart from examining the scratch resistance of polymers, a closely related quantity which is of interest would be changes in coefficient of friction. Studies relating mechanical properties (3-5,9,36,71,75,76), deformation patterns (18,33,63,71,77-81), fabrication process (3,5,35,72,77,82-86) with respect to experimental parameters, snch as temperature (18), loading effect (24,71,72,87-96), indenter geometry (21,33,75,82,95,97), and scratch velocity (21,56,57,59,64,65,96,98) have been carried ont. In addition, scratch maps for different polymers have been produced (32,33), and various scratch resistance properties estimated (33,37,56,58,59,99). 

Particles of various shapes (particulates and fibers) are produced to be used as additives for many polymers. " Incorporation of polytetrafluoroethylene has little influence on the mechanical properties of the host polymer, but substantial impact on its surface properties and coefficient of friction. Polytetrafluoroethylene is also used as mold coating. Polytetrafluoroethylene-coated molds have excellent release properties, and permit production without external or internal release agents. 

Figure 8 Basic coefficient of friction and wear behaviour at different externally applied tribological stress levels...

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