Static friction defined

For a monolayer film, the stress-strain curve from Eqs. (103) and (106) is plotted in Fig. 15. For small shear strains (or stress) the stress-strain curve is linear (Hookean limit). At larger strains the stress-strain curve is increasingly nonlinear, eventually reaching a maximum stress at the yield point defined by = dT Id oLx x) = 0 or equivalently by c (q x4) = 0- The stress = where is the (experimentally accessible) static friction force [138]. By plotting T /Tlx versus o-x/o x shear-stress curves for various loads T x can be mapped onto a universal master curve irrespective of the number of strata [148]. Thus, for stresses (or strains) lower than those at the yield point the substrate sticks to the confined film while it can slip across the surface of the film otherwise so that the yield point separates the sticking from the slipping regime. By comparison with Eq. (106) it is also clear that at the yield point oo. 

The frictional properties of plastics are of particular importance to applications in machine products and in sliding applications such as belting and structural units such as sliding doors. The range of friction properties are rather extensive. The relationship between the normal force and the friction force is used to define the coefficient of static friction. 

Fig. 32—Static friction and creep in an atomic system the creep distance is defined as the maximum value of (Xq-x), inserted panel shows the variation of iaterai force.

So far we have compared the static friction with the stick-slip transition. In both cases the system has to choose between the states of rest and motion, depending on which one is more favorable to the energy minimization. On the other hand, the differences between the two processes deserve a discussion, too. In stick-slip, when the moving surface slides in an average velocity V, there is a characteristic time, t =d.Ql V, that defines how long the two surfaces can... 

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... 

Classical, macroscopic devices to measure friction forces under well-defined loads are called tribometers. To determine the dynamic friction coefficient, the most direct experiment is to slide one surface over the other using a defined load and measure the required drag force. Static friction coefficients can be measured by inclined plane tribometers, where the inclination angle of a plane is increased until a block on top of it starts to slide. There are numerous types of tribometers. One of the most common configurations is the pin-on-disk tribometer (Fig. 11.6). In the pin-on-disk tribometer, friction is measured between a pin and a rotating disk. The end of the pin can be flat or spherical. The load on the pin is controlled. The pin is mounted on a stiff lever and the friction force is determined by measuring the deflection of the lever. Wear coefficients can be calculated from the volume of material lost from the pin during the experiment. 

The friction coefficient can be measured in two ways the static friction coefficient Qus) and the dynamic or kinetic friction coefficient (fikX The static friction coefficient is defined as the ratio of the force required to initiate relative movement and the normal force between the surfaces the dynamic or kinetic friction coefficient is defined as the ratio of the friction force to the normal force when the two surfaces are moving relative to each other. For simplicity, much of the research has focused on the dynamic friction coefficients wherein the two surfaces move at a relative constant velocity. Most of the friction studies on skin have dealt with the dynamic friction coefficient and the subscript k is usually dropped. This overview references the dynamic coefficient of friction unless otherwise noted. 

Figures 322(a) and (b) show again the conditions in a pelleting machine with concave die. Figure 322(a) depicts the mechanisms of compression and extrusion in the work area , the material volume wedged in between the press roller and die. Figure 322 explains the phenomena. Feed deposited in a layer on the die is pulled into the space between the roller and die and compressed. Neither the roll force nor the force from the die resisting extrusion (flow) are constant. The roll force increases with progressing densification while the flow-resisting force remains constant until a threshold pressure, defined by the static friction in the die holes, is surpassed. After extrusion (movement in the die holes) has started, both the resisting and the roll forces decrease.

Two types of friction are commonly measured and calculated. The static friction Fj is defined as the minimum lateral force needed to initiate sliding of one object over a second, while the kinetic friction Fk v) is the force needed to maintain sliding at a steady velocity v. Observation of static friction implies that the contacting solids have locked into a local free-energy minimum, and Fj represents the force needed to lift them out of this minimum. It is a threshold rather than an actual force acting on the system, and it limits lateral motion in any direction. No work is done by the static friction, since no motion occurs. The kinetic friction is intrinsically related to dissipation mechanisms, and it equals the work done on the system by external forces divided by the distance moved. 

Since the static friction is the force that is necessary to start sliding, it depends on the state of the system. Therefore static friction is not uniquely defined for Vq > Vq However, one can introduce the force that gives an upper limit for the actual static friction. It is defined as the smallest force above which there exists no stable state. 

N (7-6) where is the negative of the tangential force required to keep the slider moving at constant velocity. Equation 7-6 is a formal statement defining the coefficient of kinetic friction and also the expression of a phenomenological fact. Its counterpart for the coefficient of static friction is... 

In fact, the situation is more complex. If wear takes place, then energy is used in breaking up the surfaces, but this appears in the measurement as work done against friction and the figure obtained for the eoeffieient of friction is enhanced. This type of ambiguity makes it difficult not only to measure friction but also to define what it is we are measuring. A good example of this is so-called static friction. 

Static friction is sometimes defined as the force needed to start the motion between two surfaces. It is clear, however, that if a shear force is applied to two contacting surfaces and no motion takes place it may be because the surfaces arc adhering and thus it is neccs.sarv to distinguish between friction and adhesion. A car licence holder on a windscreen illustratc.s the dilemma perfectly. There is a very strong resistance to shear, but is this entirely due to friction ... 

If static friction is defined as the force needed to establish motion between two surfaces. then experimentally it is not possible to di.stingiii.sh between. stiction. or adhesion, and friction. In some circumstances this may be an appropriate measurement, but it is important to realize that a wide range of values may be obtained, since the result depends on the time available to establish adhesion. 

The relationship between the normal force and the friction force is used to define the coefficient of static friction. Coefficient of fiiction is the ratio of the force that is required to start the fiiction motion of one surface against another to the force acting perpendicular to the two surfaces in contact. Friction coefficients will vary for a particular plastic from the value just as motion starts to the value it attains in motion. The coefficient depends on the surface of the material, whether rough or smooth. These variations and others make it necessary to do careful testing for an application that relies on the fiiction characteristics of plastics. Once the fiiction characteristics are defined, however, they are stable for a particular material fabricated in a prescribed method. 

Fig. 7-5. Friction diagram. Coefficient of static friction is defined as tan 0 at the angle when the load starts to slide.

A body of weight W on a flat surface will begin to move when the surface is tilted to a certain angle termed the friction angle, 6, as defined in Fig. 1. The static friction coefficient is given by ... 

Frederich established one of the first progressions [8]. The friction function which it defines results from on site tests. The fnction is a function of the rolling speed and the normal force applied to a wheel. Unfortunately, the relations of macroscopic causes (mechanical parameters) in microscopic effects (variation of the fnction) are not physically known. Therefore, Ohyama carried out laboratory experiments with layers injected into the contact where their shear stress were expressed as a function of the ratio of two coefficients static friction ps and kinematic pd [9]. The first coefficient was defined in the stick zone while the second was in the slip zone (Figure 4). Thus the total tangential force was the integral of the tangential stresses qi (x) and q2(x) of each zone. 

The total suction lift is defined as above except the level of the liquid is below the centerline of the pump or the head is below atmospheric pressure. Its sign is negative. Total Suction Lift (TSL) = static lift plus friction head losses. 

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