Frictional force coefficient

A is the friction force coefficient B is the inertia correction coefficient and C is the resistance coefficient due to the Basset force. Equation (6.65) gives... 

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. 

Thus, the requirement that the Brownian particle becomes equilibrated with the surrounding fluid fixes the unknown value of, and provides an expression for it in tenns of the friction coefficient, the thennodynamic temperature of the fluid, and the mass of the Brownian particle. Equation (A3.1.63) is the simplest and best known example of a fluctuation-dissipation theorem, obtained by using an equilibrium condition to relate the strengtii of the fluctuations to the frictional forces acting on the particle [22]. 

Let. F > 0 be a given friction coefficient, and > 0 be a known friction force at the boundary. The conditions of given friction along the normal implies... 

Coefficient of friction f, the ratio of friction force to appHedload, is... 

Other spectral densities correspond to memory effects in the generalized Langevin equation, which will be considered in section 5. It is the equivalence between the friction force and the influence of the oscillator bath that allows one to extend (2.21) to the quantum region there the friction coefficient rj and f t) are related by the fluctuation-dissipation theorem (FDT),... 

The turbulent regime for Cq is characterized by the section of line almost parallel to the x-axis (at the Re" > 500). In this case, the exponent a is equal to zero. Consequently, viscosity vanishes from equation 46. This indicates that the friction forces are negligible in comparison to inertia forces. Recall that the resistance coefficient is nearly constant at a value of 0.44. Substituting for the critical Reynolds number, Re > 500, into equations 65 and 68, the second critical values of the sedimentation numbers are obtained ... 

The friction and wear of plastics are extremely complex subjects which depend markedly on the nature of the application and the properties of the material. The frictional properties of plastics differ considerably from those of metals. Even reinforced plastics have modulus values which are much lower than metals. Hence metal/thermoplastic friction is characterised by adhesion and deformation which results in frictional forces that are not proportional to load but rather to speed. Table 1.7 gives some typical coefficients of friction for plastics. 

The friction force can formally be expressed with the aid of the friction coefficient... 

Second, we take account of the frictional drag as the solute molecule moves through the solvent. The frictional force is taken to be proportional to the velocity of the particle, with a proportionality constant called the friction coefficient... 

The friction coefficient of 0.03 used above is so low due to the advantage of a wheel on an axle. The friction force at the axle of the pulley wheel is overcome by a smaller force applied at the rim in accord with the principle of the lever. 

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. 

All sliding friction forces are dramatically affected by surface contamination. If the surface is covered with a material that prevents the adhesive forces from acting, the coefficient is reduced. If the material is a liquid which has low shear viscosity the condition exists of lubricated sliding where the characteristics of the liquid control the friction rather than the surface friction characteristics of the materials. It is possible by the addition of surface materials that have high adhesion to increase the coefficient of friction. 

Frictional forces are not proportional to load-friction increases with increasing speed, and the static coefficient of friction is lower than its dynamic one. When two viscoelastic low-modulus materials are run against each other, additional inconsistencies result. 

If the surface over which the fluid is flowing contains a series of relatively large projections, turbulence may arise at a very low Reynolds number. Under these conditions, the frictional force will be increased but so will the coefficients for heat transfer and mass transfer, and therefore turbulence is often purposely induced by this method. 

Phenomenal studies were made to observe the frictional behavior of L-B films and SAMs and its dependence on applied load and sliding velocity, which has been summarized in a review article by Zhang [33]. It has been confirmed that in comparison to the bare surface of the substrates, the friction on molecular films is significantly reduced, with friction coefficients in a range of 0.05-0.1. Friction forces are found... 

Follow the above procedures, we obtained the friction coefficient of the unclean single crystal Si surface is about 0.06, which agrees very well with the result obtained under the same experimental condition by Bhushan et al. It is validated with the feasibility of the calibration method. Based on the friction coefficient, we can easily obtain the friction forces under the loads. 

As it is known, during the micro friction force measurement, it is difficult to obtain the real and precise friction force due to the small size of cantilever as well as the slight difference between cantilevers. According to the principle of FFM, the friction force signal can be used as the representative of the real friction force. Therefore, a friction coefficient factor is introduced in order to compare the relative micro friction characteristics among the samples. Corresponding to the relationship between the friction force and the friction... 

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