Coulomb friction coefficient

Parameters. Many parameters can influence the compression process. One of the most important variables in metal forming is the friction. In this study the friction coefficient has been studied in the shown models of the Table 1. To do this, it has been carried out an analysis with different Coulomb friction coefficients, changed from /r=0 to /r=0,5 in increments of 0,1. 

In the above equations, is the ith actuator Inertia, and are viscous damping and coulomb friction coefficients at Joint i, G is comprised of Gj s in Eq. (23), M and f are Cartesian mass matrix and force vector, and h... 

In the debonded regions L z - (L - ) and (L - )<,z L), frictional slip occurs between the fiber and matrix and the stress transfer is governed by the Coulomb friction law for a constant coefficient of friction, p... 

When an ion with charge q (coulombs) is placed in an electric field E (V/m), the force on the ion is qE (newtons). In solution, the retarding frictional force is /uep, where ncp is the velocity of the ion and/is the friction coefficient. The subscript ep stands for electrophoresis. The ion quickly reaches a steady speed when the accelerating force equals the frictional force ... 

Such a dependence is characteristic of the dry friction, i.e. it agrees with Coulomb s friction law, Ffr = /frFN. Consequently, the model of plastic behavior of a material or disperse system may be represented by two surfaces (two plates) with a mutual friction coefficient, fx, pressed against each other with normal force, FN, causing the tangential force, Ffr, to be equal to the critical shear stress of material (Fig. IX-7). 

Coulomb friction, with the shear stress being limited to a maximum value dependent on the local normal pressure. Because Coulomb friction depends on the normal stress, this is only valid for hnite element analysis in which the elasticity is included. It is most commonly applied to model the shoulder contact but requires the assumption of a constant coefficient of friction, usually calibrated via the net measured torque or indirectly through the temperature held, which reflects the fric-honal heat input. 

In area 2, the zone of elastic contact, the chip slides down the face of the tool and no further plastic deformation of the material takes place. Coulomb friction can be applied here. The friction coefficient fi may be dependent on other parameters in different ways. In order to obtain... 

Figure 8.16 shows a biaxial yield contour for principal stresses a and 02 (with (73 = 0) of PVC, PC, PS, and PMMA at room temperature, normalized with the uniaxial yield stresses of these four polymers (Raghava et al. 1973). Thus, the center of the typical elliptical von Mises yield contour is displaced toward the biaxial compression quadrant characteristic of the pressure-dependent yield formalisms of Coulomb (1773) and Mohr (1900). For PC, discussed above, a model friction coefficient /if = 0.297 is obtained from eq. (8.40). In contrast, the displaced elliptical yield contour of experiments shown in Fig. 8.16 was obtained with a best fit of /if = 0.23, which gives a somewhat larger discrepancy than that for PC alone, given through eqs. (8.36) above. This could be attributed to the fact that the Oy used for normalization is itself dependent on (Tm. 

Coulomb s friction theory for particles was based on the idea that the traction force divided by the plate area was given by an adhesion pressure K plus a friction term JA where p was the friction coefficient, i.e. 

Some results for wet sand are shown in Fig. 9.17. The macroscopic silica samples gave a friction coefficient of 0.33, whereas the finer particles gave an apparently higher value up to 0.66 for 10pm grains. Clearly, this apparent rise in Coulomb law friction follows from Equation (9.16) which leads to the idea that the apparent friction coefficient should rise for small grains at low pressures according to the equation... 

Figure 9.17. Apparent friction coefficient for wet silica powders of various sizes at lOOkPa normal pressure, showing that large particles give the true friction of 0,33 but smaller grains give up to twice that value, assuming Coulomb behavior.

Die compaction of agglomerates has been simulated in a computer sphere model by Thornton et When the particles are in a liquid paste, the liquid is usually expelled through pores in the mold, and the partieles form a filter cake. The mechanism by which this occurs has been modeled by Woodcock et The application of forces to powder beds, sometimes immersed in liquids, is the subject of soil mechanics. " This considers particles to interact via Coulomb s law, Equation (11.16), but also takes into account the hydrodynamic forces acting on the individual particles. Unfortunately, as we have seen. Coulomb s law is not correct for particles which experience molecular adhesion, so the friction coefficients found in soil mechanics theories seem to vary. Friction seems to increase as the particles get smaller because smaller particles adhere more strongly. Soil mechanics is therefore a difficult science. 

This type of dependence is a characteristic of dry friction, that is, corresponds to Coulomb s dry friction law, Ff, = pF, . Plastic behavior can be modeled by a friction element, that is, two flat plates with a friction coefficient, p, with respect to each other and compressed with a normal force Fn in such a way that the applied tangential force F would correspond to the yield stress of a given material (Figure 3.7). 

Example 6.4.2 We consider the truck with Coulomb friction between the wheels and the road. The Coulomb coefficient is assumed to be p = 0.9 (dry road). 

In addition to a characteristic line describing the friction coefficient we have to deal with Coulomb friction in points of contact between container and the deck of the ship. 

A new approach for calculating the coefficients of the matrices in the explicit form dynamic equations taking into account the friction in pairs is presented. Coulomb friction is assumed. An approach concerning stiction in joints is suggested. The numerical procedure is based on the matrix methods in kinematics and on Newtcm-Euler equations. As the procedure is numerical, all kinds of friction presented by coefficients of friction as nonlinear functions of the joint positions and velocities... 

Assuming the tangential traction/, is related to the normal traction / through Coulomb friction by the equation/ = q/, (where fi is the coefficient of friction) and defining a normalized shear force V = VfW, Eq. 16 reduces to... 

The effect of decreased normal stress on a shallow imbedded crack makes it more likely to mp-ture to the surface above a critical depth as shown by Rudnicki and Wu (1995). The Coulomb friction condition is introduced such that slip occurs when Icr l = kapparent coefficient of friction, including effects of pore-pressure differences in the fault zone. The right-hand side of integral equation above is modified such that... 

In order to verify the hypothesis that an interaction between these earthquakes may have occurred and to understand the role of the first earthquake in promoting the rupture of the second event, the Coulomb failure function (CFF) has been evaluated onto the Christchurch fault plane. The CFF is obtained by computing the stress tensor corresponding to the elastic dislocation induced by the Darfield earthquake, projecting it onto the fault plane of the Christchurch earthquake, and evaluating the relative weights of the stress components (normal and shear), assuming an certain friction coefficient. 

Coulomb sliding condition Fd < is enforced, where i is the static friction coefficient. When a contact between disks i and j breaks, Uf.. is reset to zero. This model for static friction has been implemented in a number of discrete element simulations of static and flowing granular media [8,38]. 

---