Coulomb friction

Namm R.V. (1995) On uniqueness of smooth solution to the static problem with the Coulomb friction condition and contact. Appls. Maths. Mechs. 59 (2), 330-335 (in Russian). 

Figure 5-22b shows this phenomenon. When contact is made between the surface and the rotating shaft, the coulomb friction will induce a tangential force on the rotor. This friction force is approximately proportional to the... 

When two bodies are in contact and there is a tendency for them to slide with respect to each other, a tangential friction force is developed that opposes the motion. For dry surfaces this is called dry friction or coulomb friction. For lubricated surfaces the friction force is called fluid friction, and it is treated in the study of fluid mechanics. Consider a block of weight W resting on a flat surface as shown in Figure 2-5. The weight of the block is balanced by a normal force N that is equal and opposite to the body force. Now, if some sufficiently small sidewise force P is applied (Figure 2-5b) it will be opposed by a friction force F that is equal and opposite to P and the block will remain fixed. If P is increased, F will simultaneously increase at the same rate until... 

This P -I type of response curve can also be easily shown to apply to a simple rigid-plastic mechanical system, in the manner shown in Figure 16 (see Refs. 15 and 22). Here, the spring in the system is replaced with a pure Coulomb friction element, with resisting force f, which is independent of displacement once the mass starts to move. All other symbols are defined above. 

Apart from the elastic stress transfer at the perfectly bonded interface, another important phenomenon that must be taken into account is the stress transfer by friction, which is governed by the Coulomb friction law after the interface bond fails. Furthermore, matrix yielding often takes place at the interface region in preference to interfacial debonding if the matrix shear yield strength, Xm is significantly smaller than the apparent interface bond strength, tb. It follows thus... 

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... 

Based on the Coulomb friction law, which governs the frictional stress transfer in the debonded interface, and combining Eqs. (4.12) and (4.18) yield the MAS at the interface (r = a)... 

However, some theoretical treatment considers only the special case of friction sliding of a single fiber along a mechanically bonded interface, particularly for some ceramic matrix composites, where the Coulomb friction law applies. See for example Zhou and Mai (1995) and Shetty (1988). Assuming a constant friction at the fiber-matrix interface and neglecting the Poisson effects, Shetty (1988) reported a simple force balance equation for the frictional shear strength, Tfr... 

In this section we discuss dry friction, also called solid or Coulomb friction. Solid friction occurs when two solid surfaces are in direct contact without any other components like lubricants or adsorbed surface layers involved. The reader might object that in practice no such... 

The second empirical law for dry, macroscopic friction is that of Coulomb Friction does not depend on the sliding velocity. 

Various models will be used for the interface between the fiber and the matrix. For bonded interfaces, complete continuity of all components of the velocity will be invoked. The simplest model for a weak interface is that a shear drag equal to r opposes the relative shear velocity jump across the interface. The direction of the shear drag is determined by the direction of the relative velocity. However, the magnitude of r is independent of the velocities. This model is assumed to represent friction occurring mainly because of roughness of the surfaces or due to a superposed large normal pressure on the interface. Creep can, of course, relax the superposed normal stress over time, but on a short time scale the parameter r can be assumed to be relatively invariant. No attempt will be made to account for Coulomb friction associated with local normal pressures on the interface. 

Section 22.6 has accounted for one important nonlinearity, namely the velocity limit of the valve. Another nonlinearity that can cause control problems is static friction, sometimes referred to as stiction, although more properly known as Coulomb friction. Static friction acts to prevent or impede relative motion by opposing the force applied. Its effect on valve movement may be measured as the difference between the valve s demanded travel (equal to the normalized controller output) and the actual valve travel seen on the plant. This difference will lie normally in the normalized range 0.001 to 0.005 (0.1 to 0.5% of total valve travel) for valves fitted with a valve positioning system, although the author has had experience of an important control valve with a value measured at... 

The dispersive stress evidently contributes an additional term to the force balance. This stress is strongly dependent on solids concentration. According to Hanes and Inman (100), this stress requires a finite interparticle shear strain rate and would not exist in a sliding bed of solids. In the latter case, the immersed weight of the particles would be transmitted to the pipe wall by interparticle Coulombic friction. The stress resulting from this type of contact was denoted the supported load (94). 

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. 

The average shaft resistance per unit area can be computed from the following equation based on the principles of Coulomb friction ... 

Viscous flow models have been applied to a variety of problems ranging from slow creep deformations and mud flows to more rapid fluid types of mass movement. Morgenstem (1967) described an early viscous flow analysis in which the soil shear resistance consisted of a velocity-dependent viscous component in addition to Coulomb friction. In his analysis Morgenstem (1967) derived an equation for determining the velocity required to change a slump into a turbidity current as shown in Figure 11.20. This expression is given as follows... 

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... 

Due to frictional boundary conditions, seizures of up to half the contact length and subsequently Coulomb friction with a constant friction value were assumed. However, this method is considerably more complex than a simple comparison of measured and calculated forces. 

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 this work technological parameters such as the Coulomb friction and the geometry of the workpiece (shape factor) in indentation processes have been studied. To analyze the influence of them, it has been obtained the forces to carry out the indentation process and the contact pressures between the punch and workpiece. 

Frictional sliding becomes an important phenomenon when cracks close and likely contributes to the macroscopic constitutive behavior of the porous material. For the sake of simphcity, a Coulomb friction law is assumed such that slip occurs when... 

The number of state variables of an overall model is not time-invariant but mode dependent. Due to a connection of model parts storage elements may become dependent, e.g. if a clutch is engaged or if rigid bodies stick together for a while due to Coulomb friction. 

The Coulomb friction damping due to slip among the unbonded, debrmded and... 

In the analysis of flow of granular material, two types of flow can be distinguished. The first is slow frictional flow where the particles remain in continuous contact with each other the internal forces result from Coulomb friction between contacting particles. The second type of flow is much more rapid the particles are not in constant contact with their neighbors. The energy associated with the velocity fluctuations is comparable to that of the mean motion. In this type of flow, the internal forces arise because of the transfer of momentum during collisions between particles. The constitutive relations for this rapid flow are rate-dependent. This type of flow, therefore, is referred to as viscous flow (sometimes just rapid flow). Steady,... 

The other most popular model is the frequency independent damping model. The concept of frequency independent damping arose when in 1927 Kimball and Lovell claimed that hysteretic damping is universal in nature. Since then there has been several studies which further strengthened their claim. One of the most popular models in this category is the linear Coulomb friction force model given as (Reid 1956, Muravski 2004)... 

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