Stick-slip friction models

The load-deflection response from both friction models (i.e. the continuous and stick-slip friction models) are shown in Figure 11.11 together with the experimental curve. Both friction models represent the behaviour in the experiment reasonably well. The sharp change from static fiiction Slope 1) to kinetic fiiction transition region) is slightly better represented by the stick-slip friction model. This is because... 

Figure 11.12 Component of loads acting on one laminate in the single-lap joint in the loading ( c) direction, (a) Free body diagram of force components in loading direction, (h) loads from finite element model using stick-slip friction model.

Scratches can also appear as segmented chatter marks" as depicted in Figure 17.11. A nanoscale stick slip friction model is proposed to account for such defects [10]. Lack of proper lubrication between pad and wafer surfaces could be the main attribute responsible for the generation of chatter marks. 

H.J. Kim, J.C. Yang, B.U. Yoon, H.D. Lee, T. Kim, Nanoscale stick-slip friction model for the chatter scratch generated by chemical mechanical polishing process, J. Nanosci. Nanotech. 12 (7) (2012) 5683-5686. 

Figure 11.9 Friction force microscope pictures (a, b) of a graphite(OOOl) surface as obtained experimentally with FFM and results of simulations (c, d) of the stick-slip friction using a two-dimensional equivalent of the Tomlinson model. The friction force parallel to the scan direction (a, c) and the lateral force perpendicular to the scan direction (b, d) are shown. The scan size is 20 Ax 20 A. Pictures taken from Ref. [481] with kind permission from R. Wiesendanger.

The introduction to the concept of static and kinetic friction in Chapter 7, Section 2 is admittedly simplistic. Familiarity with the experimental details of measuring friction leads to a more realistic view in behavioristic terms and also to some theoretical questions. In particular, the theory of stick-slip friction requires that be greater than and distinct from and indeed Fig. 7-5a shows a discontinuity between static and kinetic friction. But the model for the fundamental adhesive mechanism of friction does not predict such a discontinuity. 

Anisotropic friction and molecular stick-slip friction were observed on a number of polymer systems by LFM using non-functionalized and functionalized tips. The observations described in this paper can be understood within the frame of the cobblestone (interlocking asperity) model. For a quantitative description, however, important parameters such as the energy fraction dissipated during the kinetic friction process (e) are still lacking. 

In the present pqrer, we present a simple rigid body model of a spline coupling and use it to determine normal and tangential displacements in the cont region r en misalignment is imposed. We also consider the overall equilibrium and stability of the coiqrling. These results are then compared to those from a boundary element model Mdiich includes elasticity and stick-slip friction in the contact Wear depth predictions are also made. A locked spline, in which the shaft axial location is controlled by a nut and a shoulder is also examined. 

Marton L, Lantos B (2007) Modeling, identification, and compensation of stick-slip friction. IEEE Trans Ind Electron 54(1) 511-521... 

In the studies that attribute the boundary friction to confined liquid, on the other hand, the interests are mostly in understanding the role of the spatial arrangement of lubricant molecules, e.g., the molecular ordering and transitions among solid, liquid, and amorphous states. It has been proposed in the models of confined liquid, for example, that a periodic phase transition of lubricant between frozen and melting states, which can be detected in the process of sliding, is responsible for the occurrence of the stick-slip motions, but this model is unable to explain how the chemical natures of lubricant molecules would change the performance of boundary lubrication. 

Macroscopic stick-slip motion described above applies to the center of mass movement of the bodies. However, even in situations where the movement of the overall mass is smooth and steady, there may occur local, microscopic stick-slip. This involves the movement of single atoms, molecular groups, or asperities. In fact, such stick-slip events form the basis of microscopic models of friction and are the explanation why the friction force is largely independent of speed (see Section 11.1.9). 

The validity of Coulomb s law has been verified also on the nanoscale Zworner et al. [484] showed that, for different carbon compound surfaces, friction does not depend on sliding velocity in the range between 0.1 /xm/s and up to 24 /xm/s. At low speeds, a weak (logarithmic) dependence of friction on speed was observed by Gnecco et al. [485] on a NaCl(lOO) surface and by Bennewitz et al. [486] on a Cu (111) surface. This can be modeled when taking into account thermal activation of the irreversible jumps in atomic stick-slip [487],... 

F. Heslot, T. Baumberger, B. Caroli, and C Caroli, Creep, Stick-slip and Dry Friction Dynamics Experiments and a Heuristic Model, Phys. Rev., E49, 4973 (1994). 

It may be mentioned here that a recent study (Vasconcelos 1996) of a simple noncooperative (one-block) model of stick-slip motion (described by eqn (4.2) with / o = 0 or eqn (4.4) with k = 0) shows discontinuous velocity-dependent transition in the block displacement, for generic velocity-dependent friction forces. Naive generalisation of this observation for the coupled Burridge-Knopoff model would indicate a possible absence of criticality in the model. 

As argued by Fisher, pinned and sliding solutions can only coexist in some range of the externally applied force if the inertial term exceeds a certain threshold value [29]. This can lead to stick-slip motion as described in Section VI.A. For sufficiently small inertial terms, Middleton [85] has shown for a wide class of models, which includes the PT model as a special case, that the transition between pinned and sliding states is nonhysteretic and that there is a unique average value of F which does depend on vq but not on the initial microstate. The instantaneous value of Fk can nevertheless fluctuate, and the maximum of Fk can be used as a lower bound for the static friction force Fg. The measured values of Fj can also fluctuate, because unlike Fk they may depend on the initial microstate of the system [85]. 

As discussed in Section I.D, the dependence of friction on past history is often modeled by the evolution of a state variable (Eq. 6) in a rate-state model [50,51]. Heslot et al. [53] have compared one such model, where the state variable changes the height of the potential in a finite-temperature PT model, to their detailed experimental studies of stick-slip motion. They slid two pieces of a special type of paper called Bristol board and varied the slider mass M, pulling... 

Figures 17b and 17c show the response in the lateral and normal directions to a lateral constant velocity drive for the stick slip regime that occurs at low driving velocities. This behavior is similar for the presently discussed model. The separation between the plates, which is initially Zq at equilibrium, starts growing before slippage occurs and stabilizes at a larger interplate distance as long as the motion continues. Since the static friction is determined by the amplitude of the potential corrugation exp(l — Z/A), it is obvious that the dilatancy leads to a decrease of the static friction compared to the case of a constant distance between plates.

The factor that is least controllable in the deduction of static and kinetic friction values from stick-slip experiments is the condition of the contacting surfaces. This explains why Brockley and Davis [20] in their study of the influence of the time of contact on were unable to obtain repeatable results, as shown in Fig. 8-15a. For each series of determinations made with a single placement of the rider on the track, the plot of against the time of quiescent contact shows satisfactory self-consistency. But when the experiment is repeated with a fresh placement of the rider on the track, a different curve is obtained, self-consistent but not a duplicate of the previous experiment. This was traced to the variability of the surface with location on the rubbing track. Furthermore, it was demonstrated that a model of time-dependent junction growth could be made to yield the following expression ... 

The finite element model described in Section 11.2 was used here to model the friction experiments described above. However, to simulate the 16 Nm torque, a bolt pre-stress of 227 MPa was applied. This value was obtained experimentally from the axial gauges in the shank of a specially manufactured instmmented bolt, as discussed previously. For comparison, both the continuous and stick-slip [25] fiiction models (available in MSC Marc finite element code) was used to account for fiiction between the contacting interfaces. The fiiction coefficients were chosen to be 0.1, 0.3 and 0.45 between the bolt/laminate, washer/laminate and laminate/laminate interfaces, respectively. More details on fiiction coefficient selection can be found in [17]. 

An example for self-excited vibrations is the stick-slip phenomenon. In machining applications, stick-slip typically arises at the glides. The mechanical model can be seen in Fig. 12. The block of mass m is fixed to the moving wall by a spring of stiffness k and a dashpot of damping c. The wall is moving with velocity vq-The friction force acting on the block is... 

Velocity-Dependent Friction Research and development work on the numerical specification of contact and friction conditions may include mathematical formulation and implementation of friction models as well as adaptation of the numerical solution methods (Heisel et al. 2009 Neugebauer et al. 2011). Standard implementations may be illustrated using Coulomb s Law and the Friction Factor Law. These two basic models were modified using a stick-slip model. Using these models enables consideration of the relative sliding velocity between the tool and the workpiece. 

Yet another theory has emerged recently from the field of nanotribology. Surface force apparatus studies, combined with molecular dynamics simulations, of simplified model systems, such as molecularly flat mica separated by a few molecules thick lubricant layers, have identified a solid-melt transition as the cause for stick-slip motion to occur for such confined liquids (18, 106, 111-113, 144-149). A similarly confined liquid can be found in macroscopic friction systems in the boundary lubrication regime wherein thin lubricant layers are trapped between surface asperities in very close proximity. 

Stick-slip motion observed with syringes is associated with the nuxed and boundary lubrication regime. This is in agreement with current models of the occurrence of stick-slip motion for lubricated sliding systems (see Physics of Friction section). Possible causes for this phenomenon are discussed in more detail in the following. 

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