An example of stick–slip and stick–slip–separation waves

The dynamical problem of a brake-like mechanical system composed of an elastic cylindrical tube with Coulomb's friction in contact with a rigid and rotating cylinder is considered. This model problem enables us to give an example of non-trivial periodic solutions in the form of stick–slip or stick–slip–separation waves propagating on the contact surface. A semi-analytical analysis of stick–slip waves is obtained when the system of governing equations is reduced by condensation to a simpler system involving only the contact displacements. This reduced system, of only one space variable in addition to time, can be solved almost analytically and gives some interesting informations on the existence and the characteristics of stick–slip waves such as the wave numbers on the circumference, stick and slip proportions, wave celerities, tangential and normal forces. It is shown in particular that the stick–slip–separation solutions would occur for small normal pressures or high rotational speeds. Since the analytical discussion becomes cumbersome in this case, a second approach based on numerical analysis by the finite element method is performed. The existence and the characteristics of stick–slip and stick–slip–separation waves are discussed numerically.     

An example of stick–slip waves

An analytical solution representing a family of stick–slip waves is obtained in a simple example modelling the dynamic behaviour of an elastic cylindrical tube in contact with Coulomb's friction with a rigid and rotating cylinder. This family of waves, representing the non-trivial periodic responses of a continuous system of one space variable, is not classical in the literature.     

Numerical and experimental studies of stick–slip oscillations in drill-strings

Nonlinear Dynamics - The cyclic nature of the stick–slip phenomenon may cause catastrophic failures in drill-strings or at the very least could lead to the wear of expensive equipment....     

Nonlinear dynamics of hardware-in-the-loop experiments on stick–slip phenomena

A single degree-of-freedom nonlinear mechanical model of the stick–slip phenomenon is studied when the Stribeck-type friction force is emulated by means of a digitally controlled actuator. The relative velocity of the slipping contact surfaces is considered as bifurcation parameter. The original physical system presents subcritical Hopf bifurcation with a wide bistable parameter region where stick–slip and steady-state slipping are both stable locally. Hardware-in-the-loop experiments are performed with a physical oscillatory system subjected to the emulated Stribeck forces. The effect of sampling time is studied with respect to the stability and nonlinear behavior of this experimental system. The existence of subcritical Neimark–Sacker bifurcations are proven in the digital system, the stability and bifurcation characteristics of the continuous and the digital systems are compared, and the counter-intuitive stabilizing effect of sampling time is shown both analytically and experimentally. The conclusions draw the attention to the limitations of hardware-in-the-loop experiments when the corresponding systems are strongly nonlinear.     

Modeling and waveform optimization of stick–slip micro-drives using the method of dimensionality reduction

In this paper, the dynamics of piezo-actuated stick–slip micro-drives are studied experimentally and theoretically. First, the stick–slip-based force-generating test stand is introduced, and experimental results are presented. Then, a numerical model is formulated which explicitly includes the dynamics of normal and tangential properties of the contact areas in the frictional driving elements of the drive. The contact forces are simulated using the method of dimensionality reduction. We show that the experimentally observed behavior can be described without using any fitting parameters or assuming any generalized laws of friction if the explicit contact mechanics of the frictional contacts is taken into account. Furthermore, an even simpler model of the drive is developed to get a qualitative understanding of the system. It is employed to gain a new actuation method, which reduces the vibrations of the drive’s runner and therefore enhances its performance.     

High-order synchronization of stick–slip process: experiments on spring–slider system

In the last years it has been shown that the synchronization and triggering of dynamic events by weak external forcing is ubiquitous and is observed in biological systems, lasers, electronic networks, etc. In the present paper, new experimental data on the phase synchronization in frictional system induced by a weak electromagnetic or mechanical periodic forcing are analyzed. For quantitative analysis of stick–slip time series, modern tools of nonlinear dynamics were used. Stick–slip events were identified by recording acoustic emissions, which accompany slip displacements. The spring–slider system in stick–slip regime is considered as a proxy of active tectonic fault, generating earthquakes. The effect of high-order synchronization of stick–slip events by weak electromagnetic or mechanical periodic forcing, as well as the phenomenon of phase time delay of the synchronized slip events behind the forcing phase, was discovered. These findings can help to find new regularities in seismic time series.     

Structural and electrical dynamics of a grating-patterned triboelectric energy harvester with stick–slip oscillation and magnetic bistability

The majority of research work on triboelectric energy harvesting is on material science, manufacturing and electric circuit design. There is a lack of in-depth research into structural dynamics which is crucial for power generation in triboelectric energy harvesting. In this paper, a novel triboelectric energy harvester with a compact structure working in sliding mode is developed, which is in the form of a casing and an oscillator inside. Unlike most sliding-mode harvesters using single-unit films, the proposed harvester utilizes grating-patterned films which are much more efficient. A bistable mechanism consisting of two pairs of magnets is employed for broadening the frequency bandwidth. A theoretical model is established for the harvester, which couples the structural dynamics domain and electrical dynamics domain. This paper presents the first study about the nonlinear structural dynamics of a triboelectric energy harvester with grating-patterned films, which is also the first triboelectric energy harvester integrating grating-patterned films with a bistable magnetic system for power performance enhancement. Theoretical studies are carried out from the perspectives of both structural and electrical dynamics. Surface charge density and segment configuration of the films affect whether the electrostatic force influences the structural dynamics, which can be neglected under a low surface charge density. Differences in structural response and electrical output are found between a velocity-dependent model and Coulomb’s model for modelling the friction in the triboelectric energy harvesting system. The bistable mechanism can effectively improve the output voltage under low-frequency excitations. Additionally, the output voltage can also be obviously enhanced through increasing the number of the hollowed-out units of the grating-patterned films, which also results in a slight decrease in the optimal load resistance of the harvester. These findings enable innovative designs for triboelectric energy harvesters and provide fabrication guidelines in practical applications.

     

The effect of dynamic normal force on the stick–slip vibration characteristics

Nonlinear Dynamics - In the experiment, we observed such a phenomenon: the alternating normal force changes the vibration state of a friction system. A single-degree-of-freedom mathematical model...     

Understanding root cause of stick–slip vibrations in deep drilling with drag bits

In search for the root cause of stick–slip, a mode of torsional vibrations of a drilling assembly, a linear stability analysis of coupled axial–torsional vibrations has been carried out. It has been shown that in a rotary drilling system with axial and torsional degree of freedom two distinct modes of self-excited vibrations are present: axial and torsional. These axial (torsional) modes of vibrations are due to resonance between the cutting forces acting at the bit and the axial (torsional) natural modes of drillstring vibrations. It has been demonstrated that although axial and torsional modes of vibrations do affect each other the underlying mechanisms driving these modes of vibrations are completely different. In particular, the only driving mechanism of the axial vibrations is the regenerative effect, while there are two distinct mechanisms that drive the torsional vibrations: (i) the cutting action of the bit, and (ii) the wearflat/rock interaction. Moreover, in the case of the torsional vibrations the regenerative effect plays only a secondary role. The results of the present study indicate that the axial compliance can play a stabilizing role. In particular, the stabilizing role of the axial compliance increases as the ratio of the torsional to the axial natural frequency of the drillstring vibrations decreases.     

Correction to: Structural and electrical dynamics of a grating-patterned triboelectric energy harvester with stick–slip oscillation and magnetic bistability

Nonlinear Dynamics -     

Propagation of slip pulse along frictionless contact interface with local separation between two piezoelectric solids

The Stroh formalism of piezoelectric materials,Fourier analysis and singular integral equation technique were used to investigate the existence of a pulse at the fric- tionless interface in presence of local separation between two contact piezoelectric solids. The two solids were combined together by uniaxial tractions and laid in the electric field. The problem was cast into a set of Cauchy singular integral equations,from which the closed-form solutions were derived.The numerical discussion on the existence of such a slip pulse was presented.The results show that such a slip pulse,which has square root singularities at both ends of the local separation zone,can propagate in most material combinations.And the existence of such a slip pulse will not be affected by the applied mechanical and electric fields in some special material combinations.     

Adiabatic shear banding and scaling laws in chip formation with application to cutting of Ti–6Al–4V

The phenomenon of adiabatic shear banding is analyzed theoretically in the context of metal cutting. The mechanisms of material weakening that are accounted for are (i) thermal softening and (ii) material failure related to a critical value of the accumulated plastic strain. Orthogonal cutting is viewed as a unique configuration where adiabatic shear bands can be experimentally produced under well controlled loading conditions by individually tuning the cutting speed, the feed (uncut chip thickness) and the tool geometry. The role of cutting conditions on adiabatic shear banding and chip serration is investigated by combining finite element calculations and analytical modeling. This leads to the characterization and classification of different regimes of shear banding and the determination of scaling laws which involve dimensionless parameters representative of thermal and inertia effects. The analysis gives new insights into the physical aspects of plastic flow instability in chip formation. The originality with respect to classical works on adiabatic shear banding stems from the various facets of cutting conditions that influence shear banding and from the specific role exercised by convective flow on the evolution of shear bands. Shear bands are generated at the tool tip and propagate towards the chip free surface. They grow within the chip formation region while being convected away by chip flow. It is shown that important changes in the mechanism of shear banding take place when the characteristic time of shear band propagation becomes equal to a characteristic convection time. Application to Ti–6Al–4V titanium are considered and theoretical predictions are compared to available experimental data in a wide range of cutting speeds and feeds. The fundamental knowledge developed in this work is thought to be useful not only for the understanding of metal cutting processes but also, by analogy, to similar problems where convective flow is also interfering with adiabatic shear banding as in impact mechanics and perforation processes. In that perspective, cutting speeds higher than those usually encountered in machining operations have been also explored.     

The wheeled three-link snake model: singularities in nonholonomic constraints and stick–slip hybrid dynamics induced by Coulomb friction

Nonlinear Dynamics - The wheeled three-link snake model is a well-known example of an underactuated robotic system whose motion can be kinematically controlled by periodic changes of its internal...     

Couette–Poiseuille flow of Bingham fluids between two porous parallel plates with slip conditions

Analytical solutions of Couette–Poiseuille flow of Bingham fluids between two porous parallel plates are derived. This study extends the work of Tsangaris et al. [S. Tsangaris, C. Nikas, G. Tsangaris, P. Neofytou, Couette flow of a Bingham plastic in a channel with equally porous parallel walls, J. Non-Newtonian Fluid Mech. 144 (2007) 42–48] to a general situation where the slip effect at the porous walls is considered. It is found that the form of the flow inside the channel depends not only on the Bingham number Bn, the Couette number Co (related to the moving wall) and the transverse Reynolds number Re, but also on the slip parameter Cs at the porous walls. In both the Co–Re diagram and the Co–Bn diagram, the region where plug flow appears enlarges as the slip effect increases, especially in the case where Co is negative. In the case where plug flow and double shear flow coexist, the transverse position of the plug flow and the shear rate at the boundaries exhibit two opposite behaviors when Cs increases, depending on the value of the other three dimensionless numbers. In other cases, slippage always weakens the shearing deformation of the flow.     

Elastic fields and effective moduli of particulate nanocomposites with the Gurtin–Murdoch model of interfaces

A complete solution has been obtained for periodic particulate nanocomposite with the unit cell containing a finite number of spherical particles with the Gurtin–Murdoch interfaces. For this purpose, the multipole expansion approach by Kushch et al. [Kushch, V.I., Mogilevskaya, S.G., Stolarski, H.K., Crouch, S.L., 2011. Elastic interaction of spherical nanoinhomogeneities with Gurtin–Murdoch type interfaces. J. Mech. Phys. Solids 59, 1702–1716] has been further developed and implemented in an efficient numerical algorithm. The method provides accurate evaluation of local fields and effective stiffness tensor with the interaction effects fully taken into account. The displacement vector within the matrix domain is found as a superposition of the vector periodic solutions of Lamé equation. By using local expansion of the total displacement and stress fields in terms of vector spherical harmonics associated with each particle, the interface conditions are fulfilled precisely. Analytical averaging of the local strain and stress fields in matrix domain yields an exact, closed form formula (in terms of expansion coefficients) for the effective elastic stiffness tensor of nanocomposite. Numerical results demonstrate that elastic stiffness and, especially, brittle strength of nanoheterogeneous materials can be substantially improved by an appropriate surface modification.     

Interlayer shear of nanomaterials:Graphene–graphene,boron nitride–boron nitride and graphene–boron nitride

In this paper, the interlayer sliding between graphene and boron nitride(h-BN) is studied by molecular dynamics simulations. The interlayer shear force between h-BN/h-BN is found to be six times higher than that of graphene/graphene, while the interlayer shear between graphene/h-BN is approximate to that of graphene/graphene. The graphene/hBN heterostructure shows several anomalous interlayer shear characteristics compared to its bilayer counterparts. For graphene/graphene and h-BN/h-BN, interlayer shears only exit along the sliding direction while interlayer shear for graphene/h-BN is observed along both the translocation and perpendicular directions. Our results provide significant insight into the interlayer shear characteristics of 2D nanomaterials.     

Statistical modeling and comparison with experimental data of tire–soil interaction for combined longitudinal and lateral slip

The interaction of a tire with a soft terrain has multiple sources of uncertainties such as the mechanical properties of the terrain, and the interfacial properties between the tire and the terrain. These uncertainties are best characterized using statistical methods such as the development of stochastic models of tire–soil interaction. The quality of the models can be assessed via statistical validation measures or metrics. Although validation of stochastic tire–soil interaction models has recently been reported with good results, it involves longitudinal slip only without considering lateral slip which can occur simultaneously with longitudinal motion. This paper presents results of the validation of a simple stochastic tire–soil interaction model for the more complicated case of combined slip. The statistical methods used for validation include the development of a Gaussian process metamodel, the calibration of model parameters using the approach of the maximum likelihood estimate in conjunction with new test data. The validation of the calibrated model, when compared with test data, is obtained using four validation metrics with good results.