Stick-slip Transition Research Articles

Atomistic understanding of the interlayer friction of graphullerene

Graphullerene, an emerging two-dimensional carbon allotrope derived from C60, is endowed with distinctive mechanical and thermal characteristics, positioning it as a potential candidate with superior lubricating properties akin to graphene and C60. This research delves into the interlayer frictional behavior of graphullerene through molecular dynamics simulations, meticulously examining the impact of sliding velocity, normal load, flake orientation, and temperature. The findings reveal a stick-slip mode of friction with an exponential increase in friction force as sliding velocity increases. Additionally, the study captures the formation of puckering at the slider's forefront, which undergoes ballistic motion propelled by the slider's momentum. Notably, at higher velocities, a distinctive "stone skipping" effect is observed, with the graphullerene flake intermittently detaching from the substrate.

Screening of low-friction two-dimensional materials from high-throughput calculations using lubricating figure of merit

Two-dimensional materials are excellent lubricants with inherent advantages. However, superlubricity has been reported for only a few of these materials. Unfortunately, other promising two-dimentional (2D) materials with different physical properties cannot be discovered or applied in production; thus, energy consumption can be greatly reduced. Here, we carry out high-throughput calculations for 1,475 2D materials and screen for low-friction materials. To set a standard, we propose, for the first time, a geometry-independent lubricating figure of merit based on the conditions for stick-slip transition and our theory of Moiré friction. For the efficient calculation of this figure of merit, an innovative approach was developed based on an improved registry index model. Through calculations, 340 materials were found to have a figure of merit lower than 10−3. Eventually, a small set of 21 materials with a figure of merit lower than 10−4 were screened out. These materials can provide diverse choices for various applications. In addition, the efficient computational approach demonstrated in this work can be used to study other stacking-dependent properties.

Nonlinear dynamics and onset of steady precession of a ring on a vertical rod.

We report on the unexpected precessional motion that occurs when a small, rigid ring is rotated on a vertical smooth rod. Using high-speed imaging, two distinct regimes of motion are observed experimentally. (i) Oscillatory motion when the ring has a single contact with the rod (transient motion). (ii) Steady state (terminal velocity) when the ring has two instantaneously stationary contacts with the rod. These two regimes and the transition between them are analyzed through qualitative, analytical, and numerical means. One key feature of the steady-state motion is energy dissipation through rolling resistance and air drag. Our model predicts that steady-state motion occurs only when certain geometric conditions (the ratio of the radii of a ring and a rod, and the tilt angle) are fulfilled. As the steady-state regime is often found to be the preferred final state, the dynamic stability of the single contact configuration is investigated through bifurcation, phase-space, and linear stability analyses. Our numerical simulation accounts for the stick-slip transition at the contact point, and is in good agreement with experimental data across all experiments. Our findings have potential applications in various engineering fields, such as studying the vibrational detachment of threaded fasteners and developing gravity-driven centrifuges.

Dynamic modeling for continuous locomotion of bionic soft worm-like robot

In the nature, worm-like robot can bend its slender body into an arch bridge when it moves, and it will move quickly in this deformation mode to nimbly escape from enemies once encountering danger. Inspired by this locomotion mechanism, a plenty of bionic soft worm-like robots have been devised and studied adopting quasi-static method. Nevertheless, how to describe the stick-slip transition and the continuity of the entire locomotion process of soft worm-like robots is still a challenging problem. To settle the above issue, a simplified curved beam model is developed to depict a type of soft worm-like robot move forward continuously by controlling its initial curvature in this paper. Based on the curved beam model, a novel dynamic modeling method is further proposed to solve stick-slip nonlinear switchover problem of the soft robot. Since the curved beam is divided into finite segments, an angular variable of an arbitrary point is introduced to elaborate the deformed shape of the curved beam, and then the dimensionless discretized equations of motion can be established via theoretical derivation and solved by implicit integration method. Through dynamic simulation and analysis, a continuous forward locomotion and net displacement of the robot can be easily observed, and several laws of the locomotion are uncovered, which reveals the stick-slip dynamic behaviors. Distinguished from the normal quasi-static modeling approach, the law of motion of the soft worm-like robot is clarified from the dynamic point of view, which will provide important reference for structural design and optimization control of similar soft robots.

Facet-governed frictional behavior in graphene/h-BN heteronanotubes

Superlubricity, a state characterized by ultra-low friction and nearly-zero wear, has conventionally been linked to planar incommensurate interfaces between heterogeneous van der Waals layered materials. In this work, our investigation introduces a novel perspective by highlighting the pivotal role of curvature in heterostructures. Employing our recently developed anisotropic interlayer force field, we demonstrate the profound impact of size and chirality on the morphological characteristics, specifically circumferential faceting, of heterogeneous graphene/h-BN nanotubes. This exploration unravels a consequential transition from a superlubric to a high-friction state, coinciding with the transformation of nanotube cross-sections from cylindrical to faceted shapes. The induction of a faceted scenario triggers redistribution of moiré-dependent distortion deformation during sliding, resulting in a transition from a stick-slip mode to a high-friction state. This stands in stark contrast to the smooth-sliding mode (superlubric state) observed in non-faceted heterogeneous nanotubes. Our discoveries provide valuable insights for the intentional design of quasi one-dimensional van der Waals metamaterials and devices with tunable tribological properties, and expand the current understanding of superlubricity.

Development and Test of a Multimode Piezomotor With Active Contact Force Adjusting

Piezomotors have been widely used for motion generation with long stroke and fine resolution, where stick-slip mode features a high motion velocity but a low load capacity, inchworm mode has a high load capacity but a low motion velocity, and scan mode is able to realize super-high resolution but less travel range. Combining these motion modes to achieve a well-rounded piezomotor is challengeable but significant. In this study, a piezomotor with multiple motion modes is proposed. A compliant mechanism with a parallelogram mechanism and lever-type amplifiers is designed to realize various motion modes and adjust the contact force, which has a significant impact on motion performance. To prevent the backward motion and slippage during motion, two power-function based driving signals are designed and analyzed for stick-slip mode and inchworm mode, respectively. A prototype of the designed piezomotor was fabricated to validate the feasibility. According to the experiment results, the maximum motion velocity is 3.24 mm/s, the load capacity is 7.85 N, and the most fine displacement resolution is 10 nm. The proposed methodology is applicable to other types of multi-mode piezomotors.

Dynamic modeling and simulation for pneumatic landing airbag system with frictional contact

The landing airbag system, a mechanism composed of thin-walled structures, is designed to ensure the safe landing of a lander. To investigate the dynamic behavior of the landing airbag with large deformations, a novel modeling approach incorporating gas exchange and frictional contact is proposed. The Absolute Nodal Coordinate Formulation (ANCF) is introduced to model the flexible airbag. Subsequently, the gas parameters inside the airbag are calculated by integrating the Control Volume (CV) Method and the energy conservation equation. Additionally, based on master–slave techniques, a frictional contact formulation for the thin-walled structure and the rigid plane is presented, in which the normal contact force is estimated using the penalty method, and the velocity-based friction model accounting for the stick–slip transition characterizes the tangential friction. Furthermore, the bounding box technology is adopted to improve contact detection efficiency. A series of numerical examples are performed, which demonstrates the proposed model’s advantages in terms of precision and versatility. Finally, the landing dynamic characteristics of the airbag landing system for the small lunar lander are successfully revealed, and the parameter analysis for the airbag system is expected to aid the design optimization of the airbag cushioning system.

Efficient finite element modelling of helical strand cables utilising periodicity

This paper proposes a repeated unit cell (RUC) FE modelling strategy for multilayered helical strand cables subject to tensile loading and bending with an initial tensile load. The approach utilises the axial periodicity in helical structures to reduce computational domain to two cable periods. A novel mesh creation method allowing the exact geometry of helical strands to be discretised into solid elements while maintaining flat end surfaces is proposed. Periodic boundary conditions (PBC) allowing for geometric and material nonlinearity are used to implement cyclic loads to study hysteresis in single and multilayered cables. Comparisons made to existing experimental and analytical results validate the models ability to capture hysteresis due to plasticity and geometric effects such as the stick–slip transition in bending. Examination of the cross-sectional stress distribution shows plasticity initiates at contact points at loads which are 25% of the load at which the cable tensile response deviates from linearity.

Metric-based anisotropic mesh adaptation for viscoelastic flows

The computation of flows of viscoelastic fluids is expensive compared to standard fluids. Besides degrees-of-freedom for velocity and pressure, the viscoelastic stresses introduce an additional unknown to the system. While adaptive meshing techniques are commonly used for simulations of standard fluids, their application is seldom explored in the context of viscoelastic fluids. In this work, we apply an anisotropic mesh adaptation algorithm to solve the viscoelastic flow problem. Our flow solver is based on a logarithmic reformulation of the viscoelastic constitutive laws, which greatly reduces the stringent stability requirements on the mesh size and allows adaptive meshing in this context. For discretization, we use a stabilized finite element method. We present numerical results for a flow past a cylinder. The adaptive method produces near mesh-independent results up to Weissenberg number Wi=0.7. Our results indicate that with an anisotropic refinement strategy, fewer mesh elements are needed to maintain the same error level as with an isotropic refinement strategy. In a stick-slip transition flow, we demonstrate the capability of the adaptive method to produce optimal meshes even in the presence of a singularity in the solution.

Conditions of enhanced evaporation for nanofluids droplet and inhibition of coffee-ring effect under buoyancy and Marangoni convection

Evaporation of nanofluid droplets whose size is larger than capillary length is common in industrial processes, but there is currently a lack of research on the evaporation kinetics and more complex deposition patterns under the combined effects of buoyancy and Marangoni convection of large evaporating droplet. Experimental investigations on evaporation of Al2O3H2O nanofluid sessile droplet with initial contact line diameter of 4 mm on heating PTFE coating substrate are reported. The variation in contact angle, contact radius, and droplet volume over time under different conditions were obtained through experiments. The average evaporation rate is calculated. Internal flow characteristics are inferred through the surface temperature distribution detected by the top view infrared camera. The constant contact radius mode takes place at the beginning of evaporation. Then mixed evaporation mode and stick slip mode may occur for different substrate temperature, nanoparticle mass concentration and nanoparticle size. Increasing nanoparticle size causes a decrease in average evaporation rate. Whether the use of nanofluids can improve evaporation rate and heat transfer or not depends on multiple factors. Convection cells exist, and three kinds of deposition patterns are formed due to the underlying coupled transport phenomena. Under the combined effect of buoyancy and Marangoni convection in this article, the most common coffee-ring pattern does not appear. The deposition patterns are directly affected by the pinning stability, which decrease at higher temperature.

A Second-Order Dynamic Friction Model Compared to Commercial Stick–Slip Models

Friction has long been an important issue in multibody dynamics. Static friction models apply appropriate regularization techniques to convert the stick inequality and the non-smooth stick–slip transition of Coulomb’s approach into a continuous and smooth function of the sliding velocity. However, a regularized friction force is not able to maintain long-term stick. That is why dynamic friction models were developed in recent decades. The friction force depends herein not only on the sliding velocity but also on internal states. The probably best-known representative, the LuGre friction model, is based on a fictitious bristle but realizes a too-simple approximation. The recently published second-order dynamic friction model describes the dynamics of a fictitious bristle more accurately. It is based on a regularized friction force characteristic, which is continuous and smooth but can maintain long-term stick due to an appropriate shift in the regularization. Its performance is compared here to stick–slip friction models, developed and launched not long ago by commercial multibody software packages. The results obtained by a virtual friction test-bench and by a more practical festoon cable system are very promising. Thus, the second-order dynamic friction model may serve not only as an alternative to the LuGre model but also to commercial stick–slip models.

Large deformation of longitudinal-torsional-lateral coupled effect of round balance rope in mine friction hoisting system

Torsion deformable spatial beam and Costello theory are used to establish longitudinal-torsional-lateral coupled model of round balance rope. Based on Coulomb’s friction law and longitudinal-torsional-lateral coupled model, the nonlinear coupled dynamic model with friction constraint of round balance rope is established. Meanwhile, time-varying multi-segments non–equal-length element transformation method (TMN-ETM) is proposed to save computation time. Then, natural frequencies, lateral responses are calculated when the coupled stiffness coefficient is zero. And the calculations are compared with traditional solution method. The results show that only about few areas in the round balance rope loop have large stress norm value, while the rest parts have small stress values. Besides, dynamic responses of the balance rope with balance rope suspension rotor releasing are conducted. When the static friction is converted to dynamic friction, the friction torque and angle acceleration will be mutated at the switching instants, and slip-stick transition in angle acceleration occurs.

Binary Mixture Droplet Evaporation on Microstructured Decorated Surfaces and the Mixed Stick-Slip Modes.

The interactions between liquid droplets and solid surfaces during wetting and phase change are important to many applications and are related to the physicochemical properties of the substrate and the fluid. In this work, we investigate experimentally the evaporation of pure water, pure ethanol, and their binary mixture droplets, accessing a wide range of surface tensions, on hydrophobic micro-pillared surfaces varying the spacing between the pillars. Results show that on structured surfaces, droplets evaporate following three classical evaporative behaviors: constant contact radius/pinning, stick-slip, or mixed mode. In addition, we report two further droplet evaporation modes, which are a mixed stick-slip mode where the contact angle increases while the contact radius decreases in a stick-slip fashion and a mixed stick-slip mode where both the contact angle and the contact radius decrease in a stick-slip fashion. We name these evaporation modes not yet reported in the literature as the increasing and decreasing contact angle mixed stick-slip modes, respectively. The former ensues because the fluid surface tension increases as the most volatile fluid evaporates coupled to the presence of structures, whereas the latter is due to the presence of structures for either fluid. The duration of each evaporation mode is dissimilar and depends on the surface tension and on the spacing between structures. Pure water yields longer initial pinning times on all surfaces before stick-slip ensues, whereas for binary mixtures and pure ethanol, initial pinning ensues mainly on short spacing structures due to the different wetting regimes displayed. Meanwhile, mixed stick-slip modes ensue mainly for high ethanol concentrations and/or pure ethanol independent of the solid fraction and for low ethanol concentrations on large spacing. Contact line jumps, changes in contact angle and pinning forces are also presented and discussed. This investigation provides guidelines for tailoring the evaporation of a wide range of surface tension fluids on structured surfaces for inkjet printing, DNA patterning, or microfluidics applications.

Shear Wave-Induced Friction at Periodic Interfaces for Programmable Mechanical Responses

Abstract Nonlinear phononic materials enable superior wave responses by combining nonlinearity with their inherent periodicity, creating opportunities for the development of novel acoustic devices. However, the field has largely focused on reversible nonlinearities, whereas the role of hysteretic nonlinearity remains unexplored. In this work, we investigate nonlinear shear wave responses arising from the hysteretic nonlinearity of frictional rough contacts, and harness these responses to enable programmable functions. By using a numerical approach, we solve the strongly nonlinear problem of shear wave propagation through a single contact and a periodic array of contacts, accounting for frictional effects. Specifically, the Jenkin friction model with experimentally obtained properties is used to capture the effects of stick–slip transition at the contacts. Results show that friction gives rise to shear-polarized eigenstrains, which are residual static deformations within the system. We then demonstrate how eigenstrain generation in multiple contacts can enable programmable functionalities such as an acoustically controlled mechanical switch, precision position control, and surface reconfigurability. Overall, our findings open new avenues for designing smart materials and devices with advanced functionalities via acoustic waves using the hysteretic nonlinearity of frictional contacts.

Dynamic modeling and analysis for inflatable mechanisms considering adhesion and rolling frictional contact

A new modeling approach is proposed for dynamic analysis of inflatable mechanisms with large deformations, involving frictional contact and adhesion. Firstly, the Absolute Nodal Coordinate Formulation (ANCF) shell element is employed to model the flexible appendage. Then, by combining the master-slave and master-master techniques, a frictional contact formulation for the thin shell and the rigid cylinder is presented, which can capture the stick–slip transition and address both large sliding and rolling scenarios. In addition, a modified contact detection approach is proposed by optimizing the contact detection region to effectively avoid mutual over-penetration and improve detection efficiency. Furthermore, an adhesion element with failure mechanism is developed. Finally, a series of numerical examples are carried out to validate the proposed modeling approach. Together with the successful simulation against the resistance controlled deployment of an inflatable mechanism, the advantages of the proposed approach are demonstrated. Moreover, the most appropriate parameters for adhesion constitutive relationship are obtained to serve the adhesion-based controller design.

Design, analysis and experimental performances of a multi-mode friction inertial piezoelectric actuator

To enrich the output performances and application fields of friction inertial piezoelectric actuators, a multi-mode friction inertial piezoelectric actuator was proposed. It had three driving modes, i.e. the inertial stick-slip mode, the inertial impact mode and the compound driving mode. An integrated flexible mechanism (IFM) consisting of the lever-shaped flexible mechanism (LSFM) and the butterfly-shaped flexible mechanism (BSFM) was designed for achieving these three driving modes. Theoretical analysis of the IFM was performed by using the matrix-based compliance modeling method and the response surface methodology. An experimental system was established to test the output performances of the actuator under various driving modes. Experimental results indicated that the actuator in three driving modes presented different output performances, and the output displacement in the compound driving mode was equivalent to the sum of those in the two single inertial modes. In the compound driving mode, the actuator achieved larger step displacement, and it also achieved good speed, loading capacity as well as motion stability. For instance, the maximum speed was 10.04 mm/s at 250 Hz in the compound driving mode, while they were 5.06 mm/s at 250 Hz in the inertial impact mode and 10.81 mm/s at 450 Hz in the inertial stick-slip mode. Furthermore, output performances of the actuator could be easily tuned in the compound driving mode when two driving voltages were controlled separately, which provided an idea for achieving the linear smooth motion.

An Inchworm and Stick-Slip Dual Mode Piezoelectric Linear Actuator for Cell Injection

Cell injection system for biomedical engineering demands that actuators have large stroke, high resolution and speed for cell positioning and injection. Single mode piezoelectric actuators could meet some of these requirements but hardly all. Stick-slip actuator is easy to achieve high-speed operation, but it is prone to setback; The speed characteristics of the inchworm actuator are lower than those of the stick-slip actuator, but the step is more stable and the setback is lower. This study proposes an inchworm and stick-slip dual mode piezoelectric actuator (ISSPA) for cell injection. It integrates two working modes into one actuator and both modes drive the same slider. The stick-slip mode works at high frequency for fast positioning to the cell and the inchworm mode drives the needle to puncture the cell membrane and accurately locates to the specified location. The structure and working principle of the ISSPA are provided. A prototype of the proposed ISSPA is fabricated and experiments are conducted. When the driving voltage of the piezoelectric stack is 100 V and the frequency is 500 Hz,the maximum speed of the ISSPA is 2.287 mm/s in the stick-slip mode. When the driving voltage of the piezoelectric stack is 60 V, the frequency is 3 Hz and the load is 0.5 kg,the minimum step displacement is 57 nm in inchworm mode. Demonstration of cell injection is carried out by using the ISSPA to positioning and puncturing a zebrafish embryo. Fast positioning with the stick-slip mode and accurate puncture with the inchworm mode are achieved with the ISSPA alone, taking 12 seconds for the whole injection process. It could be expected to apply the ISSPA to cells with wide range of diameter, as the frequency of the stick-slick mode and the voltage of the inchworm mode could be well regulated.

Improved friction model applied to plane sliding connections by a large deformation FEM formulation

Friction is an important source of dissipation in dynamical systems. Properly considering it in the numerical model is fundamental to obtain stable and representative responses in structures and mechanisms. This is especially significant for the well-known Coulomb model due to discontinuity in force when stick-slip transition occurs. In this work an improved friction force model is proposed to smooth the force transition at null velocity, with an additional parameter obtained from the own system state. The improved model is employed in sliding connections of plane frames finite elements. A total Lagrangian Finite Element Method (FEM) formulation based on a positional description of the motion is employed. Using a variational principle, frictional dissipation is added to the total mechanical energy to develop the equations of motion. The resulting nonlinear equations are solved by the Newton-Raphson method accounting for the friction force update in the iterative process. Examples are presented to show the formulation effectiveness and possibilities in simulating dynamical systems that present the stick-slip effect.

An alternate state-space algorithm for dynamic solution, sensitivity analysis and parameter identification of dry friction systems

Dry friction is one of the most complicated nonlinear phenomena in mechanical systems, due to its discontinuous stick–slip property. This property certainly brings difficulty to the solution and identification of dry friction systems. To overcome the difficulty, an alternate state-space algorithm is proposed in this paper to transform the dry friction system into a piecewise linear system. In doing so, the stick–slip process is firstly modeled by a zero–one representation, with which the stick–slip transition conditions are deduced. Then, the transition points are detected by the transition conditions to break the system into several pure stick or slip phases; each phase corresponds to a linear system. Dynamic solution of the piecewise linear system is quickly acquired by precise time step integration over an arbitrary pure stick or slip phase and the sensitivity analysis, pertaining also to a piecewise linear equation, can proceed exactly in a similar way. As is noteworthy, the sensitivity may admit jumps at the transition points due to the discontinuity of the dry friction system and therefore, the affine relation between the sensitivity before and after a transition point is elaborately derived. Eventually, based on the acquired sensitivity and the Tikhonov regularization, a sensitivity approach is developed to inversely identify the parameters of the dry friction system. Numerical examples and an experimental case are studied to demonstrate the accuracy and efficiency of the proposed alternate state-space algorithm.

Friction-induced vibration of a stick–slip oscillator with random field friction modelling

In this paper, stochastic planar stick–slip motions are investigated using a slider-on-belt model where the coefficient of friction (COF) of the contact interface is modelled as a random field. New three-variable stick–slip transition criteria are proposed to improve the accuracy and robustness of the algorithm. Stochastic analyses are performed concerning the Peak-to-Valley value of the displacement and friction forces and the time duration of the stick state. It is found that the correlation length of the COF random field is dominantly responsible for the stochastic behaviours of the system. In contrast, the belt velocity and the mean value of the COF have a significant influence on the time duration of the stick state compared with the corresponding deterministic slider-on-belt model.