Stick-slip Research Articles

Modelling and simulation of interaction forces in tugboat-assisted docking of large marine vessels

In this paper, we address modelling and simulation of dynamics involved in docking of large marine vessels with aid of tugboats, with the aim of providing a tool for improved design of control algorithms for autonomous docking operations. Mathematical models of the docking vessel and tugboats in 3DOF are derived, with a special focus on realistic interactions through towline, contact and friction forces with stick–slip dynamics and time delays, which are typically not considered in previous publications on the topic. We also present the implementation of the developed models in the first step towards a Simulink simulator in which considers the special case of tugboat-assisted docking operations in the Narvik harbour. The developed simulator is available on GitHub (see Ørke et al. (2023)) and encompasses model dynamics, tugboat control and vessel control and guidance, although the scope of this paper is model dynamics. We present simulation results that show that we are indeed able to capture interaction dynamics in a realistic way. Finally, we include a discussion of our results and some ideas for further development, as well as some concluding remarks.

Nucleation Mechanism and Rupture Dynamics of Laboratory Earthquakes at Different Loading Rates

The loading rate of tectonic stress is not constant during long-term geotectonic activity and significantly affects the earthquake nucleation and fault rupture process. However, the mechanism underlying the loading rate effect is still unclear. In this study, we conducted a series of experiments to explore the effect of the loading rate on earthquake nucleation and stick–slip characteristics. Through lab experiments, faults were biaxially loaded at varying rates to produce a series of earthquakes (stick–slip events). Both shear strain and fault displacement were monitored during these events. The findings indicate a substantial effect of the loading rate on the recurrence interval and the shear stress drop of these stick–slip events, with the recurrence interval inversely proportional to the loading rate. The peak friction of the fault also decreases with the increasing loading rate. Notably, prior to the dynamic rupture of earthquakes, there exists a stable nucleation phase where slip occurs in a quasi-static manner. The critical nucleation length, or the distance required before the dynamic rupture, diminishes with both the loading rate and normal stress. A theoretical model is introduced to rationalize these observations. However, the rupture velocity of these lab-simulated earthquakes showed no significant correlation with the loading rate. Overall, this study enhanced our comprehension of earthquake nucleation and rupture dynamics in diverse tectonic settings.

Super/sub-loading surface model for constitutive equation of friction

In this study, an elasto–plastic constitutive model of friction incorporating the superloading surface concept was formulated as an extension of the subloading friction model. The proposed model regards the state in which the static friction coefficient is larger than the kinetic friction coefficient as the “bulkiness” of structure and the smooth transition of friction was expressed by the evolution rule of structure.The positive definiteness of the plastic multiplier, the loading condition, and a condition equation for material parameters were clearly derived. The capability of the proposed model in accordance with the subloading-friction model was confirmed in the stick–slip simulation of a mass-spring system.

Fan‐hinged shear instead of frictional stick–slip as the main and most dangerous mechanism of natural, induced, and volcanic earthquakes in the earth's crust

AbstractFrictional stick–slip instability along pre‐existing faults has been accepted as the main mechanism of earthquakes for about 60 years, since it is believed that fracture of intact rocks cannot reflect such features inherent in earthquakes as low shear stresses activating instability, low stress drop, repetitive dynamic instability, and connection with pre‐existing faults. This paper demonstrates that all these features can be induced by a recently discovered shear rupture mechanism (fan‐hinged), which creates dynamic ruptures in intact rocks under stress conditions corresponding to seismogenic depths. The key element of this mechanism is the fan‐shaped structure of the head of extreme ruptures, which is formed as a result of an intense tensile cracking process, with the creation of inter‐crack slabs that act as hinges between the shearing rupture faces. The preference of the fan mechanism over the stick–slip mechanism is clear due to the extraordinary properties of the fan structure, which include the ability to generate new faults in intact dry rocks even at shear stresses that are an order of magnitude lower than the frictional strength; to provide shear resistance close to zero and abnormally large energy release; to cause a low stress drop; to use a new physics of energy supply to the rupture tip, providing supersonic rupture velocity; and to provide a previously unknown interrelation between earthquakes and volcanoes. All these properties make the fan mechanism the most dangerous rupture mechanism at the seismogenic depths of the earth's crust, generating the vast majority of earthquakes. The detailed analysis of the fan mechanism is presented in the companion paper “New physics of supersonic ruptures” published in DUSE. Further study of this subject is a major challenge for deep underground science, earthquake and fracture mechanics, volcanoes, physics, and tribology.

A bistable energy harvester for friction-induced stick–slip vibration

A bistable energy harvester for friction-induced stick–slip vibration

Influence of rail side lubrication and slip rate dependent effects upon the corrugation on the metro small curve track

For investigating the rail corrugation characteristics of metro small curve track under the combined effect of rail side lubrication and slip rate dependence, by developing a three-dimensional vehicle-track coupling numerical model, the wheel-rail (WR) contact stick-slip (SS) characteristics under different transition areas of rail side lubrication in the presence of corrugation were analyzed. Meantime, on the basis of considering the friction slip rate dependence, the SS vibration characteristics under different rail side lubrication conditions were further analyzed to understand the effect mechanism of rail surface friction characteristics on corrugation. The results show that, when there is rail side lubrication, both inner and outer WR systems have the possibility for SS vibration, and the longitudinal SS vibration intensity is greater than the transverse SS vibration intensity; the SS vibration intensity of the inner WR system is greater than that of the outer WR system, indicating that the inner rail is more susceptible to corrugation and the corrugation is more acute. With the expansion of the rail side lubrication range, the standard deviations of longitudinal and transverse adhesion coefficients decrease, illustrating that the expansion of the lubrication range can reduce the SS vibration intensity of WR system. When the co-effects of rail side lubrication and slip rate dependence are considered, the increase of the rail side lubrication range leads to the increase of standard deviations of adhesion coefficients, which may be related to the enhancement of slip effect induced by the increase of the lubrication range. The introduction of slip rate dependent effect can reduce the standard deviation of the WR adhesion coefficient, which demonstrates that the slip rate dependent effect can ease the degree of SS vibration of WR system, thus reducing the probability of corrugation occurrence caused by the SS vibration.

Distributed model for the drill-string system with multiple regenerative effects in the bit-rock interaction

In this paper, an integrated model is presented to study the axial–torsional dynamics of a distributed drill string. The coupled axial and torsional drill string dynamics typically lead to severe phenomena such as bit-bounce and stick–slip, which are the main causes of failure and efficiency reduction. The top-drive dynamics and the Bottom Hole Assembly (BHA) dynamics are interconnected through the drill pipes. In order to preserve the infinite-dimensional feature of the drill pipes in the mathematical modeling, a distributed model in terms of Delay Differential Algebraic Equations (DDAE) is proposed to represent the dynamics of the drill string. The bit-rock interaction, which consists of the cutting and the frictional components, is responsible for the coupling between the axial and torsional dynamics. A rate-independent bit-rock interaction law is employed for both cutting and frictional components. In order to capture the global bit motion, including multiple regenerative effects, the well-bottom depth function is used to determine the depth of cut. The well-bottom pattern evolution is formulated through algebraic equations rather than Partial Differential Equations (PDEs). A new formulation for the linearized drill string system in terms of Neutral-type Delay Differential Integral Equations (NDDIEs) is proposed to investigate the initiation of the oscillations around the nominal operation. By this formulation, the local stability of the distributed system is studied by determining the right-most eigenvalue of the linearized dynamics. A simulation-based case study reflecting real-life scenarios is presented to investigate the dynamical behavior of the system under different operating conditions.

The effect of temperature-dependent interfacial interaction on the stick–slip behavior of polyamide-66/zinc-coated steel

The stick–slip behavior of polymer/metal is a complex frictional issue since the properties of polymers are highly temperature-sensitive. The present study aimed to shed light on the key factors influencing the stick–slip behavior of polyamide-66/zinc-coated steel by conducting experiments at varying temperatures. The results revealed that the stick–slip behavior and interfacial interaction are temperature-dependent. The friction behavior transitioned from stick-slip to smooth sliding at 40 °C. The transition in the interfacial interaction from adhesion to plastic deformation with increased temperature was responsible for the reduction in stick–slip intensity. The reductions in both the potential energy and static friction force were believed to cause the decreased stick–slip intensity, as evidenced by the in-situ observation of the friction pairs through the digital image correlation (DIC) method. The present study could provide a comprehensive and targeted approach to suppressing the stick–slip behavior of polymer/metal over a wide range of temperatures.

Modeling and controlling a rotary piezo actuator

In this study, a novel piezo rotary stick–slip actuator was designed and investigated. This approach employs two piezo actuators to deform a flexible mechanism in order to generate a variable stick-and-slip force that drives the rotor. The compliant mechanism is composed of the bridge amplifiers and lever mechanism. They are arranged in sequence to amplify the piezo actuator's displacement. Hence, the operating range of the actuator, which includes rotation speed and resolution, can be increased. To optimize the fundamental dimensions of the actuator, the method of finite elements was investigated. The mechanical structure is detailed, the operating principle is elucidated, and a dynamic model is developed. From experimental data, the dynamic model of the structure is identified. The actuator achieves an angular displacement resolution of 0.028 degree at an applied voltage of 45 V and an operating frequency range up to 140 Hz, allowing it to be employed in applications requiring high precision positioning. Besides, the closed-loop control scheme is proposed to control the actuator in both directions. The simulation and experimental results have demonstrated that the position of the stick–slip actuator can be effectively controlled through this proposed controller. This is expected to increase the potential application of the stick–slip actuator in industrial practice.

Experimental analysis of friction properties in omega seals: Influence of a coated surface on deformation and contact topography under compressed conditions

In this study, the intricate interplay among surface conditions, friction, and sealing behavior was investigated using a simplified omega seal as a representative model. The effects of surface conditions were examined by preparing samples with a thin coating on one set, which were then compared to uncoated reference samples. Subsequently, the impact arising from surface differences was analyzed. Findings emphasize the critical importance of surfaces characterized by a low coefficient of friction, underlining the necessity for long-term preservation. This investigation revealed a compelling link between the stick–slip phenomenon and the topographical features of the friction interface. These insights not only underscore the essential nature of tailored surface treatments but also their pivotal role in optimizing the performance of rubber seals.

Frictional boundary condition for lattice Boltzmann modelling of dense granular flows

Hydrodynamic approaches that treat granular materials as a continuum via the homogenization of discrete flow properties have become viable options for efficient predictions of bulk flow behaviours. However, simplified boundary conditions in computational fluid dynamics are often adopted, which have difficulty in describing the complex stick–slip phenomenon at the boundaries. This paper extends the lattice Boltzmann method for granular flow simulations by incorporating a novel frictional boundary condition. The wall slip velocity is first calculated based on the shear rate limited by the Coulomb friction, followed by the reconstruction of unknown density distribution functions through a modified bounce-back scheme. Validation is performed against a unique plane Couette flow configuration, and the analytical solutions for the flow velocity profile and the wall slip velocity, as functions of the friction coefficient, are reproduced by the numerical model. The transition between no-slip and partial-slip regimes is captured well, but the convergence rate drops from second order to first order when slip occurs. The rheological parameters and the basal friction coefficient are calibrated further against the discrete element simulation of a square granular column collapsing over a horizontal bottom plane. It is found that the calibrated continuum model can predict other granular column collapses with different initial aspect ratios and slope inclination angles, including the basal slip and the complex internal flow structures, without any further adjustments to the model parameters. This highlights the generalization ability of the numerical model, which has a wide range of application in granular flow predictions and controls.

Investigation of the interface stick-slip friction behavior of clay nanoplatelets by molecular dynamics simulations

As lamella and porous materials, the failure of clay soil is closely related to the microscale friction features between nano minerals sheets. This study delves into the microscale interface stick-slip friction behavior of clay minerals, with a particular focus on kaolinite and halloysite models, under varying hydrostatic pressure conditions. The research unveils several significant discoveries. Firstly, under hydrostatic pressure, the mechanical properties of clay minerals perpendicular to the mineral platelet weaken, accompanied by a gradual reduction in the space occupied by interlayer water molecules. As pressure increases, these molecules assemble into "water molecular clusters", resulting in the formation of two or three layers of water molecular films. At 6 GPa, interlayer water nearly reaches a state of stagnation. Secondly, both kaolinite and halloysite exhibit "stick-slip friction behavior" during shearing, with rising hydrostatic pressure intensifying interatomic interactions and augmenting shear stress fluctuations. Lastly, the calculated friction coefficients (μ) for the three systems (kaolinite –7 Å, halloysite –8.6 Å, and halloysite –10 Å) are 0.035, 0.048, and 0.033, respectively, while the friction angles (φ) are 2.270, 2.900, and 2.263. The cohesion values (C) for these systems, obtained through different methods, demonstrate consistency. These findings advance the understanding of clay mineral behavior under varying conditions and contribute valuable insights to the microscale failure mechanism of clay soil.

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.

Motion of a viscous slug on heterogeneous surfaces: crossover from stick–slip to steady sliding

We present a theoretical study of viscous slug motion inside a microscopically rough capillary tube, where pronounced stick–slip motion can emerge at slow displacement rates. The mathematical description of this intermittent motion can be reduced to a system of ordinary differential equations, which also describe the motion of a pendulum inside a fluid-filled rotating drum. We use this analogy to show that the stick–slip motion transitions to steady sliding at high displacement rates. We characterize this crossover with a simple scaling relation and show that the crossover is accompanied by a shift in the dominant energy dissipation mechanisms within the system.

Identification of Stribeck Model Parameters to Accurately Reveal Stick–Slip Characteristics of a Disc–Block Friction System

Stick–slip vibration is simultaneously influenced by several factors that share complicated coupling relationships. In this research, an experimental investigation was performed to analyze the evolution law of stick–slip characteristics at different working conditions using a tribometer. The results showed that the disc rotational speed and normal force had noticeable impact on both stick–slip vibration and coefficient of friction (COF). Then the Stribeck model, which can characterize COF characteristics in the stick–slip process, was employed and the parameters were identified to construct a dynamic relationship between working conditions and COF. Further, numerical simulations respectively considering and neglecting the dynamic relationship between working conditions and Stribeck model parameters were conducted via an established tribometer analytical model. It was found that the simulation results considering the influence of working conditions on Stribeck model parameters were in better agreement with the experimental results, as the stick–slip vibration depends on the combined effect of working conditions and Stribeck model parameters. Therefore, the dynamic relationship between working conditions and Stribeck model parameters is crucial to accurately reveal stick–slip characteristics.

Statistical laws of stick-slip friction at mesoscale

Friction between two rough solid surfaces often involves local stick-slip events occurring at different locations of the contact interface. If the apparent contact area is large, multiple local slips may take place simultaneously and the total frictional force is a sum of the pinning forces imposed by many asperities on the interface. Here, we report a systematic study of stick-slip friction over a mesoscale contact area using a hanging-beam lateral atomic-force-microscope, which is capable of resolving frictional force fluctuations generated by individual slip events and measuring their statistical properties at the single-slip resolution. The measured probability density functions (PDFs) of the slip length δxs, the maximal force Fc needed to trigger the local slips, and the local force gradient {k}^{{prime} } of the asperity-induced pinning force field provide a comprehensive statistical description of stick-slip friction that is often associated with the avalanche dynamics at a critical state. In particular, the measured PDF of δxs obeys a power law distribution and the power-law exponent is explained by a new theoretical model for the under-damped spring-block motion under a Brownian-correlated pinning force field. This model provides a long-sought physical mechanism for the avalanche dynamics in stick-slip friction at mesoscale.

Compensation of friction and stick-slip uncertainties in trajectory tracking control of servo DC machines considering actuation constraints

Nowadays, electric motors are common in many precision instrument industries that require high-precision control. If a suitable model of a servo system is available, accurate results can be obtained using a model-based control algorithm. The DC motor is one of the most widely used systems in precision industries, for which a high-precision controller can be designed using its mathematical model with feedback on position and velocity. In such systems and other rotating systems, it is necessary to consider friction in the control system design. Friction enters the system in the form of resistant force or torque in both static and kinetic states, which causes uncertainty in the dynamic modeling of the system, the stick-slip phenomenon, and creates a deadzone in the actuation system. In this article, considering a switching dynamic model for different states of a system subject to friction which has a saturation limit on the control input and an actuation system dependent on the angular velocity feedback, first, the stable reaching laws in two modes of position control and velocity control for different dynamic model switch modes are defined. Then, the control input that forces the tracking error to follow the corresponding reaching law for each control mode is calculated. In the next step, according to the limitations of the actuation system, such as saturation and deadzone, using the filtering mechanism and optimal search for each control mode, the desired values are filtered and it is guaranteed that the control input will be chosen within the allowed range. Finally, using the optimal switching mode selection mechanism, the optimal control mode is selected and the voltage is calculated as the next step input.

Friction modelling and the use of a physics-informed neural network for estimating frictional torque characteristics

This paper presents an exploration of friction modeling encompassing theoretical and practical aspects, utilizing a planar or 2D contact system. Various white-box friction models, including static and dynamic variants, are introduced, highlighting the superior capability of dynamic models in comprehensively capturing friction effects, substantiated through numerical simulation. Practical aspects of friction measurement and data-driven friction modeling are elucidated. The discourse extends to the development of grey-box and black-box friction models. A significant contribution lies in the proposition of a physics-informed neural network-based friction modeling approach, presenting it as an advanced and preferable alternative for friction estimation. To exemplify its efficacy, a case study of a torsion-based frictional contact scenario, employing Physics-Informed Neural Network (PINN) and the Nelder–Mead (N–M) algorithm for concurrent dynamics and friction model identification, was examined. Experimental data from a double torsion pendulum system, characterized by discontinuous dynamics, is employed for training. Results demonstrate the PINN’s superiority, providing more accurate representation of stick–slip phases at the contact zone and exhibiting faster performance compared to the N–M algorithm. The paper concludes by deliberating on challenges, prospects, and future directions in friction modeling.

Axial Impact Analysis of Torsion Impactor Based on Water Strike Effect

The stick-slip vibration phenomenon that occurs during the drilling process not only reduces the drilling speed, but also affects the performance of the drill pipe and the service life of the drill bit. In response to the problem of stick-slip vibration, a torsional impactor has been developed. The tool, through its internal throttle action, will produce a sudden change in the mass flow of fluid in the central tube and thus produce a water strike phenomenon, and the change in the axial force of the torsional impactor caused by the water strike effect can cope with the stick-slip vibration that occurs during drilling as well as increase the drilling efficiency. In this paper, the axial impact capacity of the tool is investigated based on its water impact effect. CFD simulations were used to determine the axial impact capacity of the torsional impactor at different drilling fluid flow rates, and the maximum equivalent force of the central tube under the water impact effect was analyzed and strength checks were performed. The research results show that: two axial vibrations occur in the center tube within half a working cycle; As the drilling fluid flow rate increased from 24L/s to 31L/s, the axial impact force of the torsion impactor increased from 32506N to 43189N; the maximum equivalent force of the center tube is 106.59 MPa, which meets the impact strength requirements. Finally, it was verified through field tests that the water impact effect generated inside the torsional impactor can effectively solve the stick-slip vibration problem and improve the rock-breaking efficiency under different drilling fluid flow rates.

Numerical study of hydraulic characteristics of shale fractures during unloading-induced slipping: Effects of inclination angle and unloading rate

This study investigates the roles of inclination angle of fracture (θ) and unloading rate of confining pressure (Ur) on the hydraulic characteristics of shale fractures during the unloading-induced slipping process. A series of fluid flow simulations in the directions both parallel (x-directional) and perpendicular (y-directional) to the shear direction at different shear displacements (ds) were performed. The results show that the channeling effect is more pronounced in the y-direction than that in the x-direction. As ds increases, the fluid flow becomes less anisotropic, and the ratio of permeability in the y-direction (Ky) to that in the x-direction (Kx) gradually decreases first and then remains almost constant. Both Kx and Ky greatly increase with increasing in θ. The Ur significantly affects the permeability when ds increases to a certain value (i.e., 0.8 mm in this study). The efficiency of permeability enhancement represented by ΔK/Δds is evaluated. The mean ΔK/Δds during the slipping process for samples with θ = 50° is 4.73 times and 5.25 times larger than that for samples with θ = 30° in the x-direction and y-direction, respectively. With increasing Ur, the mean ΔK/Δds slightly increases first and then decreases. The occurrence of stick–slip events may control the ΔK/Δds.