Stick-slip Effect Research Articles

Friction with Hysteresis Loop Modeled by Tensor Product

Engineers encounter the problem of friction in any mechanical system. Friction force is strongly nonlinear and varies considerably while the system is working. In the case of high-precision applications friction makes the situation even more complex, as the stick-slip effect occurs near the target position. This paper introduces a pneumatic servo-system for investigation of the behavior of friction near the target position. A new model is proposed which takes the hysteresis loop of the friction also into consideration emphasizing the importance of hysteresis. This paper presents the tensorproduct (TP) based modeling of friction which is suitable for control design. The main advantage of the TP model transformation is that due to its polytopic model form Linear Matrix Inequality (LMI) can be immediately applied to the resulting model to yield controllers with guaranteed performance. The main contribution of this paper is the application of TP model transformation making the identification of friction parameters unnecessary by utilizing directly the measured data itself.

Stick-Slip Effect in a Vibration-Driven System With Dry Friction: Sliding Bifurcations and Optimization

Vibration-driven systems can move progressively in resistive media owing to periodic motions of internal masses. In consideration of the external dry friction forces, the system is piecewise smooth and has been shown to exhibit different types of stick-slip motions. In this paper, a vibration-driven system with Coulomb dry friction is investigated in terms of sliding bifurcation. A two-parameter bifurcation problem is theoretically analyzed and the corresponding bifurcation diagram is presented, where branches of the bifurcation are derived in view of classical mechanics. The results show that these sliding bifurcations organize different types of transitions between slip and sticking motions in this system. The bifurcation diagram and the predicted stick-slip transitions are verified through numerical simulations. Considering the effects of physical parameters on average steady-state velocity and utilizing the sticking feature of the system, optimization of the system is performed. Better performance of the system with no backward motion and higher average steady-state velocity can be achieved, based on the proposed optimization procedures.

Research on the Low Velocity Accuracy Control of the Direct Drive Volume Control Electro-Hydraulic Servo System

The Direct Drive Volume Control (DDVC) Electro-hydraulic Servo System is a new Electro-hydraulic Servo System. With the development of its application, how to improve the trajectory tracking precision of the DDVC system in low velocity motions becomes more important in the field. So that, the level of the low velocity characteristic impacted the system become to an important subject. In this paper, the mathematical mode of AC asynchronism motor Direct Torque Control was established, and the simulation mode was built. In addition, the idealized model of the DDVC system which based on united simulation of AMEsim/Simulink was established, simulation was executed. In order to make the research available, the low velocity characteristic of the DDVC system was also analyzed, and the low velocity characteristic simulation model was built. Computer simulation validated that the friction is seriously influenced the system performance when the system working on the low velocity mode. An integral back stepping adaptive control law is designed to realize the friction compensation and load disturbance estimation. From the Lyapunov theory, the stability of the closed-loop system is proved. Simulation results show that LuGre friction in servo systems will lead to the effect of limit cycles and stick-slip. Moreover, the proposed compensation method can greatly reduce the effect and improve the system tacking accuracy and robustness.

Effects of stick-slip on stress intensity factors for subsurface short cracks in rolling contact

This paper theoretically investigates the effects of stick-slip in rolling contact zone on stress intensity factors (SIFs) for subsurface short cracks. New mathematical models for SIFs including stick-slip ratio are deduced in two cases. One is a subsurface short crack parallel to surface, and the numerical analysis shows that the value of K II increases with the increase of stick-slip ratio; the other is a subsurface short crack perpendicular to the surface, and the numerical analysis indicates that the positive value of K I decreases with the increase of stick-slip ratio. As ΔK I and ΔK II are necessary to evaluate the fatigue crack propagation rate or fatigue lifetime, the influences of stick-slip ratio on them are then discussed. It is found that the maximum variations of ΔK I and ΔK II are both around 3.0% due to stick-slip ratio variation.

Molecular Dynamics Simulations of Sliding Friction of Rigid Sphere with Single Crystal Copper Surface

Using LAMMPS to establish the three-dimensional sliding friction model of the nanoscale diamond hemisphere with the single-crystal copper surface. Simulation and solving the process of sliding friction, research the micro-contact area atomic states change in sliding friction process, and study the friction characteristics change when the rigid sphere sliding on rough surface of the single crystal copper with minute projections. The results indicate that, in the sliding friction process, the lattice of substrate atoms are damaged under the forces of the extrusion which also cause corresponding dislocation and deformation. In the direction of the hemisphere movement, generate the pileup and side stream phenomena, and produce furrows. Friction and normal force rapidly increase with the depth of contact, and then enter into a stable sliding phase. For the thermal motion of atoms, formation of dislocations and the stick-slip effect, the curves of friction and normal force present waves of sawtooth. Small defect on surface of the substrate almost have no effect on the process of sliding friction.

(Invited) Linear Magnetic Tape Heads and Contact Recording

Linear tape recording heads, introduced in 1984, originally were cylindrical ferrite structures having shunt-biased magnetoresistive sensors. In 2000, heads transitioned to flat-lapped, ceramic wafers and anisotropic magnetoresistive (AMR) sensors fabricated in hard disk drive (HDD) facilities. In 2008, heads transitioned to giant magnetoresistive (GMR) sensors. Engineering tape heads has meant dealing with problems related to the head-media interface. Examples include sub-nanosecond pulses in sensors having metal shields (ca. 1994), signal losses and telegraph noise caused by parasitic electrical connections and spacing due to deposits that form at low relative humidity. Wear management, especially with 'green' media, and stick-slip effects are on-going challenges. A strategy was created for protecting GMR tape heads, leading to the discovery of polycrystalline Al2O3 films.

Application of Hénon method in numerical estimation of the stick–slip transitions existing in Filippov-type discontinuous dynamical systems with dry friction

Accuracy of numerical modeling of any discontinuous dynamical system plays an important role in the proper use of the tools applied for its analysis. No less important in this matter is the numerical estimation of the phase trajectories, bifurcation diagrams, and Lyapunov exponents. This paper meets these expectations presenting application of Hénon’s method to obtain good numerical estimations of the stick–slip transitions existing in the Filippov-type discontinuous dynamical systems with dry friction. Subsequent sections are focused on the problem definition, block diagrams of the numerical procedure coded in Python, application of the method that was originally proposed for Poincaré maps, its use in estimation of phase trajectories, bifurcation diagrams of tangent points, and on estimation of the Lyapunov exponents for a selected two-dimensional system with stick–slip effect.

Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects

In this article, a discrete model of a drill-string system is developed taking into account stick-slip and time-delay aspects, and this model is used to study the nonlinear motions of this system. The model has eight degrees-of-freedom and allows for axial, torsional, and lateral dynamics of both the drill pipes and the bottom-hole assembly. Nonlinearities that arise due to dry friction, loss of contact, and collisions are considered in the development. State variable dependent time delays associated with axial and lateral cutting actions of the drill bit are introduced in the model. Based on this original model, numerical studies are carried out for different drilling operations. The results show that the motions can be self-exited through stick-slip friction and time-delay effects. Parametric studies are carried out for different ranges of friction and simulations reveal that when the drill pipe undergoes relative sticking motion phases, the drill-bit motion is suppressed by absolute sticking. Furthermore, the sticking phases observed in this work are longer than those reported in previous studies and the whirling state of the drill pipe periodically alternates between the sticking and slipping phases. When the drive speed is used as a control parameter, it is observed that the system exhibits aperiodic dynamics. The system response stability is seen to be largely dependent upon the driving speed. The discretized model presented here along with the related studies on nonlinear motions of the system can serve as a basis for choosing operational parameters in practical drilling operations.

Molecular Dynamics Simulation of Nanoscale Sliding Friction Process between Sphere and Plane

Contact surface of nanoscale sliding friction represent some new features that are different from the macro scale sliding friction, which need to seek new analysis methods. Molecular dynamics simulation is an effective method to describe microscopic phenomena. Therefore, Molecular dynamics method was used to study mechanical behavior of contact surface of nanoscale sliding friction. A molecular dynamics model of hemisphere sphere sliding on rectangular solid plane was built. State change of the micro contact area and friction force variation in the process of sliding friction were observed and analyzed after solution and simulation. The results show that, at the beginning position of the sliding, with different contact depth, contact action region of hemisphere and plane generated the atoms displacement, re-arranged and close-packed accumulation is also different. The deeper the contact depth is, the greater the atoms close-packed accumulation is, and the greater the contact deformation is. In the process of sliding friction, the contact surface of the basal body has produced lattice destruction, surface upheaval and silicon atoms close-packed accumulation, and then formed furrow scratches. At the same time the silicon atoms of the hemisphere generated atomic migration obviously and adhered on the basal body surface. The top of the hemisphere was torn and peeled, which resulted in wear. The deeper contact depth is, the more loss of the material of the hemisphere is, and wear become heavier. The curve of friction force and sliding displacement in different contact depths shows that the deeper contact depth is, the greater friction force is. The friction force increases quickly at the beginning of the sliding. Then the friction force remains steady relatively at stable sliding phase. In subsequent sliding process, due to hemisphere was worn and the original contact surface changed in size, shape and configuration state, friction force decreases obviously. Besides, in process of sliding friction, due to stick-slip effect, friction force appears obviously fluctuations. Moreover, if the sliding speed is large the changes of sliding speed have less effect on friction force when the nanoscale sphere sliding on the plane at the different speeds.

Singing sands, booming dune sands, and the stick–slip effect

The origin of the acoustic and seismic emissions from impacted singing grains and from avalanching dune sand grains is sought in modes of vibration in discreet grain columns. It is postulated that when the grains in a column are pressed together and forced to slide over one another, elastic shear bands are formed at the contact areas with distinct elastic moduli. Such contact shear bands would have implications in the formulation of the Hertz–Mindlin contact theory. The assembly of all grain columns below the impacting pestle forms the slip (slide) shear band. The transfer of energy from the pestle to the modes of vibration in such columns is effected by the stick–slip effect. The intense collective vibration of all columns in the slip shear band results in the familiar musical sound. The concept of grain flowability is used to justify the disparity between the acoustic emissions from impacted singing grains and from avalanching booming dune sand grains. The concept of grain columns is assumed to apply in the freely avalanching sand band, but with longer length to justify the lower frequencies. This approach predicts frequency spectra comprising a low-frequency content and a dominant frequency with its harmonics in agreement with the experimental evidence. Additionally, it can account for the low-frequency vibration evoked when booming sand flows through a funnel, with implications in the understanding of grain silo vibrations. It is argued that sand grains do not sing or boom because the stick–slip effect in not applicable in the contact shear bands.

Low-Speed Voltage-Input Tracking Control of a DC-Motor Numerically Modelled by a Dynamical System with Stick-Slip Friction

Stick-slip vibrations appear during relative motion between contacting surfaces of miscellaneous frictional pairs. They depend on the viscous force, Coulomb force or other velocity-dependent forces. These effects appear in almost all mechanical systems, for instance, in positioning systems like servomechanisms, impulse encoders and stepper motors which operate at, or about zero velocity of relative motion between shafts and sliding bearings. This paper presents numerical modelling of a DC-motor as a dynamical system with stick-slip effect which appears while direction of rotation of its rotor crosses zero velocity speed. These investigations are aimed on some future applications of the control technique serving for explanation of bifurcation phenomena existing in such kind of discontinuous systems. Putting emphasis on nonlinear effects we apply the well-known, but a bit extended sliding-surface method allowing for compensation of frictional effects. A limit cycle on a phase plane as well as time-histories of control inputs and system outputs were obtained using numerical simulations performed in Simulink.

A Novel Trans-Scale Precision Positioning Stage Based on the Stick-Slip Effect

This article focuses on developing a novel trans-scale precision positioning stage based on the stick-slip effect. The stick-slip effect is introduced and the rigid kinematics model of the stick-slip driving is established. The forward and return displacement equations of each step of the stick-slip driving are deduced. The relationship of return displacement and the acceleration produced by friction are obtained according to displacement equations. Combining with LuGre friction model, the flexible dynamics model of the stick-slip driving is established and simulated by using Simulink software. Simulation results show that the backward displacement will reduce with the acceleration of the slider produced by dynamic friction force, the rigid kinematics model is also verified by simulation results which are explained in further detail in the article.

Dynamics of a three-module vibration-driven system with non-symmetric Coulomb’s dry friction

In the present paper, a three-module vibration-driven system moving on a rough horizontal plane is modeled to investigate the relation among the system’s steady-state motion, external Coulomb’s dry friction force and internal excitations. Each module of the system represents a vibration-driven system composed of a rigid body and a movable internal mass. Major attention is focused on the primary resonance situation that the excitation frequency is close to the first-order natural frequency of the system. In the case that the external friction is low, the internal excitation is weak and the stick–slip motion is negligible, both methods of averaging and modal superposition are employed to study the steady-state motion of the system. Through a set of algebraic equations, an approximate value of the system’s average steady-state velocity is obtained. Several numerical examples are calculated to verify the validity of the analytical results both qualitatively and quantitatively. It is seen that big quantitative errors will appear if stick–slip motions occur. Then, two mechanisms for the possible stick–slip motions are put forward, which explain the errors on the average steady-state velocity. Numerical simulations verify our analysis on the stick–slip effects and their mechanisms. Finally, to maximize the average steady-state velocity of the system, optimal control problem is studied. It is shown that, in addition to modifying the friction coefficients, the improvement of the system’s efficiency can be provided by changing the initial phase shifts among the three internal excitations.

Modeling and Waveform Optimization of a Nano-motion Piezo Stage

Piezo actuators are used in high-precision systems that require nanometer accuracy. In this paper, we consider a nano-motion stage driven by a walking piezo actuator, which contains four bimorph piezo legs. We propose a (model-based) optimization method to derive waveforms that result in optimal driving properties of the walking piezo motor. A model of the stage and motor is developed incorporating the switching behavior of the drive legs, the contact deformation, and stick-slip effects between the legs and the stage. The friction-based driving principle of the motor is modeled using a set-valued friction model, resulting in a model in terms of differential-algebraic inclusions. For this model, we developed a dedicated numerical time-stepping solver. Experiments show a good model accuracy in both the drive direction and the perpendicular direction. The validated model is used in an optimization, resulting in waveforms with optimal driving properties of the stage at constant velocity. Besides the model-based optimization, also a direct experimental data-based waveform optimization is performed. Experiments with the optimized waveforms show that compared to existing sinusoidal and asymmetric waveforms in literature the driving properties can be significantly improved by the model-based waveforms and even further by the data-based waveforms.

Comparison of Sessile Drop and Captive Bubble Methods on Rough Homogeneous Surfaces: A Numerical Study

Quasi-static experiments using sessile drops and captive bubbles are the most employed methods for measuring advancing and receding contact angles on real surfaces. These observable contact angles are the most easily accessible and reproducible. However, some properties of practical surfaces induce certain phenomena that cause a built-in uncertainty in the estimation of advancing and receding contact angles. These phenomena are well known in surface thermodynamics as stick-slip phenomena. Following the work of Marmur (Marmur, A. Colloids Surf., A 1998, 136, 209-215), where the stick-slip effects were studied with regard to sessile drops and captive bubbles on heterogeneous surfaces, we developed a novel extension of this study by adding the effects of roughness to both methods for contact angle measurement. We found that the symmetry between the surface roughness problem and the chemical heterogeneity problem breaks down for drops and bubbles subjected to stick-slip effects.

Dynamics of a mobile system with an internal acceleration-controlled mass in a resistive medium

The dynamics of a mobile system with a movable internal mass is investigated in this paper. Due to the periodic motion of the internal acceleration-controlled mass as well as the anisotropy of the external resistance, the system can move in a resistive medium. Major attention is given to the steady-state motion and stick–slip effect of the system as a whole. For anisotropic Coulomb's dry friction, in light of the non-smooth factors in both the internal control mode and external resistance, method of averaging is adopted to obtain an approximate expression of the average steady-state velocity when the stick–slip motion is absent. Optimizing the parameters of the internal controlled mass enables one to realize a maximal average steady-state velocity of the system. In view of the stick–slip effect, the steady-state motion of the system is classified into eight types, and the characteristics of each type are analyzed. Stick–slip motion is of our interest and receives extra attention. Two strategies of control are put forward based on the characteristics of stick–slip motion. Making use of these two control strategies, directed motions of the system are possible and the direction of the motion can be simply controlled by modifying the values of internal accelerations. To achieve an always forward motion with higher average steady-state velocity, further optimization is carried out. For anisotropic linear resistance, the approximate expression of average steady-state velocity can be also obtained by the method of averaging. No stick–slip motion may occur in this instance. All the analytical results are numerically simulated in order to verify their correctness.

Movement Modeling and Testing of a Novel Trans-Scale Precision Positioning Stage Based on the Stick-Slip Effect

A novel trans-scale precision positioning stage based on the stick-slip effect was developed. Combining with LuGre friction model, the flexible movement model of the stick-slip driving was established and simulated in Simulink software. Simulation analysis got the displacement and speed curve of slider and the net displacement of each step was calculated. The movement of slider lags behind the PZT actuator. The testing prototype of the stage driving by stick-slip effect was designed and the movement parameters of forward and reverse direction was tested, the results of movement model and simulation was verified by the testing datas. The problem of the difference of forward and reverse movement was proposed.

A fluidic-muscle driven force-controlled parallel platform for physical simulation of virtual spatial force-displacement laws

Described in this paper is a six-legged Stewart-Gough parallel platform driven by a relatively new type of fluidic muscles. The advantage of the platform is that it is virtually free of stick-slip effects. Thus, the device is well-suited for fine-tuned force control and for physical simulation of virtual force-displacement laws. The legs of the platform are of type RRPS and are equipped with a coaxial coil spring and a fluidic muscle providing push and pull forces. Each leg is equipped with a force sensor, a pressure sensor, and a magnetostrictive position encoder. The control for the platform consists of six control loops for the six operated actuators with model-based force control comprising individual gas models as well as the rubber nonlinearities for each leg. The control law also includes the gas flow in the proportional directional control valve in 3/3-way function. The present paper describes the basic architecture of the platform, the dynamic models, as well as testbed results for the existing fluidic-muscle parallel platform DynaHex. It is shown that the presented control scheme leads to a stable force control of the platform for quasi-static motion. As an application, the device will be employed in fields of biomechanics, as well as in general environments requiring physical simulation.

Manufacturing and tribological properties of copper matrix/carbon nanotubes composites

The dry wear tests were introduced to investigate the tribology properties varying with the contents of carbon nanotubes, the sliding velocity and the normal loadings on martensitic S45C carbon steels and the copper matrix composites with 5, 10, 15 and 20 vol.% carbon nanotubes, which are fabricated by the vacuum sintering method. The friction coefficient increases as the content of carbon nanotubes decreases and the wear rate shows the lowest value when the carbon nanotubes content is 10–15 vol.%. The rise of stick-slip effect results in that the friction coefficient and the contact resistance increased with the increasing of sliding velocity. Because of the effect in decreasing the stick-slip phenomenon and in increasing the plow and seizing wear, the tribology properties do not change apparently with the increasing of loads. In summary, when PV value is 1.802, the wear rate is the highest.

Squeal vibrations, glass sounds, and the stick-slip effect

The origin of the squeal acoustic emissions when a chalk is rubbed on a blackboard or better on a ceramic plate, and those when a wet finger is rubbed on a smooth surface, such as a glass surface, is sought in the stick-slip effect between the rubbing surfaces. In the case of the squealing chalk, the stick-slip effect is anchored by shear modes of vibration in about a 0.3 mm thick chalk powder band at the rubbing interface, while in the case of the wet finger on glass, by such modes in a band comprising the finger skin. Furthermore, there are the interfacial bands at the contact areas that result in the decrease of the friction coefficient with relative velocity of slide, i.e., the condition for the stick-slip effect to occur. Such bands are basically composed of the asperities on the surface of the chalk band and of the epidermis ridges and the water layer, respectively.