Frictional Motion Research Articles

Slow rupture of frictional interfaces

The failure of frictional interfaces and the spatiotemporal structures that accompany it are central to a wide range of geophysical, physical and engineering systems. Recent geophysical and laboratory observations indicated that interfacial failure can be mediated by slow slip rupture phenomena which are distinct from ordinary, earthquake‐like, fast rupture. These discoveries have influenced the way we think about frictional motion, yet the nature and properties of slow rupture are not completely understood. We show that slow rupture is an intrinsic and robust property of simple non‐monotonic rate‐and‐state friction laws. It is associated with a new velocity scalecmin, determined by the friction law, below which steady state rupture cannot propagate. We further show that rupture can occur in a continuum of states, spanning a wide range of velocities from cminto elastic wave‐speeds, and predict different properties for slow rupture and ordinary fast rupture. Our results are qualitatively consistent with recent high‐resolution laboratory experiments and may provide a theoretical framework for understanding slow rupture phenomena along frictional interfaces.

光刻投影物镜可变光阑的结构设计与分析

The diaphragm structure in a lithographic projection objective is designed depending on the character demand for large adjustable ranges,small installing spaces and high adjustable precision,and the iris diaphragm has an aperture of 236 mm and adjustable precision of NA±0.003.The parameters of the iris piece are calculated in detail and the size of part is acquired.Then,the part of gear is used to reduce the mass and motion friction of the motion structure and the strength of parts such as the rivet and gears is checked to ensure the adjustable precision and material stress of the diaphragm.It is shown that the stress of all of key parts of the diaphragm meets the requirement of the system and the nature frequency of the diaphragm is no dense frequency phenomenon.These results prove the rationality of the proposed structure.

Position control of very lightweight single-link flexible arms with large payload variations by using disturbance observers

In this article, a robust control scheme for trajectory tracking of very lightweight single-link flexible arms is discussed. Since the payload is one of the most variable parameters in a manipulator, the control is designed to achieve an accurate tracking of the desired tip trajectory for any value of the robot tip mass, or even for a tip mass changing during the maneuver. The proposed controller also guarantees stability for small uncertainties in parameters such as stiffness or motor friction. In addition, the effect of spillover on the performance of the controlled system is analyzed, and it is proven that stability and a good performance are preserved independently from the non-modeled high-order dynamics. The control scheme is based on a two nested loops structure. Each of these loops implements a Generalized Proportional Integral (GPI) controller. Moreover, the outer loop includes a disturbance compensation term based on a disturbance observer, which achieves the required insensitivity to payload changes. The theoretical analysis is supported by an extensive set of numerical simulations which shows controlled system response when variations in the robot payload, or dynamics neglected in the controller design, are considered. Finally, some experiments have been carried out in order to test the performance of the tip trajectory tracking of the proposed control system.

1D Model of Precursors to Frictional Stick-Slip Motion Allowing for Robust Comparison with Experiments

In this article, we study the dynamic behaviour of 1D spring-block models of friction when the external loading is applied from a side, and not on all blocks like in the classical Burridge–Knopoff-like models. Such a change in the loading yields specific difficulties, both from numerical and physical viewpoints. To address some of these difficulties and clarify the precise role of a series of model parameters, we start with the minimalistic model by Maegawa et al. (Tribol. Lett. 38: 313, 2010) which was proposed to reproduce their experiments about precursors to frictional sliding in the stick-slip regime. By successively adding an (i) internal viscosity, (ii) interfacial stiffness and (iii) initial tangential force distribution at the interface, we manage to (i) avoid the model’s unphysical stress fluctuations, (ii) avoid its unphysical dependence on the spatial resolution and (iii) improve its agreement with the experimental results, respectively. Based on the behaviour of this improved 1D model, we develop an analytical prediction for the length of precursors as a function of the applied tangential load. We also discuss the relationship between the microscopic and macroscopic friction coefficients in the model.

Sliding mode tracking control of a very lightweight single-link flexible robot robust to payload changes and motor friction

A sliding mode control design methodology is applied to solve the position tracking problem of an uncertain very lightweight single-link flexible robot arm. Throughout this work we seek a control scheme robust with regards to payload and actuator friction changes, without the establishment of any bounding limits on these parameter variations. Based on the decomposition of the robot dynamics into the motor and flexible link submodels, two nested control loops are proposed, each one of these controlled by an independent sliding mode controller. By carrying on this model decomposition, both motor friction and payload changes become matched uncertainties in their respective models, allowing for their effective rejection using these sliding controllers. Simulations and experimental results are shown to demonstrate the performance of the control system proposed.

Kinetics and dynamics of frictional stick-slip in mesoscopic boundary lubrication

The kinetics and dynamics of frictional stick-slip motion of a slider of size extending from mesoscopic upward is analyzed within the framework of a multi-contact, earthquake-like model. The microscopic contacts are characterized by a distribution of static thresholds for individual breaking. The condition for an overall elastic instability leading to stick-slip sliding are derived and details of the slip motion are studied theoretically. The crucial model parameters emerging from this analysis include the delay time for each micro-contact to reform after breaking, the strength of elastic interaction between the contacts, the elasticity of contacts and of the slider, and the distribution of static thresholds for their breaking. The dynamics is also studied with the help of a scaling procedure. As a prototype application, we adopt parameters appropriate to describe recent surface force apparatus (SFA) boundary lubrication experiments. Despite suggestions of extremely large lubricant viscosities, the experimental data are shown to be fully compatible with ordinary, bulk-like viscosity values once the multi-contact aspects are taken into account.

Friction and Wear Properties of Laser Cladding Coatings under Boundary Lubrication Conditions

AISI 1045 steels were laser-clad with Ni-based powder by CO2 HJ-4 coherent laser. The phase composition of the laser-cladding coating was investigated by means of X-ray diffraction (XRD). The cross-section of the cladding coating was observed using a scanning electron microscopy (SEM). The friction and wear properties of the laser cladding coatings sliding against AISI 52100 steel under the lubrication of liquid paraffin containing various anti-wear and extreme pressure additives were investigated using an Optimol SRV reciprocating motion friction and wear tester. Results showed that the laser-cladding coating considerably decreased coefficient of friction and increased wear resistance in sliding against AISI 52100 steel and attributed to the change in the hardness, phase composition of the laser-cladding coating and tribochemical reactions between the laser-cladding coating and the extreme pressure and anti-wear additives.

Precise measurement of velocity dependent friction in rotational motion

Frictional losses are experimentally determined for a uniform circular disc exhibiting rotational motion. The clockwise and anticlockwise rotations of the disc, that result when a hanger tied to a thread is released from a certain height, give rise to vertical oscillations of the hanger as the thread winds and unwinds over a pulley attached to the disc. It is thus observed how the maximum height is achieved by the hanger decrements in every bounce. From the decrements, the rotational frictional losses are measured. The precision is enhanced by correlating vertical motion with the angular motion. This method leads to a substantial improvement in precision. Furthermore, the frictional torque is shown to be proportional to the angular speed. The experiment has been successfully employed in the undergraduate lab setting.

Workspace analysis of 3SPS+1PS bionic parallel test platform for hip joint simulator

In order to evaluate the movement performance of a human hip joint, a novel parallel manipulator called 3SPS+1PS bionic parallel test platform is proposed in this article. SPS denotes the spherical-prismatic-spherical leg, and PS the prismatic-spherical leg where only the prismatic joint is actuated and hence underlined. For the 3SPS+1PS bionic parallel test platform with four degrees of freedom including three rotations and one translation, the formulae for solving the inverse kinematics equations are derived based on the quaternion method. Unit quaternion is used to represent the position and orientation of a moving platform, and singularities caused by Euler angles are avoided. Combining the topological structure characteristics of the parallel manipulator, the orientation workspace of the moving platform at a given translation position is constructed. Moreover, the procedures to solve and evaluate the orientation workspace of the parallel manipulator are obtained. In order to ensure dexterity and obtain more workspace, the condition index is studied by the condition number and singular values analysis of the dimensionally homogeneous Jacobi matrix. The parallel manipulator has three rotations about the Z-axis, the Y-axis, and the X-axis applied to represent three rotation motions (flexion/extension (FE), abduction/adduction (AA), and internal/external (IE) rotation motion) of a human hip joint, respectively. The numerical results illustrate that the 3SPS + 1PS bionic parallel test platform generates ±25° to ±108° in FE, −20° to 20° in AA, and −21° to 21° in IE rotation where the maximum permissible condition numbers of Jacobi matrix are set within the range 15–20 and the parallel manipulator can provide full-scale friction motion for hip joint simulator. In the dexterous orientation workspace, the slide track on the friction counterface of hip joint prostheses can be varied consistently. By verifying the lengths of the SPS-type active legs, the parallel manipulator can provide cross-path multidirectional slide motion for hip joint prostheses. The three-dimensional model and kinematics simulation of the manipulator are established and analysed. The simulation results prove that the 3SPS + 1PS bionic parallel test platform can accurately represent human hip joint motion and provide more reliable experimental data for hip joint prostheses in clinical application. The research builds the theoretical basis for its bionic motion simulation in practical application.

Study on the Mechanical Instability of MICE Coupling Magnets

The superconducting coupling solenoid magnet is one of the key equipment in the Muon Ionization Cooling Experiment (MICE). The coil has an inner radius of 750 mm, length of 281 mm and thickness of 104 mm at room temperature. The peak induction in the coil is about 7.3 T with a full current of 210 A. The mechanical disturbances which might cause the instability of the impregnated superconducting magnet involve the frictional motion between conductors and the cracking of impregnated materials. In this paper, the mechanical instability of the superconducting coupling magnet was studied. This paper presents the numerical calculation results of the minimum quench energy (MQE) of the coupling magnet, as well as the dissipated strain energy in the stress concentration region when the epoxy cracks and the frictional energy caused by “stick-slip” of the conductor based on the bending theory of beam happens. Slip planes are used in the coupling coil and the frictional energy due to “slow slip” at the interface of the slip planes was also investigated. The dissipated energy was compared with MQE, and the results show that the cracking of epoxy resin in the region of shear stress concentration is the main factor for premature quench of the coil.

Effect of surface treatment of graphite nanoplatelet on damping properties of polyetherimide nanocomposites.

Polyetherimide (PEI) with excellent mechanical properties and thermal stability is gaining popularity as infrastructure materials in aircraft and ground transportation. Exfoliated graphite nanoplatelet (GNPs) composed of stacked 2-D graphene layer, have shown great potential as a damping property modifier, owing to their high mechanical performances and strong interlayer frictional motion. Interface bonding between the nanofiller and the polymer matrix is critical to the properties of polymer nanocomposites. This paper reports the investigation on PEI/GNP nanocomposites for their dynamic mechanical properties, specifically to fabricate polymer composites with superior damping properties. In order to determine the effects of interfacial bonding between PEI and GNPs, the GNPs were surface treated by different amounts of silane ([3-(2-aminoethylamino) propyl] triethoxysilane. Preliminary results indicated that adding both types of GNP with and without the silanization treatment does increase the storage modulus of PEI, but surface treated GNP shows much better efficiency in improving the damping capability, compared with pristine GNP, especially at high dosage of silane surfactant.

Nonlinear Vibration Characteristics of a Flexible Blade with Friction Damping due to Tip-Rub

An approximate approach is proposed in this paper for analyzing the two-dimensional friction contact problem so as to compute the dynamic response of a structure constrained by friction interfaces due to tip-rub. The dynamical equation of motion for a rotational cantilever blade in a centrifugal force field is established. Flow-induced distributed periodic forces and the internal material damping in the blade are accounted for in the governing equation of motion. The Galerkin method is employed to obtain a three-degree-of-freedom oscillator with friction damping due to tip-rub. The combined motion of impact and friction due to tip-rub produced a piecewise linear vibration which is actually nonlinear. Thus, a complete vibration cycle is divided into successive intervals. The system possesses linear vibration characteristic during each of these intervals, which can be determined using analytical solution forms. Numerical simulation shows that the parameters such as gap of the tip and the rotational speed of the blades have significant effects on the dynamical responses of the system. Finally, the nonlinear vibration characteristics of the blade are investigated in terms of the Poincare graph, and the frequency spectrum of the responses and the amplitude-frequency curves.

Nonlinear Vibration Characteristics of a Flexible Blade with Friction Damping due to Tip-Rub

An approximate approach is proposed in this paper for analyzing the two-dimensional friction contact problem so as to compute the dynamic response of a structure constrained by friction interfaces due to tip-rub. The dynamical equation of motion for a rotational cantilever blade in a centrifugal fo rce field is established. Flow-induced distributed periodi c forces and the internal material damping in the blade are accounted for in the governing equation of motion. The Galerkin method is employed to obtain a three-degree-of-freedom oscillator with frict ion damping due to tip-rub. The combined motion of impact and friction due to tip-rub produced a piecewise linear vibration which is actually nonlinear. Thus, a complete vibration cycle is divided into successive intervals. The system possesses linear vibrati on characteristic during each of these intervals, which can be determined using analytical solution forms. Numerical simulation shows that the parameters such as gap of the tip and the rotational speed of the blades have significant effects on the dynamical respons es of the system. Finally, the nonlinear vibration characte ristics of the blade are investigated in terms of the Poincare graph, and the frequency spectrum of the responses and the amplitude-frequency curves.

Dissipated energy and boundary condition effects associated to dry friction on the dynamics of vibrating structures

In turbomachines, dry friction devices (under platform dampers, shrouds, and tie-wire) are usually introduced to reduce resonant responses of bladed disks. Dry friction between rubbing elements induces a highly nonlinear dynamic behaviour which flattens the frequency response functions. It is clear that such behaviour requires an optimisation process to find the optimum parameters that lead to the minimum forced response amplitudes. However, different interpretations still remain concerning the explanation of the physical origin of this type of flattening. The most common one is based on dissipated energy. In this case, heat resulting from the relative frictional motion between contacting surfaces is supposed to bring sufficient dissipation to flatten response functions. On the other hand, a different approach considers that a decrease in vibrational amplitudes is explained by changes in boundary conditions induced by a stick/slip behaviour. In this study, a single degree-of-freedom system is used and analysed both in time and in frequency domains (Harmonic Balance Method) in order to show the contribution of respectively energy dissipation and change of contact state on peak levels.

Quasi-Static Frictional Test between Silicon Sharp Probes with in-situ TEM Observation of Real Contact Point

Frictional deformation of a nano-scaled real contact area between silicon MEMS opposing tips was in-situ visualized by a transmission electron microscope and the force to deform the real contact area was simultaneously measured. In our experiment, the initial diameter of the real contact point was 6.4 nm. During the frictional motion at 0.01 nm/s, the force applied to the contact point was gradually increased. The maximum frictional force was 61 nN when the diameter of the real contact point was 2.2 nm. After the maximum force, the force gradually decreased to zero because the real contact point was retracted and finally fractured. The friction coefficient was 0.9, which is reasonable in comparison with the previous reports. This result suggested that the friction was caused by the deformation of the real contact point.

Motion control in double-walled carbon nanotube systems using a Stone–Thrower–Wales defect cluster

The ability to control the motion of a single molecule will have an important impact in nano-mechanical systems. Multi-walled carbon nanotube systems, which have extremely low intertube friction and strong motion confinement, can form the basis for mechanically based motion control. We devise two molecular motion control units based on double-walled carbon nanotubes embedded with a Stone–Thrower–Wales defect cluster, and perform molecular dynamics simulations to determine the characteristics of these two control units. We show that one of the molecular control units is able to perform a logic operation on one logic input and produce three logic outputs, while the other is able to produce two logic outputs. Potential applications of the motion control units include molecular switches, shuttles and mechanically based logic devices.

The Dynamics of the Onset of Frictional Slip

The way in which a frictional interface fails is critical to our fundamental understanding of failure processes in fields ranging from engineering to the study of earthquakes. Frictional motion is initiated by rupture fronts that propagate within the thin interface that separates two sheared bodies. By measuring the shear and normal stresses along the interface, together with the subsequent rapid real-contact-area dynamics, we find that the ratio of shear stress to normal stress can locally far exceed the static-friction coefficient without precipitating slip. Moreover, different modes of rupture selected by the system correspond to distinct regimes of the local stress ratio. These results indicate the key role of nonuniformity to frictional stability and dynamics with implications for the prediction, selection, and arrest of different modes of earthquakes.

Dynamic modeling of a 6-degree-of-freedom Stewart platform driven by a permanent magnet synchronous motor

For an electrical six-degree-of-freedom Stewart platform, it is difficult to compute the equivalent inertia of each motor in real time, as the inertia is time-varying. In this study, an analysis using Kane’s equation is undertaken of the driven torque of the movements of motor systems (including motor friction, movements of motor systems along with the actuators, rotation around axis of rotors and snails), as well as driven torque of the platform and actuators. The electromagnetic torque was calculated according to vector-controlled permanent magnet synchronous motor (PMSM) dynamics. By equalizing the driven torque and electromagnetic torque, a model was established. This method, taking into consideration the influence of counter electromotive force (EMF) and motor friction, could be applied to the real-time dynamic control of the platform, through which the calculation of the time-varying equivalent inertia is avoided. Finally, simulations with typically desired trajectory inputs are presented and the performance of the Stewart platform is determined. With this approach, the multi-body dynamics of the electrical Stewart platform is better understood.

A proposed mechanism for squeaking of ceramic-on-ceramic hips

Ceramic-on-ceramic (COC) bearings for hip arthroplasty have shown low wear rates and low biological reactivity of wear particles. However, a clinical complication receiving increased attention is the phenomenon of squeaking in COC hips and its importance in terms of clinical performance of the bearings. The recent literature presents a wide spectrum of factors claimed to be the cause of squeaking of ceramic hips, and a clear determination of the factors leading to squeaking has been elusive. The current study documents that the ceramic ball-in-socket bearing couple alone, without any metal devices incorporated, can be made to vibrate at an audible frequency when articulated. Consideration of the geometry of current generation ceramic-on-ceramic hip bearings leads to an hypothesis of a rolling/sliding mechanism causing vibration and squeaking. The derived relationship appears to accurately model the frequencies of the noise from hip bearings. Laboratory tests using accelerometers support the predicted relationship between bearing friction and femoral head motion, providing evidence that the proposed roll/slide mechanism reflects the type of motion that occurs during flexion of a modern COC hip device.

Temperature Dependence of Friction at the Nanoscale: When the Unexpected Turns Normal

The dynamics of frictional motion have been studied for hundreds of years, yet many key aspects of these important processes are not understood. The main challenge in predicting frictional response is the complexity of highly non-equilibrium processes going on in any tribological contact. This includes the continuous detachment and reattachment of multiple microscopic junctions at the sliding interface, the kinetics of which are controlled by the interface temperature. Our experiments reveal a non-monotonic enhancement of dry nanoscale friction at cryogenic temperatures for different material classes. We propose a model that reproduces the experimental observations and shows that the peak in temperature dependence of friction emerges from two competing processes acting at the interface: the thermally activated formation as well as the rupturing of an ensemble of atomic contacts. Our experiments and simulations provide a direct link between the temperature and velocity dependencies of friction, thus offering a new conceptual framework to describe the dynamics of dry nanoscale friction.