Displacement-dependent Friction Research Articles

Identification of a Practical Digital Twin for Simulation of Machine Tools

A practical digital twin for machine tools is proposed in this study. The proposed digital twin is capable of time-domain simulation of machine tools and consists of a controller model, machining process model, and machine dynamic model. To predict the quality of the machined surface after the finishing processes, a precise dynamic model is required. The developed dynamic model consists of an interaction force model, vibration model, and friction force model. A linear auto regressive with exogenous inputs (ARX) model is adopted for the interaction and vibration models. Based on a systematic analysis of the disturbance forces of the machine tool, the friction characteristics are extracted to a displacement-dependent friction model and velocity-dependent friction model. A nonlinear Hammerstein model is adopted to identify the friction. Online identification systems based on the recursive least-squares (RLS) method are developed and tested for each model.

Dynamic process analysis of the Niumiangou landslide triggered by the Wenchuan earthquake using the finite difference method and a modified discontinuous deformation analysis

The Niumiangou landslide was the largest landslide triggered by the 2008 Wenchuan earthquake, which was significantly affected by the amplification effect of seismic acceleration. The ring-shear experiments indicated that the materials in the source area of the Niumiangou landslide were subjected to friction degradation under a big shear displacement, which may result in rapid movement of the landslide. In order to better understand the landslide movement and study the effect of the friction degradation on movement mechanisms, the dynamic process of Niumiangou landslide was simulated with a new numerical method, which combines the finite difference method (FDM) and the discontinuous deformation analysis (DDA). First, the FDM was used to study the initiation time, amplification effect and velocity of the landslide. Afterwards, these initiation velocities were applied to the blocks in the DDA model by corresponding coordination in the FDM model. A displacement-dependent friction model of the sliding surface was incorporated into DDA code to further understand the kinetic behavior of the landslide. The results show that the displacement-dependent friction strongly decreases the friction coefficient of sliding surface under a big displacement, which can obviously promote the run-out and velocity of landslide. The model output well matches the topographic map formed by the landslide. This implies that the proposed model can be applied to the simulation of earthquake-induced landslides with amplification effect, and the friction degradation model is important to clarify the movement mechanism of high-speed and long-distance landslides.

A novel steel lever viscoelastic wall with amplified damper force-friction for wind and seismic resistance

This paper presents a new steel wind- and seismic-resisting wall, called a lever viscoelastic wall (LVEW) that includes a velocity-dependent VE damper and a displacement-dependent friction damper in a device, characterized by two different motion phases. In Phase one motion (i.e., small drifts), the VE damper which is activated by a lever delivers amplified lateral force and energy dissipation to the frame structure. In Phase two motion (i.e., medium-to-large drifts), the VE damper is constrained by a stopper and the friction damper, instead, is activated to provide frictional energy dissipation to the frame. The damping is provided by incorporating VE material and sliding friction in a wall configuration, reducing both the wind and earthquake responses of structures in a single unit. The objectives of the work were to (1) develop the force transfer mechanism and kinematics of the LVEW, (2) verify the cyclic response of LVEWs at low and large drifts, and (3) evaluate the limitation of LVEWs for the applications. Three full-scale LVEW specimens were designed and tested to validate the hysteretic response in two motion phases. The hysteretic response of LVEWs obtained from the test was compared to that from the analytical formulation.

A modified Coulomb's law for the tangential debonding of osseointegrated implants.

Cementless implants are widely used in orthopedic and dentalsurgery. However, debonding-related failure still occurs at the bone-implant interface. It remains difficult to predict such implant failure since the underlying osseointegration phenomena are still poorly understood. Especially in terms of friction and adhesion at the macroscale, there is a lack of data and reliable models. The aim of this work was to present a new friction formulation that can model the tangential contact behavior between osseointegrated implants and bone tissue, with focus on debonding. The classical Coulomb's law is combined with a state variable friction law to model a displacement-dependent friction coefficient. A smooth state function, based on the sliding distance, is used to model implant debonding. The formulation is implemented in a 3D nonlinear finite element framework, and it is calibrated with experimental data and compared to an analytical model for modeIII cleavage of a coin-shaped, titanium implant(Mathieu et al. in J Mech Behav Biomed Mater 8(1):194-203, 2012). Overall, the results show aclose agreement with the experimental data, especially the peak and the softening part of the torque curve with a relative error of less than 2.25%. In addition, better estimates of the bone's shear modulus and the adhesion energy are obtained. The proposed model is particularly suitable to account for partial osseointegration.

Initiation, movement, and run-out of the giant Tsaoling landslide — What can we learn from a simple rigid block model and a velocity–displacement dependent friction law?

Tsaoling landslide is the largest and best documented landslide among several large landslides induced by the 1999 Taiwan Chi-Chi earthquake. Pliocene sedimentary rocks of about 125Mm3 in volume slid along very flat bedding planes dipping by 14° with an average speed of 35–40m/s for about 1650m, before hitting the bank of the Chinshui River during the landslide. Detailed analysis of DTMs before and after the earthquake using a GIS software leads to an accurate determination of the locations of the centroids of landslide mass, revealing the horizontal and vertical displacements of the 2524m and 524m, respectively. Those displacements and landslide mass give an apparent friction coefficient of 0.21 and the release of the potential energy of 1.6×1015J. We conducted rotary-shear high-velocity friction experiments on fault gouge from bedding-parallel faults under semi-wet conditions and at 3MPa normal stress corresponding to the overburden pressure of the landslide mass. We also compiled reported data on the frictional properties on shale powders and fault gouge from the landslide site under both dry and wet conditions, and proposed a velocity–displacement dependent friction law that can describe most experimental data. Newmark analysis of landslide motion with six scenarios for different landslide materials and conditions, assuming a simple rigid block sliding and using measured frictional parameters, revealed that the landslide did not occur with dry frictional properties, and that the landslide occurred at 38–39s with accumulated displacements of 0.62m–1.09m and reached at the river bank at 82–87s after the generation of Chi-Chi earthquake at its epicenter. Those timings are consistent with high-frequency signals at 32–40s and at 76s recorded at a nearby seismic station and with a survivor's witness that the landslide initiated 10s after he felt strong ground motion, possible S wave arrival at 25.2s. Slip-weakening is essential in initiating the landslide and low friction coefficient (0.08–0.1) allowed high-speed of the landslide possible. The landslide was caused by a few peaks of northeast-oriented strong accelerations of the ground motion. Frictional work during the sliding of the landslide mass was estimated to be of about 23% of potential energy, and the rest of the released energy is likely to have been consumed during the stopping phase of the landslide after hitting the river bank in complex processes such as fragmentation, heat dissipation, and spreading of the landslide deposits.

Frictional properties of olivine at high temperature with applications to the strength and dynamics of the oceanic lithosphere

Faulting and brittle deformation of mantle rocks occurs in many tectonic settings such as oceanic transform faults, oceanic detachment faults, subduction zones, and continental rifts. However, few data exist that directly explore the frictional properties of peridotite rocks. Improved constraints on the brittle deformation of peridotite is important for a more complete understanding of the rheological properties of the lithosphere. Furthermore, our comparatively detailed understanding of plastic deformation in olivine allows us to explore the possible role of thermally activated intracrystalline deformation mechanisms in macroscopically brittle processes. It has been hypothesized, and some experimental data indicate, that plastic yielding by dislocation glide (low temperature plasticity) determines the direct effect in the rate and state frictional constitutive formulation. Plastic flow may also have important implications for the blunting or necking at asperity contacts that influences the time and/or displacement dependent friction evolution effect and frictional healing. We present results from saw cut experiments on fine grained synthetic olivine fault gouge conducted in a gas‐medium deformation apparatus in the temperature range of 400–1000°C with 100 MPa confining pressure. We conducted velocity stepping tests to explore the rate and temperature dependence of sliding stability. We also conducted slide‐hold‐slide experiments to investigate the time and temperature dependence of fault zone restrengthening (frictional healing). The mechanical data and microstructural observations allow us to explore the role of thermally activated processes in frictional sliding. The data indicate systematic temperature dependenceof rate and state variables that can be attributed to plastic yielding at grain to grain contacts. We explore the implications of such temperature dependent behavior for controlling the base of the seismogenic zone in the oceanic lithosphere, and we seek insight into possible mechanistic models for the interactions between fracture and flow that could lead to improved constraints on the strength of the lithosphere.

2P1-E07 波動歯車減速機の摩擦モデルの構築(アクチュエータの機構と制御(3))

Modeling of hysteresis behavior of harmonic drive gearing is a difficult problem, which makes it difficult to compensate friction by using controlled actuators. Some researchers suggested to represent the hysteresis by using Maxwell-slip model, but some phenomena, such as drift and displacement-dependent friction torque, are not reproduced by Maxwell-slip model. This paper presents a new friction model that represent hysteresis, drift, and displacement-dependent friction torque. In addition, the model considers the relation between velocity and torque that can be observed through experiments. The proposed model is validated through comparison with experimental results obtained from a manipulator joint.

Hemivariational inequality approach to the dynamic viscoelastic contact problem with nonmonotone normal compliance and slip-dependent friction

We examine a mathematical model which describes dynamic viscoelastic contact problems with nonmonotone normal compliance condition and the slip displacement dependent friction. First, we derive a weak formulation of the model in the form of a hemivariational inequality. Then we embed the hemivariational inequality into a class of second-order evolution inclusions for which we provide a result on the existence of a solution. We conclude with examples of the subdifferential boundary conditions for contact with normal compliance and the slip dependent friction.

Dynamic hemivariational inequalities in contact mechanics

This paper gives a review of results on the existence and uniqueness of solutions to some mechanical contact problems. The second-order evolution problems with a general normal compliance response condition and a normal damped response one in viscoelasticity are discussed. Finally, a new result for a problem which includes the slip displacement-dependent friction and the Tresca model is provided.

Hemivariational inequality for viscoelastic contact problem with slip-dependent friction

In this paper we consider a class of hyperbolic hemivariational inequalities modeling the frictional contact between a viscoelastic body and a rigid foundation. The friction law is described by a multivalued subdifferential relation which includes the slip displacement dependent friction and the Tresca models. We establish the existence of weak solutions to the problem by using a surjectivity result for pseudomonotone mappings.

Suppression of Bending-Torsion Flutter Through Displacement-Dependent Dry Friction Damping

Flutter is an important problem in modern technology engines. Despite significant research in the area of turbomachinery aeroelasticity, flutter instabilities still occur. The flutter suppression potential of dry friction damping with displacement-dependent friction forces is investigated. Bending-torsion coupling, aerodynamic coupling, and realistic aerodynamic damping terms are all considered. The total aeroelastic system is studied under compressible flow conditions and is modeled by a set of first-order differential equations in state-space form. Through time integration studies, it is found that the nondimensional flutter speed can be significantly increased by including displacement-dependent friction forces and by moving the location of the dry friction damper. This result strongly suggests that it may be possible to design the geometry and location of frictional interfaces on airfoils so that damping may be enhanced and flutter can be better controlled. Possihle future applications might be in the area of turbine or fan and compressor hlade systems.

On the contact problem with slip displacement dependent friction in elastostatics

The problem of the static contact with slip dependent friction between an elastic body and a rigid foundation is considered. The existence of a solution is proved. The link between the equilibrium and the minimum of the energy is deduced and sufficient conditions for stability are given. The qualitative behaviour of the solution is decided by the competition between two parameters which involve the geometry, the normal stress, the elastic properties and the slip weakening of the friction force. We distinguish two cases. In the first one we prove that the solution is unique and depends continuously upon the load. In the second case we point out the loss of uniqueness and the discontinuous dependence upon the load of the solution. The existence of an homogeneous sliding is analysed and its local uniqueness is studied. We give sufficient conditions for the bifurcation of nonhomogeneous sliding from homogeneous sliding. An application to anti-plane problem is also given.

Displacement dependent friction in space structural joints

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The role of the shear mach number in earthquake source dynamics

abstract The effect of the rupture velocity upon the spatial and temporal dependence of earthquake source functions is investigated. To this end a model is suggested in which the fault zone is realized as a flexible membrane under the action of a moving force with additional stiffness forces provided by the surrounding medium. The motion of each particle of the membrane is impeded by a displacement-dependent friction and radiation damping. The particle motion along the fault is found to obey an inhomogeneous Klein-Gordon equation whose solutions are derived in closed form. In the time domain, the solutions yield a particle-motion function that has frequently been derived by analysis of earthquake seismograms. The physical parameters in the theoretical source function are found to depend strongly on the Mach number, as already predicted by the theoretical directivity function. The theory excludes the possibility of supersonic rupture and asserts a transonic rupture for major shallow earthquakes and subsonic rupture for seismic events with low and intermediate magnitudes. It predicts new functional relations between the initial particle velocity at the fault's tip, D˙0, the Mach number, M = ν/β, the rise time τ, the stress drop σ∞ and the fault length L.