Friction Oscillator Research Articles

Dynamic analysis of a class of fractional‐order dry friction oscillators

This article investigates a class of Duffing nonlinear dynamic systems with fractional‐order dry friction and conducts in‐depth research on the stability, chaotic characteristics, and erosion of the safety basin of this system; the results are verified through numerical simulation. First, the average method is used to approximate the amplitude–frequency relationship of the system, and the accuracy of the analytical results is verified through numerical experiments. Second, the Melnikov method is used to obtain the conditions for the system to enter chaos in the Smale horseshoe sense, and the Melnikov curve is drawn for further verification. Then, bifurcation diagrams are drawn for the changes in various parameters in the system, with a focus on analyzing the influence of friction factors on chaotic bifurcation. By applying the definition and calculation principle of the maximum Lyapunov exponent, and drawing and utilizing the maximum Lyapunov exponent graph, the chaotic state that the system enters under different parameters is more clearly defined. Finally, the evolution law of the safety basin under various parameter changes, especially dry friction changes, is analyzed, and the erosion and bifurcation mechanism of the safety basin is studied. Comparing with the bifurcation diagram, it reveals that chaos primarily contributes to the erosion of the safety basin.

Thermo-mechanical investigation of a friction oscillator under high-frequency excitation

The frictional behavior, temperature evolution, and system dynamics in tribological systems are closely coupled. However, in many cases, at least one of the mentioned phenomena is neglected or not modeled consistently. This paper presents a model of a thermo-mechanically coupled oscillator, where the reduction of friction force due to high-frequency excitation is analyzed. The oscillator’s equation of motion, the impulse balance, and the heat equation for the thermo-mechanical continuum are evaluated so that a set of nonlinear equations describes the coupled system. Using specific mathematical procedures like Laplace-transformation and a particular transformation ansatz for integral equations, the system can be transformed into a set of ordinary differential equations, enabling efficient simulation. Based on this equation set, an averaging method is applied to eliminate the fast time scale of the mechanical oscillation due to high-frequency excitation so that only the averaged influence of the motion goes into the heat evolution. This procedure leads to concise expressions to determine the stationary state of the system, and the quantities of interest can be calculated conveniently. These equations yield parameter combinations where the friction force can be reduced due to the high-frequency excitation, even though thermal expansion is considered. However, there are also parameter regions where the excitation yields a significantly larger friction force.

Benchmarking the quality improvement strategies of wire arc additive manufacturing process using fuzzy QFD approach

PurposeThe purpose of this paper is to improve the productivity and quality of the wire arc additive manufacturing process by benchmarking the strategies from the selected six strategies, namely, heat treatment process, inter pass cooling process, inter pass cold rolling process, peening process, friction stir processing and oscillation process.Design/methodology/approachTo overcome the lack of certainty associated with correlations and relationships in quality functional deployment, fuzzy numbers have been integrated with the quality functional deployment framework. Twenty performance measures have been identified from the literature under five groups, namely, mechanical properties, physical properties, geometrical properties, cost and material properties. Using house of quality weights are allocated to performance measures and groups, relationships are established between performance measures and strategies, and correlations are assigned between strategies. Finally, for each strategy, relative importance, score and crisp values are calculated.FindingsInter pass cold rolling process strategy is computed with the highest crisp value of 15.80 which is followed by peening process, heat treatment process, friction stir processing, inter pass cooling process,] and oscillation process strategy.Originality/valueTo the best of the authors’ knowledge, there has been no research in the literature that analyzes the strategies to improve the quality and productivity of the wire arc additive manufacturing process.

Study on the Formation Mechanism for High Rail Corrugation

This research employed a tracking investigation and numerical study to examine the initiation of high rail corrugation. Beginning with the trial operation of Metro Line 6 in Chengdu, China, we conducted a follow-up investigation for 2½ years that recorded the rail surface wear morphology of a 600-m radius curved track. The field observation results show that high rail corrugation occurred 12–17 months after the subway was officially put into operation, whereas the low rail of the same track did not show any corrugation. The distribution of high rail corrugation was discontinuous. Due to wear, the profiles of the rails and wheels changed. Two points of contact may occur between the leading outer wheel and high rail, with one contact point at the gauge corner and the other in the vicinity of the railhead (hereafter referred to as two-point contact). We developed a finite-element model that used the measured worn profiles to predict the self-excited frictional vibrations of a leading wheelset–rails system under the condition of two-point contact. We predicted the occurrence trend of self-excited frictional vibrations via the complex eigenvalue analysis. The simulation results show that in the condition of two-point contact, the self-excited frictional oscillation produced at an outer wheel–high rail interface can induce high rail corrugation. The use of straight or double S-shaped web plate wheels and an increase in railpad damping can help to reduce high rail corrugation.

Nanoscale wear evolution on a polystyrene/poly (n-butyl methacrylate) blend

We have investigated the formation of surface nanostructures caused by early-stage wear of polystyrene (PS) and poly(n-butyl methacrylate) (PnBMA) thin films as pure materials, or mixed in the form of a 1:1 blend. To this end, atomic force microscopy (AFM) was used to repeatedly scratch the sample surfaces, measure the accompanying friction forces, and image the resulting features. In the very first stage ordered ripples are formed in all cases. As the process goes on, hillocks are nucleated on the crests of the ripples, and progressively released in the form of nanoplastics while the ripples become wider and less regular. On the blend surface the more compliant PnBMA presents more corrugated ripple structures and larger friction oscillations than PS in the beginning, but the scenario becomes again more complex as the wear test is repeated and the original ‘rim and hole’ geometry of the blend is disrupted. Quite noticeably, the wear damage is reduced if the surfaces are scraped forth and back and not only in one direction. The influence of the scan pattern (distance between scan lines) and of the normal force (well below and above the force threshold of about 50 nN leading to surface ripples in the first stage) have been also addressed.

On Splitting of Separatrices Corresponding to the Working Mode of the Watt Regulator

The nonlinear problem of the Watt regulator dynamics is investigated. It is assumed to be installed on a machine that performs the specific harmonic oscillations of small amplitude along the vertical. Viscous friction forces is believed to arise in the hinges of the regulator, and these forces are small. In the main operating mode of the regulator, its rods, carrying massive weights, are deflected from the downward vertical by a constant acute angle. If friction and vertical oscillations of the machine are neglected, then we obtain an approximate problem in which the dynamics of the regulator is described by an autonomous Hamiltonian system with one degree of freedom. On the phase portrait of the approximate problem, the operating mode corresponds to a singular point of the center type. The trajectories surrounding this point lie inside the separatrix, which is a homoclinic doubly asymptotic trajectory that passes through the equilibrium position corresponding to the vertical position of the rods with weights. In the phase portrait, this position corresponds to a saddle singular point. The Melnikov method is used to obtain the splitting condition for the unperturbed separatrix in the complete perturbed problem, taking into account dissipation in the hinges and vertical vibrations of the machine.

Influence of Weak Structural Vibrations on a Machine-Driven Chain of Mechanical Oscillators with Friction under Varying Normal Forces

This work presents a real mechatronic system consisting of coupled inertia oscillators affected by relatively high-frequency structural vibrations. The system’s basic mathematical description is also provided. To simulate real structural vibrations, a vibration exciter in the form of an imbalanced rotor is incorporated into the model. The dynamic behavior of the contacting solid bodies is significantly influenced by the rotating imbalanced mass, which is in frictional contact with the body. The vertical acceleration component resulting from the rotational motion of the imbalance leads to a faster breakage of the sliding contact between the block and the belt, causing a shorter duration of the contact pair in the stick phase. Additionally, the softly coupled pendulum solid body can be utilized to effectively detect weak vibration modes of the self-excited friction oscillator that would otherwise be challenging to observe.

Identification and study of the characteristics of friction oscillations in the brake

Purpose.The task of researching modes of established frictional oscillations of the braking mechanism is to find a solution to the initial dynamic problem with friction that satisfies the periodicity conditions. At the same time, the period of motion of the dynamic system is not known in advance. This dynamic system is described by a non-linear dissipative non-autonomous system of differential equations. The methods. The developed technique of spectral analysis of the braking mechanism's oscillations is based on the assumption that its movements are periodic. If deterministic chaos occurs in the analyzed dynamic system, then the autocorrelation function of the time series of movements must have a finite carrier, that is, vanish outside a finite time interval. Findings. In the paper, the method of computational experiment is used to identify and study the characteristics of oscillatory processes in brake mechanisms. At the first stage of the computational experiment, a numerical solution of the considered dynamic problem with friction is carried out using a computational algorithm. As a result, the time series of block movements are calculated. At the second stage of the computational experiment, the obtained time series are studied. The originality. The paper uses phase diagrams in the "displacement-velocity" variables to analyze the process of establishing the oscillations of the brake mechanism and visual detection of attractors. When studying the dependence of amplitudes of displacements, velocities and accelerations of the dynamic system under consideration on changes in its parameters, the method of continuation by parameter was used with a stepwise change in the parameters of the system. Practical implementation. The developed mathematical model of vibrations of the braking mechanism and the computational algorithm for its numerical study are implemented in the form of a computer program for personal computers in the FORTRAN algorithmic language. Almost all available commercial compilers can be used to compile the program, including Compaq Visual Fortran 6.6 and Intel Visual Fortran 10, as well as non-commercial compilers distributed under the GNU license.

Discontinuous Dynamics of a 2-DOF Friction Oscillator with Rigid and Elastic Composite Constraints

Discontinuous Dynamics of a 2-DOF Friction Oscillator with Rigid and Elastic Composite Constraints

Smoluchowski–Kramers approximation with state dependent damping and highly random oscillation

<p style='text-indent:20px;'>The small mass limit (Smoluchowski–Kramers approximation) of class systems of ordinary differential equations describing motions of small mass particle with state dependent friction and high oscillation is derived by a diffusion approximation approach. In the small mass limit, due to the state dependent damping, one additional term appears in the limit equation, which leads to a stochastic differential equation (SDE) as the highly random oscillation appears as a multiplicative white noise.</p>

A switching Gaussian process latent force model for the identification of mechanical systems with a discontinuous nonlinearity

Abstract An approach for the identification of discontinuous and nonsmooth nonlinear forces, as those generated by frictional contacts, in mechanical systems that can be approximated by a single-degree-of-freedom model is presented. To handle the sharp variations and multiple motion regimes introduced by these nonlinearities in the dynamic response, the partially known physics-based model and noisy measurements of the system’s response to a known input force are combined within a switching Gaussian process latent force model (GPLFM). In this grey-box framework, multiple Gaussian processes are used to model the unknown nonlinear force across different motion regimes and a resetting model enables the generation of discontinuities. The states of the system, nonlinear force, and regime transitions are inferred by using filtering and smoothing techniques for switching linear dynamical systems. The proposed switching GPLFM is applied to a simulated dry friction oscillator and an experimental setup consisting of a single-storey frame with a brass-to-steel contact. Excellent results are obtained in terms of the identified nonlinear and discontinuous friction force for varying: (i) normal load amplitudes in the contact; (ii) measurement noise levels, and (iii) number of samples in the datasets. Moreover, the identified states, friction force, and sequence of motion regimes are used for evaluating: (1) uncertain system parameters; (2) the friction force–velocity relationship, and (3) the static friction force. The correct identification of the discontinuous nonlinear force and the quantification of any remaining uncertainty in its prediction enable the implementation of an accurate forward model able to predict the system’s response to different input forces.

Oil-lubricated sliding wear performance of TiSiCN-coated ductile iron

Improvements to internal combustion engine performance can be achieved by the application of advanced coatings to piston rings and cylinder bores. Here, the sliding wear performance of TiSiCN coatings on ductile iron was evaluated in heavy-duty diesel engine oil using a block-on-ring tribometer. The coatings were deposited by plasma-enhanced magnetron sputtering of titanium in a reactive environment containing nitrogen, acetylene, and hexamethyldisilazane. Coating characterization was conducted using X-ray spectroscopy and diffraction, electron microscopy, and nanoindentation. TiSiCN adhesion to ductile iron was qualified by Rockwell indentation testing. Wearing surface and counter surface material pairs were systematically varied. Intermittent friction oscillation was observed for self-mated TiSiCN, while tribosystems with only one TiSiCN surface exhibited improved friction stability relative to uncoated ductile iron. A 24% reduction in block wear rate was achieved by coating the block surface with TiSiCN. Solely coating ring surfaces with TiSiCN, however, increased the uncoated block wear rate by over 300%.

Multi-scale modeling of an atomic force microscope tip for the study of frictional properties and oscillation behavior

In this paper, the vibrational behavior of the atomic force microscope (AFM) on a graphene sheet sample was analyzed using a multi-scale model. The cantilever and silicone tip base were simulated using continuum mechanics and finite element modeling, while the tip apex was modeled using Tersoff potential and structural mechanics modeling. The modified Morse potential was used to model the single-layer graphene, and the Lennard-jones potential was employed as nonlinear springs to model the interactions between the graphene layers and the tip-sample. In addition, the contact behavior between the tip and graphene was investigated by measuring the friction force during the movement of the tip on the graphene sheet, and the results were compared to those obtained from a molecular dynamics simulation and an experimental test. The friction force between the tip and graphene increased by enhancing the tip radius and the contact surface between the tip and the sample. With the initial distance displacement of the tip from the sample, two curves of the tip oscillation amplitude variations and the tip oscillation and excitation vibration phase shift were plotted. In conclusion, the results of the present multi-scale model are compared with those of the MD simulation and demonstrate the strong correlation between the proposed model and the MD model.

Finite-Time Stability of Polyhedral Sweeping Processes with Application to Elastoplastic Systems

We use the ideas of Adly-Attoych-Cabot [Adv. Mech. Math., 12, Springer, 2006] on finite-time stabilization of dry friction oscillators to establish a theorem on finite-time stabilization of differential inclusions with a moving polyhedral constraint (known as polyhedral sweeping processes) of the form $C+c(t).$ We then employ the ideas of Moreau [New variational techniques in mathematical physics, CIME, 1973] to apply our theorem to a system of elastoplastic springs with a displacement-controlled loading. We show that verifying the condition of the theorem ultimately leads to the following two problems: (i) identifying the active vertex ``A'' or the active face ``A'' of the polyhedron that the vector $c'(t)$ points at; (ii) computing the distance from $c'(t)$ to the normal cone to the polyhedron at ``A''. We provide a computational guide to implement steps (i)-(ii) in the case of an arbitrary elastoplastic system and apply the guide to a particular example. Due to the simplicity of the particular example, we can solve (i)-(ii) by the methods of linear algebra and minor combinatorics.

Nonlinear dynamics of dry friction oscillator subjected to combined harmonic and random excitations

Nonlinear dynamics of dry friction oscillator subjected to combined harmonic and random excitations

A dynamic recrystallization based constitutive flow model for micro-machining of Ti-6Al-4V

The study proposes a coupled thermo-mechanical transient analysis to estimate the cutting performance during micro-machining of Titanium alloy. A constitutive flow model is used along with the effects of dynamic recrystallization which is how the strain-softening evolves at a high strain rate. The frictional stick-slip oscillations that arise from the process are introduced through a Fortran user-subroutine at the chip tool interface. Strain softening and dynamic recrystallization are observed, while the cutting strain exceeds the critical strain of 1.7, owing to strain localization. When the uncut chip thickness reduces from 3 μm to 1 μm which is lesser than the edge radius of the tool, the value of maximum residual stresses increases by a factor of 3.7 and a magnitude of chip reduction coefficient of 2.25 is observed due to a local negative rake angle. The level of residual stress, specific cutting energy and morphology of the chip are validated with literature. In addition, a user-defined material stiffening algorithm is proposed which revealed an increase of compressive residual stress at the surface by 20%.

Bifurcation analysis of stick–slip vibration in a 2-DOF nonlinear dynamical system with dry friction

This paper describes a new approach to study the nonlinear dynamical behaviors of a belt-driven two-coupled friction oscillator. First, using Buckingham’s π theorem, several dimensionless and physically meaningful parameters are derived. Their relationships with the steady state responses of the system are revealed through numerical simulations. Then a new mapping tool named as sticking phase plot is developed to record the transition process of stick–slip motion. It intuitively shows how bifurcation occurs in sticking region and transforms the dynamical responses. The bifurcation diagrams of the system are obtained by sweeping the dimensionless parameters. Some extraordinary bifurcation phenomena are observed in this system. By using sticking phase plot, it is found that the bifurcations can be broadly divided into four main categories: the Border-Collision Bifurcation, the Grazing-Sliding Bifurcation, the Multi-Sliding Bifurcation, and the Fixed-Point Bifurcation. New nonlinear phenomena are found herein, including chaos caused by the Border-Collision Bifurcation and the Sliding Bifurcations. The local and the global changes caused by the Fixed-Point bifurcation are also observed. In numerical simulation, we adopted the LVIM method proposed by the authors, which can be used to integrate non-smooth systems very accurately and efficiently.

Stick Motions and Grazing Flows in a Double Belt Friction Oscillator

This paper is concerned with the dynamics of a double belt friction oscillator which is subjected to periodic excitation, linear spring-loading, damping force and two friction forces using the flow switchability theory of the discontinuous dynamical systems. Different domains and boundaries for such system are defined according to the friction discontinuity, which exhibits multiple discontinuous boundaries in the phase space. Based on the above domains and boundaries, the analytical conditions of the stick motions and grazing motions are obtained mathematically. There are more theories about such friction oscillators to be discussed in future.

The problem of damping frictional oscillations in a two-mass oscillatory system under the action of a disturbing harmonic force

The problem of damping oscillations in a two-mass oscillatory system with two degrees of freedom under the action of a harmonic periodic force is considered. For the purpose of active infl uence when damping vibrations, two force effects of a special structure are used simultaneously.

Вплив мастильних матеріалів на довговічність трибоспряжень

The aim of the research is to determine the influence of motor oils on operating modes, durability of tribocouples and substantiation of expediency of use of motor oils of corresponding brands. A study of the tribological properties of motor oils from different manufacturers. Characteristic features of friction moment change during lubrication with ZIC and Xado oils have been studied. During friction in the ZIC oil environment, significant oppositely directed changes in the moment of friction (oscillation) were recorded, which indicates an unstable friction mode. At the beginning of the experiment, a gradual increase in the friction moment when lubricating tribocouples with Xado oil was recorded. Studies of the dynamics of temperature in the friction zone depending on the lubricating medium are performed. It was found that the maximum temperature in the friction zone was when using Xado and ZIC engine oil - 90.0 ºC and 84.5 ºC, respectively. The value of wear intensity of steel-steel tripods depending on the engine oil of different manufacturers is determined. An analysis of micrographs of surfaces before and after the experiment was performed. It is established that the amount of damage to the surface friction as a whole without drastic changes. Unidirectional light lines are the places of direct contact between two friction bodies. After the experiment with lubrication with Xado engine oil on the friction surface of the pad recorded minor accumulations in the grooves and on their peripheries. It was found that the moment of friction when using the selected motor oils for the selected modes of friction of the tribocouples differs slightly, 1.13 N ∙ m and 1.15 N ∙ m, respectively, for ZIC X5 and Xado. At the same time, it should be noted that when lubricating with Xado engine oil, a higher constancy of the friction moment was recorded, compared to working in ZIC oil environment. It is established that the dynamics of temperature rise is gradual. The intensity of linear wear when using Xado oil is 17.7% lower compared to lubrication with ZIC oil. Thus, it can be concluded that the use of Xado motor oil can increase the durability of tribocouples.