Friction-induced Oscillations Research Articles

Efficacy of velocity feedback control for suppression of the friction-induced oscillation due to mode-coupling instability in a two degrees-of-freedom mechanical system

The present article focuses on suppressing mode-coupling instability in frictional systems, which can cause unwanted vibrations such as squeal in braking systems. Mode-coupling instability occurs when two or more modes of a system approach each other. This article proposes the use of resonant velocity feedback control to eliminate friction-induced oscillations generated by mode-coupling instability. A two degree-of-freedom linear model is used to capture the instability due to friction-induced mode coupling. The efficacy of the control is demonstrated through linear stability analysis, and by optimizing control parameters using pole crossover method to minimize the transient time of the response. The robustness analysis demonstrates the ability of the control to effectively mitigate the instability even under parametric perturbations. The controlled system is simulated in MATLAB Simulink to validate analytical results. The effects of time delay, which is commonly present in feedback systems, are also investigated. Finally, the effectiveness of the control is studied in the presence of nonlinearity in the system. The nonlinear dynamics are analyzed by creating bifurcation diagrams with different bifurcation parameters.

Optimization of vibration absorbers for the suppression of rail corrugation in the sharp curved section with Cologne-egg fasteners

Rail corrugation in the sharp curved section with Cologne-egg fasteners is suppressed by vibration absorbers, in which the suppression mechanism is unclear and the optimization method of the vibration absorber needs to be further investigated. Firstly, the complex eigenvalue and dynamic transient methods are adopted to investigate the vibration inducement of rail corrugation and influence law of vibration absorber on the rail corrugation. Then, the optimization methods of absorbers are studied from the perspectives of the connection stiffness, connection damping and different installation methods of absorbers. Results show that vibration inducement of rail corrugation in the sharp curved section with Cologne-egg fasteners includes the friction-induced oscillation of the entire system and feedback oscillation of undulatory wear. The installation of the vibration absorber can effectively weaken the impact of the vibration inducement, thereby inhibiting the rail corrugation. When the vertical and lateral connection stiffness are 120 MN·m−1 and 60 MN·m−1 respectively, the vertical and lateral connection damping are 100 kN·s·m−1 and 50 kN·s·m−1 respectively, the vibration absorber has the best effect of suppressing rail corrugation. Moreover, the continuous installation on both rail webs can be adopted to achieve the better inhibitory effect of the absorber.

Controlling mode-coupling instability in friction-induced vibration by acceleration feedback

Self-excited friction-induced oscillation, such as brake squeal, railway wheel squeal, chattering in machine tools, etc., is harmful in many mechanical systems. In the present study, the efficacy of acceleration feedback control with a second order filter is theoretically studied to mitigate friction-induced mode-coupling instability. Two different control strategies based on acceleration feedback are employed to control friction-induced mode-coupling instability of a two degrees-of-freedom linear system. Linear stability analysis near the equilibrium point of the system shows the efficacy of control laws to stabilize the system. The optimum filter parameters are determined by the pole crossover optimization method to attenuate the transient response as well as to achieve greater relative stability of the system. The Robustness study confirms the ability of the controller to stabilize the system in the presence of uncertainties in system parameters. Analytical results match closely with simulation results. Finally, nonlinearity in the form of stiffness is incorporated into the system for which the dynamics of the system show the presence of subcritical, supercritical Hopf bifurcation, and cyclic fold bifurcation. In the presence of nonlinearity, the feedback control is also able to reduce the range of instability of static equilibrium as well as the amplitude of the self-excited oscillation. The method of averaging is used to determine the stability and amplitude of the limit cycle. For the nonlinear system, the bifurcation diagram is constructed in AUTO and validated with results obtained from MATLAB SIMULINK and the method of averaging.

Parametric Study of Track Support Structure to Minimize the Occurrence Possibility of Rail Corrugation

Changing the track support structure is an effective method to suppress or eliminate rail corrugation in practical engineering. Rail corrugation on small-radius curves with booted short sleepers is the main research object in the present paper. A relevant finite element model of the wheelset-track system supported by booted short sleepers is built combined with the dynamic analysis of the vehicle-track system. The effects of various parameters of booted short sleeper structure on the wheel–rail friction-induced vibration are investigated by complex eigenvalue analysis. Considering the interaction of multiple parameters in the booted short sleeper structure, the multi-parameter fitting equation forecasting the possibility of rail corrugation is obtained using the least squares algorithm. Results show that wheel–rail friction-induced oscillation is a contributing factor in the formation of rail corrugation. Controlling wheel–rail friction-induced oscillation with a frequency of about 300 Hz is beneficial to suppress the possibility of rail corrugation in sections with booted short sleepers. Lower fastener stiffness or greater vertical fastener damping make it less likely that rail corrugation will occur. Rail corrugation is not generated when the vertical stiffness of the fastener is controlled below 20 MN/m in the booted short sleeper.

On the Synchronization Behavior of Coupled Friction-Induced Oscillators Subjected to Base Excitation

Abstract The primary objective of this paper is to analyze the synchronization phenomena in a coupled friction-induced oscillator consisting of two cantilever beams with tip-masses subjected to base excitations. The coupling is achieved by connecting a linear spring between the tip-masses, which are in frictional contact with a rigid rotating disk. The Pearson time correlation coefficient is used to measure the strength and mode of synchronization between the oscillations of the coupled system. Periodicity of the motions is determined by evaluating the Poincaré map wherein the zero velocity crossing from positive to negative is considered as the Poincaré section. The fundamental frequency of the coupled motion and its harmonics are obtained from the Fast Fourier Transform (FFT) of the time responses. A bifurcation study is conducted to identify the periodicity of motion of both the uncoupled and coupled systems. The coupled system is found to be synchronized for the single-periodic, multiperiodic, and quasi-periodic motions, but not for chaotic motions. Multiple basins of attractions of initial conditions corresponding to different synchronization characteristics are observed. The coupled system shows a large dependence of the mass ratio detuning factor (MRDF) on the synchronization characteristics; in-phase synchronization is obtained for smaller MRDF, which eventually becomes out-of-phase for larger MRDF. A special study conducted confirms that the coupling can be used to control the amplitude as well as the stick-phase of motion in friction oscillators.

Study on the effect of the fastener support structure on rail corrugation in metros based on the friction-induce vibration

Rail corrugation is very serious in Cologne egg fastener track; effective control measures are still lacking. The cause of the corrugation wear on a curved metro track is analyzed based on the friction-induced vibration theory. A finite element model is established to study the frequency domain and time domain features of the friction-induced oscillation of this system. The influences of the fastener spacing and the fastener support length on the corrugation wear are investigated to develop countermeasures. The simulation results show that the friction-induced vibration of the wheel-track system is the wavelength-fixed mechanism of the corrugation wear of rail of the curved Cologne egg fastener track. There are two reasons why the low rail corrugation wear is more serious. The contact resultant force between the low rail and the wheel is obviously bigger than that between the wheel and the high rail, resulting in a higher wear rate of the low rail. The contact force fluctuation of the low rail caused by the friction-induced vibration is more severe, resulting in a higher corrugation wear evolution speed on the low rail. The friction-induced oscillation cannot be eliminated only by adjusting the fastener support length and spacing. However, the long-wavelength corrugation wear instead of the more harmful short-wavelength corrugation wear can be produced by adjusting the fastener support length and the fastener spacing to alleviate the influence of corrugation wear on the vehicle-track system.

Brake squeal analysis of disc brake

Brake squeal noise has been under analysis by automotive firms for years due to regular client complaints and high warranty prices. Brakes develop large and sustained friction-induced oscillations, referred to brake squeal. Brake squeal is considered a significant operational braking issue in passenger cars and commercial vehicles. This research works involves a method to find out the key causes of disc brake squeal incidence using finite element methods (FEM). The application of complex eigenvalue analysis in a finite element model of a disc brake system is employed to extract unstable modes. The influence of the operational parameters (friction coefficient, braking pressure and angular velocity) and contact stiffness on the dynamic stability of the brake system is brought out. Using Abaqus version 6.10 the complex eigen values are extracted and examined to identify the squeal frequency.

Time-delayed feedback control of improved friction-induced model: application to moving belt of particle supply device

In this paper, based on the original friction-induced oscillation, we propose a new friction-induced mathematical model associated with moving belt of particle supply device. Two delay feedback control methods are provided to make the new model be stable. Linear stability analysis is carried out to obtain the stability of equilibrium and the stability boundary, corresponding to the critical value of Hopf bifurcation, dividing stable and unstable regimes of equilibrium. Next, we derive explicit formulae for determining the stability of Hopf bifurcating periodic solutions and the direction of Hopf bifurcation. Finally, detailed numerical simulations using MATLAB software are presented to demonstrate the application of the theoretical results, and we also compare the efficacy of the two control forces in new friction-induced models.

Surrogate model approach for investigating the stability of a friction-induced oscillator of Duffing’s type

Parametric studies are required to detect instability regimes of dynamic systems. This prediction can be computationally demanding as it requires a fine exploration of large parametric space due to the disrupted mechanical behavior. In this paper, an efficient surrogate strategy is proposed to investigate the behavior of an oscillator of Duffing’s type in combination with an elasto-plastic friction force model. Relevant quantities of interest are discussed. Sticking time is considered using a machine learning technique based on Gaussian processes called kriging. The largest Lyapunov exponent is considered as an efficient indicator of chaotic motion. This indicator is estimated using a perturbation method. A dedicated adaptive kriging strategy for classification called MiVor is utilized and appears to be highly proficient in order to detect instabilities over the parametric space and can furthermore be used for complex response surfaces in multi-dimensional parametric domains.

Analysis of dynamical behaviors of a 2-DOF friction-induced oscillator with one-sided impact on a conveyor belt

In this paper, the flow switchability theory of discontinuous dynamical systems is used to illustrate the dynamical behavior of a 2-DOF (two degrees of freedom) friction-induced oscillator with one-sided impact on a conveyor belt. All the possible motion states such as stick and non-stick motions, impact motion, and stuck motion for such an oscillator are introduced. The phase space in system can be divided into different domains and boundaries according to the discontinuity caused by the friction force jumping and the impact between the mass and the rigid obstacle. The vector field in each domain is continuous and different from that in its adjacent domain. The flow barrier on the separation boundary is considered in this paper. Once the boundary flow leaves the boundary, the boundary flow barrier on the velocity boundary may exist and the leaving flow barriers on the velocity boundary may also exist. The G-functions on different separation boundaries are defined to illustrate the flow switching on the corresponding boundaries. The analytical conditions of the passable, stick, grazing, impact, and stuck motions are developed through G-functions and analysis of vector fields. Since the motions of the two masses interact with each other, the four-dimensional switching sets are given by the form of direct product and the four-dimensional mappings are given to describe periodic motions with different mapping structures. The analytical prediction of different periodic motions is performed through the mapping dynamics. For a better understanding of the motion switching mechanism in such a 2-DOF oscillator , the time histories of displacement, velocity, G-function and the trajectories in phase space for the passable motion, stick motion, impact motion, grazing motion, stuck motion, and periodic motion in system are given by simulation numerically. This investigation has important significance in the optimization design of machinery with friction and impact etc.

Study on the Effect of Track Curve Radius on Friction-Induced Oscillation of a Wheelset–Track System

The purpose of this article is to investigate the correlation between the friction-induced oscillation of a wheelset–track system and curve radius and to explain a general phenomenon of rail corrugation based on the viewpoint of friction-induced oscillation. The typical phenomenon of rail corrugation in metros is that corrugation generally arises when the curve radius is quite small, whereas it rarely occurs when the curve radius is larger or on a straight track. Different multibody models of the vehicle–track system and finite-element models of the multiple-wheelset–track system with different curve radii are established, respectively. According to the creep force analyses and unstable vibration analyses, the correlation between the creep force and friction-induced oscillation can be identified. Then the effect of the track curve radius on the friction-induced oscillation of the wheelset–track system can be summarized, which provides an explanation of the typical phenomenon of corrugation.

Numerical analysis of the friction-induced oscillator of Duffing's type with modified LuGre friction model

This paper focuses on analysis of a friction-induced mechanical oscillator with cubic nonlinearity and an applied dynamical model of dry friction. The studied model is based on the classical LuGre approach to friction force modelling. Lyapunov exponents spectrum of the frictional oscillator is calculated by means of a recently implemented method of their estimation for non-smooth systems. Results of the numerical research, observations of the nature of the oscillator's response and interaction of the applied dynamic friction model with the oscillator are reported.

Analysis of Discontinuous Dynamical Behaviors of a Friction-Induced Oscillator with an Elliptic Control Law

This paper develops the passability conditions of flow to the discontinuous boundary and the sticking or sliding and grazing conditions to the separation boundary in the discontinuous dynamical system of a friction-induced oscillator with an elliptic control law and the friction force acting on the mass M through the analysis of the corresponding vector fields and G-functions. The periodic motions of such a discontinuous system are predicted analytically through the mapping structure. Finally, the numerical simulations are given to illustrate the analytical results of motion for a better understanding of physics of motion in the mass-spring-damper oscillator.

A case study of rail corrugation phenomenon based on the viewpoint of friction-induced oscillation of a wheelset-track system

An interesting rail corrugation phenomenon unreported in open literature is found in Beijing metros, in which the wavelength of rail corrugation in the Cologne egg sleeper section is obviously different from that in the fixed dual short sleeper section, although both sleeper sections are located on an identical sharp curved track. Based on the viewpoint that friction-induced oscillation is the main cause of rail corrugation in some cases, three multiple-wheelset-track models in the transitional section on an identical sharp curved track are built in this paper. The phenomenon is researched by adopting the complex eigenvalue method together with the transient dynamic method. The simulation results are consistent with the corrugation measured in real metros. It can be found that the unstable oscillations mainly occur on the low rail and the relevant frequencies are noticeably different in different sleeper support sections. The dominant unstable oscillation frequencies in the fixed dual short sleeper and Cologne egg sleeper sections are about 201 and 422 Hz, respectively. However, when a sharp curved track is supported only by fixed dual short sleepers or Cologne egg sleepers, the unstable oscillation frequencies are close to each other, which are both about 420 Hz. Therefore, the corresponding wavelengths of rail corrugation are different in different conditions. The local special phenomenon can be satisfactorily explained and the viewpoint of friction-induced oscillation can be further verified.

Analysis of dynamical behaviors of a friction-induced oscillator with switching control law

In this paper, the dynamical behaviors of a friction–induced oscillator with switching control law are studied through the flow switching theory of discontinuous dynamical systems. The physical model consists of a mass on the conveyor belt and a spring-damping system with switching control law. Based on the switching control law and the friction between the oscillator and the conveyor belt, multiple domains and discontinuous boundaries are defined. The G–functions are introduced to illustrate the motion switching mechanism and the analytical conditions of the passable motion, stick motion, sliding motion and grazing motion are presented for motion switchability. The switching sets and mapping structures are adopted to describe the complex motions in this discontinuous system. The numerical simulations are also carried out from the analytical conditions and mapping structures in order to better understand the motion switching complexity of this oscillator.

Stability and nonlinear self-excited friction-induced vibrations for a minimal model subjected to multiple coalescence patterns

In certain industrial applications with frictional interfaces such as brake systems, the friction-induced vibrations created by coupled modes can lead to a dynamic instability and thus to an important deterioration in the operating condition. As a result, they are considered as a source of critical engineering problem. In addition, the presence of the nonlinearity makes necessary the consideration of the nonlinear dynamic analysis in order to explain clearly the complexity of the contribution of different frequency components due to unstable modes in the self-excited friction-induced vibrations, to get a design as reliable as possible and to avoid catastrophic failure during the operation phase of the mechanism. The present paper is based on previous works of Sinou and Jézéquel and extends them to include a developed damped four-degree-of-freedom system with frictional contact and spring cubic nonlinearities. Its essential goals are to analyze numerically the mode-coupling instability of the four-degree-of-freedom system owing to the friction between the surfaces of contact and to predict its nonlinear dynamic behavior. The numerical study of stability for the static solution of the mechanical system is performed by applying the complex eigenvalue analysis of the linearized differential equations of motion and by identifying the Hopf bifurcation points as a function of the coefficient of kinetic friction. Depending on the Runge-Kutta time-step integration scheme and the fast Fourier transforms, quantitative and qualitative nonlinear phenomena related to self-excited friction-induced oscillations and limit cycle evolutions are observed and discussed for various friction coefficients.

On Dynamical Behavior of a Friction-Induced Oscillator with 2-DOF on a Speed-Varying Traveling Belt

The dynamical behavior of a friction-induced oscillator with 2-DOF on a speed-varying belt is investigated by using the flow switchability theory of discontinuous dynamical systems. The mechanical model consists of two masses and a speed-varying traveling belt. Both of the masses on the traveling belt are connected with three linear springs and three dampers and are harmonically excited. Different domains and boundaries for such system are defined according to the friction discontinuity. Based on the above domains and boundaries, the analytical conditions of the passable motions, stick motions, and grazing motions for the friction-induced oscillator are obtained mathematically. An analytical prediction of periodic motions is performed through the mapping dynamics. With appropriate mapping structure, the simulations of the stick and nonstick motions in the two-degree friction-induced oscillator are illustrated for a better understanding of the motion complexity.

Characterization of friction force and nature of bifurcation from experiments on a single-degree-of-freedom system with friction-induced vibrations

Experimental investigation is performed on a test set-up representing a single-degree-of-freedom friction-induced system. The experimental set-up consists of a rigid mass (oscillator) connected to a fixed support through a spring and the mass in frictional contact with a moving belt. The major objectives of the experiments are to characterize (i) the nature of friction-induced oscillations, (ii) the nature of bifurcation associated with frictional instability in the system, and (iii) the nature of friction force that is responsible for the oscillations observed from the experiment. The phase portrait of the system shows significant overshoot of the oscillator velocity above the belt velocity indicating the existence of hysteretic loop around zero relative velocity (pre-sliding regime). The bifurcation diagram clearly demonstrates the subcriticality of the Hopf bifurcation associated with the system negating all empirical friction models which yield supercritical Hopf bifurcation. The friction force-relative velocity curve shows significant hysteretic behavior, both in the pre-sliding as well as in the pure sliding domains. This observation hints towards a dynamic or an acceleration-dependent friction model as an appropriate choice for representing the friction force obtained from our experimental set-up.

Friction-Induced Oscillations of a Non-Asbestos Organic Pin Sliding on a Steel Disc

Abstract Friction-induced oscillations result in deterioration of performance of disc brakes and are generally undesired. We conduct experimental study of friction-induced oscillations in a non-asbestos organic material / steel pair used in disc brakes of motor vehicles. The tests are done by use of a pin-on-disc machine in which the pin sample is supported on a deformable beam. The adjustable friction parameters are the disc velocity, contact pressure and temperature. The tests show that the friction coefficient decreases with the sliding velocity and increases with the temperature. The friction-induced tangential oscillation of the pin sample occurs with a frequency equal to the first natural frequency of the beam. The effects of the disc velocity and temperature on the oscillation characteristics are investigated. The oscillation amplitude increases with the disc velocity on the interval of velocities below 2 m/s. Temperature changes of several tens of degrees Celsius lead to the oscillation occurrence / decay. The obtained results can be useful for prognostication of friction-induced oscillations in disc brakes with non-asbestos organic pads.

SINGULARITY, SWITCHABILITY AND BIFURCATIONS IN A 2-DOF, PERIODICALLY FORCED, FRICTIONAL OSCILLATOR

In this paper, the analytical dynamics for singularity, switchability, and bifurcations of a 2-DOF friction-induced oscillator is investigated. The analytical conditions of the domain flow switchability at the boundaries and edges are developed from the theory of discontinuous dynamical systems, and the switchability conditions of boundary flows from domain and edge flows are presented. From the singularity and switchability of flow to the boundary, grazing, sliding and edge bifurcations are obtained. For a better understanding of the motion complexity of such a frictional oscillator, switching sets and mappings are introduced, and mapping structures for periodic motions are adopted. Using an eigenvalue analysis, the stability and bifurcation analysis of periodic motions in the friction-induced system is carried out. Analytical predictions and parameter maps of periodic motions are performed. Illustrations of periodic motions and the analytical conditions are completed. The analytical conditions and methodology can be applied to the multi-degrees-of-freedom frictional oscillators in the same fashion.