Friction-induced Self-excited Vibration Research Articles

Controlling stick–slip in low-speed motion with a lifting force of magnetic fluid

Stick–slip is a standard friction-induced self-excited vibration that usually occurs in the boundary or mixed lubrication regimes. Broadening of the hydrodynamic lubrication regime is conducive to suppressing stick–slip motion. In this paper, the load carrying capacity of a magnetic fluid (MF) film in the presence of a magnetic field is derived based on the modified Reynolds equation. An additional lifting force produced by MF under the magnet was applied between the tribopairs to achieve the full fluid lubrication. Thus, the stick–slip is expected to be inhibited in a lower speed scope. The effect of magnet thickness on the lifting force is investigated experimentally and theoretically. Special attention is given to the influence of the lifting force on the friction and the critical transition speed of the hydrodynamic lubrication regime. Results demonstrate that the lifting force increases with the increment of the magnet thickness. The presence of the additional lifting force expands the hydrodynamic lubrication and makes the critical transition speed move left, as shown by the friction transitions on the Stribeck curve. Therefore, stick–slip motion can be suppressed at a lower sliding speed. Such beneficial effects are more pronounced in thicker magnets. It can be confirmed that, so long as the lifting force is higher than the normal load, the friction will invariably operate in the full film lubrication and the stick-slip motion may be eliminated theoretically.

Energy harvesting from friction-induced vibrations in vehicle braking systems in the presence of rotary unbalances

A severe limitation of energy harvesting from friction-induced vibrations in vehicle brakes is that the voltage generated is significant only at low vehicle speeds. The present work suggests a strategy to overcome this limitation by the utilisation of ambient vibrations resulting from rotary unbalances of vehicle components. A realistic model for vibrations in the brake pad of a disc brake under the action of rotary unbalance is used. The brake pad vibration is modelled using a non-smooth stick–slip oscillator in the presence of Stribeck friction. A weightless shaft of rectangular cross-section rotating at constant angular speed and having an unbalanced mass concentrated at its centre is used to model rotary unbalances. It is shown that the rotary unbalance provides parametric excitation to the brake pad mass undergoing friction-induced self-excited vibration leading to synchronising patterns via Neimark–Sacker bifurcation. Such synchronisation is successful in ensuring steady voltage generation over a much wider speed bandwidth. The qualitative nature of the different solution regimes interspersed with periodic intervals are determined by Lyapunov exponents. The technique used to arrive at the Lyapunov exponents in the present discontinuous model is outlined, and MATLAB code for the same is provided in the appendix.

Analytical expressions of friction-induced self-excited vibration amplitudes of the marine rubber bearing-shaft system

By the analytical method, this paper investigates the mode-coupling friction-induced instability and the resulting stick-slip self-excited vibration of the marine stern water-lubricated rubber bearing-shaft system. The 2-DOF simplified theoretical model is reasonably developed to characterize stern water-lubricated rubber bearing-shaft system. The complex eigenvalue analysis is conducted to analyze the instability behaviors of the model. Results show the normal force and nonlinear stiffness often deteriorate the stability of the model. Subsequently, two types of analytical expressions for stick-slip vibration amplitude of the model are by the Krylov-Bogoliubbov-Mitropolsky method, which match well with the results from numerical integration. Then, parameter discussion about the influences of friction coefficient, damping, normal force and nonlinear contact stiffness on self-excited vibration amplitudes are performed. The results indicate that the bearing-shaft system can keep the steady-state static equilibrium or the oscillations with small amplitude if the proper parameter values of the variables are chosen, which will benefits controlling the friction-induced vibration of the water-lubricated rubber bearing-shaft system. The novelty of this work is to give analytical expressions for stick-slip self-excited vibration amplitude of the simplified model.

Study on long-term tracking of rail corrugation and the influence of parameters

Rail corrugation is a common form of damage in subway tracks. This paper presents the results of a 1.5-year study of track wear at two sites on the Chengdu Metro. Findings revealed the appearance of corrugation with a 30 mm main wavelength near the middle of the curve on the low rail of a 350 m radius track. As the subway's operating hours extended, the corrugation expanded toward the transition curves, and the wavelength changed. Conversely, no rail corrugation was seen on the rails of a 610 m radius curved track. A finite element model of the wheelset–rail system was established based on friction-induced self-excited vibration (FSV), and complex eigenvalue and instantaneous dynamic analysis methods were employed on the model to predict corrugation. Results showed that the increased elasticity modulus of the rail pad and baseplate pad could restrain long-pitch corrugation, and matching the material parameter of the pads reasonably reduced the frequency of short-pitch corrugation (SPC). In addition, the lack of corrugation on the 610 m radius track was studied, with results showing that the creep forces at the interface were not saturated. Thus, no FSV occurred, and no corrugation arose.

Tribo-Brake Characteristics between Brake Disc and Brake Shoe during Emergency Braking of Deep Coal Mine Hoist with the High Speed and Heavy Load

The friction wear and thermal fatigue cracking of the brake shoe and friction-induced self-excited vibration (frictional flutter) of the disc brake can easily occur during emergency braking of a deep coal mine hoist with at high speed and with a heavy load. Therefore, tribo-brake characteristics between the brake disc and brake shoe during emergency braking of a deep coal mine hoist are investigated in the present study. Scaled parameters of the disc brake of a deep coal mine hoist are determined by employing the similarity principle. Friction tests between friction disc and brake shoe are carried out to obtain the coefficient of friction in the case of high speed and large specific pressure between the friction disc and brake shoe. Coupled thermo-mechanical finite element analyses of the brake disc and brake shoe are established to investigate temperature and stress fields of the brake disc and brake shoe during emergency braking, which is validated by the engineering failure case. Effects of braking parameters on flutter characteristics between the brake disc and brake shoe are explored by employing a double-degrees-of-freedom vibration mechanism model. The results show that the maximum temperature, equivalent Von Mises stress and contact pressure are all located at the average friction radii of contact surfaces of the brake disc and brake shoe during emergency braking. The cage crashing accident in the case of high speed and heavy load in a typical coal mine shows crack marks and discontinuous burn marks at central locations of brake shoe and brake disc surfaces, respectively, which indicates frictional flutter characteristics between brake disc and brake shoe. During emergency braking, flutter time duration decreases with increasing initial braking speed and damping parameter; the flutter amplitude and frequency of the disc brake increases with increasing normal braking load and stiffness, respectively.

Sliding region and coexisting attractors of a friction-induced self-excited vibration.

This paper mainly investigates the nonlinear dynamics of a friction-induced self-excited vibration when the coefficient of static friction is larger than that of kinetic friction. First, this system is rewritten by a new theory proposed by Jeffrey, which is different from the Filippov theory. Then, the sliding region is obtained from the theory, which is also verified by the numerical simulation. Furthermore, multiple attractors, such as period-1 orbit and equilibrium point, period-2 orbit and equilibrium point, can coexist if the coefficient of static friction exceeds that of kinetic friction, but it is not true if they are equal. Finally, some sliding bifurcations, such as crossing-sliding bifurcation, switching-sliding bifurcation, and grazing-sliding bifurcation, are also found.

Friction-Induced Vibration in a Bi-Stable Compliant Mechanism

This paper investigates friction-induced self-excited vibration in a bi-stable compliant mechanism. A single-degree-of-freedom oscillator, hanged vertically, vibrates on a belt moving horizontally with a constant velocity. The oscillator is excited through the frictional input provided by the belt. The friction coefficient is defined as an exponentially decaying function of the sliding velocity. Due to the specific configuration of spring and damper, the normal contact force is variable. Therefore, the friction force is a function of the system states, namely, slider velocity and position. Employing eigenvalue analysis gives an overview of the local stability of the linearized system in the vicinity of each equilibrium point. It is shown that the normal force, spring pre-compression and belt velocity are bifurcation parameters. Since the system is highly nonlinear, a local analysis does not provide enough information about the steady-state response. Therefore, the oscillating system is studied numerically to attain a global qualitative picture of the steady-state response. The possibility of the mass-belt detachment and overshoot are studied. It is shown that one equilibrium point is always dominant. In addition, three main questions, i.e., possible mass-belt separation, location of stick-slip transition and overshoot are answered. It is proven that the occurrence of overshoot is impossible.

Vibration Instability in a Large Motion Bistable Compliant Mechanism Due to Stribeck Friction

The present paper investigates friction-induced self-excited vibration of a bistable compliant mechanism. A pseudo-rigid-body representation of the mechanism is used containing a hardening nonlinear spring and a viscous damper. The mass is suspended from above with the spring-damper combination leading to the addition of geometric nonlinearity in the equation of motion and position- and velocity-dependent normal contact force. Friction input provided by a moving belt in contact with the mass. An exponentially decaying function of sliding velocity describes the friction coefficient and, thereby, incorporates Stribeck effect of friction. Eigenvalue analysis is employed to investigate the local stability of the steady-state fixed points. It is observed that the oscillator experiences pitchfork and Hopf bifurcations. The effects of the spring nonlinearity and precompression, viscous damping, belt velocity, and the applied normal force on the number, position, and stability of the equilibrium points are investigated. Global system behavior is studied by establishing trajectory maps of the system. Critical belt speed is derived analytically and shown to be only the result of Stribeck effect of friction. It is found that one equilibrium point dominates the steady-state response for very low damping and negligible spring nonlinearity. The presence of damping and/or spring nonlinearity tends to diminish this dominance.

Physical mechanism of ice/structure interaction

ABSTRACTTo obtain the effect of velocity and structural natural frequency (structural stiffness) on ice failure, an extended dynamic Van der Pol-based single degree-of-freedom ice/structure interaction model is developed. Three basic modes of response were reproduced: intermittent crushing, frequency lock-in and continuous crushing. Further analysis on the physical mechanism of ice/structure interaction is presented on the basis of feedback mechanism and energy mechanism, respectively. Internal effect and external effect from ice and structure were both explained in the feedback branch. Based on reproduced results, energy exchanges at different configurations are computed from the energy conservation using the first law of thermodynamics. A general conclusion on the predominant type of vibration when the ice velocity increases during the interaction process is forced, self-excited and forced in each of the three modes of responses. Ice force variations also show that there is more impulse energy during the lock-in range. Moreover, ice-induced vibration demonstrates an analogy of friction-induced self-excited vibration. Finally, the similarity between strain-stress curve and Stribeck curve shows that static and kinetic friction force variations are attributed to ice force characteristic, and can be used to explain the lower effective pressure magnitude during continuous crushing than the peak pressure during intermittent crushing.

Nonlinear control of stick-slip oscillations by normal force modulation

The present paper investigates the efficacy of controlling friction induced vibration by normal load modulation. Friction-induced self-excited vibration, attributed to the low-velocity drooping characteristics of friction (Stribeck effect), is modelled by a mass-on-belt model where the normal force of the mass is being modulated based on the acceleration feedback followed by a second order filtering. Polynomial model is employed to study the friction phenomenon between the mass and the belt. The pole crossover design (to ensure faster transient and greater relative stability) is implemented to optimize the filter parameters with an independent choice of the belt velocity and control gain. These sets of optimized parameter values are then used to construct local stability boundaries in the plane of control parameters. Numerical simulations in a MATLAB SIMULINK model and bifurcation diagrams obtained in AUTO (while using belt velocity as the bifurcation parameter) indicate that a significantly small-amplitude limit cycle resulting from a supercritical Hopf bifurcation stabilizes the extreme low velocity region at higher values of the control gain. With the increase of the control gain the subcritical nature of Hopf bifurcation changes to a supercritical one. The efficacy of this optimization (based on numerical results) in the delicate low velocity region is also enclosed.

Tangential acceleration feedback control of friction induced vibration

Tangential control action is studied on a phenomenological mass-on-belt model exhibiting friction-induced self-excited vibration attributed to the low-velocity drooping characteristics of friction which is also known as Stribeck effect. The friction phenomenon is modelled by the exponential model. Linear stability analysis is carried out near the equilibrium point and local stability boundary is delineated in the plane of control parameters. The system is observed to undergo a Hopf bifurcation as the eigenvalues determined from the linear stability analysis are found to cross the imaginary axis transversally from RHS s-plane to LHS s-plane or vice-versa as one varies the control parameters, namely non-dimensional belt velocity and the control gain. A nonlinear stability analysis by the method of Averaging reveals the subcritical nature of the Hopf bifurcation. Thus, a global stability boundary is constructed so that any choice of control parameters from the globally stable region leads to a stable equilibrium. Numerical simulations in a MATLAB SIMULINK model and bifurcation diagrams obtained in AUTO validate these analytically obtained results. Pole crossover design is implemented to optimize the filter parameters with an independent choice of belt velocity and control gain. The efficacy of this optimization (based on numerical results) in the delicate low velocity region is also enclosed.

Experimental and numerical studies of the effects of a rail vibration absorber on suppressing short pitch rail corrugation

The effects of a rail vibration absorber on suppressing short pitch rail corrugation are studied. Firstly, a rail vibration field test is carried out to analyze the vibration response of the rail with and without the vibration absorbers. Secondly, based on the hypothesis that friction-induced self-excited vibration of a wheel-rail system causes rail corrugation; two finite element models of a wheel-rail system and a wheel-rail-absorber system are established and analyzed. Both sets of rail vibration test results and theoretical results show that the rail absorbers can effectively reduce the friction-induced self-excited vibration of the wheel-rail system in the frequency range of 200-800 Hz, which corresponds to frequencies of short pitch rail corrugation. This may be a main reason that the rail vibration absorber can suppress the formation of short pitch rail corrugation.

Chatter vibration phenomenon of pipeline inspection gauges (PIGs) in natural gas pipeline

Pipeline inspection gauges (PIGs) are needed for operations such as cleaning and internal inspection of the natural gas pipelines to facilitate improvement in efficiency and safety. There is chatter vibrations appeared in PIGs when they run in the dry pipe with the wear of rubber sealing disc. Dry friction-induced self-excited vibration between sealing disc and pipe is the source of chatter vibration on PIG. In this paper, an experimental setup for measuring chatter vibration response signal of a typical bi-directional PIG running in a real dry steel pipe was implemented. The reason that cause self-excited vibration which manifest as chatter vibration on PIG, was explained through the analysis of classic dry-friction model. A self-excited vibration model based on LuGre friction model was proposed for better understanding of the phenomenon of chatter vibration during the process that PIG running through the natural gas pipeline, and the model was solved by MATLAB/SIMULINK. Our results show that the PIG runs in dry pipe with chatter vibration at a certain period within micro-vibrations in the single ladder period. Dry friction-induced self-excited vibration between sealing disc and pipe is the source of chatter vibration on PIG, and lead to the wear of PIG's sealing disc in natural gas pipeline; the negative damping of system in dry friction contact is the reason that causes self-excited vibration; the simulation of the numerical model can validate the PIG's self-excited phenomenon well. These results provide a better understanding of the complex behavior of PIG motion within natural gas pipelines.

A Transient Dynamics Study on Wear-type Rail Corrugation on a Tight Curve due to the Friction-induced Self-excited Vibration of a Wheelset-track System

Rail corrugation has been perplexing metro tracks over the years. It is of great significance in both theory and application to study the generation mechanism for rail corrugation. Based on the viewpoint of friction-induced self-excited vibration of a wheelset-track system causing rail corrugation, an elastic vibration model of a wheelset-track system when a vehicle negotiates a tight curve at a steady state is established, which includes a wheelset, two rails and a series of sleepers. In the model, the creep forces between the wheels and rails are assumed to be saturated and equal to the normal contact forces multiplied by the friction coefficient. The motion stability of the model is analyzed and transient dynamics of friction-induced self-excited vibration of the wheelset-track system is simulated using ABAQUS package. Dynamic vibrations of the rails and time histories of the contact normal forces are obtained due to self-excited vibration of the wheel-track system. Results show that there is a serious fluctuation of the contact normal force between the inner wheel and low rail. The mechanism for the fluctuating contact normal force causing rail corrugation is discussed.

Active control of friction self-excited vibration using neuro-fuzzy and data mining techniques

Vibration caused by friction, termed as friction-induced self-excited vibration (FSV), is harmful to engineering systems. Understanding this physical phenomenon and developing some strategies to effectively control the vibration have both theoretical and practical significance. This paper proposes a self-tuning active control scheme for controlling FSV in a class of mechanical systems. Our main technical contributions include: setup of a data mining based neuro-fuzzy system for modeling friction; learning algorithm for tuning the neuro-fuzzy system friction model using Lyapunov stability theory, which is associated with a compensation control scheme and guaranteed closed-loop system performance. A typical mechanical system with friction is employed in simulation studies. Results show that our proposed modeling and control techniques are effective to eliminate both the limit cycle and the steady-state error.

The Investigation of the Influence of Dynamics Parameters on the Friction-Induced Self-Excited Vibration

A one degree of freedom nonlinear dynamics model of self-excited vibration induced by dry-friction is built firstly, the numerical method is taken to study the impacts of dynamics parameters on self-excited vibration. The calculation result shows that Along with the variation of system dynamics parameters such as initial velocity or normal pressure the self-excite vibration has the weakened trend or the enhanced trend, so the self-excite vibration could be controled through the control of dynamics parameters.

The Investigation of the Influence of Structure Parameters on the Friction-Induced Self-Excited Vibration

A one degree of freedom nonlinear dynamics model of self-excited vibration induced by dry-friction was built firstly, the numerical method was taken to study the impacts of structure parameters on self-excited vibration. The calculation result shows that the variation of stiffness can change the vibration amplitude and frequency of the self-excited vibration, but can not eliminate it, Along with the increase of system damping the self-excite vibration has the weakened trend and there a ritical damping, when damping is greater than it the self-excite vibration will be disappeared.

Active control of friction-induced self-excited vibration using adaptive fuzzy systems

Vibration caused by friction is harmful to engineering systems. Understanding the mechanism of such a physical phenomenon and developing some strategies to effectively control the vibration have both theoretical and practical significance. Based on our previous work, this paper deals with a problem of active compensation control of friction-induced self-excited vibration using adaptive fuzzy systems. Comparative studies on control performance are carried out, where a class of adaptive compensation control schemes with various friction models are applied to control a motion dynamics with friction. It is observed that our proposed modeling and control techniques are powerful to eliminate the limit cycle and the steady-state error. Furthermore, robustness of the proposed controller with respect to external disturbances is discussed. Simulation results show that the active controller with adaptive fuzzy friction compensation outperforms other active controllers with compensation terms characterized by three well-known friction models.

Pole assignment of friction-induced vibration for stabilisation through state-feedback control

Friction-induced self-excited linear vibration is often governed by a second-order matrix differential equation of motion with an asymmetric stiffness matrix. The asymmetric terms are product of friction coefficient and the normal stiffness at the contact interface. When the friction coefficient becomes high enough, the resultant vibration becomes unstable as frequencies of two conjugate pairs of complex eigenvalues (poles) coalesce (when viscous damping is low). This short paper presents a receptance-based inverse method for assigning complex poles to second-order asymmetric systems through (active) state-feedback control of a combination of active stiffness, active damping and active mass, which is capable of assigning negative real parts to stabilise an unstable system.

Non-linear control of friction-induced self-excited vibration

The present paper introduces a new method of controlling friction-driven self-excited vibration. The control law is primarily derived using the Lyapunov's second method. A single degree-of-freedom oscillator on a moving belt represents the primary model of the system. The control action is achieved by modulating the normal load at the frictional interface based on the state of the oscillatory system. The basic mechanism of the control action utilises subcritical Hopf bifurcation of the equilibrium followed by cyclic-fold bifurcation (of limit cycle oscillations) to globally stabilise the equilibrium. The basic mechanism is qualitatively independent of the exact model of friction. Different models of friction, like, algebraic model, LuGre model and switch model with time-dependent static friction are considered to substantiate the above claim. An approximate method for estimating the critical value of the control parameter that ensures global stability of the equilibrium is also proposed.