Frictional Self-excited Vibrations Research Articles

Comparison of modeling methods and mitigation measures for curve squealing

Predicting and mitigating curve squealing has always been difficult. This study employed various modeling methods to unify the existing models and establish three finite element models (FEMs) of wheelset–track systems to predict curve squealing. The FEMs of the wheelset–track systems, which incorporated solid fasteners, negative friction–velocity slopes, and multiple wheelsets, were examined using complex eigenvalue analysis to determine their relative capacity to predict curve squeal. The inhibitory effects of damping treatments on curve squeal in both wheels and rails were also studied. The results indicate that, in an improvement on the initial model, the FEMs developed in this study can effectively predict curve squeal with frequencies of 482, 1,205, and 2154 Hz. The wheelset–track system was more likely to produce frictional self-excited vibrations under negative damping and interference from multiple wheelsets, but the impact was small. In addition, the rubber block angle of the resilient wheel was set at 15°. Increasing the damping of the rail vibration absorbers and selecting a continuous–discrete under-rail vibration absorber effectively suppressed the generation of curve squeal.

Study on the friction-induced vibration and wire corrugation of metro rigid overhead wire-pantograph systems

Most recently, metro rigid overhead wire-pantograph systems are subjected to severe wear of overhead wires and current collectors throughout China, which are difficult to completely solve up to now. The severe wear of metro rigid overhead wire-pantograph systems is probably brought about by the medium-high frequency vibration of the metro rigid overhead wire-pantograph systems. Coincidentally, corrugation is frequently found in rigid overhead wire systems, but rarely in flexible catenary systems. A frictional self-excited vibration model of a rigid overhead wire-pantograph system was set up. The self-excited vibration characteristics were investigated using the transient analysis and the motion stability analysis. Results show that when the friction coefficient is greater than 0.07, the rigid overhead wire-pantograph system is more prone to self-excited vibration. The self-excited vibration frequencies cover a range of 20–1000 Hz. The simulated overhead wire corrugation approaches the measured corrugation in wavelength. The influence factor analysis displays that the friction coefficient, zigzag layout of rigid catenary wires, and sliding direction of pantographs have significant effects on overhead wire corrugation, and but the train speed, normal force, main spring stiffness, and span of two positioning clips have a little effect.

Study on the Effect of the Modeling Method of Railway Fastener on Rail Corrugation Prediction Model

Taking the typical corrugation phenomenon on a curved track in a metro line as the research object, the modeling method of railway fastener in the friction self-excited vibration model of a wheel–rail system is studied in this article. Firstly, according to the difference of the track support structure in the actual metro line, finite element models of the leading wheel–track system under different track forms, including the short sleeper with a DTVI2 fastener, the shock-absorbing track with a Cologne egg damping fastener, and the ladder sleeper track with a DTIII2 fastener, were established. The rail corrugation on a curved track with a small radius with three different sleepers is studied through complex eigenvalue analysis. In addition, the difference in rail corrugation finite element prediction model with a spring–damper pair model, solid-connected model, and solid-connectmodel is studied. The stability and vibration characteristics of a wheel–rail system with different tracks are studied by complex eigenvalue analysis. The research shows that the frictional self-excited vibration of a wheelset–track system occurs under saturated creep force, and the deformation caused by unstable vibration mainly occurs in the low rail and inner wheel, which can explain why the rail corrugation of a curved track with a small radius mainly occurs in the low rail. Compared with the spring–damper pair fastener model, the calculation result using the solid element fastener model (the solid-connected model and the solid-contact model) is closer to the measured data of the rail corrugation of the curved line with a small radius on the site. Of the two solid element fastener models, the latter is significantly more accurate than the former in predicting rail corrugation on the metro lines.

Effect of wheelset eccentricity on the out-of-round wheel of high-speed trains

Wheelset geometric eccentricity and mass eccentricity are generally considered to be the main reasons behind the formation of the 1st order out-of-round (OOR) wear (or eccentric wear) of railway wheels. Based on finite element simulation, the relationship between wheelset geometric eccentricity and the high-order OOR wheels of high-speed trains was studied in this paper. Moreover, the reason for the phase difference between the polygonization on the left and right wheels of a railway wheelset was discussed. The results show that, when the train runs at a high speed of 237 km/h, a wheelset’s geometric eccentric value greater than 0.7 mm can lead to longitudinal creep forces on the left and right wheels to periodically reach saturation during operation, causing frictional self-excited vibrations of about 605 Hz in the wheel-rail systems; and resulting in 24th ∼ 25th order wheel polygonal wear. The phase difference between the geometric eccentric directions of the left and right wheels can cause the phase difference between the saturation states of the creep forces on these wheels, resulting in the phase difference between the 1st and 24th ∼ 25th order OOR shapes on these wheels. In addition, during the assembly of the trailer wheelset, when the phase difference between the residual static unbalance values of the wheel and brake disc is 180°, the unbalanced force couple caused by the wheelset mass eccentricity is minimal, which then slows down the formation of 1st order OOR shapes on the trailer wheels.

Study on the Different Effects of Power and Trailer Wheelsets on Wheel Polygonal Wear

The wheels of power and trailer wheelset show different polygonal characteristics since their structures are obviously different. Therefore, the frictional self-excited vibration models of wheelset-track systems are established based on the viewpoint of the frictional self-excited vibration in reducing the wheel polygonal wear. Then, the motion stability of wheelset-track systems is studied by using the complex eigenvalue method. The results show that when the creep force between the wheel and rail is saturated, the unstable vibration frequency of the power wheelset is prone to induce 19-20th-order polygonal wear of the wheel, and the trailer wheelset is prone to induce 20-21th-order polygonal wear of the wheel. Meanwhile, the wheel polygonal wear can be effectively alleviated through changing the gearbox position of the power wheelset. And avoiding disc braking at high speeds can suppress the occurrence of wheel polygonal wear. In addition, the development tendency of wheel polygonal wear can be reduced by increasing the Young’s modulus of the brake pad, but Poisson’s ratio has little effect on the development tendency.

Study on the Mechanism of the Abnormal Phenomenon of Rail Corrugation in the Curve Interval of a Mountain City Metro

An abnormal phenomenal of rail corrugation was found in the transition and circular curve interval of the mountain city metro, in which the rail corrugation on the outer rail is more serious and earlier than that on the inner rail, and the wavelengths are also different. In the present article, the frictional self-excited oscillation of the wheel–rail system and the feedback vibration of the rail corrugation are considered comprehensively to study the mechanism of rail corrugation. According to the dynamic analysis of the vehicle track system on the high-incidence section of rail corrugation, finite element models of wheelset–track systems on the smooth track and wear track are established. Then, the unstable vibration mode and dynamic response of the wheelset–track system are calculated by complex eigenvalue analysis and transient dynamic analysis. The consistency of the numerical simulation and field test indicates that the generation of rail corrugation may be affected by the frictional self-excited vibration of the wheelset–track system. Furthermore, the feedback vibration induced by the previous rail corrugation not only aggravates the original rail corrugation but also induces new rail corrugation.

Study on the mechanism for the wheel polygonal wear of high-speed trains in terms of the frictional self-excited vibration theory

In the paper, the frictional self-excited vibration of a wheelset-track system caused by the saturated wheel-rail creep force is proposed as a possible mechanism for wheel polygonal wear of high-speed trains. The wheelset-track system model is established, which consists of a wheelset, two rails, some sleepers and a slab. The stability of the wheelset-track system is studied through the complex eigenvalue method. Results show that the unstable vibration frequency of the wheelset-track system is f= 495.01 Hz, which can lead to the 18th-order wheel polygonal wear. This simulation result is approximately consistent with the field measurement result. Furthermore, the parameters sensitivity analysis shows that increasing the vertical damping of the fastener to a certain extent can suppress or eliminate wheel polygonal wear. In addition, a transient dynamic analysis of the wheelset-track system with the wheelset eccentricity is conducted. Results indicate that the wheelset eccentricity is an important factor affecting wheel polygonal wear.

Effect of the unstable vibration of the disc brake system of high-speed trains on wheel polygonalization

This paper conducts a detailed investigation into the formation mechanism of wheel polygonalization in high-speed trains and its influence factors through numerical simulation. A finite element model including two rails, one wheelset, and three disc brake units is set up to study the formation mechanism of wheel polygonalization in high-speed trains based on the point of view of frictional self-excited vibration. Using the finite element complex analysis, the dynamic stability of the wheelset–track–disc brake system is studied. In addition, the influence factors on the wheel polygonalization are investigated. Results show that when the longitudinal creep force is unsaturated, the 21-order polygonal wear of wheels occurs easily due to the self-excited vibration of the disc brake unit. When the longitudinal creep force is saturated, the 12-order polygonal wear of wheels probably occurs due to the self-excited vibration of the disc brake unit. The bigger the friction coefficient between the brake disc and pad, the greater the occurrence propensity of the polygonal wear of wheels. Vertical fastener damping that is too large or too small is disadvantageous for suppressing wheel corrugation. However, increasing the lateral fastener damping is beneficial for reducing the polygonal wear of wheels. When the vertical fastener stiffness is 25 MN/m, 7-order, 9-order, and 14-order wheel polygonalization can easily occur. A higher lateral fastener stiffness is beneficial for the suppression of wheel polygonalization.

Frequency domain model for railway wheel squeal resulting from unsteady longitudinal creepage

Railway wheel squeal is an unresolved noise pandemic facing the railway industry. Wheel squeal results from frictional self-excited vibration occurring in the wheel-rail contact. Solving the problem of squeal requires researchers to work towards a squeal model that can predict squeal wholly and in every situation. This will allow for squeal to be resolved during the design stages. The current research presents a frequency domain model for the excitation of squeal due to longitudinal creepage with rising, constant and falling friction. In this model the time varying part of the longitudinal creep force is modelled as a feedback loop and tested for stability with the Nyquist criterion. Crucial to the instability is modelling the dynamics of a wheel taking into consideration the moving load nature of the rotating wheel. If wheel rotation is accounted for in the model, modes in a doublet can become unstable through mode-coupling in the presence of large longitudinal creepage. The results of the model provide good agreement with that of squeal occurring on-track. Positive flow of energy for the modelled case of squeal results from the dynamic friction and normal forces being in phase with one another as well as the friction force causing normal displacement at the wheel-rail contact that is in phase with the normal displacement that caused the normal force in the first place. This closed phase loop causes positive interference of the normal vibration in the wheel-rail contact and allows the vibration amplitude to grow. Extending the model to include lateral creepage shows that the vibration of the wheel-rail contact can be unstable due to unsteady longitudinal creepage for more directions of the resulting creep force compared to unsteady lateral creepage in a case with constant friction.

Field investigation and numerical study of the rail corrugation caused by frictional self-excited vibration

Rail corrugation is one of the most serious problems in metro lines, and its formation is affected by several factors. According to the field investigations and research reviews, rail corrugations generally occur on the low rails of sharp curved tracks. Based on the viewpoint of frictional self-excited vibration causing rail corrugation in the present paper, both the field measurement and numerical simulation are performed to study the formation mechanism of rail corrugation found on the rubber-booted short sleeper section of a sharp curved track. In the field measurement, the vibration signals of rails at three different positions are measured when the vehicle runs across the sharp curved track supported by the rubber-booted short sleepers. In the numerical simulation, an elastic vibration model of a leading wheelset-track system on a sharp curved track supported by the rubber-booted short sleepers is established. The dynamic responses and unstable vibration modes are calculated utilizing the transient dynamic analysis together with the complex eigenvalue analysis. The good agreement between the results of the field measurement and numerical simulation further verifies that the saturated creep forces between the leading wheelset and rails can induce the frictional self-excited vibration of the wheelset-track system on a sharp curved track, which is able to cause rail corrugation. It can be found that the vertical vibration acceleration on the rail surface has a significant fluctuation when the wheelset travels through the relevant measuring point, which means that the friction-induced vibration is happening. Meanwhile, the oscillation amplitude of vibration acceleration and normal contact force on the low rail is much larger than that on the high rail. Therefore, the rail corrugation caused by the frictional self-excited vibration mainly occurs on the low rail of sharp curved track. And the wavelength of rail corrugation caused by frictional self-induced vibration is consistent with that measured at the test site in the actual metro line.

Investigation into rail corrugation in high-speed railway tracks from the viewpoint of the frictional self-excited vibration of a wheel–rail system

A finite element vibration model of a multiple wheel–rail system which consists of four wheels, one rail, and a series of sleepers is established to address the problem of rail corrugation in high-speed tracks. In the model, the creep forces between the wheels and rail are considered to be saturated and equal to the normal contact forces times the friction coefficient. The oscillation of the rail is coupled with that of wheels in the action of the saturated creep forces. When the coupling is strong, self-excited oscillation of the wheel–rail system occurs. The self-excited vibration propensity of the model is analyzed using the complex eigenvalue method. Results show that there are strong propensities of unstable self-excited vibrations whose frequencies are less than 1,200 Hz under some conditions. Preventing wheels from slipping on rails is an effective method for suppressing rail corrugation in high-speed tracks.

Experimental Study on Corrugation of a Sliding Surface Caused by Frictional Self-Excited Vibration

abstractA series of tests is conducted on a pin-on-disc tester to study the effect of frictional self-excited vibration on evolution of the scar profiles. A laser displacement sensor is used to measure the profile size of the worn scars. An accelerometer is used to measure vibration of the pin specimen. The test results show that a sustained frictional self-excited vibration easily occurs under dry friction. When the vibration lasts for a long enough time, corrugation is generated on the sliding surface of the disc specimen. The wavelength of corrugation is approximately equal to the sliding speed multiplied by the period time of the friction-induced vibration.

Internal synthesis of motion and the dynamic characteristics of external friction

On the example of a simple tribosystem in the form of a body sliding (rolling) over an inclined plane, it is demonstrated that the kinematic concept of external friction based on the Amonton-Coulomb law of modifications is not appropriate as a base for the study of the dynamics of external friction. The obtained dynamic friction characteristics in respect to the velocity and acceleration prove that the velocity of motion varies and that the dynamic equations are nonlinear both in respect to velocity and acceleration. The mechanism of dynamic feedback in tribosystems ensures both subordination to external effects and the capacity for effective synthesis of relevant motion types. The problem is analyzed of selecting adequate design types of motion elements of a tribosystem in relation to the frictional self-excited vibrations and the metrology of measuring the coefficients of sliding and rolling friction. In view of the high complexity of a priori modeling of external friction, it is concluded that methods of experimental tribodynamics should be developed.

Squeal and chatter phenomena generated in a mountain bike disc brake

This paper examines squeal and chatter phenomena generated experimentally in mountain bike disc brakes. There are two kinds of frictional self-excited vibrations in the bike disc brakes, called squeal with frequency of 1 kHz and chatter with frequency of 500 Hz. In order to reproduce the squeal and chatter, a bench test apparatus using an actual bike was set up to determine the associated frequency characteristics experimentally. The results show the frequencies to be independent of pad temperature and disc rotating speed. Squeal is shown to be in-plane vibration in the direction of the disc surface which is caused by the frictional characteristics having negative slope with respect to the relative velocity in the vibrating system, which includes brake unit, spokes and hub. Chatter is generated within a limited high temperature region. Again, it is frictional vibration in which the squeal and out-of-plane vibration of the disc due to Coulomb friction combine through the internal resonance relation between in-plane and out-of-plane nonlinear vibration caused by the temperature increase of the disc during braking.

Thermo-mechanical model of frictional self-excited vibrations

A novel thermo-mechanical model of frictional self-excited stick-slip vibrations is proposed. Contrary to the tribo-mechanical models known in literature, the proposed model does not include any massless elastic parts. The applied friction force depends on a relative velocity of the sliding bodies. The period of vibrations depends on both heating expansion conditions and on conditions of heat taking up (giving up). Stability of the stationary solutions is studied. A computation of contact parameters during heating of the bodies is performed. Possibility of the existence of frictional auto-vibrations is shown.

Dynamics of a two-degrees-of-freedom system with friction and heat generation

A novel thermomechanical model of frictional self-excited stick-slip vibrations is proposed. A mechanical system consisting of two masses which are coupled by an elastic spring and moving vertically between two walls is considered. It is assumed that between masses and walls a Coulomb friction occurs, and stick-slip motion of the system is studied. The applied friction force depends on a relative velocity of the sliding bodies. Stability of stationary solutions is considered. A computation of contact parameters during heating of the bodies is performed. The possibility of existence of frictional auto-vibrations is illustrated and discussed.

Experimental Investigation on Squeal and Chatter Phenomena in Bicycle Disk Brakes (1st Report, Regeneration Experiments of Squeal and Chatter and Their Characteristics)

This paper deals experimentally with the squeal and chatter phenomena generated in mountain bike disk brakes. First, the authors performed the traveling test using actual bicycle on downhill road in a mountain. As the results, there are two kinds of frictional self-excited vibrations in the bicycle disk brakes called by squeal with frequency of 1 kHz and by chatter with frequency of 500 Hz. In order to regenerate the squeal and the chatter, a bench test apparatus by actual bicycle was set up and their characteristics were experimentally examined. By using the bench test apparatus, it was made clear that their frequencies were independent of temperature of pad and rotating speed of rotor, and the chatter was generated in a certain limited region of high temperature though the squeal occurred in arbitrary temperature region of pad.

Significance of the normal degree of freedom and natural normal vibrations in contact friction

An apparatus has been devised for studying contact friction and self-excited frictional vibrations at constant driving velocities ranging from~1−10 −9cm/sec. The essential features of the apparatus are a total absence of vibrations due to the actuating mechanism and the possibility of damping both natural and self-excited vibrations. It has been shown experimentally that both the negative friction-velocity slope and the frictional self-excited vibrations are closely associated with the freedom of normal displacements of the slider. Whenever the latter are absent the force of contact friction becomes practically independent of the relative velocity of sliding and the self-excited vibrations disappear. Direct interferometric observations have shown that the tangential “darts” of the slider in the process of self-excited vibrations are invariably accompanied by simultaneous upward jumps so that stick-slip sliding is a succession of bumps rather than mere forward darts. Self-excited vibrations in sliding vanish in two cases: (1) at velocities lower than a certain critical value below which the force-velocity curve acquires a positive slope and (2) when the normal vibrations are damped by external means. The value of the critical velocity may be roughly estimated in terms of the creep viscosity of the rubbing solids, their yield strength, the friction coefficient and both the height and spacing of the surface asperties. The sliding friction oscillograms obtained with and without normal vibration damping have revealed some facts which prove the existence of natural normal microvibrations whose frequency is determined by the contact stiffness and mass of the slider. It has been shown that these microvibrations strongly affect both the magnitude of the frictional force and the stability of sliding. Special interferometric measurements have been undertaken to show the high sensitivity of the frictional force to normal slider displacements. The same method has enabled the contact stiffness to be determined as a function of the normal slider displacement. The existence of the normal natural contact microvibrations of the slider and their influence on the frictional force suggests the possibility of sharply reducing friction by low-power forced vibrations at resonance frequency. This has been checked experimentally with the aid of Rochelle salt vibrators glued on the upper surface of the slider. The friction-frequency curves invariably showed a distinct resonance minimum, the percentage friction drop at resonance frequency ranging between 35 and 85%.