Finite element modelling for the investigation of in-plane modes and damping shims in disc brake squeal

Squeal propensity of the in-plane modes and the constrained-layer type damping shims for disc brake system is investigated by using the finite element method. Theoretical formulation is derived for a rotating disc in contact with two stationary vibrating pads attached to the damping shim components. By the conversion from the theoretical to FE brake model, the full equations of motion for the actual disc brake system describes the disc rotation, the in-plane friction characteristics and damping shims in association with squeal vibration. It is concluded from the results that the in-plane torsion modes can be generated by the negative friction slope, but they cannot be controlled by the damping shims. The in-plane radial mode is also investigated and found to be very insensitive in squeal generation.     

LINING-DEFORMATION-INDUCED MODAL COUPLING AS SQUEAL GENERATOR IN A DISTRIBUTED PARAMETER DISC BRAKE MODEL

A distributed-parameter model of a disc brake is developed, which is used for simulation of friction-induced vibrations in the form of high-frequency squeal. The effect of different squeal generation mechanisms is investigated. The comparison of measured and calculated frequencies shows a good agreement and this study indicates that lining-deformation-induced modal coupling can act as a squeal generator in disc brakes.     

EXPERIMENTAL ACTIVE CONTROL OF AUTOMOTIVE DISC BRAKE ROTOR SQUEAL USING DITHER

This paper presents an experimental investigation into the application of “dither” control for the active control and suppression of automobile disc brake squeal. Dither control is characterized by the application of a control effort at a frequency higher than the disturbance to be controlled. In the particular system considered here, a vibro-acoustic analysis of a disc brake system during squeal determined the acoustic squeal signature to be emanating from the brake rotor. This squeal was eliminated, and could even be prevented from occurring, through the application of a harmonic force with a frequency higher than the squeal frequency. The harmonic force was generated by a stack of piezoelectric elements placed within the brake's caliper piston. The harmonic force represented a small variation about the mean clamping force exerted by the brake upon the rotor. The high-frequency vibration in the brake system due to the action of the control system was not heard if an ultrasonic control frequency was used. More importantly, the active control system is shown to be able to prevent squeal from even occurring. This gives rise to a possible active control system integrated into the brake system of automobiles to prevent squeal.     

Coupling analysis of a matched piezoelectric sensor and actuator pair for vibration control of a smart beam

This paper presents a theoretical and experimental study of the in-plane and out-of-plane coupling of a matched piezoelectric sensor/actuator pair bonded on a beam. Both the sensor and actuator are triangularly shaped polyvinylidene fluoride (PVDF) transducers and are intended to provide a compact sensor/actuator system for beam vibration control. The measured sensor-actuator frequency response function has shown an unpredicted increase in magnitude with frequency, which was found, to be due to in-plane vibration coupling. An analytical model has been developed to decompose the sensor-actuator response function into an in-plane contribution and an out-of-plane contribution. This in-plane coupling can limit the feedback control gains when a direct velocity feedback control is applied. A method called the j omega s compensation method is proposed to identify the effect of the in-plane vibration coupling at low frequencies. Even after this compensation, however, there was unexpected strong out-of-plane coupling at even modes, which may have been caused by a lack of accuracy in the shaping of the PVDF sensor and actuator. Numerical simulations have confirmed the sensitivity of the matched sensor/actuator pair with shaping errors.     

Experimental and numerical investigations of resonant vibration characteristics for piezoceramic plates.

Electronic speckle pattern interferometry (ESPI) is a full field, non-contact technique for measuring the surface displacement of a structure subjected to static loading or, especially, to dynamic vibration. In this article we employ an optical system called the amplitude-fluctuation ESPI with out-of-plane and in-plane measurements to investigate the vibration characteristics of piezoceramic plates. Two different configurations of piezoceramic plates, namely the rectangular and the circular plates, are discussed in detail. As compared with the film recording and optical reconstruction procedures used for holographic interferometry, the interferometric fringes of AF-ESPI are produced instantly by a video recording system. Because the clear fringe patterns will be shown only at resonant frequencies, both the resonant frequencies and the corresponding mode shapes are obtained experimentally at the same time by the proposed AF-ESPI method. Excellent quality of the interferometric fringe patterns for both the in-plane and out-of-plane vibration mode shapes is demonstrated. The resonant frequencies of the piezoceramic plates are also measured by the conventional impedance analysis. From experimental results, we find that the out-of-plane vibration modes (type A) with lower resonant frequencies cannot be measured by the impedance analysis and only the in-plane vibration modes (type B) will be shown. However, both the out-of-plane (bending) and in-plane (extensional) vibration modes of piezoceramic plates are obtained by the AF-ESPI method. Finally, the numerical finite element calculations are also performed, and the results are compared with the experimental measurements. It is shown that the numerical calculations and the experimental results agree fairly well for both the resonant frequencies and the mode shapes.     

The method of feed-in energy on disc brake squeal

Brake squeal is studied in this paper by feed-in energy analysis. Based on the brake closed-loop coupling model, a calculation method of feed-in energy for squeal mode is derived. Result of the feed-in energy indicates squeal tendency of the brake system, while formula for calculating it discloses the relation among brake squeal phenomenon and structural parameters, such as frictional coefficient, geometric shape of brake pads, elastic modulus of frictional material, substructure modal shape, etc. The method also helps to analyze the effectiveness of various structural modification schemes attempted to eliminate the squeal noise. Finally, this method is illustrated by application to a typical squealing disc brake.     

Out-of-plane exchange bias and magnetic anisotropy in MnPd/Co multilayers

Magnetic and structural properties in [MnPd/Co]₁₀ multilayers deposited onto Si(1 1 1) substrates have been investigated. The dependences of anisotropy and exchange bias on the thicknesses of both MnPd and Co layers have been studied. In most of the samples, the out-of-plane magnetic anisotropy and both large out-of-plane and in-plane exchange biases have been observed at cryogenic temperature below the blocking temperature T_B≈240 K. With appropriate MnPd and Co thicknesses, we have obtained samples with a large out-of-plane exchange bias along with a large out-of-plane magnetic anisotropy. The origin of the out-of-plane magnetic anisotropy in the samples has been suggested to be due to the formation of CoPd interfacial alloys which have tensile in-plane strains, while the spin structure of the antiferromagnetic layer at the interface which is believed to be responsible for exchange bias may be the same as that of the bulk material. Also, the present study shows that the interplay between the out-of-plane magnetic anisotropy and exchange bias is evident in our multilayers and plays an important role in the out-of-plane exchange-bias mechanism.     

Analysis of disc brake squeal using the complex eigenvalue method

A new functionality of ABAQUS/Standard, which allows for a nonlinear analysis prior to a complex eigenvalue extraction in order to study the stability of brake systems, is used to analyse disc brake squeal. An attempt is made to investigate the effects of system parameters, such as the hydraulic pressure, the rotational velocity of the disc, the friction coefficient of the contact interactions between the pads and the disc, the stiffness of the disc, and the stiffness of the back plates of the pads, on the disc squeal. The simulation results show that significant pad bending vibration may be responsible for the disc brake squeal. The squeal can be reduced by decreasing the friction coefficient, increasing the stiffness of the disc, using damping material on the back plates of the pads, and modifying the shape of the brake pads.     

LINEAR VIBRATION CHARACTERISTICS OF CABLE-BUOY SYSTEMS

A theoretical model for the linear vibration of a cable tensioned by a subsurface buoy is developed. The equilibrium of the cable-buoy system subject to drag is evaluated using an approximate closed-form solution whose range of validity is confirmed through comparison with numerical solutions. The three-dimensional equations of cable-buoy motion are linearized about this equilibrium and then used to assess vibration characteristics. The characteristic equations for the natural frequencies of both in-plane and out-of-plane vibration modes are derived. The in-plane natural frequency spectrum exhibits the curve veering phenomena due to asymmetry of the associated mode shapes. Parameter studies reveal the dependencies of the in-plane and out-of-plane vibration modes on the cable tension, the buoy mass, and the current velocity.     

Effect of damping on the propensity of squeal instability: an experimental investigation

Friction induced vibrations in automotive brakes is recognized as a major problem in industry. Squeal is a difficult subject because of its unpredictability caused by a not completely understood sensitivity to variation of the system parameters. In the literature several analytical and numerical studies deal with the relationship between damping and system propensity to have instability. These studies highlight the existence of a nonintuitive effect of damping distribution on modal coupling that gives rise to the unstable vibrations. The complexity of commercial brakes and the difficulties to identify the values of modal damping in brake assemblies lead to the necessity to rely on experimental analysis using simplified test rigs. This paper presents an experimental investigation of the relationship between the distribution of modal damping and the propensity to develop squeal in a beam-on-disk setup, which reliably reproduces squeal events with easy control and measurement of the damping of the disk and the beam, respectively. The experiments highlight the key role played by the modal damping distribution on squeal: A nonuniform repartition of the modal damping causes an increase of the squeal propensity.     

Cable connected active tuned mass dampers for control of in-plane vibrations of wind turbine blades

In-plane vibrations of wind turbine blades are of concern in modern multi-megawatt wind turbines. Today?s turbines with capacities of up to 7.5 MW have very large, flexible blades. As blades have grown longer the increasing flexibility has led to vibration problems. Vibration of blades can reduce the power produced by the turbine and decrease the fatigue life of the turbine. In this paper a new active control strategy is designed and implemented to control the in-plane vibration of large wind turbine blades which in general is not aerodynamically damped. A cable connected active tuned mass damper (CCATMD) system is proposed for the mitigation of in-plane blade vibration. An Euler–Lagrangian wind turbine model based on energy formulation has been developed for this purpose which considers the structural dynamics of the system and the interaction between in-plane and out-of-plane vibrations and also the interaction between the blades and the tower including the CCATMDs. The CCATMDs are located inside the blades and are controlled by an LQR controller. The turbine is subject to turbulent aerodynamic loading simulated using a modification to the classic Blade Element Momentum (BEM) theory with turbulence generated from rotationally sampled spectra. The turbine is also subject to gravity loading. The effect of centrifugal stiffening of the rotating blades has also been considered. Results show that the use of the proposed new active control scheme significantly reduces the in-plane vibration of large, flexible wind turbine blades.     

Modal stability of inclined cables subjected to vertical support excitation

In this paper the out-of-plane dynamic stability of inclined cables subjected to in-plane vertical support excitation is investigated. We compute stability boundaries for the out-of-plane modes using rescaling and averaging methods. Our study focuses on the 2:1 internal resonance phenomenon between modes that occurs when the excitation frequency is twice the first out-of-plane natural frequency of the cable. The second in-plane mode is excited directly, while the out-of-plane modes can be excited parametrically. An analytical model is developed in order to study the stability regions in parameter space. In this model we include nonlinear coupling effects with other modes, which have thus far been omitted from previous models of parametric excitation of inclined cables. Our study reflects the importance of such effects. Unstable parameter regions are defined for the selected cable configuration. The validity of the proposed stability model was tested experimentally using a small-scale cable actuator rig. A comparison between experimental and analytical results is presented in which very good agreement with model predictions was obtained.     

The vibration discomfort of standing persons: 0.5-16-Hz fore-and-aft, lateral, and vertical vibration

To minimise the discomfort of standing people caused by vibration of a floor, it is necessary to know how their sensitivity to vibration depends on the frequency of the vibration. This study was designed to determine how the discomfort of standing people exposed to horizontal and vertical vibration depends on vibration frequency over the range 0.5-16 Hz. Using the method of magnitude estimation, sixteen subjects judged the discomfort caused by fore-and-aft, lateral, and vertical sinusoidal vibration at each of the sixteen preferred one-third octave centre frequencies from 0.5 to 16 Hz at each of nine magnitudes. Subjects also reported the main cause of their discomfort. Equivalent comfort contours were constructed, reflecting the effect of frequency on subject sensitivity to vibration acceleration. With horizontal vibration, at frequencies between 0.5 and 3.15 Hz the discomfort was similar when the vibration velocity was similar, whereas at frequencies between 3.15 and 16 Hz the discomfort was similar when the vibration acceleration was similar. At frequencies less than 3.15 Hz, the subjects experienced problems with their stability, whereas at higher frequencies vibration discomfort was mostly experienced from sensations in the legs and feet. With vertical vibration, discomfort was felt in the lower-body and upper-body at all frequencies. The frequency weightings in current standards for predicting the vibration discomfort of standing persons have been greatly influenced by the findings of studies with seated subjects: the weightings are consistent with the experimentally determined frequency-dependence of discomfort caused by vertical vibration but inconsistent with the experimentally determined frequency-dependence of discomfort caused by horizontal vibration. The results suggest that the responses of seated and standing people are similar for vertical vibration, but differ for horizontal vibration, partly due to greater instability in standing persons.     

Effect of substrate temperature on the magnetic properties and internal stresses of CoPt/AlN multilayer deposited by dc magnetron sputtering

Magnetic properties and internal stresses of AlN(20 nm)/[CoPt(2 nm)/AlN(20 nm)]₅ multilayer structure deposited at different substrate temperatures by dc magnetron sputtering have been studied. It is found that with increasing the substrate temperature from room temperature to 400 °C, in-plane magnetic anisotropy field of the film becomes smaller, and the out-of-plane magnetization becomes stronger. Especially when the film is deposited at substrate temperature of 400 °C, the out-of-plane magnetization becomes as strong as the in-plane magnetization. On the other hand, the total in-plane residual stress of the film changes gradually from compressive to tensile. The compressive intrinsic stress is generated during deposition process and decreases with increasing the substrate temperature. After annealing at high temperatures, the films show strong perpendicular magnetic anisotropy. With increasing the annealing temperature, the in-plane thermal stress also increases and becomes dominant, which is considered to result in the perpendicular magnetic anisotropy of the films.     

In-plane and out-of-plane ferroelectric instabilities in epitaxial SrTiO3 films

The in-plane and out-of-plane ferroelectric instabilities in compressed (100)-epitaxial SrTiO3 films were examined by infrared reflection spectroscopy. The strongly stiffened in-plane soft mode frequency softened very slowly on cooling. On the other hand, the silent mode appeared at around 150 K, indicating an out-of-plane ferroelectric transition. This behavior points to a split of in-plane and out-of-plane ferroelectric instability temperatures due to the lowered symmetry of the SrTiO3 lattice caused by mechanical misfit strain. Infrared spectroscopy provides a possibility to detect such an effect in the strained epitaxial ferroelectric films.     

Eigenvalue optimization against brake squeal: Symmetry,mathematical background and experiments

Brake squeal is still a challenge for design engineers and scientists. Due to cost reasons for the avoidance of brake noise only passive measures are meaningful for a broad industrial range. Many countermeasures against squeal are based on the introduction of damping, for example by using shims. In the literature on the modeling of brake squeal, the structural properties of the brake disc are most often not considered. It has however been shown analytically and experimentally that the stiffness properties of the disc are important and that splitting of double modes of the disc has a stabilizing effect. This knowledge can be used for structural optimization of brake rotors. The goal of this paper is to exploit the potential and to discuss some mathematical difficulties. Furthermore, experimental evidence for the relation of rotor asymmetry and squeal is given.     

Experimental and numerical investigation of friction-induced vibration of a beam-on-beam in contact with friction

The vibrations generated by friction are responsible for various noises such as squealing, squeaking and chatter. Although these phenomena have been studied for a long time, it is not well-understood. In this study, an experimental and numerical study of friction-induced vibrations of a system composed of two beams in contact is proposed. The experimental system exhibits periodic steady state vibrations of different types. To model and understand this experimental vibratory phenomenon, complex eigenvalue and dynamic transient analyses are performed. In the linear complex eigenvalue analysis, flutter instability occurs via the coalescence of two eigenmodes of the system. This linear study provides an accurate value of the experimental frequency of vibration. To understand what happens physically during friction-induced instability, a dynamic transient analysis that takes account of the non-linear aspect of a frictional contact is performed. In this analysis, friction-induced instability is characterized by self-sustained vibrations and by stick, slip and separation zones occurring at the surface of the contact. The results stemming from this analysis show that good correlation between numerical and experimental vibrations can be obtained (in time and frequency domains). Moreover, time domain simulations permit understanding the physical phenomena involved in two different vibratory behaviours observed experimentally.     

Brake squeal reduction of vehicle disc brake system with interval parameters by uncertain optimization

An uncertain optimization method for brake squeal reduction of vehicle disc brake system with interval parameters is presented in this paper. In the proposed method, the parameters of frictional coefficient, material properties and the thicknesses of wearing components are treated as uncertain parameters, which are described as interval variables. Attention is focused on the stability analysis of a brake system in squeal, and the stability of brake system is investigated via the complex eigenvalue analysis (CEA) method. The dominant unstable mode is extracted by performing CEA based on a linear finite element (FE) model, and the negative damping ratio corresponding to the dominant unstable mode is selected as the indicator of instability. The response surface method (RSM) is applied to approximate the implicit relationship between the unstable mode and the system parameters. A reliability-based optimization model for improving the stability of the vehicle disc brake system with interval parameters is constructed based on RSM, interval analysis and reliability analysis. The Genetic Algorithm is used to get the optimal values of design parameters from the optimization model. The stability analysis and optimization of a disc brake system are carried out, and the results show that brake squeal propensity can be reduced by using stiffer back plates. The proposed approach can be used to improve the stability of the vehicle disc brake system with uncertain parameters effectively.