Squeal Instability Research Articles

Optimal disc brake design for reducing squeal instability using slip-dependent complex eigenvalue analysis

This paper proposes an improved disc brake system optimization method for squeal instability reduction using slip-dependent eigenvalue results. Although complex eigenvalue analysis is widely used for minimizing brake squeal instability, conventional optimization approaches still have the limitation of not being able to reflect slip rate-varying squeal instability characteristics. While relative angular velocity between the pad and disc declines due to braking, disc brake system instability gradually increases up to a specific peak velocity point and decreases until the vehicle stops, which means a maximum instability point exists during the braking process. Therefore, instability optimization should target the prevention of a maximum value during a braking scenario. The proposed optimization formulation is conducted considering maximum instability during full braking. To obtain braking time profiles, a model-based design method is employed and utilized instead of full finite element transient dynamic analysis to reduce computational cost. Kriging surrogate modeling is also used for solving the optimization problem and better express the multi-variable squeal problem. The proposed optimal design method produces minimal squeal instability during the full vehicle braking time range. The effectiveness of the proposed disc brake optimal design is demonstrated via acceleration power value comparison of the structure acceleration with that derived by conventional optimization approach.

Experimental and Numerical Study on the Squeal of a Rotary Compressor

This study predicts the squeal instability of a rotary compressor using a full-size finite element model. A complex eigenvalue extraction method was used to study the tendency toward squeal of the rotary compressor during working. The numerical results showed that the unstable vibration frequency of the rotary compressor was 6,908 Hz, which corresponded to the frequency of the rotary compressor squeal. The squealing vibration of the rotary compressor was also measured, with results showing that the measured squeal frequency was in good agreement with that predicted by the finite element model. Transient dynamic analysis results showed that when squeal occurred, the main frequency of the normal acceleration of the upper flange was the same as that of the tangential acceleration. This phenomenon showed that the coupling of the normal vibration and tangential vibration of the upper flange was a main reason for the compressor squeal. Also, the greater the friction coefficient, the higher the likelihood of a squeal occurrence.

An efficient numerical strategy to predict the dynamic instabilities of a rubbing system: application to an automobile disc brake system

This paper deals with the modelling and the prediction of the dynamic instabilities for a rubbing system. Two hybrid approaches are introduced for dynamic instability analysis and applied to a reduced disc brake system. The methods are based on stochastic algorithms coupled with the finite element method (FEM) using the complex eigenvalue analysis technique. By considering the input parameters as random variables, the uncertainty analysis is performed through two approaches to predict the unstable frequencies of a braking system (1) Monte-Carlo (MC) using Mersenne-Twister (MT19937) algorithm and (2) periodic sampling technique. Since the mechanism of brake squeal involves many design parameters, stochastic finite element approaches will be coupled with sensitivity algorithms, e.g. Variance-Based Sensitivity Analysis and Fourier Sensitivity Analysis Test, to analyze the contribution of each random variable on the dynamic instabilities. First, a comparison between the two stochastic algorithms is performed on standard analytical models. The objective is to validate the accuracy and to assess the numerical efficiency that FAST presents to (1) propagate the uncertainties upstream of the model and (2) to compute the partial variances of the model output. Secondly, the coupling of the previous stochastic algorithms with FEM is carried out and tested through a reduced brake system consisting of a rotating disc with two flat pads. Results show that the hybrid approach FAST-FE is more robust and computationally more efficient compared to the widely used MC-FE for these types of problems. FAST-FE solver converges, within a reasonable computing time, either to approximate the probability density function of the random variables or to compute the partial variances of the dynamic instabilities. Hence, it can be considered as an efficient numerical method for squeal instability analysis in order to reduce squeal noise of such a mechanical system.

Rendering optimal design under various uncertainties

PurposeThe purpose of this paper is to propose a unified optimization design method and apply it to handle the brake squeal instability involving various uncertainties in a unified framework.Design/methodology/approachFuzzy random variables are taken as equivalent variables of conventional uncertain variables, and a unified response analysis method is first derived based on level-cut technique, Taylor expansion and central difference scheme. Next, a unified reliability analysis method is developed by integrating the unified response analysis and fuzzy possibility theory. Finally, based on the unified reliability analysis method, a unified reliability-based optimization model is established, which is capable of optimizing uncertain responses in a unified way for different uncertainty cases.FindingsThe proposed method is extended to perform squeal instability analysis and optimization involving various uncertainties. Numerical examples under eight uncertainty cases are provided and the results demonstrate the effectiveness of the proposed method.Originality/valueMost of the existing methods of uncertainty analysis and optimization are merely effective in tackling one uncertainty case. The proposed method is able to handle the uncertain problems involving various types of uncertainties in a unified way.

Squeal propensity characterization of brake lining materials through friction noise measurements

Disc brake systems are a technology widely adopted within the automotive and rail industry, especially when high performance is needed. The interaction between the disc and the pads is responsible for friction-induced vibrations, leading often to squeal noise emission. Squeal vibrations are generated by the onset of an unstable mode, which is triggered by an external excitation. Local phenomena occurring at the contact interface, and resulting in friction noise, can be responsible of the dynamic excitation triggering the squeal instability. This work proposes a new approach for characterizing friction lining materials, by measuring the friction noise coming from the contact between different pad materials and a disc rotor, in order to quantify and compare the attitude of materials to trigger squeal. Then, a parametrical analysis has been carried out with the aim of highlighting the influence of the main parameters on the friction noise. When testing the same set of materials on a full brake disc system, the measured friction noise indexes resulted to be strongly correlated with the squeal occurrence, validating the proposed characterization method for the squeal propensity of lining materials.

An optimization method for brake instability reduction with fuzzy-boundary interval variables

In some special engineering circumstances, it is likely that all parameters of an uncertain automotive structure can only be treated as interval variables due to limited knowledge, but meanwhile their lower and upper bounds can just be modeled as fuzzy variables rather than as deterministic values due to ambiguous information. To handle this dual uncertainties case, a reliability-based optimization method with fuzzy-boundary interval variables is developed in this study, and it is further extended to carry out squeal instability analysis and reduction of brake involving both limited and vague information. In the proposed method, fuzzy-boundary interval variables are utilized to cope with the above dual uncertainties of structure parameters and help to build up the structure response analysis model. First, the structure responses are derived on the basis of α-cut strategy, Taylor series expansion, subinterval analysis, and central difference method. Then, with the aid of fuzzy possibility theory, a reliability analysis model of structure response is developed, which can make use of extra reliability information and thus quantify the reliability more accurately. Next, a reliability-based optimization model involving fuzzy-boundary interval variables is established by integrating the uncertain response analysis model and the reliability analysis model. Finally, the proposed method is extended to carry out automotive brake squeal instability analysis and optimization. The numerical investigations demonstrate the applicability and effectiveness of the proposed method.

An improved method for fuzzy–interval uncertainty analysis and its application in brake instability study

Most of the existing methods of brake squeal instability analysis are merely available to handle single type of uncertain case. In this study, an improved unified method is developed for uncertainty quantification, which is capable of handling two types of fuzzy–interval cases. In the first fuzzy–interval case, uncertain parameters of engineering structures are assumed as either fuzzy variables or interval variables, which exist in structures simultaneously and independently. In the second fuzzy–interval case, all uncertain parameters are represented by interval variables, but their lower and upper bounds just can be expressed as fuzzy variables instead of deterministic values. In the proposed method, fuzzy–boundary interval variables are introduced to handle fuzzy–interval uncertainties, and based on which an improved response analysis model is established. In the improved model, the fuzzy–boundary interval variables are firstly converted into interval-boundary variables by level-cut technique. Then by temporarily neglecting boundary uncertainties, the initial interval responses can be approximated via conducting once Taylor series expansion and subinterval analysis. Next, Taylor series expansion and central difference method are combined twice to deal with boundary uncertainties, and the interval responses of the structures with interval-boundary variables are yielded. Finally, the fuzzy–interval responses of the structures are derived on the basis of interval union operation and fuzzy decomposition theorem. The improved method is subsequently extended to quantify the uncertainties in brake squeal instability analysis involving two types of fuzzy–interval uncertainties. The effectiveness of the proposed method on tackling fuzzy–interval problems is demonstrated by numerical examples.

A unified method and its application to brake instability analysis involving different types of epistemic uncertainties

• A unified method is proposed for epistemic uncertainty analysis. • Different types of epistemic uncertainties are considered. • Seven uncertainty cases of brake instability analysis are well processed. • The method presents good computational accuracy and efficiency compared with MCM. The key idea of the proposed method is the use of the equivalent variables named as evidence-based fuzzy variables, which are special evidence variables with fuzzy focal elements. On the basis of the equivalent variables, an uncertainty quantification model is established, in which the unified probabilistic information related to the uncertain responses of engineering systems can be computed with the aid of the fuzziness discretization and reconstruction, the belief and plausibility measures analysis, and the interval response analysis. Monte Carlo simulation is presented as a reference method to validate the accuracy of the proposed method. The proposed method then is extended to perform squeal instability analysis involving different types of epistemic uncertainties. To illustrate the feasibility and effectiveness of the proposed method, seven numerical examples of disc brake instability analysis involving different epistemic uncertainties are provided and analyzed. By conducting appropriate comparisons with reference results, the high accuracy and efficiency of the proposed method on quantifying the effects of different epistemic uncertainties on brake instability are demonstrated.

A new hybrid uncertainty analysis method and its application to squeal analysis with random and interval variables

A new hybrid uncertainty analysis method with random and interval variables is proposed in this paper. In the proposed method, the uncertain parameters with sufficient information are treated as random variables, while the uncertain parameters with limited information are modeled as interval variables. Both random variables and interval variables can be viewed as special evidence variables. From this special point of view, both random variables and interval variables are represented by equivalent evidence variables in this study, and a unified framework for hybrid uncertainty analysis is developed based on evidence theory and subinterval perturbation technique. The effects of the mixture of random and interval uncertainties on uncertain output are assessed by belief measure and plausibility measure. On the base of the proposed method, the squeal analysis model of automotive disc brakes involving both random and interval uncertainties can be developed. A numerical example of brake squeal analysis is provided to illustrate the effectiveness of the proposed method. The analysis results show that the equivalent evidence variables can be explored to represent random variables and interval variables reasonably and the proposed method has good accuracy and efficiency in the hybrid uncertainty analysis of squeal instability The proposed method gives a unified framework to tackle several types of uncertain cases, and it is quite general and not only limited to the uncertainty analysis of brake squeal.

Uncertainty quantification of squeal instability under two fuzzy-interval cases

Automotive brake systems are always subjected to various kinds of uncertain factors and the uncertainty analyses of brake squeal have been investigated for decades. However, most of the existing methods of squeal analysis are merely effective in tackling single uncertain case. In this study, a unified method is developed for the uncertainty quantification of disc brake squeal, which is able to handle two fuzzy-interval cases. Due to subjective opinions or limited data, in the first fuzzy-interval case, the uncertain brake parameters are expressed as either fuzzy variables or interval variables, which exist in brake systems simultaneously and independently; whereas, the uncertain brake parameters are all treated as interval variables, but their lower and upper bounds are expressed as fuzzy variables in the second fuzzy-interval case. In the developed method, the first fuzzy-interval case is equivalently treated as a special case of the second one. On the basis of fuzzy-boundary interval variables, an uncertainty quantification model under two fuzzy-interval cases is established, in which the unified uncertain response is computed with the aid of the combination of level-cut strategy, Taylor series expansion, subinterval analysis and Monte Carlo simulation. The unified method is then extended to quantify the uncertainty in disc brake squeal analysis. The studies of several numerical examples demonstrate that the proposed method is able to quantify the uncertainty of squeal instability effectively. In addition, the proposed method can also help to carry out reliability analysis and optimization to reduce the likelihood of squeal occurrence.

A universal approach to squeal analysis of the disc brakes involving various types of uncertainty

On the basis of fuzzy random variables, a universal approach to squeal analysis of the disc brakes involving various types of uncertainty is proposed in this paper. In the proposed approach, first, the brake stability analysis function related to reliability is constructed with fuzzy random variables. Next, the fuzziness represented by fuzzy random variables is decomposed into interval uncertainties by using a level-cut strategy. Then, the expectations and the variances of the brake stability analysis function are approximately solved by the random moment method at different cut levels, and the lower bounds and the upper bounds of the expectations and the variances are calculated by using a first-order Taylor expansion and a subinterval analysis. Finally, by combining the different interval solutions with the corresponding cut levels, the fuzzy solutions of the brake stability analysis function are obtained, which can be employed to evaluate the brake squeal instability. The proposed approach provides a universal framework for dealing with various types of uncertainty that may exist in automotive brakes. The universality, the accuracy and the efficiency of the proposed approach to the squeal instability analysis of the brakes involving various types of uncertainty are verified by the analysis results from nine different numerical examples.

A unified approach for squeal instability analysis of disc brakes with two types of random-fuzzy uncertainties

Automotive brake systems are always subjected to various types of uncertainties and two types of random-fuzzy uncertainties may exist in the brakes. In this paper, a unified approach is proposed for squeal instability analysis of disc brakes with two types of random-fuzzy uncertainties. In the proposed approach, two uncertainty analysis models with mixed variables are introduced to model the random-fuzzy uncertainties. The first one is the random and fuzzy model, in which random variables and fuzzy variables exist simultaneously and independently. The second one is the fuzzy random model, in which uncertain parameters are all treated as random variables while their distribution parameters are expressed as fuzzy numbers. Firstly, the fuzziness is discretized by using α-cut technique and the two uncertainty analysis models are simplified into random-interval models. Afterwards, by temporarily neglecting interval uncertainties, the random-interval models are degraded into random models, in which the expectations, variances, reliability indexes and reliability probabilities of system stability functions are calculated. And then, by reconsidering the interval uncertainties, the bounds of the expectations, variances, reliability indexes and reliability probabilities are computed based on Taylor series expansion. Finally, by recomposing the analysis results at each α-cut level, the fuzzy reliability indexes and probabilities can be obtained, by which the brake squeal instability can be evaluated. The proposed approach gives a general framework to deal with both types of random-fuzzy uncertainties that may exist in the brakes and its effectiveness is demonstrated by numerical examples. It will be a valuable supplement to the systematic study of brake squeal considering uncertainty.

How do grooves on friction interface affect tribological and vibration and squeal noise performance

Experimental studies on the effect of grooved disc on tribological properties, and vibration and noise properties are performed in two different contact configurations: ball-on-disc and pad-on-disc configurations. Experimental results show that certain sizes of grooves on the disc surface are capable of significantly affecting tribological behaviour and reducing squeal noise. Moreover, the grooves are found to play different roles in reducing squeal noise in these two different contact configurations. A disc sample with just one groove on the disc surface sufficiently validates the different abilities of grooves in suppressing squeal noise in both contact configurations. In addition, numerical analysis is performed to further demonstrate the effect of grooves in affecting squeal instability in both contact configurations.

An imprecise probability approach for squeal instability analysis based on evidence theory

An imprecise probability approach based on evidence theory is proposed for squeal instability analysis of uncertain disc brakes in this paper. First, the squeal instability of the finite element (FE) model of a disc brake is investigated and its dominant unstable eigenvalue is detected by running two typical numerical simulations, i.e., complex eigenvalue analysis (CEA) and transient dynamical analysis. Next, the uncertainty mainly caused by contact and friction is taken into account and some key parameters of the brake are described as uncertain parameters. All these uncertain parameters are usually involved with imprecise data such as incomplete information and conflict information. Finally, a squeal instability analysis model considering imprecise uncertainty is established by integrating evidence theory, Taylor expansion, subinterval analysis and surrogate model. In the proposed analysis model, the uncertain parameters with imprecise data are treated as evidence variables, and the belief measure and plausibility measure are employed to evaluate system squeal instability. The effectiveness of the proposed approach is demonstrated by numerical examples and some interesting observations and conclusions are summarized from the analyses and discussions. The proposed approach is generally limited to the squeal problems without too many investigated parameters. It can be considered as a potential method for squeal instability analysis, which will act as the first step to reduce squeal noise of uncertain brakes with imprecise information.

Analysis of automotive disc brake squeal considering damping and design modifications for pads and a disc

The squeal noise occurring from the disc brakes of passenger cars has been analyzed by using the complex eigenvalue method numerically. The contact between a disc and two pads was analytically modeled as many linear springs and dampers in an effort to develop the improved equation of motion derived on the basis of Lagrange’s equation and the assumed mode method. The finite element modal analysis results for disc brake components constitute an eigenvalue matrix in the analytical equation of motion. The complex eigenvalue analyses based on the equations of motion are able to examine the dynamic instability of a brake system, which is an onset of squeal, by considering the disc rotational effect. Numerical analyses showed that the modes unstable in an undamped analysis became stable in a damped case, which illustrates the important effect of damping on the squeal instability in a brake squeal simulation. Then several modified brake models were suggested and investigated how effectively they suppressed the occurrence of squeal noise. The brake parts such as a pad chamfer and a disc vane were modified and the influence of pad chamfer and vane shapes on squeal occurrence was proved to be significant. The numerical results showed that proper structural modification of a disc brake system can suppress the brake squeal to some extent.

Squeal Noise of Friction Material With Groove-Textured Surface: An Experimental and Numerical Analysis

In this work, an experimental and numerical study is performed to understand squeal generation and suppression of a pad-on-disk friction system. Several friction material specimens having various orientation degrees of grooves cut on their surfaces are tested. Numerical studies using the methods of complex eigenvalue analysis and dynamic transient analysis are conducted to simulate the experimental process with the finite element (FE) software abaqus. Both experimental and numerical results show that surface modifications of friction material specimens have a significant influence on the squeal instability: cutting a 45 deg or 90 deg groove on the material surface can significantly reduce squeal noise, cutting a 135 deg groove just reduces squeal noise moderately and cutting a 0 deg groove cannot reduce squeal noise. Moreover, the contact pressure distributions for the original surface and modified surfaces are studied to provide a physical explanation of the noise phenomenon. The major finding that friction-induced noise can be reduced by means of suitable structural modifications of the contact interface is expected to have important and much wider applications.

Uncertainty quantification of squeal instability via surrogate modelling

One of the major issues that car manufacturers are facing is the noise and vibration of brake systems. Of the different sorts of noise and vibration, which a brake system may generate, squeal as an irritating high-frequency noise costs the manufacturers significantly. Despite considerable research that has been conducted on brake squeal, the root cause of squeal is still not fully understood. The most common assumption, however, is mode-coupling.Complex eigenvalue analysis is the most widely used approach to the analysis of brake squeal problems. One of the major drawbacks of this technique, nevertheless, is that the effects of variability and uncertainty are not included in the results. Apparently, uncertainty and variability are two inseparable parts of any brake system. Uncertainty is mainly caused by friction, contact, wear and thermal effects while variability mostly stems from the manufacturing process, material properties and component geometries. Evaluating the effects of uncertainty and variability in the complex eigenvalue analysis improves the predictability of noise propensity and helps produce a more robust design.The biggest hurdle in the uncertainty analysis of brake systems is the computational cost and time. Most uncertainty analysis techniques rely on the results of many deterministic analyses. A full finite element model of a brake system typically consists of millions of degrees-of-freedom and many load cases. Running time of such models is so long that automotive industry is reluctant to do many deterministic analyses. This paper, instead, proposes an efficient method of uncertainty propagation via surrogate modelling. A surrogate model of a brake system is constructed in order to reproduce the outputs of the large-scale finite element model and overcome the issue of computational workloads. The probability distribution of the real part of an unstable mode can then be obtained by using the surrogate model with a massive saving of computational time and cost. The established model can be used subsequently for design, reliability analysis and optimisation.

Numerical study of friction-induced vibration and noise on groove-textured surface

A numerical study was performed to predict the squeal instability when a sphere sliding on a groove-textured surface through complex eigenvalue analysis, which was discussed with the experimental results. It is shown that the friction system had a propensity to cause squeal instability. Mode coupling was found when squeal occurred. The calculated dominant frequency of squeal was close to the experimental measured one. The numerical model created can be used to predict the squeal instability of the friction system. Sphere sliding along groove showed potential in reducing squeal instability compared to the case of sphere sliding across groove.

A numerical investigation into the squeal instability: Effect of damping

Between the NVH issues, brake squeal is a harmonic acoustic emission (between 1 and 20 kHz) caused by friction induced vibrations. The onset of squeal is due to an unstable behaviour of the system leading to limit cycle vibrations. A general approach used by several authors to determine the system instabilities is the CEA: Complex Eigenvalues Analysis. This work presents a numerical investigation into the squeal instability on a simplified disc-brake system addressed to analyse the effect of damping on the squeal instability. The mode lock-in instability is reproduced by a parametrical analysis. The relationship between the distribution of damping on the system components and the propensity of the brake to develop squeal is investigated. The numerical results are validated by the experimental ones, presented in a previous work. The behaviour of the system eigenvalues highlights that, while a homogenous distribution of damping stabilizes the system, a non-uniform repartition of damping can increase the squeal propensity.

Uncertainty model for contact instability prediction

Contact between sliding bodies can cause vibrations leading to instability. The problem of squeal due to high frequency noise from brake systems is due to unstable vibrations generated at the contact interface between the pad and disk. Squeal noise is characterized by extreme unpredictability due to large uncertainties on the values of parameters of the system. Parametrical complex eigenvalue analysis is a common tool used to predict squeal instability. In this paper a substructured linear finite element model of a simplified brake system is studied. A parametrical analysis is focused on a test case and compared to experimental results. The analysis is developed as a function of the parameters assumed to be the most influential but also the most uncertain: friction coefficient and the parameters driving the dynamics of the system. The uncertainties are accounted for by considering parameters such as random variables. A Monte Carlo simulation and a probabilistic technique are performed simultaneously to study the probability of squeal occurrence. Finally, a reduced model based on the transfer function calculated at the contact is developed to perform the analysis with reduced computational effort.