scholarly journals On the interrelation of equilibrium positions and work of friction forces on brake squeal

2021 ◽  
Author(s):  
Sebastian Koch ◽  
Holger Gödecker ◽  
Utz von Wagner
Keyword(s):  
Equilibrium Position ◽  
Initial Conditions ◽  
Decisive Role ◽  
Essential Elements ◽  
Multiple Equilibrium ◽  
Brake Squeal ◽  
Camera System ◽  
Friction Forces ◽  
Decisive Influence ◽  
Brake Pressure

AbstractBrake noise, in particular brake squeal, is a permanent topic both in industry and academia since decades. Nonlinearities play a decisive role for this phenomenon. One nonlinear effect widely ignored so far is that the brake can engage multiple equilibrium positions with severe consequences on the noise behavior. In fact in an automotive disk brake, the essential elements carrier, caliper and pad are elastically coupled with each other and their behavior is nonlinear that multiple equilibrium positions are possible. The engaged equilibrium position depends, for example, on the initial conditions, external disturbances, and the transient application of the brake pressure, and in consequence configurations with or without self-exciting characteristics of the friction forces result. Obviously, a self-exciting characteristic of the friction force is a necessary precondition for the occurrence of squeal. The authors recently published some corresponding results (Koch et al. FU Mech Eng, 2021. https://doi.org/10.22190/FUME210106020K) demonstrating that for same operating parameters with respect to brake pressure (i.e., brake torque), rotational speed and temperature the engaged equilibrium position has decisive influence whether squeal occurs or not. While in Koch et al. (2021) it has just been detected whether there is squeal or not, the excitation characteristic of the friction forces becomes, beside the engaged equilibrium position, the additional focus in the present paper. Therefore, a work criterion already successfully applied in earlier publications for squeal tendency is considered. For the experimental application of the work criterion, accelerometers have to be mounted. The accelerometers’ location to be applied can be determined in the chosen setup by the camera system anyway necessary for the measurement of the engaged equilibrium position. With this refined setup, it is possible to specify the states squeal, close to squeal and far from squeal. The test series again demonstrate the decisive influence of the engaged equilibrium position (for constant operation parameters) on the occurrence of the respective state. These findings can have consequences for simulations (consideration of multiple equilibrium positions in models and respective linearization with consequences on system’s eigenvalues), but also for the design (avoidance of equilibrium positions suspicious for squeal) and experimental setups (determination of special positions) of brakes.

A new hyperchaotic particle motion system and its control

2019 ◽  
Vol 30 (12) ◽  
pp. 2050004
Author(s):  
Ning Cui ◽  
Junhong Li
Keyword(s):  
Particle Motion ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Multiple Equilibrium ◽  
Hopf Bifurcations ◽  
Hyperchaotic System ◽  
Motion System ◽  
The Rich ◽  
Theoretical Analyses ◽  
Multiple Equilibrium Points

This paper formulates a new hyperchaotic system for particle motion. The continuous dependence on initial conditions of the system’s solution and the equilibrium stability, bifurcation, energy function of the system are analyzed. The hyperchaotic behaviors in the motion of the particle on a horizontal smooth plane are also investigated. It shows that the rich dynamic behaviors of the system, including the degenerate Hopf bifurcations and nondegenerate Hopf bifurcations at multiple equilibrium points, the irregular variation of Hamiltonian energy, and the hyperchaotic attractors. These results generalize and improve some known results about the particle motion system. Furthermore, the constraint of hyperchaos control is obtained by applying Lagrange’s method and the constraint change the system from a hyperchaotic state to asymptotically state. The numerical simulations are carried out to verify theoretical analyses and to exhibit the rich hyperchaotic behaviors.

scholarly journals New closed analytical solutions for geometrically thick fluid tori around black holes

2018 ◽  
Vol 614 ◽  
pp. A75 ◽  
Author(s):  
V. Witzany ◽  
P. Jefremov
Keyword(s):  
Black Hole ◽  
Initial Conditions ◽  
Rest Mass ◽  
Decisive Role ◽  
Rotational Instability ◽  
Asymptotic State ◽  
Rotation Curves ◽  
Perfect Fluids ◽  
Order Of Magnitude ◽  
Orbital Periods

Context. When a black hole is accreting well below the Eddington rate, a geometrically thick, radiatively inefficient state of the accretion disk is established. There is a limited number of closed-form physical solutions for geometrically thick (nonselfgravitating) toroidal equilibria of perfect fluids orbiting a spinning black hole, and these are predominantly used as initial conditions for simulations of accretion in the aforementioned mode. However, different initial configurations might lead to different results and thus observational predictions drawn from such simulations. Aims. We aim to expand the known equilibria by a number of closed multiparametric solutions with various possibilities of rotation curves and geometric shapes. Then, we ask whether choosing these as initial conditions influences the onset of accretion and the asymptotic state of the disk. Methods. We have investigated a set of examples from the derived solutions in detail; we analytically estimate the growth of the magneto-rotational instability (MRI) from their rotation curves and evolve the analytically obtained tori using the 2D magneto-hydrodynamical code HARM. Properties of the evolutions are then studied through the mass, energy, and angular-momentum accretion rates. Results. The rotation curve has a decisive role in the numerical onset of accretion in accordance with our analytical MRI estimates: in the first few orbital periods, the average accretion rate is linearly proportional to the initial MRI rate in the toroids. The final state obtained from any initial condition within the studied class after an evolution of ten or more orbital periods is mostly qualitatively identical and the quantitative properties vary within a single order of magnitude. The average values of the energy of the accreted fluid have an irregular dependency on initial data, and in some cases fluid with energies many times its rest mass is systematically accreted.

ABSOLUTE INSTABILITY OR CHAOS? — A TRIBUTE TO DR. DAVID G. CRIGHTON

2002 ◽  
Vol 10 (04) ◽  
pp. 407-419
Author(s):  
SEAN F. WU
Keyword(s):  
Elastic Plate ◽  
Equilibrium Position ◽  
Flexural Vibration ◽  
Critical Value ◽  
Flow Speed ◽  
Multiple Equilibrium ◽  
Absolute Instability ◽  
Mean Flow ◽  
Structural Nonlinearities ◽  
The Mean

The stabilities of an elastic plate clamped on an infinite, rigid baffle subject to any time dependent force excitation in the presence of mean flow are examined. The mechanisms that can cause plate flexural vibrations to be absolute unstable when the mean flow speed exceeds a critical value are revealed. Results show that the instabilities of an elastic plate are mainly caused by an added stiffness due to acoustic radiation in mean flow, but controlled by the structural nonlinearities. This added stiffness is shown to be negative and increase quadratically with the mean flow speed. Hence, as the mean flow speed approaches a critical value, the added stiffness may null the overall stiffness of the plate, leading to an unstable condition. Note that without the inclusion of the structural nonlinearities, the plate has only one equilibrium position, namely, its undeformed flat position. Under this condition, the amplitude of plate flexural vibration would grow exponentially in time everywhere, known as absolute instability. With the inclusion of structural nonlinearities, the plate may possess multiple equilibrium positions. When the mean flow speed exceeds the critical values, the plate may be unstable and jump from one equilibrium position to another. Since this jumping is random, the plate flexural vibration may seem chaotic.

Links Between Disc Brake Squeal and Pad In-Plane Motion

2003 ◽  
Author(s):  
Fulun Yang ◽  
Valery Pilipchuk ◽  
Chin An Tan
Keyword(s):  
Degrees Of Freedom ◽  
Time History ◽  
Bending Moment ◽  
Dominant Frequency ◽  
Plane Motion ◽  
Mode Shapes ◽  
Theoretical Interpretation ◽  
Disc Brake ◽  
Brake Squeal ◽  
Friction Forces

This paper is focused on links between disc brake squeal and in-plane vibration of pads. A special experimental setup is developed in order to determine correlation between squeal acoustical signals and longitudinal accelerations of both pads. A strong coherence between spectral properties of squeal and pad vibrations is found and quantified. In particular, the dominant frequency of the acoustical and mechanical responses appears to be same. Essentially unharmonic temporal mode shapes of the pad vibrations are detected. Such mode shapes reveal the information about multiple frequency friction forces applied to the disc and pads with a possibility of resonance with their coupled elastic modes. Experimental time history records also show a significant out-of-phase component in the pad motions, which is associated with a bending moment applied to the disc. Major experimental observations admit theoretical interpretation based on a two degrees of freedom model. Theoretical conclusions and experimental results are found to be in a good agreement.

scholarly journals Wave run-up prediction and observation in a micro-tidal beach

2017 ◽  
Author(s):  
Diana Di Luccio ◽  
Guido Benassai ◽  
Giorgio Budillon ◽  
Luigi Mucerino ◽  
Raffaele Montella ◽  
...  
Keyword(s):  
Ad Hoc ◽  
Initial Conditions ◽  
Numerical Models ◽  
Remote Sensing Data ◽  
Video Camera ◽  
Extreme Weather Events ◽  
Tyrrhenian Sea ◽  
Camera System ◽  
Run Up ◽  
Offshore Wave

Abstract. Extreme weather events have significant impacts on coastal human activities and related economy. In this scenario the forecast of sea storms and wave run-up events is a challenging goal to mitigate the wave effects on shores, piers and coastal structures. To do this, we used a computational model chain based on both community and ad hoc developed numerical models in an operational context to evaluate the beach inundation levels. At this aim, we compared the results of simulated and observed wave run-up levels on a micro-tidal beach located on the northern Tyrrhenian Sea. The offshore wave simulations have been performed by WaveWatch III model, implemented by Campania Center for Marine and Atmospheric Monitoring and Modelling (CCMMMA) – University of Naples Parthenope, which were used as initial conditions for run-up calculations using different formulas. The validation of the simulated waves was done with different observation systems. The offshore wave simulations were matched with remote sensing data, while the run-up levels calculated with different formulas were compared with observations taken from a video camera system. The usual statistical errors were taken as a measurement of the modelling system capability to properly simulate the beach run-up during a storm.

scholarly journals Influence of Material-Dependent Damping on Brake Squeal in a Specific Disc Brake System

2021 ◽  
Vol 11 (6) ◽  
pp. 2625
Author(s):  
Juraj Úradníček ◽  
Miloš Musil ◽  
L’uboš Gašparovič ◽  
Michal Bachratý
Keyword(s):  
Dynamic Instability ◽  
Friction Material ◽  
System Stability ◽  
Brake System ◽  
Brake Disc ◽  
Disc Brake ◽  
Fe Model ◽  
Brake Squeal ◽  
Friction Forces ◽  
General Material

The connection of two phenomena, nonconservative friction forces and dissipation-induced instability, can lead to many interesting engineering problems. We study the general material-dependent damping influence on the dynamic instability of disc brake systems leading to brake squeal. The effect of general damping is demonstrated on minimal and complex models of a disc brake. Experimental analyses through the frequency response function (FRF) show different damping of the brake system coalescent modes, indicating possible dissipation-induced instability. A complex system including material-dependent damping is defined in commercial finite element (FE) software. A FE model validated by experimental data on the brake-disc test bench is used to compute the influence of a pad and disc damping variations on the system stability using complexe igenvalue analysis (CEVA). Numerical analyses show a significant sensitivity of the experimentally verified unstable mode of the system to the ratio of the damping between the disc and the friction material components.

scholarly journals Design of an Optimal Fuzzy Controller of an Under-Actuated Manipulator Based on Teaching-Learning-Based Optimization

2019 ◽  
Vol 13 (3) ◽  
pp. 166-172
Author(s):  
Mohammad Javad Mahmoodabadi ◽  
Amineh Yazdizadeh Baghini
Keyword(s):  
Control Method ◽  
Fuzzy Controller ◽  
Initial Conditions ◽  
Absolute Error ◽  
State Variables ◽  
Friction Forces ◽  
Time Integral ◽  
Tlbo Algorithm ◽  
Teaching Learning Based Optimization ◽  
Teaching Learning

Abstract In this paper, an optimal fuzzy controller based on the Teaching-Learning-Based Optimization (TLBO) algorithm has been presented for the stabilization of a two-link planar horizontal under-actuated manipulator with two revolute (2R) joints. For the considered fuzzy control method, a singleton fuzzifier, a centre average defuzzifier and a product inference engine have been used. The TLBO algorithm has been implemented for searching the optimum parameters of the fuzzy controller with consideration of time integral of the absolute error of the state variables as the objective function. The proposed control method has been utilized for the 2R under-actuated manipulator with the second passive joint wherein the model moves in the horizontal plane and friction forces have been considered. Simulation results of the offered control method have been illustrated for the stabilization of the considered robot system. Moreover, for different initial conditions, the effectiveness and the robustness of the mentioned strategy have been challenged.

Flutter Amplitude Saturation by Nonlinear Friction Forces: Reduced Model Validation

2014 ◽  
Author(s):  
Carlos Martel ◽  
Roque Corral ◽  
Rahul Ivaturi
Keyword(s):  
Initial Conditions ◽  
Oscillation Amplitude ◽  
Reduced Model ◽  
Limit Cycle Oscillation ◽  
Nonlinear Friction ◽  
Disk Model ◽  
Friction Forces ◽  
Elastic Oscillation ◽  
Time Modulation ◽  
Bladed Disk

The computation of the final, friction saturated Limit Cycle Oscillation amplitude of an aerodynamically unstable bladeddisk in a realistic configuration is a formidable numerical task. In spite of the large numerical cost and complexity of the simulations, the output of the system is not that complex: it typically consists of an aeroelastically unstable traveling wave (TW), which oscillates at the elastic modal frequency and exhibits a modulation in a much longer time scale. This slow time modulation over the purely elastic oscillation is due to both, the small aerodynamic effects and the small nonlinear friction forces. The correct computation of these two small effects is crucial to determine the final amplitude of the flutter vibration, which basically results from its balance. In this work we apply asymptotic techniques to consistently derive, from a bladed-disk model, a reduced order model that gives only the time evolution on the slow modulation, filtering out the fast elastic oscillation. This reduced model is numerically integrated with very low CPU cost, and we quantitatively compare its results with those from the bladed-disk model. The analysis of the friction saturation of the flutter instability also allows us to conclude: (i) that the final states are always nonlinearly saturated TW, (ii) that, depending on the initial conditions, there are several different nonlinear TWs that can end up being a final state, and (iii) that the possible final TWs are only the more flutter prone ones.

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