Dynamics and Stability of a Nonlinear Brake Model

2001 ◽  
Author(s):  
Jörg Wauer ◽  
Jürgen Heilig
Keyword(s):  
Stability Analysis ◽  
Lyapunov Exponent ◽  
Nonlinear Model ◽  
Numerical Evaluation ◽  
Critical Speed ◽  
Initial Conditions ◽  
Brake Disc ◽  
Disc Brake ◽  
Brake Pad ◽  
The Stability

Abstract The dynamics of a nonlinear car disc brake model is investigated and compared with a simplified linear model. The rotating brake disc is approximated by a rotating ring. The brake pad is modeled as a point mass which is in contact with the rotating ring and visco-elastically suspended in axial and circumferential direction. The stability analysis for the nonlinear model is performed by a numerical evaluation of the top Lyapunov-exponent. Several parameter studies for the nonlinear model are discussed. It is shown that dynamic instabilities of the nonlinear model are estimated at subcritical rotating speeds lower than 10% of the critical speed. Further, the sensitivity of the nonlinear model to the initial conditions and the stiffness ratios is demonstrated.

scholarly journals Impact Analysis of Brake Pad Backplate Structure and Friction Lining Material on Disc-Brake Noise

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Gongyu Pan ◽  
Lei Chen
Keyword(s):  
Layer Structure ◽  
Brake System ◽  
Mode Analysis ◽  
Bench Test ◽  
Brake Disc ◽  
Disc Brake ◽  
Complex Eigenvalue ◽  
Brake Pad ◽  
Six Dof ◽  
The Stability

This study proposes a three-layer brake pad design, on which a six-DOF dynamic model of brake disc-brake pad is established, and the factors affecting the system instability are analyzed. The analysis shows that the change of mass and stiffness of the brake pad will affect the stability of the system. From the linear complex eigenvalue analysis, the unstable vibration modes of the brake system are predicted, and the effectiveness of the complex mode analysis model is verified by the brake system bench test. Brake pads with different structural shapes are designed, and their influence on the stability of the brake system is analyzed. The results show that the design of the three-layer structure and the slotting design of the brake pad can effectively reduce the occurrence of the brake squeal, especially that of the high-frequency squeal noise.

Numerical Modeling and Simulation Analysis of Temperature Field of Disc Brake on Trains

2011 ◽  
Vol 199-200 ◽  
pp. 1492-1495 ◽  
Author(s):  
Guo Shun Wang ◽  
Rong Fu ◽  
Liang Zhao
Keyword(s):  
Temperature Field ◽  
Temperature Gradient ◽  
High Speed ◽  
Large Scale ◽  
Working Condition ◽  
Constant Speed ◽  
Brake Disc ◽  
Disc Brake ◽  
Brake Pad ◽  
Finite Element Software

The simulation calculation on the temperature field of the disc brake system on high-speed trains under the working condition of constant speed at 50Km/h is made. A steady-state calculation model is established according to the actual geometric size of a brake disc and a brake pad, and the analog calculation and simulation on the temperature field of the brake disc and the brake pad by using the large-scale nonlinear finite element software ABAQUS are carried out. The distribution rules of the temperature field of the brake disc and the brake pad under the working condition of constant speed are made known. The surface temperature of the brake disc at friction radius is the highest, with a band distribution for temperature. There exists a temperature flex point in the direction of thickness, of which the thickness occupies 15% of that of the brake disc; due to the small volume of the brake pad, the temperature gradient of the whole brake pad is not sharp, and larger temperature gradient occurs only on the contact surface.

scholarly journals Simulation Study on Friction and Wear Law of Brake Pad in High-Power Disc Brake

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
S. Zhang ◽  
Q. Hao ◽  
Y. Liu ◽  
L. Jin ◽  
F. Ma ◽  
...  
Keyword(s):  
High Power ◽  
Friction And Wear ◽  
Element Model ◽  
Calculation Model ◽  
Brake Disc ◽  
Disc Brake ◽  
Wear Depth ◽  
Brake Pad ◽  
Wear Calculation ◽  
Wear Law

For the serious and uneven wear of the brake pad in the high-power disc brake during braking, the dynamic variation of the brake disc and the brake pad interface variable is considered, the wear calculation model is established based on the friction and wear mechanism, and the wear depth and volume of the brake pad can be calculated by equations. A finite element model of the brake disc and the brake pad is established by DEFORM software which can analyze wear of the brake pad directly. The variation trend of wear during braking is studied, and influences of braking load and initial braking speed on the wear are analyzed. The results show that the amount of the wear increases rapidly in the early wear stage of braking, and it becomes slow in the later stage; the wear of the brake pad is serious at the friction inlet and outlet, and the middle area of the brake pad is lightly worn; heavy braking load and high initial braking speed can exacerbate the wear of the brake pad.

Experimental Verification of Critical Speed Ranges for Elastic Closed Loop Linkage Systems

1992 ◽  
Vol 114 (1) ◽  
pp. 126-130 ◽  
Author(s):  
S. Nagarajan ◽  
D. A. Turcic
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Critical Speed ◽  
Closed Loop ◽  
Local Maximum ◽  
Experimental Methods ◽  
Strain Response ◽  
Maximum Value ◽  
Speed Range ◽  
The Stability

In this work critical speed ranges are determined and verified for an elastic four bar crank rocker mechanism where all links are modeled as elastic members. The procedure used for the dynamic stability analysis is described in Nagarajan and Turcic (1991). The speed range of interest where the stability analysis is performed is 195–390 rpm. The values of the critical speeds obtained in the above speed range are then verified using independent theoretical and experimental methods of analysis. The steady state strain response is obtained both theoretically and experimentally for a number of speeds in the speed range of 195–390 rpm. From these responses plots different strain characteristics versus operating speeds are obtained. These plots exhibit peaks in the response at certain speeds indicating that the dynamic response at these speeds reaches a local maximum value. The critical speed ranges determined are found to correspond quite closely to the speeds where the peaks occur. This indicates that the critical speed ranges are indeed speeds where the response of the system is larger when compared to neighboring speeds and that the methods of determining them are accurate for the application considered.

Non-linear stability analysis of floating ring bearings using Hopf bifurcation theory

2011 ◽  
Vol 225 (12) ◽  
pp. 2804-2818 ◽  
Author(s):  
A Amamou ◽  
M Chouchane
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Limit Cycles ◽  
Critical Speed ◽  
Design Parameters ◽  
Stable Limit ◽  
Non Linear ◽  
The Stability

Floating ring bearings are used to support and guide rotors in several high-speed rotating machinery applications. They are usually credited for lower heat generation and higher vibration suppressing ability. Similar to conventional hydrodynamic bearings, floating ring bearings may exhibit unstable behaviour above a certain stability critical speed. Linear stability analysis is usually applied to predict the stability threshold speed. Non-linear stability analysis, however, is needed to predict the presence and the size of stable limit cycles above the stability threshold speed or unstable limit cycles below the stability critical speed. The prediction of limit cycles is an important step in bearing stability analysis. In this article, a non-linear dynamic model is derived and used to investigate the stability of a perfectly balanced symmetric rigid rotor supported by two identical floating ring bearings near the critical stability boundaries. The fluid film hydrodynamic reactions of the floating ring bearings are modelled by applying the short bearing theory and the half Sommerfeld solution. Hopf bifurcation theory is then utilized to determine the existence and the approximate size of stable and unstable limit cycles in the neighbourhood of the stability critical speed depending on the bearing design parameters. Numerical integration of the non-linear equations of motion is then carried out in order to compare the trajectories obtained by numerical integration to those obtained analytically using Hopf bifurcation analysis. Stability boundary curves for typical bearing design parameters have been decomposed into boundaries with supercritical stable limit cycles and boundaries with subcritical unstable limit cycles. The shape and size of the limit cycles for selected bearing parameters are presented using both analytical and numerical approaches. This article shows that floating ring stability boundaries may exhibit either stable supercritical limit cycles or unstable subcritical limit cycles predictable by Hopf bifurcation.

scholarly journals Stability study of finite-difference-based lattice Boltzmann schemes with upwind differences of high order approximation

2015 ◽  
pp. 196-204
Author(s):  
Г.В. Кривовичев ◽  
С.А. Михеев
Keyword(s):  
Stability Analysis ◽  
Finite Difference ◽  
Linear Approximation ◽  
Lattice Boltzmann ◽  
Initial Conditions ◽  
Order Approximation ◽  
Stability Study ◽  
High Order Approximation ◽  
Spatial Variables ◽  
The Stability

Исследуется устойчивость трехслойных конечно-разностных решеточных схем Больцмана третьего и четвертого порядков аппроксимации по пространственным переменным. Проводится анализ устойчивости по начальным условиям с использованием линейного приближения. Для исследования используется метод Неймана. Показано, что устойчивость схем можно улучшить за счет аппроксимации конвективных членов во внутренних узлах сеточного шаблона. В этом случае удается получать большие по площади области устойчивости, чем при аппроксимации в граничных узлах шаблона. The stability of three-level finite-difference-based lattice Boltzmann schemes of third and fourth orders of approximation with respect to spatial variables is studied. The stability analysis with respect to initial conditions is performed on the basis of a linear approximation. These studies are based on the Neumann method. It is shown that the stability of the schemes can be improved by the approximation convective terms in internal nodes of the grid stencils in use. In this case the stability domains are larger compared to the case of approximation in boundary nodes.

Stability Analysis on a Crack Rotor System in the Special Speeds

2013 ◽  
Vol 675 ◽  
pp. 116-120 ◽  
Author(s):  
Feng Lan Wang
Keyword(s):  
Experimental Study ◽  
Stability Analysis ◽  
Theoretical Analysis ◽  
Stability Problem ◽  
Critical Speed ◽  
Transverse Crack ◽  
Crack Depth ◽  
Rotor System ◽  
Single Disk ◽  
The Stability

In this paper, the single disk rotor system with a transverse open and close crack has been taken as an example; the stability problem on the system in the special speeds has been discussed by theoretical analysis and experimental study. First, the conditions, positions and areas of the stable vibrations and the unstable vibrations on a rotor system with a transverse crack have been studied quantitatively theoretically. Not only the conclusions of other authors are verified，but also that the unstable vibrations are found in the regions near the rotational speed at 2/5and 2/7 of the critical speed in the large crack and the small damping case. Then the influence of some factors such as the crack depth parameters and the damping on stability of the system is qualitatively discussed.

Vibration Characteristics of Elastic Disc Brake Pad Device

2011 ◽  
Vol 101-102 ◽  
pp. 29-32 ◽  
Author(s):  
Ji Min Zhang ◽  
Kuan Yang
Keyword(s):  
Mathematical Model ◽  
Friction Force ◽  
Friction Surface ◽  
Railway Vehicle ◽  
Brake Disc ◽  
Disc Brake ◽  
Brake Pad ◽  
Braking Performance ◽  
Simulation Results ◽  
Elastic Disc

A new elastic disc brake pad device is designed. A mathematical model on railway vehicle elastic disc brake is established compared with the non-elastic brake pad by uni-wheel set braking simulation. The simulation results show that the elastic brake pad could guarantee the vehicle braking performance as same as the non-elastic brake pad. When the friction surface of the brake disc or pad has defects, the elastic brake pad can effectively reduce the vibration of the friction force between the brake pad and the brake disc. It has been proved that the correctness and rationality of the design. A new idea for the design and analysis of the disc brake system is provides.

Symmetry Properties in the Symmetry-Breaking of Nonsmooth Dynamical Systems

2009 ◽  
Vol 5 (1) ◽  
Author(s):  
Alessio Ageno ◽  
Anna Sinopoli
Keyword(s):  
Group Theory ◽  
Stability Analysis ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Simply Supported ◽  
Symmetry Properties ◽  
Existence Conditions ◽  
Asymmetric Responses ◽  
The Stability ◽  
Nonsmooth Dynamical Systems

In this paper, the block simply supported on a harmonically moving ground is assumed as a system well representing a typical nonsmooth dynamical behavior. The aim of the work is to carry out the existence conditions of asymmetric responses; an analysis that comes first in any stability investigation. By using simple definitions belonging to the symmetry group theory, it is possible to completely clarify the relationships between the various initial conditions that allow simple asymmetric responses, and to develop tools, which will be very useful in the stability analysis of more complex asymmetric responses.

scholarly journals Stability of Vertically Traveling, Pre-tensioned, Heavy Cables

2018 ◽  
Vol 13 (8) ◽  
Author(s):  
Abhinav Ravindra Dehadrai ◽  
Ishan Sharma ◽  
Shakti S. Gupta
Keyword(s):  
Stability Analysis ◽  
Governing Equation ◽  
Initial Conditions ◽  
Slenderness Ratio ◽  
Equation Of Motion ◽  
Rate Of Change ◽  
Bending Rigidity ◽  
Stable Regime ◽  
Varying Coefficients ◽  
The Stability

We study the stability of a pre-tensioned, heavy cable traveling vertically against gravity at a constant speed. The cable is modeled as a slender beam incorporating rotary inertia. Gravity modifies the tension along the traveling cable and introduces spatially varying coefficients in the equation of motion, thereby precluding an analytical solution. The onset of instability is determined by employing both the Galerkin method with sine modes and finite element (FE) analysis to compute the eigenvalues associated with the governing equation of motion. A spectral stability analysis is necessary for traveling cables where an energy stability analysis is not comprehensive, because of the presence of gyroscopic terms in the governing equation. Consistency of the solution is checked by direct time integration of the governing equation of motion with specified initial conditions. In the stable regime of operations, the rate of change of total energy of the system is found to oscillate with bounded amplitude indicating that the system, although stable, is nonconservative. A comprehensive stability analysis is carried out in the parameter space of traveling speed, pre-tension, bending rigidity, external damping, and the slenderness ratio of the cable. We conclude that pre-tension, bending rigidity, external damping, and slenderness ratio enhance the stability of the traveling cable while gravity destabilizes the cable.

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