Sensitivity study of the contact situation between the brake pad and the disc

The contact situation between the brake pad and the disc during the braking process is of particular importance concerning the squeal behavior of brake systems. After the braking process, the surface topography of brake pads can be measured using a confocal microscope. An algorithm to calculate the contact between two surfaces has been developed at the Institute of Dynamics and Vibrations. The algorithm calculates the deflection of asperities under a normal load regarding an elastic material behavior. A normal load is applied to a measured surface topography of the brake pad; the counter body (brake disc) is represented by a flat surface. The potential contact area, the locally distributed forces, deflections and normal stiffness of the pad are computed. Since there is an uncertainty in the relative position between the pad and the disc and hence the real contact situation during the braking process is not known, different contact situations must be considered during the simulations. Concerning various tilt angles of the pad that can arise during the vibrations of the brake system, a sensitivity study has been carried out. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Cyclic Thermomechanical Coupled Problem of Thermal Gradients in Friction Railway Disc Brakes

The emergency braking distance of a TGV train at a speed of 320 km/h is almost 3000 m. Dry running brakes are reliable due to their predictable response to external stress and are thus used in such applications. The kinetic energy is dissipated proportionately into the brake disc and brake pad. This induced dissipation of energy and the high frequency of brake application cause high temperatures. These immense temperature changes could cause macroscopic cracks leading to failure of discs and accidents [1]. Generally, hot spotting describes the development of thermal localizations and can lead to early damage, early wear, pad performance loss, and squeal noise [2]. The aim of the present study is to improve a disc-pad transient numerical model by use of a coupled thermomechanical method. It is based on full 3-d thermomechanical calculations taking disc rotation into account. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Coupled Thermo-Mechanical and Wear Effects on the Analysis of High Speed Railway Brake Systems

The high speed railway brakes transfer a large amount of kinetic energy into heat. The temperature during a brake operation could reach values higher than 90 °C. The dynamics of the brake system is rather complicated with respect to the multiphysical phenomena. In this paper, the thermo-mechanical coupling are investigated combined with the loos of brake material due to wear. The coupled model is discretized by conventional finite element method. Different coupled algorithms have been tested. Various scenarios have been simulated and shown reasonable results. The temperature and deformation on pad and disc, especially the thermal deformation of disc the so–called coning effect can also be prescribed with this coupled multiphysics model. Furthermore, the tapered wear on brake pads is also discussed as a requirement of railway brake design in terms of durability. Thereby, the Ehlers's model is normally used to minimize tapered wear by selecting an adequate point of applied braking force. An extended Ehlers's model is also presented here, which concerns wear effect based on Archard's model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The interaction of surface topography and friction dynamics in brake systems described by a Cellular Automaton

The friction coefficient μ , which is the quotient of the friction force R and the normal force N is in principal not a stationary material parameter, but also dependent on for instance the relative velocity, the normal load, the temperature, the climate conditions, the location and the event itself. The dynamics in the boundary layer between a brake disc and a brake pad is closely linked with the surface topography dynamics. Growing and destroying processes of hard, thin patches, carrying the friction power, determine the time-dependence of the friction coefficient. This interaction between friction and wear has already been simulated with a set of differential equations [2-4], which give an idea about the equilibrium of flow in the contact zone and which are able to describe the fading effect, for example. Based on this assumption we discretised the boundary layer with a Cellular Automaton [5], which makes it possible to have a more detailed look at the processes in the contact area. This paper will show new conclusions concerning the interdependencies of the friction behaviour and the surface topography. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear response of a beam under distributed moving contact load

In this paper, the nonlinear behavior of a one-dimensional model of the disc brake pad is examined. The contact normal force between the disc brake pad lining and rotor is represented by a second order polynomial of the relative displacement between the two elastic bodies. The frictional force due to the sliding motion of the rotor against the stationary pad is modeled as a distributed follower-type axial load with time-dependent terms. By Galerkin discretization, the equation governing the transverse motion of the beam model is reduced to a set of extended Duffing system with quasi-periodically modulated excitations. Retaining the first two vibration modes in the governing equations, frequency response curves are obtained by applying a two-dimensional spectral balance method. For the first time, it is predicted that nonlinearity resulting from the contact mechanics between the disc brake pad lining and rotor can lead to a possible irregular motion (chaotic vibration) of the pad in the neighborhood of simple and parametric resonance. This chaotic behavior is identified and quantitatively measured by examining the Poincaré maps, Fourier spectra, and Lyapunov exponents. It is also found that these chaotic motions emerge as a result of successive Hopf bifurcations characterized by the torus breakdown and torus doubling routes as the excitation frequency varies. Various aspects of the numerical difficulties in the solution of the nonlinear equations are also discussed.     

Estimation of dry road braking distance considering frictional energy of patterned tires

This paper is concerned with the braking distance estimation of tire controlled by anti-lock brake system (ABS) according to a numerical–analytical method. While the frictional heat dissipation at disc pad is derived analytically, the tire frictional energy loss is computed by the 3D dynamic rolling analysis of patterned tire. Since the tire rolling analysis to obtain the time history of the frictional energy rate for the entire braking period is impractical, we alternatively seek the tire frictional energy rate curve versus the lapse of time by interpolating the discretized frictional energy rates computed at intervals of 10 km/h. The effect of ABS is numerically implemented by specifying the corresponding tire angular velocity to the dynamic rolling analysis. Applying the energy conservation law to each speed interval determines the interval-wise braking times and distances from which the total braking time and distance are predicted. Illustrative numerical experiment is presented together with the comparison with the experimental estimation.     

Damage and fracture behavior in dynamic tension tests: Modelling and numerical simulations

The continuum damage model is based on a general thermodynamic framework for the modeling of rate and temperature dependent behavior of anisotropically damaged elastic-plastic materials subjected to fast deformation. The introduction of damaged and fictitious undamaged configurations allows the definition of damage tensors and the corresponding free energy functions lead to material laws affected by damage and temperature. The damage condition and the corresponding damage rule strongly depend on stress triaxiality. Furthermore, the rate and temperature dependence is reflected in a multiplicative decomposition of the plastic hardening and damage softening functions. The macro crack behavior is characterized by a triaxiality dependent fracture criterion. The continuum damage model is implemented into LS-DYNA as user defined material model. Corresponding numerical simulations of unnotched and notched tension tests with high strain rates demonstrate the plastic and damage processes during the deformation leading to final fracture numerically predicted by an element erosion technique. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of dynamic brake pad properties on automotive disk brake squeal

Comparing different methods of characterizing dynamic properties of brake pad materials clearly shows, that those properties strongly depend on the boundary conditions as well as on amplitude and frequency in the excitation. Actually simulations of brake squeal suffer on the missing of correct material parameters identified under conditions relevant for squeal. The present paper gives inside into a method for the measurement and identification of linear and nonlinear brake pad material parameters identified under correct boundary conditions. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of engine design and operating parameters on the performance of a spark ignition (SI) engine with steam injection method (SIM)

The effects of engine design and operating parameters such as equivalence ratio (ER), compression ratio (CR), cycle pressure ratio (CPR), cycle temperature ratio (CTR), bore-stroke length ratio (D/L) inlet pressure, inlet temperature, friction coefficient (FC), mean piston speed (MPS) and engine speed on the performance characteristics such as brake thermal efficiency (BTE) and brake power output (BPO) are investigated for a steam injected gasoline engine (SIGE) with a simulation model validated with experiments using a realistic finite-time thermodynamics model (FTTM). Moreover, the energy losses arising from exhaust output (EO), heat transfer (HT), friction (FR) and incomplete combustion (IC), are illustrated by using graphs. The optimum values of engine speed, compression ratio, equivalence ratio, cycle temperature ratio and pressure ratio are presented by grid curves. Also, they are called performance maps. The results showed that the performance characteristics improve with enhancing inlet pressure, cycle pressure ratio and cycle temperature ratio; with diminishing inlet temperature and friction coefficient. The BPO can be increased up to 42%, 55% and 62% by using the optimum values of cycle pressure ratio, cycle temperature ratio and inlet pressure, respectively. Also, the BTE can be increased up to 8%, 12% and 15%, by the same way. On the other hand, the performance characteristics can improve or deteriorate with respect to different conditions of compression ratio, engine speed, equivalence ratio, stroke length and mean piston speed. Therefore, the optimum values should be determined to obtain the maximum performance conditions.     

A low-Mach number method for the numerical simulation of complex flows

A new numerical procedure which considers a modification to the artificial acoustic stiffness correction method (AASCM) is here presented, to perform simulations of low Mach number flows with the compressible Navier–Stokes equations. An extra term is added to the energy fluxes instead of using an energy source correction term as in the original model. This new scheme re-scales the speed of sound to values similar to the flow velocity, enabling the use of larger time steps and leading to a more stable numerical method. The new method is validated performing Large Eddy Simulations on test problems. The effect of a crucial numerical parameter alpha is evaluated as well as the robustness of the method to variations of the Mach number. Numerical results are compared to the existing experimental data showing that the new method achieves good agreement increasing the time-step, and therefore accelerating the computation for low-Mach convective flows.     

Nonlinear explicit analysis and study of the behaviour of a new ring-type brake energy dissipator by FEM and experimental comparison

The aim of this paper is to comprehensively analyse the performance of a new ring-type brake energy dissipator through the finite element method (FEM) (formulation and finite element approximation of contact in nonlinear mechanics) and experimental comparison. This new structural device is used as a system component in rockfall barriers and fences and it is composed of steel bearing ropes, bent pipes and aluminium compression sleeves. The bearing ropes are guided through pipes bent into double-loops and held by compression sleeves. These elements work as brake rings. In important events the brake rings contract and so dissipate residual energy out of the ring net, without damaging the ropes. The rope’s breaking load is not diminished by activation of the brake. The full understanding of this problem implies the simultaneous study of three nonlinearities: material nonlinearity (plastic behaviour) and failure criteria, large displacements (geometric nonlinearity) and friction-contact phenomena among brake ring components. The explicit dynamic analysis procedure is carried out by means of the implementation of an explicit integration rule together with the use of diagonal element mass matrices. The equations of motion for the brake ring are integrated using the explicit central difference integration rule. The presence of the contact phenomenon implies the existence of inequality constraints. The conditions for normal contact are and gλ=0, where λ is the normal traction component and g is the gap function for the contact surface pair. To include frictional conditions, let us assume that Coulomb’s law of friction holds pointwise on the different contact surfaces, μ being the dynamic coefficient of friction. Next, we define the non-dimensional variable τ by means of the expression τ=t/μλ, where μλ is the frictional resistance and t is the tangential traction component. In order to find the best brake performance, different dynamic friction coefficients corresponding to the pressures of the compression sleeves have been adopted and simulated numerically by FEM and then we have compared them with the results from full-scale experimental tests. Finally, the most important conclusions of this study are given.     

Instable Waves between Rough Elastic Bodies in Sliding Contact

Most sliding bodies are not perfectly flat, but show a rough surface topography or tribological layer. This paper analyses a sliding system consisting of two elastic bodies with continuous contact and steady sliding. Surface topographies are taken into account by an inertia film on one of the sliding surfaces. A linear model is developed that allows an analytical solution. As a typical tribological system, the contact between pad and disc in a brake system is discussed. It can be shown that unstable elastic waves travel through the contact between both bodies. This instability is opened only when a tribological layer on the brake pad is taken into account. This microscopic excitation can cause a loss of stability of the entire (brake) system. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth of Nanophase Clusters and Potential Energy Minima: Hysteresis, Oscillations, and Phase Transitions

The structures of small Lennard-Jones clusters (local and global minima) in the range n = 30 - 55 atoms are investigated during growth by random atom deposition using Monte Carlo simulations. The cohesive energy, average coordination number, and bond angles are calculated at different temperatures and deposition rates. Deposition conditions which favor thermodynamically stable (global minima) and metastable (local minima) are determined. We have found that the transition from polyicosahedral to quasicrystalline structures during cluster growth exhibits hysteresis at low temperatures. A minimum critical size is required for the evolution of the quasicrystalline family, which is larger than the one predicted by thermodynamics and depends on the temperature and the deposition rate. Oscillations between polyicosahedral and quasicrystalline structures occur at high temperatures in a certain size regime. Implications for the applicability of global optimization techniques to cluster structure determination are also discussed.     

Nonlinear dynamics of a simplified engine-propeller system

This paper presents a procedure for studying dynamical behaviors of a simplified engine-propeller dynamical system consisting of a number of bodies of plane motions. The equation of motion of the complex system is obtained using the Lagrange equation and solved numerically using the 4th order Runge–Kutta method. Various simulations were performed to investigate the transient and steady state behaviors of the multiple body system while taking into consideration the engine pressure pulsations, nonlinear inertia of moving bodies, and nonlinear aerodynamic load. Sub-harmonics and super harmonics in the steady state responses for different power and propeller pitch settings are obtained using the fast Fourier transform. Numerical simulations indicate that the 1.5 order is the dominant order of harmonics in the steady state oscillatory motion of the crankshaft. The findings and procedure presented in the paper are useful to the aerospace industry in certifying reciprocating engines and propellers. The crankshaft oscillatory velocities obtained from the simplified rigid body model are in good agreement with the experimental data for a SAITO-450 engine and a SOLO propeller at a 6″ pitch setting.     

A numerical study on the effect of cavitation erosion in a diesel injector

The consequences of geometry alterations in a diesel injector caused by cavitation erosion are investigated with numerical simulations. The differences in the results between the nominal design geometry and the eroded one are analyzed for the internal injector flow and spray formation. The flow in the injector is modeled with a three-phase Eulerian approach using a compressible pressure-based multiphase flow solver. Cavitation is simulated with a nonequilibrium mass transfer rate model based on the simplified form of the Rayleigh–Plesset equation. Slip velocity between the liquid-vapor mixture and air is included in the model by solving two separate momentum conservation equations. The eroded injector is found to result in a loss in the rate of injection but also lower cavitation volume fraction inside the nozzle. The injected sprays are then simulated with a Lagrangian method considering as initial conditions the predicted flow characteristics at the exit of the nozzle. The results obtained show wider spray dispersion for the eroded injector and shorter spray tip penetration.     

Validation of LES predictions for turbulent flow in a Confined Impinging Jets Reactor

This work focuses on the prediction of the turbulent flow in a three-dimensionial Confined Impinging Jets Reactor with a cylindrical reaction chamber by using Large Eddy Simulation. Three-dimensional unsteady simulations with different sub-grid scale models, numerical schemes and boundary conditions were performed for various flow rates, covering different flow regimes. First, a qualitative analysis of the flow field was carried out and then predictions of the mean and fluctuating velocities were compared with micro Particle Image Velocimetry data. Good agreement was found both for the mean velocity components and the fluctuations. For low to moderate Reynolds numbers the sub-grid scale model was found not to be very relevant, since small scales are of less importance, as long as scalar transport and chemical reaction are not in play. An important finding is the good prediction of the high velocity fluctuations detected in particular at higher Reynolds number due to the natural instability of the system, strongly enforced by the jets unsteadiness.     

Wear and fluid-solid-thermal transient coupled model for journal bearings

In this study, the transient interactions between the sliding wear behaviour and fluid–solid–thermal (FST) characteristics of journal bearings are revealed using an established mathematical model. The calculated temperature distribution is validated by a comparison with experimental results from the literature. Furthermore, a wear test for lubricated journal bearings is conducted to verify the predicted wear rate. The time-varying wear and FST performances of the journal bearing, including the wear rate, wear depth, fluid pressure, contact pressure, and maximum temperature are calculated numerically. Through numerical simulations, the effects of the boundary friction coefficient and surface roughness on the wear and FST performances are evaluated. To demonstrate the importance of considering the three-dimensional (3D) thermal effect during the wear analysis of lubricated journal bearings, the numerical results predicted by the isothermal model and the thermal model are compared systematically within a wide range of operating conditions. The numerical results reveal that the worn surface profile slightly decreases the maximum temperature. Additionally, the worn region is primarily located at both edges of the bearing, and the time-varying worn surface profile may be beneficial for improving the hydrodynamic effect. Furthermore, the effect of the 3D thermal characteristics on the wear prediction of journal bearings cannot be ignored when the external load, boundary friction coefficient, surface roughness are relatively large.     

CFD simulation of industrial bubble columns: Numerical challenges and model validation successes

Although bubble columns are widely used in many industrial situations, there are very few studies of such devices operating at high superficial velocities. Numerical simulations using an Euler–Euler methodology are reported here across a wide range of operating conditions, where we discuss model assumptions and model validation. Key to obtaining physically correct results is the choice of closure assumptions. Particular emphasis is placed on the various solution methods that can be employed. In particular, we show that massive speed-up is possible using the new Eulerian multiphase NITA solver in ANSYS Fluent 16. Comparison of results from ANSYS CFX and ANSYS Fluent show that both do a good job of capturing the main features of the flow, the mixing time and the oxygen transfer rate.     

Friction induced flutter instability - on modeling and simulation of brake-squeal -

The issue of this contribution are self–excited vibrations due to sliding friction between moving elastic bodies. Starting from Hamiltons principle, the normal contact is implemented by two different approaches. Assuming discretizations in a spatial coordinate frame, the structure of the resulting equations of motions is outlined. For a simple model of a disc–brake, stability charts of the steady–state are presented, which show a considerable influence of the motion of the disc on the stability behavior. Finally, the influence of penalty approaches to the normal contact is addressed shortly. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)