Time/frequency analysis of contact-friction instabilities. Application to automotive brake squeal.

Robust design of silent brakes is a current industrial challenge. Braking systems enter in the more general context of unstable systems featuring contact friction interaction. Their simulation requires time integra- tion schemes usually not adapted to combination of large industrial models (over 600,000 DOF) and long simulations (over 150,000 time steps). The paper first discusses selection of the contact/friction model and adaptations of the integration scheme. The relation between the nominal steady state tangent modes and the system evolution over time is then evaluated. The time response shows a nearly periodic response that is analyzed as a limit cycle. It is shown that instantaneous dynamic stability predictions show stable/unstable transitions due to changes in the contact/friction state. These transitions are thought to give an understanding of the mechanism that limits levels for these self sustained vibrations. The concept is exploited to suggest novel ways to analyze complex modes

Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part I: template-based generic programming

An approach for incorporating embedded simulation and analysis capabilities in complex simulation codes through template-based generic programming is presented. This approach relies on templating and operator overloading within the C++ language to transform a given calculation into one that can compute a variety of additional quantities that are necessary for many state-of-the-art simulation and analysis algorithms. An approach for incorporating these ideas into complex simulation codes through general graph-based assembly is also presented. These ideas have been implemented within a set of packages in the Trilinos framework and are demonstrated on a simple problem from chemical engineering

Switchable Genetic Oscillator Operating in Quasi-Stable Mode

Ring topologies of repressing genes have qualitatively different long-term dynamics if the number of genes is odd (they oscillate) or even (they exhibit bistability). However, these attractors may not fully explain the observed behavior in transient and stochastic environments such as the cell. We show here that even repressilators possess quasi-stable, travelling-wave periodic solutions that are reachable, long-lived and robust to parameter changes. These solutions underlie the sustained oscillations observed in even rings in the stochastic regime, even if these circuits are expected to behave as switches. The existence of such solutions can also be exploited for control purposes: operation of the system around the quasi-stable orbit allows us to turn on and off the oscillations reliably and on demand. We illustrate these ideas with a simple protocol based on optical interference that can induce oscillations robustly both in the stochastic and deterministic regimes.Comment: 24 pages, 5 main figure

AN ALGORITHM FOR RESPONSE AND STABILITY OF LARGE ORDER NON-LINEAR SYSTEMS — APPLICATION TO ROTOR SYSTEMS

International audienceA numerical algorithm to calculate the periodic response, stability and bifurcations of a periodically excited non-conservative, Multi-Degree of Freedom (MDOF) system with strong local non-linearities is presented. First, the given large order system is reduced using a fixed-interface component mode synthesis procedure (CMS) in which the degrees of freedom associated with non-linear elements are retained in the physical co-ordinates while all others, whose number far exceeds the number of non-linear DOF, are transformed tomodal coordinates and reduced using real mode CMS. A shooting and continuation method is then applied to the reduced system to solve for the periodic response. Floquet stability theory is used to calculate stability and bifurcations of the periodic response. The algorithm is applied to study the response to imbalance, stability, and bifurcations of a 24 DOF flexible rotor supported on journal bearings. The results indicate that the proposed algorithm, though approximate, can yield very accurate information about dynamic behavior of large order non-linear systems, even with few numbers of retained component modes. The algorithm, which imposes less demand on computer time and memory, is believed to be of considerable potential in analyzing a variety of practical problems

Understanding friction induced damping in bolted assemblies through explicit transient simulation

The design of joints is seeing increased interest as one of the ways of controlling damping levels in lighter and more flexible aeronautic structures. Damping induced by joint dissipation has been studied for more than a decade, mostly experimentally due to the difficulty of simulating large structures with non-linearities. Experimentally fitted meta-models were thus used for damping estimation at design stage without a possible optimization. The aim of this paper is to demonstrate that damping estimation using local friction models is feasible and that it can be usable for design. The simulation methodology is based on an explicit Newmark time scheme with model reduction and numerical damping that can be compensated for the modes of interest. Practical simulation times counted in minutes are achieved for detailed models. The illustration on a lap-joint shows how simulations can be used to predict the amplitude dependence of modal damping, answer long standing questions such as “does the modeshape change?” or analyze the evolution of pressure fields during a cycle

Use and limitations of the Harmonic Halance Method for rub-impact phenomena in rotor-stator dynamics

International audienceIn the present paper, a Harmonic Balance Method (HBM) coupled with a pseudo-arc length continuation algorithm is presented for the prediction of the steady state behaviour of a rotor-stator contact problem. The ability of the HBM to reproduce the four most common phenomena encountered during rotor to stator contact situations (i.e. 'no-rub', 'full annular rub', 'partial rub' and 'backward whirl/whip') is investigated. A modified Jeffcott rotor model is used and results of the proposed algorithm are compared with traditional time marching solutions and analytical predictions. The advantages and limitations of the HBM for this kind of problem are analyzed. It is shown that the HBM is orders of magnitude faster than transient simulations, and provides very accurate results. However, in its current form it is unable to predict quasi-periodic behaviour. Detailed analysis of the transient solutions yields valuable information for the future extension of the HBM to efficient quasi-periodic simulations