Hartmut Hetzler

A Multiscale Study on the Wall Slip Effect in a Ceramic–Steel Contact With Nanometer-Thick Lubricant Film by a Nano-to-Elastohydrodynamic Lubrication Approach

A novel nano-to-elastohydrodynamic lubrication (EHL) multiscale approach, developed to integrate molecular-scale phenomena into macroscopic lubrication models based on the continuum hypothesis, is applied to a lubricated contact problem with a ceramic–steel interface and a nanometric film thickness. Molecular dynamics (MD) simulations are used to quantify wall slip occurring under severe confinement. Its dependence on the sliding velocity, film thickness, pressure, and different wall materials is described through representative analytical laws. These are then coupled to a modified Reynolds equation, where a no-slip condition applies to the ceramic surface and slip occurring on the steel wall is described through a Navier-type boundary condition. The results of this nano-to-EHL approach can contradict the well-established lubrication theory for thin films. In fact, slip can occur over the whole contact length, leading to a significant modification of the lubricant flow and consequently of the film thickness. If both walls move at the same velocity, the flow is reduced at the contact inlet and the film thickness decreases. If the nonslipping wall entrains the fluid, this one is accelerated resulting in a larger mass flow; nevertheless, the surface separation is reduced as the lubricant flows even faster in the contact center. The opposite effect occurs if the slipping surface entrains the fluid, causing a lower mass flow but higher film thickness. Finally, friction is generally smaller compared to the classical no-slip case and becomes independent of the sliding velocity as total slip is approached.

Zur Stabilität von Systemen bewegter Kontinua mit Reibkontakten am Beispiel des Bremsenquietschens

Die vorliegende Arbeit befasst sich mit reibungsinduzierten Schwingungen bewegter elastischer Festkorper. Zunachst werden die Bewegungsgleichungen fur verschiedene Kontaktformulierungen angegeben und nach einer Diskretisierung die zugehorigen linearisierten Storungsgleichungen ermittelt. Es folgen Betrachtungen zur Stabilitat mit Fokus auf die zirkulatorischen Einflusse. Schlieslich wird ein analytisches Bremsenmodell hergeleitet und der Einflus verschiedener Terme auf die Stabilitat diskutiert.

Dynamic Stability of a Steady Flow in a Planar Channel

In flexible channels with internal flow the steady state may loose stability by divergence or flutter, thus leading to undesirable dynamic behaviour. A lot of investigations have already been done on this subject. The aim of this contribution is to investigate and compare systematically the influence of various parameters on the stability behaviour of the coupled problem. Therefore, a simple, yet general model is built. The fluid is assumed to be inviscid and irrotational and both compressible and incompressible fluid are considered. The steady flow is bounded by a planar channel with a rigid and a thin, flexible wall. The latter is modelled as a continuum on a viscoelastic foundation, which exhibits bending and extensional stiffness. The influence of the various characteristics on the complex eigenvalues and therefore on the stability of the steady state is discussed.

Fast Solution of Transient Elastohydrodynamic Line Contact Problems Using the Trajectory Piecewise Linear Approach

In order to obtain a fast solution scheme, the trajectory piecewise linear (TPWL) method is applied to the transient elastohydrodynamic (EHD) line contact problem for the first time. TPWL approximates the nonlinearity of a dynamical system by a weighted superposition of reduced linearized systems along specified trajectories. The method is compared to another reduced order model (ROM), based on Galerkin projection, Newton–Raphson scheme and an approximation of the nonlinear reduced system functions. The TPWL model provides further speed-up compared to the Newton–Raphson based method at a high accuracy.

Nonlinear Vibrational Behaviour of an Elasto-Pneumatic Training Tool

This paper deals with the nonlinear vibrational response of a stepping-board with nonlinear elasto-pneumatic force elements. Experimental investigations often show too high vertical ground reaction forces (VGRF) between the test persons and the training tool during exercises. The goal of this contribution is to identify the main factors of the dynamical behaviour and thus the biomechanical impact on humans of this training tool. Therefore this paper presents a mechanical model in order to investigate the interaction between the nonlinear behaviour of the board and the athlete. The multiphysical modelling consists of the linear-elastic structural stiffness part and the nonlinear part due to the pneumatic components. This leads to a nonlinear ordinary differential equation.

Bifurcation Analysis for Brake Squeal

This article presents a perturbation approach for the bifurcation analysis of MDoF vibration systems with gyroscopic and circulatory contributions, as they naturally arise from problems involving moving continua and sliding friction. Based on modal data of the underlying linear system, a multiple scales technique is utilized in order to find equations for the nonlinear amplitudes of the critical mode. The presented method is suited for an algorithmic implementation using commercial software and does not involve costly time-integration. As an engineering example, the bifurcation behaviour of a MDoF disk brake model is investigated. Sub- and supercritical Hopf-bifurcations are found and stationary nonlinear amplitudes are presented depending on operating parameters of the brake as well as of tribological parameters of the contact.Copyright

Friction Induced Brake Vibrations at Low Speeds: Experiments, State-Space Reconstruction and Implications on Modeling

Today, low frequency disc-brake noises are commonly explained as self-sustained stick-slip oscillations. Although, at a first glance this explanation seems reasonable, there are indices that cast doubt on it. For instance, the basic frequency of the observed oscillations does not scale with the disc-speed as it is with stick-slip oscillations and the classical model does not explain the observed ending of the vibrations beyond a certain speed. Indeed, our experimental studies on groaning noises reveal two different vibration patterns: stick-slip vibrations at almost vanishing relative speed and a second, differing vibration pattern at low to moderate relative speeds. Yet, these two patterns produce a very similar acoustic impression. While the experiment provides a vast amount of data, the dimension and structure of the underlying oscillation is not known a priori – hence, constructing phenomenological minimal models usually must rely on assumptions, e.g. about the number of DOF, etc. Due to noise and complexity, the measured raw data did only allow for a first straight forward insight, rendering further analysis necessary. Hence, time-delay embedding methods together with a principle component analysis were used to reconstruct a pseudo-phase space together with the embedded attractor to analyse for the systems dimension and to separate signal from noise.Copyright

Analytical Investigation of Hopf Bifurcations Occurring in a 1DOF Sliding-Friction Oscillator With Application to Disc-Brake Vibrations

This article deals with analytical investigations on stability and bifurcations due to declining dry friction characteristics in the sliding domain of a simple disc-brake model, which is commonly referred to as “mass-on-a-belt”-oscillator. Sliding friction is described in the sense of Coulomb as proportional to the normal force, but with a friction coefficient μS which depends on the relative velocity. For many common friction models this latter dependence on the relative velocity can be described by exponential functions. For such a characteristic the stability and bifurcation behavior is discussed. It is shown, that the system can undergo a subcritical Hopf-bifurcation from an unstable steady-state fixed point to an unstable limit cycle, which separates the basins of the stable steady-state fixed point and the self sustained stick-slip limit cycle. Therefore, only a local examination of the eigenvalues at the steady-state, as is the classical ansatz when investigating conditions for the onset of friction-induced vibrations, may not give the whole picture, since the stable region around the steady state fixed point may be rather small. The analytical results are verified by numerical simulations. Parameter values are chosen for a model which corresponds to a conventional disc-brake.Copyright