Karl Popp

A Historical Review on Dry Friction and Stick-Slip Phenomena

This article gives a historical overview of structural and mechanical systems with friction. Friction forces between sliding surfaces arise due to complex mechanisms and lead to mathematical models which are highly nonlinear, discontinuous and nonsmooth. Humankind has a long history of magnificent usage of friction in machines, buildings and transportation. Regardless, our state of knowledge of the friction-influenced dynamics occurring in such systems as well as in our daily lives was, until recently, rather primitive. To represent our understanding of friction in nonlinear dynamics, we first trace examples from the earliest prehistoric technologies and the formulation of dissipation laws in mechanics. The work culminates with examples of friction oscillators and stick-slip. This review article contains 304 references.

Dynamics of oscillators with impact and friction

Abstract In the present paper two types of nonsmooth oscillators are investigated: an impact oscillator and a self-sustained friction oscillator. Both are nonsmooth one degree of freedom oscillators with harmonic external excitation. Here the different types of motion, bifurcation diagrams and Poincare maps are determined from experiments. These results will be compared with numerical results on the basis of the identified impact and friction models. The nonsmooth third-order systems show rich bifurcational behaviour which is analysed by numerical simulations but also using mapping approaches. Two different formalisms for the calculation of the Lyapunov exponents are applied. The latter one requires special considerations in the given case of nonsmooth systems. Furthermore, the embedding dimension is gained applying the method of false nearest neighbours. In the case of coexisting solutions further analysis is done by means of bifurcation and stability analysis and the cell-mapping approach.

Bifurcation and stability analysis for a non-smooth friction oscillator

SummaryFriction-induced self-sustained oscillations, also known as stick-slip vibrations, occur in mechanical systems as well as in everyday life. On the basis of a one-dimensional map, the bifurcation behaviour including unstable branches is investigated for a friction oscillator with simultaneous self-and external excitation. The chosen way of mapping also allows a simple determination of Lyapunov exponents.

Dynamical behaviour of a friction oscillator with simultaneous self and external excitation

Friction-induced self-sustained oscillations, also known as stick-slip vibrations, occur in mechanical systems as well as in everyday life. In engineering applications these vibrations are undesirable and should be avoided. In the present paper it is shown how the very robust limit cycles of stick-slip vibrations can be broken up by a harmonic disturbance. Based on a simple model of a friction oscillator with simultaneous self and external excitation the resulting bifurcation behaviour and the routes to chaos are investigated for a wide range of system parameters. The influence of different types of friction characteristics is elaborated and the admissibility of smoothing procedures is examined by comparing results gained for non-smooth and smoothed friction characteristics.

Vibration Control to Avoid Stick-Slip Motion

Friction-induced self-sustained oscillations result in a very robust limit cycle that characterizes stick-slip motion. This type of motion should be avoided under any circumstances because it creates noise, wear, and damage. In this paper we show, by simple models, how stick-slip motion can be avoided. Effective methods are: (i) appropriate increase of internal damping that compensates the negative damping induced by a friction characteristic, which decreases with increasing sliding speed; (ii) external excitation that breaks up the limit cycle (however, this often leads to chaotic motion); (iii) passive vibration control by fluctuating normal forces. The last mentioned mechanism is new and will be investigated in detail. The stick-slip oscillator is extended by an additional degree of freedom, which couples the slipping motion to the normal force. The dynamic behavior of the system has been worked out by analytical investigations and numerical integration. Scanning a broad range of values, parameters of the additional system, called the dynamic vibration absorber, have been found that prevent stick-slip and minimize the amplitude of the residual limit cycle. For this task the evaluation of the system behavior has been achieved by observing its energy content. The feasibility of the proposed dynamic vibration absorber is demonstrated by an experiment.

Vibration Damping by Friction Forces -Theory and Applications

In this paper, we deal with the vibrational behavior of mechanical structures interconnected by contacts with friction. The focus is set on the utilization of friction forces that are generated in the contact interfaces with the objective to increase damping and to reduce vibration amplitudes in order to prevent structures from failures owing to high resonance stresses. We present a comparison and classification of different contact models that are most commonly used, including the derivation of a three-dimensional contact model under consideration of rough surfaces. We give different solution methods for problems with non-linear friction elements. The effectiveness of friction damping devices is pointed out by a single-degree-of-freedom friction oscillator, beam-like structures with frictional interfaces and different underplatform dampers in turbo-machinery applications. It can be shown that in many practical applications friction damping devices provide a remarkable decrease of vibration amplitudes.

Interaction of elastic wheelsets and elastic rails: modelling and simulation

The model of a railway vehicle running on a straight track is presented, in which the wheelsets and the rails are modelled as elastic bodies. The influence of the structural elasticities of the wheelsets and the rails on the running behaviour, especially the hunting motion of the vehicle, is investigated.

Asymmetrical Underplatform Dampers in Gas Turbine Bladings: Theory and Application

During operation, the rotating blades of a gas turbine are subjected to centrifugal forces as well as fluctuating gas forces, resulting in blade vibrations. In addition to material damping, aerodynamical and blade root damping, underplatform dampers are widely used to increase the amount of damping and to decrease blade vibration amplitudes. The friction forces generated by the relative displacements between the underplatform damper and the blade platforms provide a significant amount of energy dissipation. In practice, a number of different underplatform damper designs are applied. Basically, these are wedge dampers with flat contact areas, cylindrical dampers with curved surfaces or asymmetrical dampers with both flat contact surfaces on one side and curved contact surfaces on the other. The latter damper type combines the advantages of both the wedge and the cylindrical damper by preventing the damper from pure rolling on the one hand as it has been observed for cylindrical dampers and on the other hand, avoiding a diverged plane area contact in case of a wedge damper, causing a damper lift-off. This paper will focus on the investigation of cylindrical and asymmetrical underplatform dampers. A comparison between measurements of rotating assemblies in Siemens PG gas turbines (V84.2, V64.3A and V94.3A(2)) under test and real operating conditions with cylindrical and asymmetrical underplatform dampers and the predictions of the developed theoretical model are presented. Special attention is paid to the frequency shift due to the application of an underplatform damper, since in particular for stationary gas turbines, in addition to the amplitude reduction, the accurate prediction of the resonance frequency is of major interest.Copyright

Optimization of Interblade Friction Damper Design

The vibration amplitudes of bladed disk assemblies can be reduced significantly by means of friction damping devices such as shrouds, damping wires and interblade friction dampers. In practice, interblade friction dampers are applied in rotating arrangements with various geometries showing curved or flat surfaces like so-called wedge-shaped dampers. This paper is focusing on a computation method to predict the dynamical behaviour of turbine blades with friction dampers including both, curved and wedge-shaped dampers with Hertzian and non-Hertzian contact conditions, respectively. The presented computation method uses a 3D contact model to calculate the contact forces, including normal and tangential stiffnesses, roughness and microslip effects. The relative displacements in the contact area can be expressed by means of 6 DOF of the blade platforms and 6 rigid body DOF of the damper including translational and rotational displacements. The relative displacement of the friction damper with respect to the adjacent blades can be derived from the contact kinematics of the blade-damper-blade system and the equations of motion of the friction damper. Thus, the model can be applied to investigate spatial motions of the bladed disk assembly including bending and torsional vibrations. A comparison of different friction damper designs with respect to an optimal damper geometry and damper mass is presented. The advantages and disadvantages of each design will be discussed. Experimental results are shown to validate the developed computation method.Copyright

Machine Tool with Active Magnetic Guides

Abstract High speed and high dynamic machining strategies require specific solutions for the components. The limits for speed and accuracy mainly depend on the machine structure, the drives and the guides. In this paper the development of a new high speed machining centre with actively controlled linear magnetic guides will be presented. The stiffness and damping properties of this innovative component will be discussed. The machining centre is equipped with linear direct drives in all three axes and uses lightweight slides on a solid concrete base. The machine structure and first results will be presented and compared to conventional machine tools.