Andreas Otto

Fraunhofer Institute for Machine Tools and Forming Technology IWU | IWU · Business Unit Machine Tools and Production Systems

In general we are interested in dynamical systems coupled to complex hysteresis. Therefore as a first step we did some investigation on the dynamics of a periodically driven damped harmonic oscillator coupled to independent Ising spins with a local quenched disorder at zero temperature in the past. Although such a system does not produce hysteresis...

We aim at an understanding of the dynamical properties of a periodically driven damped harmonic oscillator coupled to a \ac{RFIM} at zero temperature, which is capable to show complex hysteresis. The system is a combination of a continuous (harmonic oscillator) and a discrete (\ac{RFIM}) subsystem, which classifies it as a hybrid system. In this pa...

We aim at an understanding of the dynamical properties of a periodically driven damped harmonic oscillator coupled to a Random Field Ising Model (RFIM) at zero temperature, which is capable of showing complex hysteresis. The system is a combination of a continuous (harmonic oscillator) and a discrete (RFIM) subsystem, which classifies it as a hybri...

Recently, it was shown that certain systems with large time-varying delay exhibit different types of chaos, which are related to two types of time-varying delay: conservative and dissipative delays. The known high-dimensional turbulent chaos is characterized by strong fluctuations. In contrast, the recently discovered low-dimensional laminar chaos...

Recently, it was shown that certain systems with large time-varying delay exhibit different types of chaos, which are related to two types of time-varying delay: conservative and dissipative delays. The known high-dimensional Turbulent Chaos is characterized by strong fluctuations. In contrast, the recently discovered low-dimensional Laminar Chaos...

The expansion of inverter-connected generation facilities (i.e. wind and photovoltaics) and the removal of conventional power plants is necessary to mitigate the impacts of climate change. Whereas conventional generation with large rotating generator masses provides stabilizing inertia, inverter-connected generation does not. Since the underlying p...

The increasing availability of sensor data at machine tools makes automatic chatter detection algorithms a trending topic in metal cutting. Two prominent and advanced methods for feature extraction via signal decomposition are wavelet packet transform (WPT) and ensemble empirical mode decomposition (EEMD). We apply these two methods to time series...

A new type of dynamics called laminar chaos was recently discovered through a theoretical analysis of a scalar delay differential equation with time-varying delay. Laminar chaos is a low-dimensional dynamics characterized by laminar phases of nearly constant intensity with periodic durations and a chaotic variation of the intensity from one laminar...

We demonstrate that a time-varying delay in nonlinear systems leads to a rich variety of dynamical behaviour, which cannot be observed in systems with constant delay. We show that the effect of the delay variation is similar to the Doppler effect with self-feedback. We distinguish between the non-resonant and the resonant Doppler effect correspondi...

Time delays play an important role in many fields such as engineering, physics or biology. Delays occur due to finite velocities of signal propagation or processing delays leading to memory effects and, in general, infinite-dimensional systems. Time delay systems can be described by delay differential equations and often include non-negligible nonl...

Chatter detection from sensor signals has been an active field of research. While some success has been reported using several featurization tools and machine learning algorithms, existing methods have several drawbacks such as manual preprocessing and requiring a large data set. In this paper, we present an alternative approach for chatter detecti...

The expansion of inverter-connected generation facilities (i.e. wind and photovoltaics) and the removal of conventional power plants is necessary to mitigate the impacts of climate change. Whereas conventional generation with large rotating generator masses provides stabilizing inertia, inverter-connected generation does not. Since the underlying p...

Machining processes are most accurately described using complex dynamical systems that include nonlinearities, time delays and stochastic effects. Due to the nature of these models as well as the practical challenges which include time-varying parameters, the transition from numerical/analytical modeling of machining to the analysis of real cutting...

The increasing availability of sensor data at machine tools makes automatic chatter detection algorithms a trending topic in metal cutting. Two prominent and advanced methods for feature extraction via signal decomposition are Wavelet Packet Transform (WPT) and Ensemble Empirical Mode Decomposition (EEMD). We apply these two methods to time series...

Recently, it was shown that there is a hitherto unknown dichotomy for systems with time-varying delay [Phys. Rev. Lett. 118, 044104 (2017)]. There are systems with conservative delays, which are equivalent to time delay systems with constant delay. On the other hand, there are dissipative delays leading to completely new dynamics, which are not kno...

We investigate the dynamical properties of time-delay systems with time-varying delay, where we focus on the influence of the functional structure of the delay. Two universality classes of systems with time-varying delays are presented which lead to fundamental differences in the dynamics of the related systems, as for example the scaling behavior...

The occurrence of chatter in milling processes was investigated in this study. The prediction of the stability lobes of metal cutting processes requires a model of the cutting force and a model of the dynamic machine tool behavior. Parameter uncertainties in the models may lead to significant differences between the predicted and measured stability...

In this paper we investigate the effect of the tool-workpiece mode interaction on the stability of a flexible-tool, flexible-workpiece turning process. The workpiece dynamics are modeled by classical beam theory while for the tool we consider a description in terms of eigenmodes with an arbitrary orientation. The focus here is on elucidating the co...

We show that the output of systems with time-varying delay can exhibit a new kind of chaotic behavior characterized by laminar phases, which are periodically interrupted by irregular bursts. Within each laminar phase the output intensity remains almost constant, but its level varies chaotically from phase to phase. In scalar systems, the periodic d...

Synchronization in networks of identical oscillators with heterogeneous coupling delays is studied. A decomposition of the network dynamics is obtained by block diagonalizing a newly introduced adjacency lag operator which contains the topology of the network as well as the corresponding coupling delays. This generalizes the master stability functi...

The effect of torsional vibrations on the dynamics of metal cutting processes is studied. An extended dynamic process model is presented, where the spindle angle and the time delay are dynamic variables resulting in delay differential equations with state-dependent delay. Stability lobes are calculated based on the new extended process model and co...

The Turing (wave) instability is only possible in reaction-diffusion systems with more than one (two) components. Motivated by the fact that a time delay increases the dimension of a system, we investigate the presence of diffusion-driven instabilities in single-species reaction-diffusion systems with delay. The stability of arbitrary one-component...

The influence of torsional vibrations on the milling dynamics is studied. In the new model the spindle speed changes in response to the cutting torque. For an ideal process without runout this passive spindle speed variation is periodic with the tooth passing period but does not result in a variable delay, which means that its influence on the mill...

In this paper, we investigate the influence of the retarded access by a time-varying delay on the dynamics of delay systems. We show that there are two universality classes of delays, which lead to fundamental differences in dynamical quantities such as the Lyapunov spectrum. Therefore, we introduce an operator theoretic framework, where the soluti...

In this paper, we deal with the control of a transport PDE/nonlinear ODE cascade system in which the transport coefficient depends on the ODE state. We develop a PDE-based predictor-feedback boundary control law, which compensates the transport dynamics of the actuator and guarantees global asymptotic stability of the closed-loop system. The stabil...

We study mechanical vibrations in milling with non-uniform pitch and variable helix tools. The process is modeled by a periodic delay differential equation with distributed delay, which takes into account, for example, the nonlinear cutting force behavior, the effect of runout, and the exact delay distribution due to the unequally spaced flutes. We...

The transformation from systems with time-varying delays or state-dependent delays to systems with constant delays is studied. The transformation exists if the delay is defined by a transport with a variable velocity over a constant distance. In fact, time-varying or state-dependent delays, which are generated by such a mechanism, are common in eng...

We show that the dynamics of systems with a time-dependent delay is fundamentally affected by the functional form of the retarded argument. Associating with the latter an iterated map, the access map, and a corresponding Koopman operator, we identify two universality classes. Members in the first are equivalent to systems with a constant delay. The...

In the present paper we investigate the influence of the retarded access by a time-varying delay on the dynamics of delay systems. We show that there are two universality classes of delay which lead to fundamental differences in dynamical quantities such as the Lyapunov spectrum. Therefore we introduce an operator theoretic framework, where the sol...

The equivalence between systems with state-dependent delays and systems with constant delays is studied. Systems with state-dependent delays appear when the dynamics of the system does not only depend on the instantaneous configuration but also on a delayed configuration of the system, and the size of the delay depends on the state of the system. I...

In this thesis a new frequency domain approach for the analysis of time delay systems is presented. After linearization of a nonlinear delay differential equation (DDE) with constant distributed delay around a constant or periodic reference solution the so-called Hill-Floquet method can be used for the analysis of the resulting linear DDE. In addit...

A universal frequency domain approach for studying the dynamics of metal cutting with a flexible workpiece and a compliant tool is derived. The method is used for the identification of the position-dependent stability lobes in turning. It enables a fast, accurate, and systematic stability analysis of turning processes in the parameter space, which...

Chatter vibrations in machining are studied. Special attention is paid to the effect of structural vibrations in the cutting speed direction. These so-called tangential vibrations may dominate the dynamics in drilling, sawing or grinding, where the torsional dynamic stiffness is much lower than the lateral, axial or radial dynamic stiffness. The in...

The identification of the stability lobes for machine-tool vibrations is presented for interrupted turning processes with round inserts. An analytic cutting force model for round inserts is derived, where the directional factors depend nonlinear and non-homogeneous on the depth of cut. Furthermore, the effect of vibrations in the cutting speed dire...

Chatter vibrations in cutting processes are studied in the present paper. A unified approach for the calculation of the stability lobes for turning, boring, drilling and milling processes in the frequency domain is presented. The method can be used for a fast and reliable identification of the stability lobes and can take into account nonlinear she...

In the present paper the chatter instability of variable speed machining is studied. Though, there exist numerical methods for the computation of the stability lobes for variable speed machining, especially in turning processes the potential of an active spindle speed variation for chatter suppression is mostly unexploited. In the case of a slowly...

The stability of chatter vibrations in milling processes with variable helix tools is studied. Variable helix tools are characterized by different helix angles at different teeth of the cutter. With the tool rotation a distributed time delay, specifying the time between two subsequent cuts, arises in the model equations for the description of the m...

In this paper an analytical approach for the stability analysis of milling with variable pitch and variable helix tools is presented. An important parameter, which affects the occurrence of unstable regenerative chatter vibrations, is the time delay between two subsequent cuts. For variable pitch or variable helix tools a distributed time delay ari...

In this paper the chatter stability of turning and full-immersion milling operations with spindle speed variation is studied. We present a method to calculate the stability lobes in the limit of very low and very high frequencies of the delay modulation. These approx-imations help to classify the results of numerically exact methods, as for example...

To understand the dynamics of systems with fluctuations in the retarded argument, the Lyapunov spectra of a scalar, linear delay differential equation (DDE) are studied. Depending on the structure of the deviated argument some Lyapunov exponents can be equal to minus infinity, which indicate the difference between the dimension of the state space a...