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The digital balancing of the Furuta pendulum is studied when the time delay related to the digital control and the dynamics of the actuator have essential effects on stability. Such cases occur when the sampling rate of the digital control is low, that is, the control cycles are slow due to complex signal processing strategies and/or the implementation of cheap low-capacity microprocessors. A corresponding difficulty is that no direct velocity measurement is available. Critical sampling times are identified and stability charts are constructed and validated by experiments including the possible existence of quasi-periodic self-excited oscillations. [ABSTRACT FROM AUTHOR]

The stability of a body suspended asymmetrically by means of an inelastic rope is investigated. The rope is attached to the body at two points and passed over a frictionless hook or a nail in the vertical plane. The equilibrium points of the system and their stability are described as a function of the rope length, the distance of the attachment points and the position of the center of mass. Depending on the choice of the parameters, one, two or three equilibrium positions exist: their structural change manifests itself in the form of cusp bifurcations of co-dimension two, which is determined in exact analytical form. [ABSTRACT FROM AUTHOR]

In this paper, the stability properties of milling processes are presented when the axial component of the cutting force is also taken into account as a compressive force acting on the cutting tool. The mechanism of the material removal operation is described by a one degree-of-freedom oscillator subjected to the so-called surface regeneration effect. This can be represented mathematically by a nonlinear, time-periodic, delay differential equation. The regenerative compression affects the natural frequency of the system, which is modelled through the lateral stiffness variation of the bearing support of the main spindle. This extension of the general milling model leads to the birth of stable islands within the originally unstable parameter domain. Since the exploitation of these regions may open new ways in practice for increasing the efficiency of machining, the domain of attraction is investigated qualitatively near the stability boundaries of the stable island by means of a semi-analytical method. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics of a fuzzy controlled polishing machine where the effect of temporal sampling is also taken into account. Chaotic and transient chaotic behaviors are experienced for certain control parameter combinations. In the case of transient chaotic motion, closed-form algebraic expressions are determined for the expected value of the kickout number and for the corresponding standard deviation. [ABSTRACT FROM AUTHOR]

The robustness of dynamical systems against external perturbations is crucial in engineering; however, it is often overlooked for the lack of methods for rapidly computing it. This paper proposes a novel algorithm for estimating the robustness of systems subject to time delay. More precisely, the algorithm iteratively estimates the so-called local integrity measure (LIM), that is, the radius of the largest hypersphere centered at the fixed point and located within its basin of attraction. Since time-delayed systems are infinite dimensional, initial conditions are restricted to a constrained type of initial functions. The semi-discretization method is used for rapidly simulating the dynamics of the systems, while trajectories are classified as converging or diverging using a subdivision of the reduced phase space into cells. The algorithm was tested on four different mechanical systems, and in all cases it very quickly provided an accurate estimation of the LIM. Moreover, it enabled the study of LIM trends in a multi-dimensional parameter space, which would have been unfeasible with alternative methods. This breakthrough in computational efficiency has important implications for engineering design, allowing for careful consideration of dynamical integrity and enhancing the safety and reliability of engineered systems, especially in the presence of time delays. • An algorithm for estimating the dynamical integrity of equilibria is developed. • The algorithm works for time-delayed dynamical systems. • The algorithm works iteratively, it is very quick and has no memory issues. • It enables one to consider dynamical integrity during engineering design. • Several case studies demonstrate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

This paper reviews the dynamics of machining and chatter stability research since the first stability laws were introduced by Tlusty and Tobias in the 1950s. The paper aims to introduce the fundamentals of dynamic machining and chatter stability, as well as the state of the art and research challenges, to readers who are new to the area. First, the unified dynamic models of mode coupling and regenerative chatter are introduced. The chatter stability laws in both the frequency and time domains are presented. The dynamic models of intermittent cutting, such as milling, are presented and their stability solutions are derived by considering the time-periodic behavior. The complexities contributed by highly intermittent cutting, which leads to additional stability pockets, and the contribution of the tool's flank face to process damping are explained. The stability of parallel machining operations is explained. The design of variable pitch and serrated cutting tools to suppress chatter is presented. The paper concludes with current challenges in chatter stability of machining which remains to be the main obstacle in increasing the productivity and quality of manufactured parts. [ABSTRACT FROM AUTHOR]

In spatial contact problems of rigid bodies, Coulomb friction results in dynamical systems with codimension-2 discontinuity manifolds, which are outside the scope of piecewise smooth dynamical systems. This motivated the authors to extend Filippov systems to codimension-2 discontinuity manifolds, which leads to the definition of extended Filippov systems. In these systems, sliding and crossing regions can be defined analogously to those of standard Filippov systems. A convex construction of the sliding vector is also presented in the paper. The developed methods are demonstrated on mechanical problems with spatial Coulomb friction. [ABSTRACT FROM AUTHOR]

We show that an unstable scalar dynamical system with time-delayed feedback can be stabilized by quantizing the feedback. The discrete time model corresponds to a previously unrecognized case of the microchaotic map in which the fixed point is both locally and globally repelling. In the continuous-time model, stabilization by quantization is possible when the fixed point in the absence of feedback is an unstable node, and in the presence of feedback, it is an unstable focus (spiral). The results are illustrated with numerical simulation of the unstable Hayes equation. The solutions of the quantized Hayes equation take the form of oscillations in which the amplitude is a function of the size of the quantization step. If the quantization step is sufficiently small, the amplitude of the oscillations can be small enough to practically approximate the dynamics around a stable fixed point. [ABSTRACT FROM AUTHOR]

A single degree-of-freedom nonlinear mechanical model of the stick–slip phenomenon is studied when the Stribeck-type friction force is emulated by means of a digitally controlled actuator. The relative velocity of the slipping contact surfaces is considered as bifurcation parameter. The original physical system presents subcritical Hopf bifurcation with a wide bistable parameter region where stick–slip and steady-state slipping are both stable locally. Hardware-in-the-loop experiments are performed with a physical oscillatory system subjected to the emulated Stribeck forces. The effect of sampling time is studied with respect to the stability and nonlinear behavior of this experimental system. The existence of subcritical Neimark–Sacker bifurcations are proven in the digital system, the stability and bifurcation characteristics of the continuous and the digital systems are compared, and the counter-intuitive stabilizing effect of sampling time is shown both analytically and experimentally. The conclusions draw the attention to the limitations of hardware-in-the-loop experiments when the corresponding systems are strongly nonlinear. [ABSTRACT FROM AUTHOR]

Parallel turning operations offer considerable potential in increasing productivity, since they ensure high material removal rates and high feasible accuracy simultaneously. According to preliminary calculations, the stable parameter region for a 2-cutter turning system can significantly be extended by its dynamical detuning via modifying the natural frequency of one of the tools. Mechanical models are presented for a 2-cutter turning tool fixture to predict the dynamics and stability properties of the system. First, a 2-degree-of-freedom (DoF) model with dynamically uncoupled cutters is analysed. A test fixture incorporating 2 cutters was built, in order to verify theoretical predictions on cutting stability. Measurement results resulted in the extension of the mechanical model with another DoF, which captures the physical coupling between the tools. Experiments indicate that for close natural frequencies, the corresponding modal dampings are essentially different, consequently, the damping properties of the 3-DoF model can properly be modelled by non-proportional damping only. It is also shown that the presence of this non-proportional damping results in a significant increase in the robust chip width limit of stable cutting, which enhances the effect of detuning the tool frequencies in the 2-cutter turning system even further. [ABSTRACT FROM AUTHOR]

The output of an accelerometer often has coupled components of displacement and acceleration, and is rarely used individually for balancing tasks. In order to balance a wheeled inverted pendulum like the Segway, the conventional control usually requires gyroscopes or a combination of accelerometers and gyroscopes. In this paper, we prove that even in the presence of time delay, a wheeled inverted pendulum can be well stabilized with only one accelerometer as the sensor when the mechanical structure is slightly modified. The key idea is the introduction of an additional damper that does not have a physical connection with the wheels. Moreover, we show that balancing can be achieved with an appropriately selected accelerometer position over a range of time delays. [ABSTRACT FROM AUTHOR]

For the stability analysis of time-delay systems, the available methods usually require the exact evaluation of some quantities. The definite integral stability method, originated from the Argument Principle or the Cauchy Theorem, is effective because it only requires a rough estimation of the testing integral over a finite interval to judge stability. However, no general rule is given in the literature for properly choosing the upper limit of the testing integral. In this paper, two simple algorithms are presented for finding the parameter-dependent critical upper limit and a parameter-independent upper limit without any restriction on the number of time delays. These results improve and complete the definite integral stability method. As illustrated by the numerical examples, the proposed algorithms work effectively and accurately. [ABSTRACT FROM AUTHOR]

Mechanical systems with feedback control commonly contain time delays which usually tend to destabilise the system. With increasing accuracy requirements of data acquisition and calculation, investigation of the effect of the feedback delay including the computational time, actuating time, and signalling time is crucial for developing advanced chassis control. A 2-dimensional vehicle handling model with feedback control torque is introduced to analyse the dynamics of vehicle stability control system. A revised version of the PAC-2002 tyre model is used to create two qualitatively different steering characteristics by tuning the contact friction coefficients at the front and rear wheels. The stability charts in the space of the control gains are constructed. In understeer and oversteer cases, the control gains are optimised to achieve the fastest settling signals against small perturbations. While the optimised gains provide global stability of the cornering manoeuvres in the oversteer case, the gains should be further tuned in the understeer case to ensure fast settling signals and also global stability. The optimisation procedure is presented for various realistic time delays. • Delayed dynamic model establishment for vehicle stability control. • Stability analysis of vehicle stability control with closed-form representation of critical time delay. • Analytical description of system stability w.r.t various time delays. • Parameter optimisation of delayed vehicle stability controller based on local maximal decay rate and global stability. [ABSTRACT FROM AUTHOR]

The stability of an elastic beam is studied when the beam is subjected to a longitudinal force governed by a feedback loop. The setup of the simplified mechanical model is motivated by a basic problem of electroacoustics. The corresponding governing equation is the 1D wave equation with delayed boundary conditions. By means of the D׳Alembert solution, the system can be transformed into a delay differential equation of neutral type that includes two time delays. The intricate stability chart is constructed analytically in the parameter plane of the gain parameter and the ratio of the time delays. The complete chart extends the numerical results of the literature, while it also draws attention to the numerical difficulties of finite degree of freedom approximations and to the extreme sensitivity of the dynamics with respect to the time delay parameters of the system. [ABSTRACT FROM AUTHOR]

Helical milling tools of nonuniform helix angles are widely used in manufacturing industry. While the milling tools with these special cutting edges are already available in the market, their cutting dynamics has not been fully explored. Also, there have been several attempts to introduce complex harmonically varied helix tools, but the manufacturing of harmonic edges is extremely difficult, and their effect on cutting dynamics is not clear either. In this study, a general mechanical model is introduced to predict the linear stability of these special cutters with optional continuous variation of the helix angle. It is shown that these milling, tools cause distribution in regeneration. The corresponding time-periodic distributed delay differential equations are investigated by semi-discretization. This work points out how the nonuniform and harmonically varied helix cutters behave in case of high and low cutting speed applications. [ABSTRACT FROM AUTHOR]

Dimension reduction properties of the act-and-wait controller for systems with feedback delay are analysed. The point of the act-and-wait concept is that the feedback is switched on and off periodically. Earlier works have shown that if the switch-off (waiting) period is longer than the feedback delay, then the system can be described by an n × n monodromy matrix with n being the dimension of the delay-free system. In this study, it is shown that for certain combinations of the waiting and the acting (or switch on) periods, the system can be still be transformed to a finite, kn-dimensional system with k ≥ 2 even if the waiting period is shorter than the delay. It is shown that the control technique can be a candidate as a solution to the Brockett problem posed for systems with feedback delay. [ABSTRACT FROM PUBLISHER]

Abstract: The paper addresses dynamic and control issues related to a dynamical model called the classical shimmying wheel. The classical shimmying wheel models the rolling dynamics of many physical rolling systems such as aircraft nose wheels, motorcycles, automotive systems, and tractor-trailer systems. Such a system can exhibit undesirable unstable rolling motion, that is, shimmying, which can often lead to disastrous results. Prior work with this particular model has focused on the stability of the system as well as an analysis of the qualitative nature of its dynamics, including numerical observation of possible chaotic behavior. Such behavior is observed when the rolling element is allowed to slip under certain conditions, which is intended to realistically model real physical rolling systems. In cases where the rolling dynamics of the system are unstable, the dynamics are characterized by the presence of an attractor wherein the system repeatedly switches back and forth between rolling and slipping. We present a slightly different, but more realistic, condition for the rolling element to switch from pure rolling to a slipping state and observe similar behavior. Additionally, we present a controller for the system designed using the method of feedback linearization. This controller stabilizes the purely rolling system but fails to always stabilize the system that is allowed to slip. We investigate the conditions under which the controller stabilizes the slipping system and propose an effective alternative control strategy for the slipping system for the case when the original controller fails to stabilize the system and where the uncontrolled rolling system is unstable. Finally, we investigate the stability of the system about operating points that are not equilibrium points, which models a physical system executing a turn. [ABSTRACT FROM AUTHOR]

No doubt, the COVID-19 pandemic has been and is one of the greatest challenges of the mankind in its recent history. Though not unexpectedly, it has come abruptly. The reaction of the educated community has been abrupt, accordingly. Independent from the professional background, it must be said that almost everybody has a share in the global fight against the global consequences. It is not surprising, for example, when mechanical engineers have their own immediate contribution to satisfy the sudden extreme need in hospital equipment, the fast design and manufacturing of ventilators, test tools, to mention a few only. However, it is a welcome surprise when mechanicians and mechanical engineers have relevant and important comments on the underlying problem, the global spread of the virus. Actually, this article of Professor Bala Balachandran of the University of Maryland, College Park, MD, and his group represents just one... [ABSTRACT FROM AUTHOR]

Examines the microchaotic behavior in the advanced design work of digitally controlled machines. Importance of time delay featured in both analog and digital controllers; Estimation of the distribution of vibration amplitudes; Description of the inverted pendulum used in analyzing microchaos motion.

Routh reduction presents the minimum number of differential equations that uniquely describe the state of nonlinear mechanical systems where the state variables can be separated into essential ones and cyclic ones. This work extends Routh reducibility for a relevant set of controlled mechanical systems. A chain of theorems is presented for identifying the conditions when reduced order rank conditions can be applied for determining the Kalman controllability of Routh reducible mechanical systems where actuation takes place along the cyclic coordinates only, while some of the essential coordinates and their derivatives are observed. Four mechanical examples represent the advantages of using reduced rank conditions to check and/or to exclude linear controllability in such systems. [ABSTRACT FROM AUTHOR]

Postural sway is a result of a complex action–reaction feedback mechanism generated by the interplay between the environment, the sensory perception, the neural system and the musculation. Postural oscillations are complex, possibly even chaotic. Therefore fitting deterministic models on measured time signals is ambiguous. Here we analyse the response to large enough perturbations during quiet standing such that the resulting responses can clearly be distinguished from the local postural sway. Measurements show that typical responses very closely resemble those of a critically damped oscillator. The recovery dynamics are modelled by an inverted pendulum subject to delayed state feedback and is described in the space of the control parameters. We hypothesize that the control gains are tuned such that (H1) the response is at the border of oscillatory and nonoscillatory motion similarly to the critically damped oscillator; (H2) the response is the fastest possible; (H3) the response is a result of a combined optimization of fast response and robustness to sensory perturbations. Parameter fitting shows that H1 and H3 are accepted while H2 is rejected. Thus, the responses of human postural balance to "large" perturbations matches a delayed feedback mechanism that is optimized for a combination of performance and robustness. [ABSTRACT FROM AUTHOR]

Kinematic oscillation of railway wheelsets is investigated in the case of a straight track, focusing on the nonlinear effects of the geometry of wheel and rail profiles. Euler angles are used to describe the motion of the wheelset, the contacting bodies are modelled by two-parametric rigid surfaces. The surface parameters of the current contact points are followed during the calculations. The curvatures and their variations are also included in the analysis. From the implicit form of the geometric constraints, the dynamics is determined by means of Taylor expansion. Equations of the local nonlinear motion are derived and the qualitative behaviour of the system is given. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In this study, surface error calculations and stability conditions are presented for milling operations in case of slender parts. The dynamic behavior of the flexible beam-type workpiece is modeled by means of finite element method (FEM), while the varying dynamical properties related to the feed motion as well as the material removal process are incorporated in the model. The FEM-generated direct frequency response function is verified through a closed-form solution based on the distributed transfer function method. Relative errors and convergence of the FEM are investigated based on the analytical solutions of the continuum model, from which appropriate element size and mode number can be selected for modal coordinate transformations. The pattern in the variation of the natural frequencies is explored using the analytical model in case of high radial depth of cut relative to the original cross section of the beam-like workpiece. Both the stability conditions and the resulted surface errors are predicted as a function of the tool position. The presented approach and the results are validated by laboratory tests. [ABSTRACT FROM AUTHOR]

Machine tool vibrations in turning processes are analyzed by taking into account the nonlinearity of the cutting force characteristics. Unstable limit cycles are computed for the governing nonlinear delay-differential equation in order to determine the bistable technological parameter region where stable stationary cutting and large-amplitude machine tool vibrations coexist. Simple closed-form formulas are derived for the amplitude of limit cycles and for the size of the bistable region considering a general cutting force characteristics. The analytical results are determined by the method of averaging, which can be used to treat the nonlinearities without their third-order approximation. The results are confirmed by numerical continuation and using Melnikov's integral. • Nonlinear dynamics of turning processes is analyzed on an orthogonal cutting model. • Periodic solutions are computed analytically via the method of averaging. • Simple closed-form formula is derived to determine bistable parameter regions. [ABSTRACT FROM AUTHOR]

A modal-based model of milling machine tools subjected to time-periodic nonlinear cutting forces is introduced. The model describes the phenomenon of bistability for certain cutting parameters. In engineering, these parameter domains are referred to as unsafe zones, where steady-state milling may switch to chatter for certain perturbations. In mathematical terms, these are the parameter domains where the periodic solution of the corresponding nonlinear, time-periodic delay differential equation is linearly stable, but its domain of attraction is limited due to the existence of an unstable quasi-periodic solution emerging from a secondary Hopf bifurcation. A semi-numerical method is presented to identify the borders of these bistable zones by tracking the motion of the milling tool edges as they might leave the surface of the workpiece during the cutting operation. This requires the tracking of unstable quasi-periodic solutions and the checking of their grazing to a time-periodic switching surface in the infinite-dimensional phase space. As the parameters of the linear structural behaviour of the tool/machine tool system can be obtained by means of standard modal testing, the developed numerical algorithm provides efficient support for the design of milling processes with quick estimates of those parameter domains where chatter can still appear in spite of setting the parameters into linearly stable domains. [ABSTRACT FROM AUTHOR]

This paper extends two numerical methods for the stability analysis of a class of time-periodic hybrid time-delay systems. In particular, the pseudospectral tau and spectral element methods are extended to hybrid systems. The analyzed delay-differential equation involves delayed terms with both continuous and piecewise constant arguments, in other words, it involves delays both without and with zero-order hold, respectively. The analyzed class of hybrid systems can be used to describe time-periodic hereditary processes subjected to digital feedback control. The proposed numerical algorithms are applied to the mathematical models of haptic systems and milling processes subjected to digital feedback control. [ABSTRACT FROM AUTHOR]

There are several practical methods to reduce machine tool vibrations that have negative effects especially on the quality of the machined surface. The most intricate vibration is the regenerative one originated in a delay effect of cutting processes. One group of the methods that may be successful in avoiding regenerative vibrations is the appropriate variation of the corresponding time delay. This study presents the stability analysis of milling processes in case of an especially intricate way of varying the delay in time: the radial depth of cut is varied in face milling resulting in a wavy tool path. The combination of the semi-discretization method and the implicit subspace iteration method is introduced to present an efficient way of calculating stability charts that provide conclusions regarding the use of this method in eliminating chatter. [ABSTRACT FROM AUTHOR]

Parallel turning is an excellent candidate for keeping up with current trends set by manufacturing industry, namely, to increase accuracy and productivity simultaneously. In the field of manufacturing of cylindrical parts, these cutting processes offer huge potential in increasing productivity, since they ensure high material removal rates and appropriate accuracy at the same time. The above benefits can yet only be harvested if the process is free of chatter vibration, which affects the workpiece surface quality. In this study, it is shown that by means of tuning the dynamical properties of cutting tools, it is possible to expand the stable machining parameter regions in order to eliminate adverse chatter. A parallel turning system is investigated, where tuning of the system is realized by varying the overhang of one of the tools, that is, by modulating the frequency ratio of the cutters. Measurements have been carried out for the validation of the theoretical predictions of robustly stable chip width limits, below which the turning operation is stable for all spindle speed values. [ABSTRACT FROM AUTHOR]

Prediction of machine tool chatter requires the characterization of dynamic of the machine-tool-workpiece system by means of frequency response functions (FRFs). Uncertainties of the measured FRFs result in uncertainties of the calculated stability diagrams, therefore robustness of stability prediction against parameter perturbations is of high importance. Although there exist methods to determine robust stability in terms of stability radii, these methods either give a conservative estimate of the real uncertainties or are limited to perturbations of a few modal parameters, only. In this paper, a frequency-domain approach is presented to determine robust stability boundaries using the measured FRFs directly without any modal parameter identification. The method is based on an envelope fitting around the measured FRFs combined with some considerations of the single-frequency method. The application of the method is demonstrated in case of a turning operation, where the machine tool structure is characterized by a series of FRF measurements. [ABSTRACT FROM AUTHOR]

The system of a vessel and a direct spring operated pressure relief valve is extended by a downstream pipe. The presented mathematical model consisting of ordinary and partial differential equations can be transformed to a system of differential difference equations by means of the travelling wave solutions of the partial differential equations. This model contains a time delay originated in the pipe length and the speed of sound in the pipe. The linear stability analysis presents stability charts in a parameter plane characterising the environment where the valve is built in. The boundary lines and the corresponding vibration frequencies of the self-excited vibrations are determined as compact closed form expressions. Several analogies are identified with other physical systems modelled by delayed oscillators. Both the stability charts and the vibration frequencies are checked with numerical simulations of the original nonlinear system consisting of coupled ordinary and partial differential equations. The connection between the travelling wave solution and the standard quarter standing wave approximation is explained. A qualitatively relevant phenomenon is identified, namely the appearance of the quasi-periodic vibration at certain parameter combinations. • Construction of delay differential equations for vessel–valve–pipe system. • Closed form stability boundaries and stability charts. • Closed form expressions of vibration frequencies at stability boundaries. • Analytical expression for pipe-length independent stability. • Identification of quasi-periodic oscillations. • Numerical validation of stability charts. [ABSTRACT FROM AUTHOR]

Multi-cutter turning systems bear huge potential to increase the machining productivity of cylindrical parts. The reason for this is that the application of multi-cutter turning heads enables to raise thematerial removal rate, since the rate is multiplied by the number of cutters involved. Multi-cutter turning technology is not only applied to increase cutting performance but also to ensure highest possible accuracy, which is one of the most important quality measures for cutting technologies. In this study, a further benefit of multi-cutter turning operations is shown, which is the possible elimination of adverse chatter vibrations by means of optimal tuning of system parameters. Based on numerical stability calculations, the stable machining parameter region can significantly be expanded for dynamically uncoupled and optimally tuned cutters. Results have been validated by measurements. [ABSTRACT FROM AUTHOR]

The forced periodic vibrations of milling processes with helical tools are modelled and analysed. By means of analytical and numerical techniques, the so-called superchart of milling is constructed that includes the conventional stability chart with the stability lobes and also the amplitudes of the stable forced vibrations, which is correlated to many surface quality numbers like surface location error, surface waviness and surface roughness. The existences of trivial and non-trivial appropriate axial immersions are presented for a single degree of freedom mechanical model of the machine tool structure. At these appropriate axial immersion parameters, if the cutting is stable, the surface quality parameters will be also optimal even in those spindle speed domains where the system is near to resonance and the cutting efficiency is high. Experiments are performed with a large industrial milling machine using a flexible test rig with an essential flexibility in one direction. The calculated and the measured forced vibration signals in the stable domains of the stability chart are in good correlation, which validates the simple analytical predictions for the non-trivial appropriate axial immersion parameters. [ABSTRACT FROM AUTHOR]

The act-and-wait concept is a recently developed type of controller, which is receiving growing interest because of its promising features with respect to the control of systems with feedback delay. Although most of its advantages have been widely discussed and verified experimentally, a detailed analysis of the nonlinear behavior of this type of controller is still missing. In this paper, we apply the act-and-wait controller to the digital position control of a single-degree-of-freedom system. The analysis shows both the linear stability and the post-bifurcation behavior of the system, comparing the system with a regular proportional-differential controller and with the act-and-wait controller. The performed investigation confirms most of the advantages of the act-and-wait controller, already known in the literature, regarding the enlargement of the stable region and the possibility of achieving deadbeat control, also in the presence of delay. On the other hand it shows some drawbacks of this controller, related to the post-bifurcation behavior, which presents unbounded motions, and to the robustness of the stability, which appears to be limited. [ABSTRACT FROM AUTHOR]

The observation that time-delayed feedback can stabilize an inverted pendulum motivates the formulation of models of human balance control in terms of delay differential equations (DDEs). Recently the intermittent, digital-like nature of the neural feedback control of balance has become evident. Here, semidiscretization methods for DDEs are used to investigate an unstable dynamic system subjected to a digital controller in the context of a switching model for postural control. In addition to limit cycle and chaotic ("microchaos") oscillations, transiently stabilized balance states are possible even though both the open-loop and the closed-loop systems are globally unstable. The possibility that falls can be an intrinsic component of neural control of balance may provide new insights into how the risk of falling in the elderly can be minimized. [ABSTRACT FROM AUTHOR]

In this paper we present an analysis of the stability of a two-degree-of-freedom system, modeling a robotic arm connected to the actuator through an elastic joint and subject to digital position control. The system consists of two lumped masses connected to each other through a spring and a damper. In the model there is only one actuator, so the system is underactuated in a certain sense; two cases are considered, referring to a collocated and a noncollocated configuration. Stability analysis is presented using both a continuous and a discrete time approach. The discrete time approach is related to the case of a digital controller, typical in real applications. This samples the position and the velocity signals at discrete time intervals and, therefore, it generates a piecewise constant control force, introducing a delay in the control system as well. The stability charts are presented in the parameter space of the sampling time and the control gains. Their differences highlight the role played by the resonances between the finite sampling frequency and the natural frequency of the system in achieving robust stability with respect to parameter variations. [ABSTRACT FROM PUBLISHER]

Abstract: The machining behaviour of special serrated milling tools are investigated. These cutters are most commonly used for roughing operations of superalloys such as titanium and nickel based alloys which prevent high cutting speeds due to their high cutting forces and low thermal conductivity. During the experimental study, these drawbacks were avoided with the usage of aluminium alloy that allows more convenient machining circumstances and high tooth passing frequencies compared to the frequencies of the essential vibration modes. By means of a general cutting force model, simulations point out the fact that the serrated cutters require lower drive torque than their non-serrated counterparts, while our corresponding measurements validate our model. A regenerative dynamic model is constructed up directly in the modal space using the modal representation of the tool/toolholder/spindle structure and linear stability analyses are performed by the so-called semi-discretization method. The significantly larger parameter domains of stable cutting and their predicted feed dependency for these serrated mills are confirmed by chatter tests. As a result of these investigations, the practical advantages of the serrated cutters are confirmed: while they remove the same specific amount of materials using lower drive torque, their productivity can also be increased using higher stable depth of cuts compared to their non-serrated counterparts even in case of difficult-to-cut materials like titanium. The constructed mechanical model also provides an adequate tuning of the cutting parameters and the serration waves in order to optimize the process for easy-to-cut materials like aluminium. [Copyright &y& Elsevier]

Chatter suppression is investigated when time-periodic axial load is applied during the turning process of slender workpieces. The Euler–Bernoulli beam theory is used to construct the mathematical model of the workpiece that is clamped at the chuck and pinned at the tailstock. To improve the stability of the turning process, the workpiece is excited by a periodic compressive force with various waveforms like sinusoidal, triangular and square-like ones. These modulations lead to intricate patterns in the stability chart, which are originated in the induced time-periodic variation of the lateral stiffness of the workpiece. It is revealed in a multi-dimensional parameter space that the modulation of the axial force greatly improves the stability properties of turning, which is a realistic option for low cutting speeds. [ABSTRACT FROM AUTHOR]

The paper presents the first results of an exploratory research work, aiming the experimental evaluation of the mechanical contact between conforming surfaces of metallic bodies. The proposed procedure—that is based on the measurement of electric potentials—is able to determine the actual contact pattern and estimate the force distribution on the opposing surfaces. In the present paper, the contact properties along a curve are evaluated, but the basic principles supporting the solution of the more general surface contact problem are also laid down. The goal of this research work is to provide a reliable basis for the investigation of contact-related effects on the modal properties of structures and machines. The distribution of electric contact resistivity can also be assessed using this method, opening the way to the refined characterization of electric switches and connectors. During the application of the method, measured electric voltage values are processed by a neural network trained on a data set generated by finite element software. The resulting electric contact conductivity distribution is used to determine the contact force distribution, taking into account the equilibrium of forces and moments. The results are also checked by available alternative experimental methods. [ABSTRACT FROM AUTHOR]

The unsafe zone in machining is a region of the parameter space where steady-state cutting operations may switch to regenerative chatter for certain perturbations, and vice versa. In the case of milling processes, this phenomenon is related to the existence of an unstable quasi-periodic oscillation, the in-sets of which limit the basin of attraction of the stable periodic motion that corresponds to the chatter-free cutting process. The mathematical model is a system of time-periodic nonlinear delay differential equations. It is studied by means of a nonlinear extension of the semidiscretization method, which enables the estimation of the parameter ranges where the unsafe (also called bistable) zones appear. The theoretical results are checked with thorough experimental work: first, step-by-step parameter variations are adapted to identify hysteresis loops, then harmonic burst excitations are used to estimate the extents of the unsafe zones. The hysteresis loops are accurately distinguished from the dynamic bifurcation phenomenon that is related to the dynamic effect of slowly varying parameters. The experimental results confirm the existence of the bistable parameter regions. This article is part of the theme issue 'Nonlinear dynamics of delay systems'. [ABSTRACT FROM AUTHOR]

This work presents dynamic finite element simulations of various pellet impacts in order to investigate their applicability during impulse excitation in modal analysis. Compared to the classical impulse excitation with modal hammer, the approach of pellet shots provides shorter impact time and reduces the multi-hitting effect leading a wider relevant frequency range of the frequency response function (FRF). However, the estimation of the contact characteristics requires the complete understanding of the material behaviour of the investigated commercial airsoft pellets and steel bearing balls. The behaviour of the airsoft pellet shows elastic, yielding and viscous properties during the impact, whereas the deformation of the bearing ball is mostly elastic. The commercial FE software ABAQUS offers the two-layer viscoplastic model to capture the complex material behaviour of the airsoft pellet. Based on the FE simulations of both pellets an estimation is provided for the relevant frequency range, where the force spectrum is considered to be mostly constant and the FRF is proportional with the FFT of the output signal. In order to highlight the benefits and the applicability of the excitation with pellet shots experimental work has been carried out. The comparison of the measured FRFs shows that using this novel approach wide relevant frequency domain can be reached with excellent accuracy and repeatability, which could benefit in the modal analysis of structures with high natural frequencies. [ABSTRACT FROM AUTHOR]

Chatter detection is usually based on the analysis of measured signals captured during cutting processes. These techniques, however, often give ambiguous results close to the stability boundaries, which is a major limitation in industrial applications. In this paper, an experimental chatter detection method is proposed based on the system’s response for perturbations during the machining process, and no system parameter identification is required. The proposed method identifies the dominant characteristic multiplier of the periodic dynamical system that models the milling process. The variation of the modulus of the largest characteristic multiplier can also be monitored, the stability boundary can precisely be extrapolated, while the manufacturing parameters are still kept in the chatter-free region. The method is derived in details, and also verified experimentally in laboratory environment. [ABSTRACT FROM AUTHOR]

This paper presents new observations of delayed AD (acceleration-derivative) controller in active vibration control and in bifurcation control of a Duffing oscillator. Based on the stability analysis of the linear delayed oscillator, it is found that combination of the two delays in acceleration feedback and velocity feedback has a significant influence on the stable region in the parameter plane of the gains. By calculating the real part of the rightmost characteristic roots of the controlled oscillator with fixed delays, it is shown that a delayed acceleration feedback with positive gain can work much better than the corresponding delayed negative acceleration feedback, which is used in classic control theory. For given feedback gains, by calculating the critical delay values, it is shown that a delayed positive acceleration feedback can result in a much larger stable delay interval than the corresponding delayed negative acceleration feedback does. As an application of these results to a delayed Duffing oscillator with acceleration-derivative feedback, a delayed positive acceleration feedback can be well used to postpone the occurrence of Hopf bifurcation in the delayed nonlinear oscillators. [ABSTRACT FROM AUTHOR]

This paper presents an application of the spectral element method for the stability analysis of regenerative machine tool chatter models in milling operations. An extension of the spectral element method is introduced in order to handle the discontinuities in the cutting force in an efficient way. The efficiency of the method is demonstrated on some well-known machine tool chatter models taken from the literature. Efficiency is characterized by the computational time, the convergence of the stability boundaries, and the convergence of critical characteristic multipliers. Results show that compared to the most widespread methods in machining literature, the spectral element method provides significant improvements in computational time while maintaining high accuracy levels. [ABSTRACT FROM AUTHOR]

In this work we present a quantitative measurement-based method to describe the stability behaviour of a periodic dynamical system. In-process response for impulse during milling is analysed to provide operational stability prediction. The proposed method combines chatter detection techniques with the theory of time-periodic delay differential equations applied for general milling operations. Signal processing based on dynamic modal decomposition approach not only presents qualitative properties (like stability/instability) but also quantifies a measure of stability through the determination of the Floquet multipliers. The corresponding monodromy operator of the milling process is approximated from the measured system's response during machining operation. By changing the technological parameters, the variation of the modulus of the Floquet multipliers can be monitored. The stability limit can precisely be interpolated with the unitary multiplier; furthermore, the stability limit can be extrapolated while the manufacturing parameters remain in the chatter-free region. The presented approach is validated by numerical results and laboratory tests. • Measurement-based method to quantify stability of milling operation. • In-process impulse response is analysed to provide operational stability prediction. • It combines chatter detection techniques with the theory of time-periodic systems. • Extrapolation of stability limit opens ways for efficient cutting parameter optimization. • Results are supported by theoretical, numerical and experimental parts. [ABSTRACT FROM AUTHOR]

Abstract: The large-amplitude motions of a one degree-of-freedom model of orthogonal cutting are analysed. The model takes the form of a delay differential equation which is non-smooth at the instant at which the tool loses contact with the workpiece, and which is coupled to an algebraic equation that stores the profile of the cut surface whilst the tool is not in contact. This system is approximated by a smooth delay differential equation without algebraic effects which is analysed with numerical continuation software. The grazing bifurcation that defines the onset of chattering motion is thus analysed as are secondary (period-doubling, etc.) bifurcations of chattering orbits, and convergence of the bifurcation diagrams is established in the vanishing limit of the smoothing parameters. The bifurcation diagrams of the smoothed system are then compared with initial value simulations of the full non-smooth delay differential algebraic equation. These simulations mostly validate the smoothing technique and show in detail how chaotic chattering dynamics emerge from the non-smooth bifurcations of periodic orbits. [ABSTRACT FROM AUTHOR]

In hardware-in-the-loop (HIL) experimental environment, a local softening character of the emulated cutting force is observed during the emulation of turning, which affects the stability properties of the process. The real workpiece is substituted by a dummy one that is clamped to the real main spindle. It is excited in the lateral direction by an electromagnetic actuator. The position of the dummy workpiece is monitored by contactless laser-based sensors to close the feedback loop. The previous and the present position of the workpiece is stored to attain the effect of surface regeneration. The desired cutting force characteristic is calculated by means of a high performance real-time computer. The experimental results gained for the linear loss of stability of the process and for the spindle speed dependent dynamics leads to the conclusion that the dominant frequency decreases as the virtual depth of cut and thus the emulated cutting force increases. This is identified for a wide range of real spindle speeds and virtual depth of cuts. The measurement results are supported by theoretical stability analysis and the variation of the dominant frequency is tracked by means of the unexpected local softening nonlinearity of the electromagnetic actuator emulating the real cutting forces, which are also confirmed analytically. These results are needed in future development of a portable HIL system, to analyse chatter phenomena in the presence of cutting force nonlinearities and to test specific cutting tools before prototyping. Image 1 • Stability of machining processes is investigated in hardware-in-the-loop setup. • The chatter frequency is influenced by the nonlinearity of the actuator force. • The digressive character of the setup is revealed by stability tests. [ABSTRACT FROM AUTHOR]

The prediction of chatter-free machining parameters is not reliable for industrial applications without guaranteed robustness against modeling uncertainties. Measurement inaccuracies, fitting uncertainties, simplifications and modeling errors typically lead to a mismatch between the mathematical model and the real physical system. This paper presents the robust stability analysis of milling operations based on a pseudospectral approach to take into account the effect of bounded parametric uncertainties both in the cutting coefficients and in the modal parameters. In order to make the predictions more accurate, the operational modal analysis of the spindle during rotation was conducted. The natural frequencies and damping ratios of the dominant vibration modes were identified from the impact tests of the rotating tool at different spindle speeds. The uncertainties of the fitted parameters were included in the computation of the pseudospectral radius of the monodromy operator of the time-periodic system. The solver is tested in a case study and experimental chatter tests are also included for demonstration purposes. • A robust pseudospectral method is presented for milling operations considering uncertainties in both modal parameters and cutting coefficients. • The stability analysis is based on a collocation method using Chebyshev polynomials. • Modal parameters of the rotating spindle are determined by operational modal analysis. • A case study with experimental chatter tests is included. [ABSTRACT FROM AUTHOR]

Orthogonal planing experiments are conducted with high-speed camera recordings and simultaneous cutting force measurements in order to analyze chip formation during machine tool vibrations. By means of carefully designed periodic forcing of the cutting tool, non-stationary cutting experiments are performed including wave generation, wave removal and wave-on-wave cutting, which are then compared to stationary cutting tests. The experiments are performed to address how the cutting force is affected by the chip thickness variation, the surface waviness and the fluctuation of the cutting direction. The results are used to assess some theoretical models that involve shear angle variation and chip segmentation. • Non-stationary cutting experiments are performed by orthogonal planing. • Wave generation, wave removal and wave-on-wave cutting are investigated. • High-speed camera recordings and simultaneous cutting force measurements are evaluated. • The effects of chip thickness variation, surface waviness and cutting direction fluctuation are analyzed. [ABSTRACT FROM AUTHOR]

Cutting capacity can be seriously limited in heavy duty face milling processes due to self-excited structural vibrations. Special geometry tools and, specifically, variable pitch milling tools have been extensively used in aeronautic applications with the purpose of removing these detrimental chatter vibrations, where high frequency chatter related to slender tools or thin walls limits productivity. However, the application of this technique in heavy duty face milling operations has not been thoroughly explored. In this paper, a method for the definition of the optimum angles between inserts is presented, based on the optimum pitch angle and the stabilizability diagrams. These diagrams are obtained through the brute force (BF) iterative method, which basically consists of an iterative maximization of the stability by using the semidiscretization method. From the observed results, hints for the selection of the optimum pitch pattern and the optimum values of the angles between inserts are presented. A practical application is implemented and the cutting performance when using an optimized variable pitch tool is assessed. It is concluded that with an optimum selection of the pitch, the material removal rate can be improved up to three times. Finally, the existence of two more different stability lobe families related to the saddle-node and flip type stability losses is demonstrated. [ABSTRACT FROM AUTHOR]