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Abstarct: This work presents a theoretical framework for the safety‐critical control of time delay systems. The theory of control barrier functions, that provides formal safety guarantees for delay‐free systems, is extended to systems with state delay. The notion of control barrier functionals is introduced, to attain formal safety guarantees by enforcing the forward invariance of safe sets defined in the infinite dimensional state space. The proposed framework is able to handle multiple delays and distributed delays both in the dynamics and in the safety condition, and provides an affine constraint on the control input that yields provable safety. This constraint can be incorporated into optimization problems to synthesize pointwise optimal and provable safe controllers. The applicability of the proposed method is demonstrated by numerical simulation examples. [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]

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]

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]

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]