Janez Gradišek

Machine Tool Chatter and Surface Location Error in Milling Processes

A two degree of freddom model of the milling process is investigated. The governing equation of motion is decomposed into two parts: an ordinary differential equation describing the periodic chatter-free motion of the tool and a delay-differential equation describing chatter. The stability chart is derived by using the semi-discretization method for the delay-differential equation corresponding to the chatter motion. The periodic chatter-free motion of the tool and the associated surface location error (SLE) are obtained by a conventional solution technique of ordinary differential equations. It is shown that the SLE is large at the spindle speeds where the ratio of the dominant frequency of the tool and the tooth passing frequency is an integer. This phenomenon is explained by the large amplitude of the periodic chatter-free motion of the tool at these resonant spindle speeds. It is shown that large stable depths of cut with a small SLE can still be attained close to the resonant spindle speeds by using the SLE diagrams associated with stability charts. The results are confirmed experimentally on a high-speed milling center.

Nonlinear Dynamics of High-Speed Milling—Analyses, Numerics, and Experiments

High-speed milling is often modeled as a kind of highly interrupted machining, when the ratio of time spent cutting to not cutting can be considered as a small parameter. In these cases, the classical regenerative vibration model, playing an essential role in machine tool vibrations, breaks down to a simplified discrete mathematical model. The linear analysis of this discrete model leads to the recognition of the doubling of the so-called instability lobes in the stability charts of the machining parameters. This kind of lobe-doubling is related to the appearance of period doubling vibrations originated in a flip bifurcation. This is a new phenomenon occurring primarily in low-immersion high-speed milling along with the Neimark-Sacker bifurcations related to the classical self-excited vibrations or Hopf bifurcations. The present work investigates the nonlinear vibrations in the case of period doubling and compares this to the well-known subcritical nature of the Hopf bifurcations in turning processes. The identification of the global attractor in the case of unstable cutting leads to contradiction between experiments and theory. This contradiction draws the attention to the limitations of the small parameter approach related to the highly interrupted cutting condition.

Analysis of acoustic emission signals and monitoring of machining processes

Monitoring of a machining process on the basis of sensor signals requires a selection of informative inputs in order to reliably characterize and model the process. In this article, a system for selection of informative characteristics from signals of multiple sensors is presented. For signal analysis, methods of spectral analysis and methods of nonlinear time series analysis are used. With the aim of modeling relationships between signal characteristics and the corresponding process state, an adaptive empirical modeler is applied. The application of the system is demonstrated by characterization of different parameters defining the states of a turning machining process, such as: chip form, tool wear, and onset of chatter vibration. The results show that, in spite of the complexity of the turning process, the state of the process can be well characterized by just a few proper characteristics extracted from a representative sensor signal. The process characterization can be further improved by joining characteristics from multiple sensors and by application of chaotic characteristics.

Automatic chatter detection in grinding

Two methods for automatic chatter detection in outer diameter plunge feed grinding are proposed. The methods employ entropy and coarse-grained information rate (CIR) as indicators of chatter. Entropy is calculated from a power spectrum, while CIR is calculated directly from fluctuations of a recorded signal. The methods are verified using signals of the normal grinding force and RMS acoustic emission. The results show that entropy and CIR perform equally well as chatter indicators. Based on the normal grinding force, they detect chatter in its early stage, while only cases of strong chatter are detected based on RMS acoustic emission.

A New Method for Chatter Detection in Grinding

Abstract A new method for automatic chatter detection in outer-diameter grinding is proposed which exploits significant changes in grinding dynamics caused by the onset of chatter. The method is based on monitoring of a non-linear statistic called the coarse-grained entropy rate. The entropy rate is calculated from the fluctuations of the normal grinding force. Values of the entropy rate close to zero are typical of chatter, whereas larger values are typical of chatter-free grinding. If the entropy rate is normalized, a threshold value can be set which enables automatic distinction between chatter-free grinding and chatter.

A chaotic cutting process and determining optimal cutting parameter values using neural networks

A model of an orthogonal cutting system is described as an elastic structure deformable in two directions. In the system, a cutting force is generated by material flow against the tool. Nonlinear dependency of the cutting force on the cutting velocity can cause chaotic vibrations of the cutting tool which influence the quality of a manufactured surface. The intensity and the characteristics of vibrations are determined by the values of the cutting parameters. The influence of cutting depth on system dynamics is described by bifurcation diagrams. The properties of oscillations are illustrated by the time dependence of tool displacement, the corresponding frequency spectra and phase portraits. The corresponding strange attractors are characterized by correlation dimension. The vibrations are characterized by the maximum Lyapunov exponent. The manufactured surface at the first cut is taken as the incoming surface in the second cut, thus incorporating the influence of the rough surface in the model. Again, bifurcation diagrams, the correlation dimension and the maximum Lyapunov exponent are employed to describe the effects of parametrical excitation on the cutting dynamics. A cost function is defined which describes the dependence of the cutting performance on cutting depth. The cost function is empirically modeled using a self-organizing neural network. A conditional average estimator is applied to determine the optimal value of the cutting depth applicable as a control variable of the cutting process.

On Stability and Dynamics of Milling at Small Radial Immersion

Stability and dynamics of milling at small radial immersion are investigated. Stability charts are predicted by the Semi Discretization method. Two types of instability are predicted corresponding to quasiperiodic and periodic chatter. The quasiperiodic chatter lobes are open and distributed along the spindle speed axis only, while the periodic chatter lobes are closed curves distributed in the plane of spindle speed and depth of cut. Experiments confirm the stability predictions, revealing the two principal types of chatter, the bounded periodic chatter lobes, and some special chatter cases. The recorded tool deflections in these cutting regimes are studied. The experiments also show that the modal properties of a slender tool may depend on spindle speed.

On stability prediction for low radial immersion milling

ABSTRACT Stability boundaries for milling are predicted by the zeroth-order approximation (ZOA) and the semi-discretization (SD) methods. For high radial immersions, the methods predict similar stability boundaries. As radial immersion is decreased, the disagreement between the predictions of the two methods grows considerably. The most prominent difference is an additional type of instability predicted only by the SD method. The experiments confirm the predictions of the SD method. Three different types of tool motion are observed: periodic chatter-free, quasiperiodic chatter, and periodic chatter motion. Tool displacements recorded during each of the three motion types are analyzed.

Analysis of data from periodically forced stochastic processes

A method for analysis of periodically-forced stochastic processes is presented. The method enables extraction of the deterministic and random components of process dynamics from measured data, provided the forcing frequency is known and the data is sampled stroboscopically. The method is illustrated by three examples employing synthetic and experimental data.

MACHINE TOOL CHATTER AND SURFACE QUALITY IN MILLING PROCESSES

Two degree of freedom model of milling process is investigated. The governing equation of motion is decomposed into two parts: an ordinary differential equation describing the stable periodic motion of the tool and a delay-differential equation describing chatter. Stability chart is derived by using semidiscretization method for the delay-differential equation corresponding to the chatter motion. The stable periodic motion of the tool andthe associatedsurface locationerror are obtainedby a conventional solution technique of ordinary differential equations. Stability chart and surface location error are determined for milling process. It is shown that at spindle speeds, where high depths of cut are available through stable machining, the surface location error is large. The phase portrait of the tool is also analyzed for different spindle speeds. Theoretical predictions are qualitatively confirmed by experiments.