Stability analysis of titanium alloy milling by multiscale entropy and Hurst exponent

Eur. Phys. J. Plus (2015) 130: 194 DOI 10.1140/epjp/i2015-15194-1 THE EUROPEAN PHYSICAL JOURNAL PLUS Regular Article Stability analysis of titanium alloy milling by multiscale entropy and Hurst exponent Rafal Rusinek and Marek Borowieca Department of Applied Mechanics, Lublin University of Technology, Nadbystrzycka 36, 20-618, Lublin, Poland Received: 22 April 2015 / Revised: 28 August 2015 Published online: 7 October 2015 c The Author(s) 2015. This article is published with open access at Springerlink.com  Abstract. This paper discusses the problem of stability in a milling process for titanium super-alloy Ti6242. The phenomenon of chatter vibration is analysed by the multiscale entropy method and Hurst exponent. Although this problem is often considered based on stability lobe diagrams, theoretical findings do not always agree with experimental results. First, a stability lobe diagram is created based on parameters determined by impact testing. Next, cutting forces are measured in an experiment where the axial cutting depth is gradually increased. Finally, the obtained experimental signals are investigated with respect to stability using the multiscale entropy method and Hurst exponent. 1 Introduction The problem of stability in cutting and milling processes, particularly under high speed machining (HSM) conditions, is very important in engineering practice. Instability is caused by chatter phenomena which can be generated by regenerative and frictional mechanisms [1]. The regenerative chatter is one of the most common in the literature. However, Wiercigroch et al. [2,3], Lipski et al. [4], Rusinek et al. [5,6] show that the frictional effect is also important because it can produce the so-called frictional (primary) chatter and can even lead to chaotic vibrations [7,8]. Chatter vibrations generated in cutting operations are undesired because they can deteriorate the surface of a finished product, shorten tool life or even destroy the tool or the work piece. This, combined with the properties of hard, difficult-tomachine materials like titanium alloy, poses serious problems in machining [9–13]. Specific properties of titanium alloys such as high strength and their resistance to heat and corrosion are desirable in the civil and military aviation industry to produce extremely loaded components. Therefore, these alloys are often applied in the production of aircrafts, racing cars, and many other devices. Given the demand for steadily growing productivity, there is a tendency to increase cutting parameters such as cutting speed and feed rate in manufacturing processes. This, however, can lead to self-excited chatter vibrations generated by a regenerative mechanism. To avoid regenerative chatter, the cutting parameters must be defined properly. To this end, the so-called stability lobe diagrams (SLDs) are created, usually based on modal parameters of the toolholder system, where a rotational speed and depth of cut determine conditions of stable cutting. An advantage of the SLD technique is that it can predict an unstable region of the cutting parameters prior to machining; however, its correctness depends on the accuracy of the modal test. From another point of view, the cutting process can be controlled online by measuring forces, displacements or accelerations in order to prevent instabilities from occurring in a system. Therefore, some researchers measure acoustic emission during the cutting process to obtain experimental SLDs, e.g. in [14]. Others use the recurrence plot (RP) technique [15–17], Hilbert-Huang transform (HHT) [18], flickernoise spectroscopy [19] and the Hurst exponent [20]. In some cases, however, the dynamics of a system requires the use of a multiscale approach. This is particularly true with complex systems which usually exhibit nonlinear behaviour. For this reason, such systems can be best analysed by the increasingly popular sample entropy method [21–23]. This analysis approach provides a relative level of complexity for measured finite length time signals. The method is widely used in medicine diagnostics [24], for measuring physiologic output signals, particularly blood pressure, heart rate or electrical brain activity [25]. Also, it can be used for detecting early symptoms of cardiac arrhythmias [26]. Apart from the sample entropy method, complex behaviours of mechanical systems can also be analysed by multiscale entropy. a e-mail: Page 2 of 8 Eur. Phys. J. Plus (2015) 130: 194 Fig. 1. Scheme of the experimental setup. The authors of the paper [27] adopted this method to analyse the time series of a bistable laminate plate. They examined its dynamic response, showing the presence of single well and snap-through vibrations of both periodic and chaotic character. The authors of other papers, [15,17], used the multiscale entropy analysis (M SE) to observe fluctuations describing chatter in the milling process of a composite material. This approach was also adopted for time series analysis of vehicle suspension [28,29]. The M SE proved useful in identifying system behaviour during driving tests. This paper uses the composite multiscale entropy analysis (CM SE) [30,31] to investigate the milling of the titanium alloy. This method is applied to monitor complex dynamics of machining, particularly with respect to chatter phenomena. Here, the stability of the milling process for titanium alloy Ti6242 is investigated by two approaches: multiscale entropy and Hurst exponent analysis. With these methods, chatter vibrations in machining can be predicted just before they occur. 2 Experiment The experimental investigations are conducted on a titanium alloy Ti6242 using a Haas MiniMill CNC milling machine. The tests are performed under laboratory conditions at the L  ódź University of Technology. Presented schematically in fig. 1, the experimental setup consists of two parts: a modal analysis system (left) and a force measurement system (right). The former, which is used to measure viscoelastic properties of the machine-tool system, consists of a PCB 086C03 modal hammer, a PCB 352B10 accelerometer and an NI9234 data acquisition card (DAQ). The latter is used to measure three components (Fx , Fy and Fz ) of the resultant cutting forces and torque (Mz ) by means of a Kistler 9123C piezoelectric rotating dynamometer. The dynamometer is connected to a Kistler 5223 signal conditioner and a 2855A4 data acquisition card. Both experimental rigs are integrated in computer system and controlled by the DynoWare software to record measured signals. The measurements are taken in two steps. First, a single point impact test is performed to determine stiffness, natural vibration frequency and damping ratio of the spindle-tool system in order to predict regions of stable milling. To this end, the modal hammer is used to excite the tool and then the output signal is measured by a low mass accelerometer mounted at the tip of the tool. Next, the modal parameters for x and y (...truncated)