Permutation Entropy Based Speckle Analysis in Metal Cutting

摘要

Machine tool chatter is an unfavorable phenomenon during metal cutting, which results in heavy vibration of cutting tool. With increase in depth of cut the cutting regime changes from chatter- free cutting to one with chatter. In this paper, we propose the use of permutation entropy (PE), a conceptually simple and computationally fast measure to detect the onset of chatter from the time series generated using laser speckle pattern recorded using Charge Couple Device (CCD) camera. Laser speckle is an interference pattern produced by light reflected or scattered from different parts of the illuminated surface. It is the superposition of many wave fronts with random phases, scattered from different parts of the rough surface. If a speckle pattern is produced by coherent light incident on a rough surface, then surely the speckle pattern, or at least the statistics of the speckle pattern, must depend upon the detailed surface properties. Therefore we propose PE as an ideal measure, which can efficiently distinguish regular and complex nature of any signal, to extract information about the roughness of the reflecting surface. In the present study two work pieces, one taper cut and one step cut are machined to form cylindrical pieces, by continuously varying the depth of cut. As the depth of cut increases the surface finish is expected to deteriorate, mainly due to the onset of chatter vibrations. To analyze the surface texture characteristics, the speckle pattern is obtained by illuminating this curved surface using a collimated laser beam (5mW Diode Laser at 676nm wavelength.). The laser beam is made to incident obliquely to the curved surface of the work piece, and the speckle pattern is recorded using a CCD camera. The beam is scanned along the axis of the work-piece and the speckle pattern is recorded at different regions at constant intervals. A time series is generated from the speckle data and analyzed using PE. Permutation entropy is a complexity measure suitable for regular, chaotic, noisy or reality-based signals. PE work efficiently well even in the presence of dynamical and/or observational noise. Unlike other nonlinear techniques PE is easier and faster to calculate as the reconstruction of the state space from time series is not required. Increasing value of PE indicates increase in complexity of the system dynamics. PE of the time series is calculated using a one-sample shift sliding window technique. PE of order n>=2 is calculated from Shanon entropy where the sum runs over all n! permutations of order n. PE gives the information contained in comparing n consecutive values of the time series. The calculation of PE is fast and robust in nature. Under situations where the data sets are huge and there is no time for preprocessing and fine-tuning, PE can effectively detect dynamical changes of the system. This makes PE an ideal choice for online detection of chatter, which is not possible with other conventional methods.