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1

Multiple regenerative effect governing chatter behaviour after onset

Sato H.

Journal of Machine Engineering

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2013

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Vol. 13, No. 3

51--76

EN

Chatter is the self-excited vibration that occurs during cutting. The entire structure of a self-excited vibration comprises two core mechanisms, i.e., stability limit and sustained vibration with finite amplitude after onset. The latter mechanism remained unnoticed until the discovery of the multiple regenerative effect (MRE) in 1980. However, its effects have not yet been recognized correctly. This paper summarizes the problems that could be resolved by considering the MRE in the analysis from the theoretical and practical viewpoints. In conventional stability limit analyses,tool traces never intersect; however, after the onset of chatter in an actual system, traces immediately intersect. This resultsin tool-workpiece separation, chip thickness variation during the separation period, and chip breakage. A solution for equation of motion considering the MRE agrees well with chatter behaviour in actual applications. In addition, the solution yields the phase relationship between the displacement of work motion and the cutting force, although this relationship is not considered in the equation of motion. Further, the relationship between the penetrating cutting speed and the resistive force, confirmed experimentally, is introduced in equation of motion, which verifies the widening of the stability region at low cutting speeds.

2

Lie tensor product manifolds

Sato H., Yamaguchi K.

Demonstratio Mathematica

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2012

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Vol. 45, nr 4

909-927

EN

We study the geometric structures of parabolic geometries. A parabolic geometry is defined by a parabolic subgroup of a simple Lie group corresponding to a subset of the positive simple roots. We say that a parabolic geometry is fundamental if it is defined by a subset corresponding to a single simple root. In this paper we will be mainly concerned with such fundamental parabolic geometries. Fundamental geometries for the Lie algebra of (…) type are Grassmann structures. For (…) types, we investigate the geometric feature of the fundamental geometries modeled after the quotients of the real simple groups of split type by the parabolic subgroups. We name such geometries Lie tensor product structures. Especially, we call Lie tensor metric structure for (…) or (…) type and Lie tensor symplectic structure for (…) type. For each manifold with a Lie tensor product structure, we give a unique normal Cartan connection by the method due to Tanaka. Invariants of the structure are the curvatures of the connection.

3

Growth and scintillation propertiesof Ce-doped PrF₃ single crystals

Kamada K., Yoshikawa A., Satonaga T., Sato H., Beitlerova A., Nikl M., Solovieva N., Fukuda T.

Opto-Electronics Review

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2004

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Vol. 12, No. 4

365-368

EN

The scintillation characteristics of the Ce-doped PrF₃ single crystals have been studied to find out their potential as for heavy scintillators. Crystal growth was performed in a vacuum-tight micro-pulling down (µ-PD) system. PrF₃ crystal was prepared with various concentrations (0, 0.1, 0.5, 1, 3, 5, 10, 20, 60, 80, 100%) of Ce³⁺. The crystals were transparent (CeF₃) or of greenish colour, 3 mm in diameter and 15-50 mm in length. Neither visible inclusions nor cracks were observed. At room temperature, the radio- and photoluminescence spectra and the decay kinetics were measured for the sample set.