Keijin Sato

Analysis of chatter suppression in vibration cutting

Abstract The occurrence of chatter is strongly influenced by the tool geometry in conventional cutting. Therefore, the tool geometry is regarded as a very important factor. On the other hand, it is known that vibration cutting is capable of cutting hardened steels. However, the theoretical explanation for finish hard-cutting with vibration cutting is still unknown. In this paper, experimental investigations show that chatter is effectively suppressed without relying on the tool geometry, and the work displacement amplitudes are reduced from a wide range of 10–102 μm to the range of 3–5 μm by applying vibration cutting. In order to study the precision machining mechanism of vibration cutting, a new cutting model which contains a vibration cutting process is proposed. Simulations of the chatter model exhibit the main feature of chatter suppression in vibration cutting. The simulation results are in good agreement with the measurement values and accurately predict the work displacement amplitudes of vibration cutting.

The effect of tool nose radius in ultrasonic vibration cutting of hard metal

A tool edge with a small nose radius can alleviate the regenerative chatter. In general, it is important for conventional cutting to use the smallest possible tool nose radius. However, a sharp tool shape has an adverse effect on tool strength and the instability of machining process still occurs. Previous researches have shown that vibration cutting has a higher cutting stability as compared with conventional cutting. In the present paper, the influence of tool nose radius on cutting characteristics including chatter vibration, cutting force and surface roughness is investigated by theory. It is found from the theoretical investigation that a steady vibration created by motion between the tool and the workpiece is still obtained even using a large nose radius in vibration cutting. This article presents a vibration cutting method using a large nose radius in order to solve chatter vibration and tool strength problem in hard-cutting. With a suitable nose radius size, experimental results show that a stable and a precise surface finish is achieved.

Bifurcation sets and chaotic states of a gear system subjected to harmonic excitation

The gear dynamics is described by a time-varying nonlinear differential equation due to the time dependence of tooth stiffness and backlash. To discuss whether or not distinctive new phenomena occur in the gear system with its backlash and time-variable characters is an important and interesting problem from a practival viewpoint of estimating the dynamic load or gear noise as well as an academic one of contribution to nonlinear mechanics. In this study, the bifurcation sets of periodic solutions under some gear parameters are obtained and chaotically transitional phenomena are investigated by using the Poincaré map.

The non-linear phenomena in vibration cutting system: The establishment of dynamic model

Abstract It is well-known that vibration cutting is an effective method to cut materials with accuracy. However, it often suffers from unevenness of surface roughness caused by the non-linear vibration phenomena in tool–work vibration system. To solve this problem, we propose a vibration cutting model described by two-dimensional differential equations to analyze the non-linear phenomena. This non-linear model reproduces the basic features of the real vibration cutting systems, that is, the reduction of the cutting force and the displacement of work by pulsing of the cutting force. In this report, our experiment shows that various non-linear phenomena exist in the vibration cutting system. Our non-linear model for the vibration cutting produce behaviors which qualitatively agree with these various non-linear phenomena. These behaviors can be classified by the Lyapunov exponents.

Characterization of reverse rotation in chaotic response of mechanical pendulum

Characterization of reverse rotation in chaotic responses of a parametrically excited damped pendulum is experimentally investigated. For this purpose, a statistical mechanical analysis by dynamical structure functions is used. The results showed that the difference of the two chaotic responses of the pendulum, one stably keeping a direction of rotation and the other having the possibility of reverse rotations that randomly arise in the response, can be characterized by a peak at negative q in q-weighted variance, and that the peak may act as an identifier of the possibility of the reverse rotation in the chaotic response of the pendulum.

Optical method of measuring angular displacement when the axis of rotation inclines.

An optical method is studied which permits one to measure the angular displacement using a pair of 2-D position sensitive detectors (PSD) and a microcomputer, even if the axis of rotation inclines. From the coordinates of two light spots imaged on the PSD, which are reflected with small double mirrors pasted on the object, the angular displacement and inclination are obtained. According to the experimental results and the spherical trigonometric estimation, it is possible to measure the angle in reciprocal movement of ~200 Hz, and to speed up the procedure tenfold.

A study on lateral impact of Timoshenko beam

The impact of solid bodies occurs in machines and it is the primary reason of noise and vibration. To understand the quantitative characteristics of noise and vibration, it is necessary to understand the motion of solid bodies, especially the deformation of the surface. In this study the authors analyze theoretically and numerically the impact phenomena on a falling body of a Timoshenko beam. Also we have compared a Bernoulli-Euler hinged-hinged beam and a Timoshenko hinged-hinged beam with regard to the impact of a cylindrical body on each of them. The conclusions are as follows: (1) the impact force, the deflection and the bending moment of the Timoshenko beam, and the displacement of the falling body can be calculated precisely according to the equations derived from this study, (2) the examination of the Timoshenko beam are compared with that of the Bernoulli-Euler beam, (3) the Timoshenko beam deflections with the passage of time are illustrated.

Characterization of chaotic vibration without system equations

Abstract This paper studies a method that enables us to get information about how a chaotic system behaves as its parameters are changed. This method is an application of theory based on statistical mechanics developed by Tomita and others. In a previous paper, in order to apply the theory to time series analysis, we proposed a method that can calculate quantities based on statistical mechanics, rather than on system equations. The results showed that our method is effective for characterization of non-linear systems whose equations are not known. This paper focuses on effect of instrumental noise on our method because it is a significant problem if our method is used for time series analysis. The results showed that a q β -phase transition may become invalid as an identifier of chaos or disappears altogether.

Optical method of measuring angular displacement using a 2-D charge coupled device

We investigated a quick noncontact method of measuring angular displacement with a simple system comprising a 2-D CCD and a personal computer. According to this method the angular displacement can be measured even when the rotational axis is not known, and even when the system moves parallel to the plane.

Optical method of measuring angular displacement using a diffraction pattern

We investigate a method of measuring the angular displacement of an aperture when the diffraction pattern rotates. The data that are on a rectangular coordinate are transformed into the data on a polar coordinate. We calculate a cross-correlation function between the diffraction pattern that is rotated and the reference pattern. When the angular displacement is within +/-5 degrees , the error is <0.050. Then, we calculated the angular displacement of the pattern on a spherical coordinate system by personal computer simulation. Consequently, when the azimuth and the elevation of its rotation axis are within +/-6 degrees , the error is <0.1 degrees .