Sumio Yamamoto

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.

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 .

Optical method of measuring angular displacement using two photodiode arrays

A method of measuring angular displacement is investigated that uses two pairs of photodiode arrays arranged in a square and crossed linear images produced with two cylindrical mirrors. According to this method the measurement error can be greatly reduced even when inclination of the rotation axis exists.

Light-beam trajectory propagating in a parabolic-index fiber with random radial dielectric-constant gradient

The trajectory of a light beam is investigated by using the autocorrelation function of the random fluctuations of the radial dielectric-constant gradient ∊2(z) in a parabolic-index fiber. In the limiting case, the influences of ∊2(z) on the beam trajectory are discussed using an approximation.

Influence of randomness of the refractive-index distribution parameter on the trajectory in a GRIN-rod lens array.

To study the influence of scattering of the distribution parameter in a gradient-index rod lens on ray tracing by statistical linearization, a method of obtaining the mean and variance is presented. According to examples studied, it is found that the ray trajectory is remarkably affected by the amount of scattering of the parameter.

Measurement of activated sludge coagulation based on image processing

This paper proposes a new method for the evaluation of activated sludge coagulation based on image processing. In order to evaluate coagulation patterns, we employ a technique based on the fractal dimension. The result shows that the coagulation process can be evaluated by the variance of fractal dimensions.