CHAOTIC DYNAMICS OF REPEATED IMPACTS IN VIBRATORY BOWL FEEDERS

The vibratory bowl feeder is widely used to convey small engineering parts, and can be considered as a typical non-linear dynamic system experiencing repeated impacts with friction. This paper presents a simplified model and analysis for the dynamic behavior of a single part on the vibrating track of the bowl feeder. While the previous studies are restricted to the sliding regime, the presented analysis is focused on the hopping regime where the high conveying rate is available. The periodic and chaotic regions in the hopping regime are identified through numerical simulation and experimental analysis. It is verified experimentally that the conveying rate in the chaotic region is roughly independent of variations of external parameters. The dynamic effects from the variation of several physical parameters are examined and the important features for the effective design of the vibratory feeder are presented. This research holds much potential for leverage over design problems of a wide range of mechanisms and tools with repeated collisions.     

FREE VIBRATION ANALYSIS OF A SPINNING FLEXIBLE DISK-SPINDLE SYSTEM SUPPORTED BY BALL BEARING AND FLEXIBLE SHAFT USING THE FINITE ELEMENT METHOD AND SUBSTRUCTURE SYNTHESIS

Free vibration of a spinning flexible disk-spindle system supported by ball bearing and flexible shaft is analyzed by using Hamilton's principle, FEM and substructure synthesis. The spinning disk is described by using the Kirchhoff plate theory and von Karman non-linear strain. The rotating spindle and stationary shaft are modelled by Rayleigh beam and Euler beam respectively. Using Hamilton's principle and including the rigid body translation and tilting motion, partial differential equations of motion of the spinning flexible disk and spindle are derived consistently to satisfy the geometric compatibility in the internal boundary between substructures. FEM is used to discretize the derived governing equations, and substructure synthesis is introduced to assemble each component of the disk-spindle-bearing-shaft system. The developed method is applied to the spindle system of a computer hard disk drive with three disks, and modal testing is performed to verify the simulation results. The simulation result agrees very well with the experimental one. This research investigates critical design parameters in an HDD spindle system, i.e., the non-linearity of a spinning disk and the flexibility and boundary condition of a stationary shaft, to predict the free vibration characteristics accurately. The proposed method may be effectively applied to predict the vibration characteristics of a spinning flexible disk-spindle system supported by ball bearing and flexible shaft in the various forms of computer storage device, i.e., FDD, CD, HDD and DVD.     

First observation of double-twisted helical structure in a banana-shaped achiral molecule

The double-twisted helical structure was confirmed for the first time for the smectic phase of a banana-shaped molecular system from observation of the microscopic pattern. Optically polarized microscopic textures and phase transitions of 1,3-phenylene bis[4-(3-chloro-4- n-octyloxyphenyliminomethyl) benzoate (PBCOB) and related compounds are described. The chloro-substituent introduced into the 3-position of the Schiff's base moiety of the banana-shaped molecule destabilized the smectic phase and enhanced new mesomorphic properties. The mesophases exhibited by the octyloxy homologue of the chloro-substituted compound were of the smectic phases, SmX1 and SmX2. The mixing behaviour between chloro-substituted and non-chloro-substituted compounds resulted in the appearance of a wide miscibility gap and enlargement of the SmX1 phase which can be seen in a lateral chloro-substituted compound.     

Theory and simulation of electrolyte mixtures

Monte Carlo simulation and theoretical results on some aspects of thermodynamics of mixtures of electrolytes with a common species are presented. Both charge symmetric mixtures, where ions differ only in size, and charge asymmetric but size symmetric mixtures at ionic strength ranging generally from I = 10^?4 to 1.0 M, and in a few cases up to I = 2 M, are examined. The theoretical methods explored are: (i) the symmetric Poisson-Boltzmann theory, (ii) the modified Poisson-Boltzmann theory and (iii) the hypernetted-chain integral equation. The first two electrolyte mixing coefficients w ₀ and w ₁ of the various mixtures are calculated from an accurate determination of their osmotic pressure data. The theories are seen to be consistent among themselves, and with certain limiting laws in the literature, in predicting the trends of the mixing coefficients with respect to ionic strength. Some selected relevant experimental data have been analysed and compared with the theoretical and simulation trends. In addition the mean activity coefficients for a model mimicking the mixture of KC1 and KF electrolytes are calculated and hence the Harned coefficients obtained for this system. These calculations are compared with the experimental data and Monte Carlo results available in the literature. The theoretically predicted Harned coefficients are in good agreement with the simulation results for the model KC1-KF mixture.     

Development of an Artificial Compressibility Methodology with Implicit LU-SGS Method

A numerical method has been developed to solve the steady and unsteady incompressible Navier-Stokes equations in a two-dimensional, curvilinear coordinate system. The solution procedure is based on the method of artificial compressibility and uses a third-order flux-difference splitting upwind differencing scheme for convective terms and second-order center difference for viscous terms. A time-accurate scheme for unsteady incompressible flows is achieved by using an implicit real time discretization and a dual-time approach, which introduces pseudo-unsteady terms into both the mass conservation equation and momentum equations. An efficient fully implicit algorithm LU-SGS, which was originally derived for the compressible Eulur and Navier-Stokes equations by Jameson and Toon [1], is developed for the pseudo-compressibility formulation of the two dimensional incompressible Navier-Stokes equations for both steady and unsteady flows. A variety of computed results are presented to validate the present scheme. Numerical solutions for steady flow in a square lid-driven cavity and over a backward facing step and for unsteady flow in a square driven cavity with an oscillating lid and in a circular tube with a smooth expansion are respectively presented and compared with experimental data or other numerical results.     

A QUANTITATIVE EVALUATION OF ELASTIC WAVE IN SOLID BY STROBOSCOPIC PHOTOELASTICITY

We have developed a method for visually measuring and evaluating stresses emitted from an ultrasonic probe into a model solid similar to the actual material, by using image-processing techniques and stroboscopic photoelasticity. The visualization of wave stress (sound pressure) distribution can be achieved by synthesizing two photoelastic pictures, in which the directions of the principal axes of linear polariscopes are different by 45 degrees. The sound pressure field generated by commercial ultrasonic probes was measured by using the proposed method.     

CORRECTED SOLVABILITY CONDITIONS FOR NON-LINEAR ASYMMETRIC VIBRATIONS OF A CIRCULAR PLATE

An investigation into non-linear asymmetric vibrations of a clamped circular plate under a harmonic excitation is made. We re-examined a primary resonance studied by Sridhar, Mook and Nayfeh, in which the frequency of excitation is near the natural frequency of an asymmetric mode of the plate. We corrected their solvability conditions and found that in the absence of internal resonance, the steady state response can have not only the form of standing wave but also the form of travelling wave, which is a remarkable contrast to their conclusion.