Eisuke Takano

Behaviour of granular materials in the field of vibration

Vibration has been widely used in various industrial operations dealing with granular materials. Classification, conveying and packing provide typical examples of the vibration technique. In spite of these actual uses, the behaviour of granular materials is poorly understood. Most of the knowledge related to handling of particulates is empirical and no generalized approach for the analysis of the response of granular materials to external forces exists. This paper presents an investigation into the development of a numerical method for size segregation, which is the typical behavior of granular materials in the field of vibration. This numerical method is modified on the basis of the discrete element method proposed by Cundall. In order to consider the shape anisotropy of particles, they are first treated as elliptic models. Then mechanical units such as spring, dashpots and friction sliders are used to express the contact forces. The effect of the size ratio and the shape of each particle on the response of granular materials is considered.

Vibratory Conveyance of Granular Materials Comprising Elliptic Particles

The flow model of granular materials on vibratory conveyors is derived by using an improved discrete element method. Granular materials are first assumed as cylindrical bodies with elliptic cross sections to take into account the dependence of shape anisotropy on the flow patterns. Then mechanical elements such as springs, dashpots and friction sliders model the contact forces and the equation of motion for the particles is numerically solved. It is shown that the mean velocity of transport of granular materials depends on the frequency and amplitude of the vibratory input as well as various physical parameters. By comparing the experimental with calculated results, the flow patterns obtained by this method appear realistic.

Oscillations Caused by Solid Friction in a Hydraulic Driving System : In the Case of Maximum Static Friction Equal to Kinetic Friction without Slipping

Oscillations caused by solid friction in a hydraulic driving system are treated theoretically. The system includes a table lying on a rectilinear sliding surface, an actuator cylinder, a 4-way servo valve, a relief valve, and an oil pump. The solid friction force considered is assumed to vary with the relative sliding velocities between the table and sliding surface, namely, the friction-velocity charscteristic is given by a polygon having two straight-line segments and the critical value of static friction is equal to the value of kinetic friction without slipping. The stick-slip motions of the table are analyzed considering the 4-way valve pressure-flow characteristic, the friction-velocity relation, oil compressibility and the sizes of the hydraulic driving elements. Several types of limit cycles and the regions in which they occur are shown in figures according to the parameters mentioned above. Lastly, the steady-state displacement waves of the table are described and the curves of amplitudes and their periods are given.