Mathematical modeling of vibrational systems for transverse grinding by wheel periphery

Abstract

The object of research is the vibrational systems of grinding processes. One of the problem areas of the research object is the determination of the way in which the regularities of mutual influence of the main parameters of the system's motion will be taken into account. The question of taking into account the energy dissipation in elastic elements in the study of the vibrations of an elastic system is quite complex, since internal friction depends on a number of factors whose influence is quite complex and practically not subject to direct account. In the course of the work, analytical methods of research are used, based on the basic principles of the theory of mechanical vibrations and theoretical developments of scientists in this field. Analytical dependences of the grinding system motion with longitudinal feed in the form of differential equations that take into account the dimensions of the «drive – machine - grinding tool – workpiece » system are obtained and determine their interdependence. This allows to conduct theoretical studies of processes to establish appropriate grinding modes. With the use of Nielsen algorithm, the dependencies of the vibrational system motion are obtained without taking into account the roughness of the grinding wheel, profile which allows to predict the position of the grinding tool during processing at any time. This makes it possible to study in detail the conditions of the vibrational grinding system under various conditions and to develop measures to improve the efficiency of the grinding process by selecting the correct grinding conditions (feed rate, grinding wheel rotation velocity, grinding depth, etc.).