Mathematical Modeling of Vibrational Systems for Transverse Grinding by Wheel Periphery

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\u27s 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.)

Modernization of the Technique for Rotary Shape-formation of Outer Profiled Surfaces

We have proposed a technique for obtaining outer profiled surfaces, which is characterized by affordability and low cost of equipment used. The technique is based on that a regular rotating center is fixed in a lathe's tool holder in a special way. A basic socket head of the required profile is applied as a profile-forming matrix. A tool holder's rotation angle ensures a fracture angle of the rotating center's axis relative to the axis of a workpiece rotation. A value for the fracture angle reaches 1.5°. The end surface edge of the matrix executes a reciprocating motion per every rotation of the lathe chuck along the surface of a workpiece. In this case, the end surface of the matrix and a workpiece are in contact at a single point, going deeper by the magnitude of feed per every rotation of the chuck.Application of a given technique is an alternative to existing technique of rotational shape-formation of outer profiled surfaces, whose implementation requires specialized equipment and specialized cutting tools, the price for which is quite high (UAH 57,000 and UAH 6,000, respectively). In addition, changing the size or shape of the required profile necessitates installing a new cutting tool, replacing which requires additional adjustment.The tests were carried out when manufacturing the twelve-point outer surface the size of S10. An analysis of vibrograms from the shape-formation process has established the most rational variant of equipment for manufacturing profiled outer surfaces. We have manufactured pilot outer profiled surfaces, such as hexagon the size of S10, the TORX surface the size of E14, and others. They confirmed a possibility for successful manufacturing of different profiled outer surfaces using the proposed tooling.Using the proposed technique, which implies low cost and does not require specialized equipment, could significantly expand the scope of application of conjugated surfaces with a profiled shape in mechanical engineerin