CREATION OF A MATHEMATICAL MODEL OF THE MECHANICAL PROCESSING OF A COMPLEX-PROFILE PART FIXED IN A FRACTAL VISE

Abstract

The article is devoted to the issue of creating a mathematical model of the milling process of a part fixed in a fractal vice. The history of the creation of a universal vice is briefly given. The representation of fractal vices in the market of machine tool equipment is analyzed based on the analysis of several domestic and global e-commerce platforms. Several existing works in the direction are analyzed. The main principle of fractal vise operation is defined – self-adjustment on any surface of the part. Several assumptions are made for further modeling, for example, that the fractal jaws acquire the properties of a monolith after clamping the part. A mathematical model based on the principles of kinetostatics and static balance is proposed, which consists of a system of three differential equations of the second order with lumped coefficients. The mathematical model is suitable for its implementation on modern specialized software for modeling, simulation, and analysis of dynamic systems. Recommendations for approximation of the mathematical model to the natural experiment are provided.