Analytical relations for fields and currents in magnetic-pulsed «expansion» of tubular conductors of small diameter

Abstract

Introduction. This work was initiated by the problems of cardiovascular diseases, which are one of the main causes of mortality of the population of our planet. More than ten years ago, in 2012, approximately 3.7 million people died of acute coronary syndrome worldwide. The fight against such pathologies is carried out with the help of so-called stents, the manufacture of which can be carried out by the method of magnetic pulse «expansion» from hollow metal cylinders. The limited production possibilities of magnetic pulse «expansion» were caused by the minimum cross-sectional size of the inductor-instrument, which can be practically manufactured. Other tools are required to perform this operation. Novelty. A system of magnetic-pulse expansion of thin-walled pipes of small diameter with an inductor that excites an azimuthal electromagnetic field in the case of direct current passing through the processing object and in the absence of its connection in an electric circuit with an inductor is proposed. Purpose. The main analytical dependencies for the characteristics of the electromagnetic processes taking place in the inductor systems for the expansion of cylindrical conductive pipes of small diameter when direct passage of current through the processed object and when it is not connected to an electric circuit with an inductor (insulated billet) is derived. Methods. The solution of the boundary value problem with given boundary conditions was carried out by applying Laplace transforms and integrating Maxwell’s equations. Results. Analytical expressions were obtained for the main characteristics of the processes: the intensities of the excited electromagnetic fields and currents in the system depending on the parameters of the studied systems. The analysis of possible technical schemes for solving the given problem indicated the choice of the optimal variant of an effective system of magnetic-pulse «stretching» of thin-walled cylindrical conductors of small diameter. Practical value. Based on the qualitative analysis of the obtained results, recommendations for the practical implementation of the proposed system were formulated. The obtained dependences allow us to give numerical estimates of the effectiveness of excitation of magnetic pressure forces on the object of processing and to choose directions for further improvement of the magnetic pulse technology for solving such problems. References 23, figures 2.

Keywords

• pulsed electromagnetic fields
• cylindrical conductors of small diameter
• solution of a boundary value problem
• laplace transforms