The methods to calculate the winding inductance of electrical devices without a ferromagnetic core have been discussed. The methods for calculating the self- and mutual inductances of windings are suggested based on the analytical calculations of the magnetic field and taking into account the design features of the windings. These suggestions are implemented in the MATLAB environment and can be integrated into electrical CAD systems as an additional calculation module, allowing for the selection of a reasonable calculation method for a specific winding design. The results of testing the developed methods are presented, and the results obtained using each method are compared with those calculated using the field models. The results of this work can be used to develop digital twins of designed devices for preliminary characterization of their key parameters in different operating modes.
The paper outlines the methodology and results for mathematical modeling of the mechanical state of a biomechanical system comprised by the femur and the stem of the hip endoprosthesis. The femoral component of the endoprosthesis was manufactured from metamaterials with a through porosity of about 70 %, defined by unit cells of strut-based and surface-based structures made of a biocompatible titanium alloy. We considered four classes of unit cells comprising the metamaterial: two strut-based cells and two TPMS-based cells. The structural strength and the stress state of bone tissue were evaluated under two representative configurations. In the first case, it was assumed that the pore space of the metamaterial was filled with soft, undifferentiated tissue corresponding to the initial implantation stage of the endoprosthesis. In the second case, the pore space was filled with bone tissue evolving during the later stages of bone regeneration. We conducted a series of finite-element simulations aimed at stress–strain analysis of the system under specific loading scenarios, reproducing the common types of human motor activity: normal walking, upstairs and downstairs walking. From the standpoint of structural strength, our findings indicate that priority should be given to strut-based structures, as their yield strength is typically not exceeded across the entire set of scenarios. Surface-based structures are acceptable provided that a safety margin is maintained specifically for the most high-load scenarios of motor activity, along with local geometry adjustments in the transition zone and restrictions on minimum strut thicknesses. This reinforcement reduces the risk of local stress concentrators appearing, serving to improve the overall stress state of the structure.
In this paper, we prove an abstract formula for regularized traces of discrete operators in a separable Hilbert space. This formula is a generalization of the formula for the first regularized trace to the case of higher-order traces. We also discuss applications of the formula obtained to a wide class of discrete operators acting in the Bergman space that are generalizations of the Gribov operator from Reggeon field theory.
Despite great progress made in neurosurgery, stable spinal reconstruction after total en bloc spondylectomy remains a challenge. While the common tactic is to replace the vertebral body with an implant and perform transpedicular fixation, the standard implants do not always provide the necessary support and natural load distribution, increasing the risks of instability and subsidence of the implant. It is therefore of utmost importance to construct customized implants based on additive technologies. Our study considers five implants: one made of polymer and four made of metamaterials similar in properties to cortical tissue of the vertebrae. Two of the implants were made of lattice metamaterials (Body-centered Cube and Diamond) and two of TPMS metamaterials (Fischer – Koch and Gyroid). Stress–strain analysis of the reconstructed spine was carried out for each implant for six basic movements: flexion, extension, right bending, left bending, right rotation and left rotation. Our findings led us to conclude that the metamaterial implants have an almost identical influence on the biomechanics of the lumbar spine in terms of strength. Furthermore, even though higher stresses were observed in the system in this case, metamaterials can still be recommended for use in implants as they stimulate ingrowth of bone tissue into the implant.
The construction of new nuclear power plants under the NPP-2006 project required Leningradsky Metallichesky Zavod (LMZ) to implement an electronic and hydraulic turbine regulation and protection system (TRPS) in the design of a large capacity condensing turbine K-1200-6,8/50, based on the experience, design and circuit solutions for a similar system of a high-speed turbine-analogue K-1000-60-3000 manufactured by LMZ. Despite the preservation of the turbine layout in relation to the turbine-analogue (2LP module + HP module + 2LP module), the turbine control concept through the TRPS and the available references at the stage of commissioning of the Novovoronezh NPP-2 power units (before the power unit was turned on to the grid), as experience has shown, there were cases of incorrect operation of the TRPS due to the ambiguity of the assembly or hidden inconsistencies. The elimination of the causes of incorrect operation of hydraulic assemblies is often directly related to the search for the root cause "from the inside", i.e. disassembly of equipment is required. The presented article shows cases of incorrect operation of the TRPS and ways to solve them from the experience of commissioning on a high-capacity turbine K-1200-6,8/50 with a brief description of the problematic TRPS hydraulic components, the amount of refinement of structural elements. The experience of commissioning described in this article is still relevant today due to regular scheduled preventive repairs at commissioned power units of the NPP-2006 project, during which a routine audit of the hydraulic elements of the steam distribution organs is carried out, as well as a pre-start check of the interaction of the hydraulic and electronic parts of the TRPS. In addition, the commissioning of nuclear power plants with turbine K-1200-6,8/50 is currently underway abroad (in People's Republic of Bangladesh) where the described experience can be applied on occasion.
