Mechanics and Advanced Technologies

Formalization of Technological Processes Based on Vector and Tensor Analysis

Volodymyr Zabashta — 2025-12-29

The work further develops the results of studies [1]–[5] based on a systematic analysis using an interpretative-formal approach in a new scientific and technical direction – the technological interpretation of provisions of vector and tensor analysis that are similar in meaning. This allows expanding the formal field of representation of technological processes within the concept of their “technological meaning” and increasing the formal capacity of TP description. The results of research are revealed in the practical and production aspects related to TP, providing for the application of vector and tensor analysis in the coordinate approach, technological space, scalar product, matrix tensor, as well as examples of tensor and vector analysis in composite AKZ technology. It is determined that vectors (tensors) can be specified in different ways, depending on the technological context (polymer composite materials technology – PCM), and the set of components is only its representation in a certain (in terms of detail) basis. A coordinate approach is used, as well as the possibility of other methods of specifying and working with vectors (tensors) using the example of ordinary vectors and simple second-rank tensors, characterized by the powerful idea of orthogonality. Since the second vector and tensor represent real technological objects, including: autonomous dynamic systems (ADS), structural and technological solutions (STS), technological processes (TP), in the form of contravariant and covariant vectors, etc.
The interpretative correspondence of the technological interpretation of contravariant and covariant coordinates of a vector is shown, and the nature of the relationships between technological contravariant and technological covariant coordinates is established.
The example demonstrates the invariance of the enlarged stages of a complex technological process in different coordinate systems, which confirms the invariance of the technological vector under the condition of transformation of its coordinates.

Properties of Ti-6Al-4V Lattice Structures with In-Situ Alloying and Functional Gradient

Svitlana Kyrylakha — 2025-12-29

Problem statement. The object of research is lattice structures made of Ti-6Al-4V titanium alloys, manufactured using selective laser melting (SLM) and laser powder bed fusion (LPBF), including in-situ alloyed and functionally graded variants. The problem lies in the lack of systematized data on the relationship between process parameters of additive manufacturing, the resulting microstructure, and mechanical properties, which limits the application of such materials in aerospace industry. Purpose of the study. To determine the influence of in-situ alloying and functional gradient lattice structures on the formation of microstructure, elastic modulus, strength, and energy absorption capacity of Ti-6Al-4V produced by SLM/LPBF. Methodology. Experimental specimens of Ti-6Al-4V–3 % Cr were fabricated by SLM/LPBF under controlled energy density and scanning parameters. The structure was analyzed using X-ray diffraction (XRD), electron microscopy (SEM, EBSD, EDS), and lattice geometry evaluation. In parallel, finite element modelling (FEM) was applied to predict mechanical behavior. Results. The results demonstrate that in-situ alloying with Cr stabilizes the b-phase and controls the distribution of a + b microstructure, thereby increasing alloy strength and stiffness (UTS up to 1050 MPa, elongation 8–10 %). Lattice structures of elliptical and spiral geometry exhibited maximum elastic moduli of 0.76 GPa and 0.41 GPa respectively, while reducing structural mass. Functionally graded lattices with variable strut diameter (1–1.2 mm) ensured more efficient stress transfer and controlled local stiffness. The effect is attributed to substrate preparation and cyclic heating during LPBF, which promoted a¢ martensite decomposition, b-phase stabilization, and stress reduction in critical regions. Conclusions. The novelty of the study lies in the combination of in-situ alloying and functional geometry gradient, which enables achieving an optimal strength-to-weight ratio, improving energy absorption, and providing controlled mechanical response throughout the component volume. Potential applications cover aerospace engineering, where weight reduction under high stiffness and strength is crucial, as well as structural elements with increased resistance to local loading.

Integrated Geometric Confinement and Ejection-Driven Drainage Flow for Splash Suppession in High-Speed Abrasive Waterjet Machining

Xianding Xue — 2025-12-29

Abrasive waterjet machining (AWJM) is widely used in aerospace and precision manufacturing due to its cold-cutting nature. However, the residual high-energy jet column penetrating the workpiece frequently impacts the support structure, generating intense splashback that leads to surface contamination and secondary damage. To address this, we propose a composite anti-splash support structure integrating a concave bowl surface with a Venturi-induced negative pressure mechanism. Using VOF multiphase modeling combined with finite element validation, we elucidate the synergistic control mechanism: the curved bowl promotes wall-adherent liquid sliding to reduce radial momentum, while the Venturi throat creates a ~0.15 MPa negative pressure zone that captures droplets into the downstream channel for dissipation. Results demonstrate that compared to conventional supports, the design reduces mixture peak velocity by ~35%, decreases droplet diffusion height by 40%, and curtails radial spread by 30%, effectively constraining contamination areas. Static analysis further confirms the structure maintains high safety margins even under extreme loads. These outcomes not only enhance AWJM processing environments but also provide a validated engineering paradigm for high-speed fluid interaction control. Looking forward, the mechanism resonates with splash suppression needs in photolithography, food packaging, electronic encapsulation, and metal cutting, paving the way for a universal design and evaluation system for splash control in advanced manufacturing.

Options for Cold Extrusion of Axially Symmetrical Hollow Semi-Finished Products for Further Drawing with Thinning

Volodymyr Dragobetskyi — 2025-12-29

Problems. Cold extrusion of hollow semi-finished products is used as the first stamping step in the manufacture of shell casings and bodies of certain caliber. In the context of mass production of semi-finished products, the task of increasing the stability of the deforming tool during cold forming is of paramount importance, which will lead to a reduction in the cost of semi-finished products. Increased durability can be achieved by reducing extrusion forces and specific forces on the deforming tool, in particular on punches and dies. To produce hollow semi-finished products, a reverse extrusion scheme is currently widely used, in which the diameter of the workpiece is the same as the outer diameter of the semi-finished product. Hot-rolled round billets are produced from hot-rolled round steel by waste-free shear cutting in dies on presses. The use of forward extrusion with feeding and reverse extrusion with feeding in a moving die results in a lower deformation force compared to reverse extrusion and requires the use of smaller billets with the same external dimensions of semi-finished products. Reducing the diameter of rolled products for the manufacture of blanks by shear separation leads to an increase in the geometric accuracy of the resulting blanks, which is the second objective when extruding hollow semi-finished products.

Objective. A comparative analysis of cold extrusion of hollow semi-finished products for further drawing with thinning using the schemes of reverse extrusion, direct extrusion with dispensing and reverse extrusion with dispensing in a moving die based on computer modeling by the finite element method.
Methods of realization. By simulating the cold extrusion of hollow semi-finished products according to three molding schemes, parameters are established, based on the analysis of which a rational scheme is selected for use in production.
Results. Using the finite element method (FEM), the processes of cold extrusion of round hollow semi-finished products were modeled according to the schemes of traditional reverse extrusion, direct extrusion with dispensing, and reverse extrusion with dispensing in a moving die. The dependence of the forces of extrusion, removal of punches from semi-finished products, and pushing semi-finished products out of dies on the movement of the deforming tool was determined. The specific forces on the punch, die, and ejector were determined. The distributions of temperature and strain intensity in the deformed metal at the end of extrusion were determined. The development of the metal structure by cold plastic deformation along the width of the walls and in the bottom parts of hollow semi-finished products was evaluated. The scheme of reverse extrusion in a moving die provides reduced values of the deformation force and requires the use of a smaller diameter billet compared to the reverse extrusion and has increased productivity compared to the direct extrusion.

Laser-Assisted Synthesis of Diamond-Reinforced Coatings on Cast Steel with CuSn10 (Bro10) Binder

Oleksii Goncharuk — 2025-12-29

The selection of a binder material for the working layer with diamond grains is of critical importance in the production of diamond-containing abrasive tools. The object of the study is the process of forming diamond-reinforced coatings on cast steel 40L using a powder bronze binder of CuSn₁₀ (BrO10) composition as a matrix material. The possibility of applying a CuSn₁₀ (BrO10) binder for thermomechanical laser sintering of diamond-containing coatings on 40L steel is considered, with the aim of ensuring a reliable metallurgical bond between the working layer and the substrate and obtaining a dense, defect-free structure.
Using a fourth-generation Maxphotonics fibre laser (λ = 1.06 µm, power 500‑1000 W, exposure time 0.18‑1.8 s) under an inert atmosphere, a dense defect-free diamond-containing coating was synthesised on the steel substrate. A strong metallurgical bond was formed at the bronze/steel interface due to atomic diffusion of Cu and Fe, as well as a dense contact with the diamond particles. The morphology, chemical composition, geometry and microhardness of the deposited bead at the diamond/binder interface were analysed. The phase composition and element redistribution in the matrix region were determined as a function of laser power density.
The bonding strength is explained by the combined effect of Cu‑Fe atomic diffusion, the formation of intermetallic phases at the interface, and an increase in the real contact area with diamonds as a result of microstructural rearrangement under local heating.
A distinctive feature of the obtained results is the formation of a dense defect-free structure with high adhesion, which differentiates laser sintering from conventional powder pressing and sintering. This minimises the risk of delamination and enhances tool reliability under load. The findings can be applied to the manufacture of diamond abrasive tools intended for machining hard materials.

Research and Simulation of Heat Treatment of Steel Elements of Metal Molds for Semi-Dry Vibrocompression

Valentin Gordienko — 2025-12-29

This work investigates the full cycle of heat treatment (carburizing and quenching) of steel elements of metal molds used in the production of concrete products manufactured by the semi-dry vibrocompression method.
Severe abrasive wear of the working surfaces of metal molds necessitates the optimization of chemical–heat treatment. Traditional methods do not allow accurate prediction of the final phase composition or hardness profile, particularly considering the complex influence of carbon concentration on quenching kinetics. Therefore, a numerical model for process prediction and quality control is required.
A coupled multiphysics 2D model (diffusion, heat transfer, and phase transformations) was developed and implemented for a steel specimen with dimensions 100 × 100 × 20 mm. Carburizing simulations were performed for two initial carbon concentrations (0.08 and 0.2 wt.%) achieving a final surface concentration of up to 0.9 wt.%. After water quenching (typical heat-transfer coefficient h ≈ 5000 W/(m²·K)), the simulations demonstrated the formation of 80–85% martensite in the carburized layer. However, an increased content of retained austenite (15–20 %) was observed in the near-surface region.
The presence of retained austenite in the carburized layer is explained by the significant reduction of the martensite-start temperature (MS) due to high local carbon enrichment. This confirms that even at high cooling rates (h ≈ 5000 W/(m²·K)), complete martensitic transformation does not occur, indicating the need for additional heat-treatment operations.
The use of the Koistinen–Marburger model with concentration-dependent MS(c) and a locally refined mesh enabled accurate determination of the boundaries of the carburized and quenched layers. This provided a quantitative evaluation of the final phase composition profile, which is essential for hardness prediction.
The simulation results can be applied by process engineers to optimize carburizing parameters (temperature and duration) and quenching conditions (cooling rate) to increase the service life of steel metal molds, as well as to justify the necessity of low-temperature tempering.

Numerical Analysis of 2D Elastic Torsion Problem for a Rod by the Method of Matched Sections

Kostiantyn Slovak — 2025-12-29

Torsion problem is treated here as Saint Venant’s semi-inverse task for prismatic bars, which allows to consider 2D geometry instead of 3D one. The novelty of the paper is that at the first time it tackles the problem by the method of matched section, MMS, – a new numerical approach for multiphysics problems. Like finite element method it supposes the continuous distribution of all parameters within the element, and like volume element method it keeps the conservation laws and equilibrium for each element and the body as a whole. The main idea of MMS is to substitute the partial differential equations (stemmed from required conservation laws) by the ordinary ones by introducing the additional constants, which can be later found from the continuity conditions at the center of element. The governing equations for torsion are broken out on two independent (along each coordinate axis passed through the centers of the opposite sides) equations, which relate two governing parameters (angle of rotation and torque) at the beginning with those at the end of the element. Each element contains 8 unknowns, so 4 above connection equations are supplemented by continuity conditions between elements and the boundary conditions. In addition to rectangular element the simplified version of the triangular one is proposed which is used to account for the outer boundary configuration. Numerical verification is performed for different shapes of cross-section and for composite cross-section. The results show the efficiency of the method, and high accuracy is attained even for small grids.

Optimization Characteristics of Revision Knee Joint Endo-Prostheses

Yehor Ovcharenko — 2025-12-29

The study addresses the problem of reducing the mass of patient-specific revision knee joint endoprostheses while preserving their load-bearing capacity through the introduction of internal cavities. The relevance of this research is driven by the need to decrease mechanical loading on bone tissue, improve patient comfort, and reduce titanium alloy consumption in the production of individualized implants. Additive manufacturing technologies, in particular selective laser melting (SLM), allow the creation of complex internal geometries that are unattainable by conventional machining methods. The aim of this work is to determine the optimal balance between mass reduction and preservation of strength characteristics by means of finite element analysis of two hollow stem configurations based on a 75 mm long reinforced stem. Numerical simulations were conducted using the Ansys Student 2024 R2 software package. Quantitative results demonstrated mass reduction of 25–35% accompanied by a corresponding increase in maximum stresses of 6–20%, depending on cavity configuration. The findings confirm the feasibility of achieving a substantial reduction in implant weight with an acceptable increase in stresses that does not exceed the structural safety margin.

Biomechanics of Osteosynthesis by Titanium Miniplates of Bones of the Lower Jaw Damaged by a Fracture

Mykola Kryshchuk — 2025-12-29

The main task of osteosynthesis of jaw bones damaged by fractures is to align the fragments in an anatomically correct position and securely hold them in place for a specified period of consolidation using fixation devices. The processes that develop in bone tissue after the installation of a fixator for jaw bones damaged by a fracture significantly depend on the conditions of the force load. The stability of fixation of bones damaged by a fracture affects the course of reparative biological processes and determines each other, which must be taken into account during their osteosynthesis. To determine strategies for osteosynthesis of damaged bones with titanium miniplates with screws, mathematical models of the stress-strain state of connected heterogeneous bodies of biological origin and technological manufacture of the fixator under static loads were formed. Numerical modeling of the biomechanics of osteosynthesis of 3D digital twins of biomechanical osteosynthesis systems was performed in the ANSYS software environment, taking into account the isotropic properties of their structural elements. The patterns of influence of the design features of titanium miniplates and the conditions of their fixation on the stiffness and stress-strain state of the simulation model of the lower jaw damaged by a lateral fracture were established. Calculations of the amplitudes and stress gradients of biomechanical osteosynthesis system models in a numerical experiment helped to determine the parameters of the required stiffness and topology of the location of two types of miniplates and screws that affect the diastasis and density of interfragmentary contact of fragments in the jaw fracture area. Empirical data on the stiffness of lower jaw osteosynthesis systems with titanium miniplates were obtained from cadaver samples. The established levels of deformation of biomechanical systems natural objects in the area of fixation of bone fragments with miniplates are a decisive factor in assessing the risk of excessive displacement of fragments in the postoperative period.

Influence of the Fillet Radius on the Performance of an Ultrasonic Stepped Velocity Transformer

Andrii Movchanuk — 2025-12-29

This study presents the results of a numerical investigation into the influence of geometric parameters, particularly the fillet radius, on the dynamic characteristics of an ultrasonic stepped velocity transformer. Such transformers are employed in high-frequency electromechanical systems to match the acoustic impedances between the transducer and the load, as well as to increase the amplitude of mechanical vibrations. Modeling was carried out using the finite element method (FEM), which enables consideration of the spatial distribution of stresses and strains within the transformer volume. The effects of the step diameter and acoustic length on the resonance frequency and amplification coefficient were analyzed. It has been established that an increase in the step diameter leads to a decrease in the resonance frequency, whereas an increase in the fillet radius results in its rise. Quantitative relationships between the fillet radius, transformation coefficient, and resonance frequency were obtained, allowing for approximate determination of optimal design parameters. It was shown that enlarging the fillet radius reduces stress concentration in the transition zone between steps, thereby enhancing the fatigue strength of the structure. An empirical relationship was proposed for preliminary estimation of the fillet radius to ensure agreement between the actual and the calculated resonance frequencies. The results obtained can be applied in the design and optimization of ultrasonic amplification systems and transducers used in ultrasonic welding, material processing, and surface modification technologies.

Mechatronic Module with Alternative-Probability Control

Oleksandr Gubarev — 2025-12-29

This article presents control algorithms for adaptive mechanical systems. Object of research: processes occurring in industrial hydraulic drive systems during their operation. Subject of research: dependence of operational efficiency of industrial hydraulic drive systems on the term and operating modes, and applied fundamental circuit solutions and technical means that affect the functional, energy, and cost indicators of the system.The problems solved in the presented article are actual tasks. They involve the use of previous experience in the operation of a specific mechatronic system in specific conditions, for the formation of an adaptive control algorithm. The study is based on the creation of logical interpretations in the algorithm for decision-making. The simultaneous consideration of logical connections and the probability of the component “success of system actions” is considered. On the basis of which a two-component structure of logical expressions of control commands is formed. Accordingly, examples are given for evaluating each of the operation options. The article presents the scope and conditions of practical use of the obtained results. They are based on several examples, namely, the technical implementation of the manipulator macromodule with alternative probabilistic control is considered. It is possible to use the success of the system’s actions and the choice of the option for distributing attempts by digits or/and the basis of logarithmic weight. The peculiarity of the obtained results lies in the use of the criterion of “volume of involved memory” in the control system. This makes it possible to prioritize one of the alternative reactions of the system to external excitation, which provides a basis for the formation of control commands.

Upper-Bound Estimate of Reduced Pressure and Optimisation of Scheme Parameters for Direct Extrusion of Parts with a Conical Cavity

Anton Hranovskyi — 2025-12-29

The object of the study is the process of direct cold extrusion of parts with a conical cavity. The problem addressed is the absence of general analytical estimates of the reduced pressure that simultaneously take into account the geometry of the bottom and wall of conical cavity, contact friction and the parameters of the deformation-zone partition, while remaining suitable for engineering calculations.
The aim of the work is to develop a parametric scheme for partitioning the deformation zone and to determine the partition parameters for which the reduced pressure is minimal.
The deformation zone is divided into a compression and flow-turning region in the bottom and a compression region in the wall of conical cavity; the reduced pressure is represented as the sum of the contributions of these regions. For the bottom, closed-form expressions for the optimal geometric parameters are obtained; for the wall, the minimisation problem is reduced to a one-dimensional search with respect to the partition parameter at a fixed number of similar triangular elements.
It is shown that increasing the relative radius of the cavity from 0.25 to 0.7 and the cone angle of the wall from 5° to 30°, as well as decreasing the relative bottom thickness from 1.5 to 0.75, leads to an increase in reduced pressure by approximately 1.5–2 times. A threshold dependence on the number of similar elements in the wall of conical cavity is revealed: for small relative radii the minimum is achieved with one element, whereas for larger radii the optimal number ranges from two to five.
The partition parameters are not prescribed in advance but are determined from the minimum-pressure condition, which allows the partitions of the bottom and wall to be treated as two kinematic modules. The proposed model accounts for geometry, friction and the number of similar rigid elements and can be used for preliminary design of extrusion processes for parts with a conical cavity and combined extrusion schemes.