Complex Geometric Shapes Research Articles

Numerical modeling of the wind regime on the beaches of the wash of the artificial storage facilities for mineral processing waste

A 2D numerical model has been developed to estimate the airflow velocity field when flowing around the dam of an artificial storage facility for mineral processing waste. To solve the aerodynamic problem of determining the air flow velocity field when flowing around such hydraulic structures with a complex geometric shape, a potential motion model was applied. The numerical integration of the equation for the velocity potential is carried out using the Liebman method. The geometric shape of the tailings storage facility is formed in a discrete model using the marking method. A computer program was created to implement the developed numerical aerodynamics model. Based on the processing of the results of computational experiments, coefficients were obtained that allow us to quickly determine the value of the air flow velocity at the beginning and end of the tailing pond beach, i.e. in the area of the most intense dust emission. This allows for a quick prediction of the risk of dust air pollution at different tailing pile heights.

Abstract 2024: Elucidating The Role Of Shape In Aortic Disease State Pathology With Machine Learning

Maximum aortic diameter has been the mainstay metric for aortic disease management and surgical intervention for decades, specifically acute aortic dissection and aneurysm. While this size metric has been effective at separating patient populations into groupings associated with required intervention and monitoring for eventual intervention respectively, size alone ignores the role of complex geometric shape and how it may be further indicative of disease state. Analyses of aortic shape in addition to size have been discussed at length in literature, however the representations and methods to convey shape are siloed and often highly subjective. Machine learning methodologies offer a means to explore high dimensional feature spaces and can identify a sparse set of metrics which result in a division of patient responses parametrized by physical and interpretable variables. Additionally, by introducing a modeling workflow which contains engineered parameters designed to describe aortic shape, in addition to traditional size metrics, the exploration of shape dependence on intervention outcomes becomes more comprehensive across size-shape parameter spaces. The engineered parameters presented primarily incorporate estimations of integrated Gaussian surface curvature into features that contain both the magnitude and spatial variation in shape of the aortas. The models discussed accurately classify over two hundred aortic disease patients spanning aneurysm, dissection, and other modalities with accuracies above 90% and performance across multiple modeling methodologies is discussed. The classification success of the geometrically informed feature space suggests the underlying dependence on pathology shape on the success of the intervention outcome. The most clinically effective models will preserve the wealth of information in modern medical diagnostics and imaging into descriptive, and physically interpretable, parameters to aid in clinical decision making.

Voronoi-based 3D phase field model and numerical simulations of granite crack propagation

The distribution of mineral grains within underground rocks and materials is crucial for understanding geological processes and the stability of engineering structures. However, numerical simulation methods that consider 3D mineral particles are still immature. This study presents a 3D phase-field fracture model of mineral grains based on Voronoi polygons, making some beneficial attempts in this regard. The phase-field method does not rely on mesh reconstruction or crack path tracking and can simulate complex crack propagation behavior. Meanwhile, the Voronoi polygon can better describe the microscopic structure of rock with grain boundaries. Rooted in Voronoi polygons, this model efficiently captures the complex geometric shapes of mineral grains and accurately characterizes their positions, shapes, and sizes. Therefore, this study combines Voronoi polygons to establish a 3D phase-field model. Through two numerical simulation cases, the model demonstrates its effectiveness in simulating the impact of three-dimensional mineral grains on crack propagation behavior, showing that cracks tend to propagate at the boundaries or inside softer mineral grains. The modeling approach proposed in this paper has good reference value for numerical simulation studies considering the microscopic structure of rocks.

BrepMFR: Enhancing machining feature recognition in B-rep models through deep learning and domain adaptation

Feature Recognition (FR) plays a crucial role in modern digital manufacturing, serving as a key technology for integrating Computer-Aided Design (CAD), Computer-Aided Process Planning (CAPP) and Computer-Aided Manufacturing (CAM) systems. The emergence of deep learning methods in recent years offers a new approach to address challenges in recognizing highly intersecting features with complex geometric shapes. However, due to the high cost of labeling real CAD models, neural networks are usually trained on computer-synthesized datasets, resulting in noticeable performance degradation when applied to real-world CAD models. Therefore, we propose a novel deep learning network, BrepMFR, designed for Machining Feature Recognition (MFR) from Boundary Representation (B-rep) models. We transform the original B-rep model into a graph representation as network-friendly input, incorporating local geometric shape and global topological relationships. Leveraging a graph neural network based on Transformer architecture and graph attention mechanism, we extract the feature representation of high-level semantic information to achieve machining feature recognition. Additionally, employing a two-step training strategy under a transfer learning framework, we enhance BrepMFR's generalization ability by adapting synthetic training data to real CAD data. Furthermore, we establish a large-scale synthetic CAD model dataset inclusive of 24 typical machining features, showcasing diversity in geometry that closely mirrors real-world mechanical engineering scenarios. Extensive experiments across various datasets demonstrate that BrepMFR achieves state-of-the-art machining feature recognition accuracy and performs effectively on CAD models of real-world mechanical parts.

Analysis of the technology of manufacturing a semi-finished part for a hollow part of a complex geometric form using the technology of hot volume stamping

Abstract. Background. Today, the actual issues in the production of metal products are the saving of materials and the productivity of production, as this has a significant impact on the cost of finished products. This especially applies to hollow products with a complex geometric shape. Such products include parts or semi-finished products that have hollow cavities and additional elements in the design in the form of flanges, or variable wall thickness along the height of the product. Such parts are widely distributed in mechanical engineering, aircraft construction and in the production of special purpose products, in particular in the field of ammunition production. Therefore, the manufacturing technology of such parts should ensure mass production and have an economic effect. Goal. By calculation, using the finite element method (FEM) in the DEFORM software environment, determine the option of stamping, from blanks of different diameters, a semi-finished product of a hollow part of a complex geometric shape using the technology of hot three-dimensional stamping, and analyze the proposed technological process of obtaining a semi-finished product. Methodology of implementation. Using MSE in the DEFORM software environment, simulation of hot three-dimensional stamping of a semi-finished product was carried out for a hollow part of a complex geometric shape made of blanks of different diameters. In this way, the option of obtaining a semi-finished product with a minimum number of transitions and a guaranteed possibility of implementing the technological process of mold formation was chosen. For the selected option, an analysis of the force modes of forming, normal stresses on the contact surfaces of the workpiece with the tool, and the stress-strain state of the deformed metal was performed. The results. A semi-finished product manufacturing technology for a hollow part of a complex geometric shape using hot three-dimensional stamping technology is proposed. This technology will be implemented in the production of the adapter housing part, which is used in the design of the 120 mm mine. By calculation, with the help of MSE in the DEFORM software environment, the variant of semi-finished product molding for the "Body-adapter" part was determined using the technology of hot three-dimensional stamping, and an analysis of the technological operation of semi-finished product molding was carried out. The temperature regime of the process, technological efforts, parameters of the stress-strain state of the deformed material, the distribution of normal stresses on the deforming tool are determined. The results of the conducted computer modeling make it possible to take into account the design features and select the necessary technological equipment for mass production. Conclusions. The technology for serial production of semi-finished products by hot volumetric stamping has been developed and substantiated. This technology made it possible to increase the rate of material utilization by two times compared to the technology of obtaining a part by mechanical processing from graded rolled steel.

MODELLING OF MASS TRANSFER IN WASTEWATER FACILITIES

Problem statement. The design of wastewater treatment systems is a complex process and requires the use of special mathematical models. As a rule, empirical models are used at the stage of designing structures of water drainage systems, which allow obtaining only an “integral” characteristic of the efficiency of wastewater treatment. But in a number of cases, it is important to have information about the spatial distribution of the impurity concentration in the structure. To solve this problem, you need to have three-dimensional mathematical models. In the future, there is a shortage of such models, so the creation of three-dimensional multifactorial models for the analysis of the efficiency of drainage system structures is an urgent task. The purpose of the article. Development of a three-dimensional numerical model for the analysis of the mass transfer process to determine the impurity concentration in the clarifier. Methodology. The analysis of impurity concentration fields in the clarifier is carried out by numerical integration of the three-dimensional equation for the velocity potential and the three-dimensional equation of the convective-diffusion transport of the impurity. For the numerical integration of the Laplace equation for the velocity potential, the variable-triangular method and the Liebmann method are used. Finite-difference splitting schemes are used for numerical integration of the three-dimensional equation of convective-diffusion transport of impurities. Scientific novelty. A dynamic multifactorial numerical model was created for the analysis of the process of mass transfer of impurities in a settling tank by conducting a computational experiment. Practical value. The built multifactorial numerical model makes it possible to analyze the efficiency of wastewater treatment in clarifiers that have a complex geometric shape and cannot be calculated on the basis of existing engineering methods. Conclusions. On the basis of the developed three-dimensional numerical model, a computer code was created, which allows you to quickly obtain information about the distribution of the impurity concentration in the settling tank.

The Past, Present, and Future of Tubular Melt Electrowritten Constructs to Mimic Small Diameter Blood Vessels - A Stable Process?

Melt Electrowriting (MEW) is a continuously growing manufacturing platform. Its advantage is the consistent production of micro- to nanometer fibers, that stack intricately, forming complex geometrical shapes. MEW allows tuning of the mechanical properties of constructs via the geometry of deposited fibers. Due to this, MEW can create complex mechanicsonly seen in multi-material compounds and serve as guiding structures for cellular alignment. The advantage of MEW is also shown in combination with other biotechnological manufacturing methods to create multilayered constructs that increase mechanical approximation to native tissues, biocompatibility, and cellular response. These features make MEW constructs a perfect candidate for small-diameter vascular graft structures. Recently, studies have presented fascinating results in this regard, but is this truly the direction that tubular MEW will follow or are there also other options on the horizon? This perspective will explore the origins and developments of tubular MEW and present its growing importance in the field of artificial small-diameter vascular grafts with mechanical modulation and improved biomimicry and the impact of it in convergence with other manufacturing methods and how future technologies like AI may influence its progress.

Graph convolution network-based surrogate model for natural convection in annuli

This work develops a model for natural convection in annuli with internal heat sources based on Graph Convolution Network (GCN), achieving rapid prediction by directly establishing the mapping relationship between the geometric features and the temperature field. The GCN learns node features and connections between nodes in data structures. Compared with traditional machine learning networks, GCN exhibits greater advantages in handling complex geometric shapes and unstructured nodes. In this study, numerous data samples were constructed with various geometric features, e.g., varying sizes, positions, and quantities of internal heat sources. The results indicate that a fully trained GCN was capable to adaptively predict temperature field distributions with arbitrary heat source sizes, positions, and quantities. The mean prediction errors of GCN for the temperature field are around 0.17 %, 0.32 %, and 0.85 %, for the single, double, and triple heat sources cases, respectively. Furthermore, the GCN prediction performance was also compared with surrogate models by the convolutional, and fully connected neural networks (CNN and FNN), which shows an improvement of 88.1 % and 84.8 %, respectively. Therefore, compared with numerical results and other surrogate models, the proposed model presents superior geometric adaptability, high prediction accuracy and a remarkable enhancement in computational efficiency (three orders of magnitude).

One-Dimensional Modeling of the Pressure Loss in Concrete Pumping and Experimental Verification

An accurate formula for calculating the pressure loss in concrete pumping plays a significant guiding role in the design and service process of pump trucks. Based on the flow characteristics of concrete pumping, a straight pipe one-dimensional model for the pressure loss is developed, in which both the viscous force of the mortar in the lubrication layer and the blocking effect of coarse aggregate particles are considered. First, the complex geometrical shapes of the aggregate particles are geometrically reconstructed by using a HandySCAN noncontact scanner and the reverse modeling software Geomagic Design X (v.19.0.2). Then, the equivalent spherical size of nonspherical aggregate particles is calculated according to the equal hydraulic radius principle. The blocking effect of the aggregate particles is converted into the wall roughness. Finally, an explicit expression for the pressure loss in concrete pumping is deduced by using Modi’s equation, Bernoulli’s equation, and Darcy’s formula, and the calculated value is compared with the measured value at a corresponding experimental site. The results indicate that the pressure loss values calculated with the one-dimensional flow model are closer to the actual pumping pressure loss values. The relative error between the results and the actual pumping pressure loss value is about 20.2%.

ANALYSIS OF THE EFFICIENCY OF THE USE OF PROTECTIVE SCREENS TO REDUCE THE LEVEL OF AIR POLLUTION

The task of assessing the areas of chemical pollution near the highway, where protective screens of different geometric shapes are located, is considered. The purpose of the work is to develop numerical models for calculating pollution zones formed near protective screens, as well as conducting a laboratory experiment to analyze the patterns of formation of pollution zones near screens of a complex geometric shape. For mathematical modeling of the process of formation of pollution zones near the protective screen, the equation of convective-diffusion transfer of impurities is used. This equation takes into account atmospheric diffusion, wind speed, emission intensity of a chemically hazardous substance, the location of the emission source, and the shape of the protective screen. The Navier-Stokes equation and the Laplace equation for the velocity potential are used to solve the problem of aerodynamics. Finite-difference methods are used for numerical integration of modeling equations. A package of application programs was created on the basis of the developed numerical models. Numerical models and a package of programs have been built, allowing to study the process of the formation of areas of pollution near the highway in almost real time. The results of the computational experiment are presented.

Vat photopolymerization 3D printing of yttria-stabilized ZrO2 ceramics: effects of a sintering additive (Na2O – 2SiO2), biocompatibility, and osteointegration

Effects of a liquid-phase sodium disilicate additive on the properties of ZrO2 ceramics containing 3 mol.% of Y2O3 and 2 wt% of Al2O3 are presented, including phase composition, microstructure, shrinkage, porosity, and bending strength. The distribution of elements along grain boundaries and the composition in a selected area of a lamella were investigated by transmission electron microscopy in pure and additive-containing samples. As a result of the introduction of the additive, sintering activity of the material increased, and the sintering temperature diminished down to 1150 °C. Thus, dense nanocrystalline materials with a crystallite size of 50–70 nm and a bending strength of up to 450 MPa were obtained. Optimized polymer-ceramic suspensions were used to produce objects with complex geometric shapes by 3D molding technology through layer-by-layer vat polymerization. According to in vitro assays, the obtained samples are nontoxic and cytocompatible with human osteosarcoma MG-63 cells, and according to in vivo experiments, are biocompatible and showing osseointegrative properties when implanted into the rat tibia.

An Interdisciplinary Educational Proposal in Junior High School: The Fractal Geometry in Science, Computer Science and Art Lessons

The purpose of this study is to provide an interdisciplinary approach to fractals within the traditional school curriculum. The proposed activities are expected to help teachers to provide a comprehensive and engaging learning experience for students that fosters deeper understanding, creativity, and connections within the sciences. Fractals are complex geometric shapes that are self-similar, and therefore exhibit similar patterns at every scale. They are created by repeating a simple process over and over. Fractals differ from traditional geometric shapes because they are non-regular, but are very common in nature, such as clouds, mountains, trees and snowflakes. Also fractals are impressive mathematical creations and can contribute a lot to the understanding of Junior High School mathematics because they could be fun and at the same time an exciting way to introduce many areas of mathematics and physics. By connecting fractals to different mathematical concepts and applications, Junior High School students can develop their problem-solving skills and gain a deeper appreciation for the beauty and complexity of mathematics.

Contribution to the formability improvement in sheet metal stamping by a novel technique to control press kinetics

The thickness variation during sheet deep drawing process has an impact on the quality of the final product and can lead to local material fractures. To minimize this phenomenon caused by varying degrees of stretching in different areas of the sheet, various methods can be employed. This research paper introduces a novel technique for metal sheet deep drawing, specifically designed for parts with complex geometric shapes that exhibit significant variations in deformation levels across different areas. The objective of this method is to enhance the quality of the deep drawing process by reducing thickness variations in the final part. In this proposed approach, the vertical movement of the punch is accomplished through two vertical rotational movements. This increases the flexibility of the deformation process, ensuring that the active tools elements occupy the most advantageous positions determined by the material flow in the die. As a result, the material's deformability is improved, allowing for a higher degree of deformation. Additionally, this new method offers a relatively simple design and kinematics solutions for the press and eliminates the need for lengthy assembly-disassembly times.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ НЕИЗОТЕРМИЧЕСКОГО ТЕЧЕНИЯ ДВУХФАЗНЫХ СРЕД В ОБЛАСТЯХ СЛОЖНОЙ ГЕОМЕТРИЧЕСКОЙ ФОРМЫ

Mathematical modeling of non-isothermal flow of two-phase media in areas of complex geometric shape, which are often working units of various types of technological equipment, is considered. To construct a mathematical model describing the flow of a two-phase medium in channels and pipes of complex shape, the equations of conservation of mass, momentum and energy of the mechanics of multiphase media were used with the corresponding closing relations for the force of interphase interaction, the physical parameters of the two-phase medium and the rheological law of the state of the mixture in the form of the Ostwald-de Ville. The conservation equations, taking into account the flow features close to one-dimensional, are written in an orthogonal coordinate system associated with the region, which allows them to be significantly simplified. An algorithm for conducting a computational experiment has been constructed. As a numerical method for conducting a computational experiment, a modified method of equal flow surfaces was used. In this case, changes in the physical parameters of a two-phase medium depending on temperature are taken into account, which significantly complicates the calculations. Numerical calculations were carried out for areas of parabolic and conical shapes, which are determined in the general conservation equations written in a curvilinear orthogonal coordinate system by specifying the corresponding Lame coefficients. In this case, the location and number of equal flow surfaces varied over a wide range, and the input values of the longitudinal velocity and temperature on the streamlines were specified. A computational experiment was implemented for various values of the parameters of the flow region, the rheological law of the state of the medium, taking into account changes in the effective viscosity of the medium from temperature, heat transfer modes and the flow of a two-phase medium. As a result of the computational experiment, various flow regimes and the influence of various geometric characteristics of the flow region, mass forces, and parameters of the rheological law of the state of the medium on the hydrodynamic situation were studied. The various longitudinal velocity and temperature profiles specified at the input developed to a certain steady state, which do not depend on the choice of the initial profile. The temperature values of the medium on the streamlines monotonically approach their asymptotes. The locations of the asymptotic values are determined by the temperature values on the channel walls and the initial temperature of the medium at the inlet. At the same wall temperatures, a symmetrical pattern of heating of the medium is observed, but when the wall temperatures are different, no symmetry is observed. The results of mathematical modelling and computational experiment can be used in the calculation of various technological processes occurring in non-isothermal flows of two-phase media in areas of complex geometric shape.

A novel prediction model of the freckle defects for single-crystal superalloy blades

The freckle is a typical surface defect formed during the directional solidification of SC (single crystal) components of Ni-based superalloys. It generally appears as a long and narrow trail of equiaxed grains aligned roughly parallel to the direction of gravity, which breaks the integrity. Once appears, the freckle can never be avoided by further treatment. With the turbine blade requirements increasing, the state-of-the-art methods include adding more refractory elements into Ni-based SC superalloys, and the design of blades with a more complex geometric shape make the freckle defects grow easier at the special surface zones. This leads to a significant challenge in controlling grain defect formation in SC blades and vanes for freckles. The current consensus to freckle formation is described as the Rayleigh-Taylor instability (RTI) flow that occurred in the interdendritic zone. During solidification, the compositional segregation (CS) occurred as soon as the solid interface forwarding led to the density changes between the interdendritic melting phases and the residual liquids. For nickel-based superalloys, the enrichment of low-density solutes like Al, and Ti at the interdendritic zone will make the liquid lighter. However, the widely used Ra model can’t correctly match the freckle tendency of the components with complex shapes (called geometrical effects of freckles), especially for blades. Recent reports indicate that the freckles occur at the preferred positions in the casting. In this work, a novel model is designed to quantitatively discuss the geometrical effects on freckle formation and to combine existing Ra number models with solidification models to enable freckle predictions at a smaller scale. The proceeding of this work can make the design of complex blades easier.

Adaptive Ultrasonic Full Matrix Capture Process for the Global Imaging of Complex Components with Curved Surfaces.

This work proposes a new global FD-RTM method to solve the problem of ultrasonic inspection of parts with complex geometric shapes. With this method, the frequency domain reverse time migration (FD-RTM) algorithm is used to adapt to the complex refraction of ultrasonic waves by the surface, while an interface solution algorithm based on tangent fitting is used to solve the interface position with high precision through the full matrix reception data. Based on high-precision interface information, a hybrid extrapolation algorithm and a situation-specific probe movement strategy are used to enable the probe to find the next sampling point according to the direction of the workpiece surface, allowing complex surface topography features to be identified without relying on the workpiece CAD drawing. This makes it possible to achieve the automated inspection of workpieces. To verify the proposed method's effectiveness, an aluminum alloy model with side-drilled holes (SDH) is used. The geometry of the model consists of multiple convex and concave surfaces. By comparing the local FD-RTM imaging with images synthesized using the entire scan path, it is shown that gFD-RTM improved the imaging performance. Compared with FD-RTM, the average signal-to-noise ratio of gFD-RTM was increased by 20%, and the array performance index (API) was reduced by 70%, indicating effective detection coverage.

Analysis of Stability and Oscillations of Porous Power and Sigmoid Functionally Graded Sandwich Plates by the R-Function Method

In this paper, the R-function method is used for the first time to study the stability and oscillations of porous functionally graded (FG) sandwich plates with a complex geometric shape. It is assumed that the outer layers of the plate are made of functionally graded materials (FGM), and the filler is isotropic, namely ceramic. The differential equations of motion were obtained using the usual first-order shear deformation theory with a given shear coefficient (FSDT). Two models of porosity distribution according to the power (P-law) and sigmoid (S-law) laws were studied. Analytical expressions for calculating the effective mechanical characteristics of FG materials with even and uneven porosity distribution were obtained. The proposed approach takes into account the fact that the subcritical state of the plate can be heterogeneous, and therefore, first of all, the stresses in the middle plane of the plate are determined, and then the eigenvalue problem is solved in order to find the critical load. To determine the critical load and plate frequencies, the Ritz method was used along with the R-function method. The developed algorithms and software are tested on test examples and compared with known results obtained using other methods. A number of problems of stability and oscillations of the FG of porous sandwich plates with a complex geometric shape for various layer stacking schemes, various boundary conditions and laws of porosity distribution have been solved.

Dynamic analysis of functional gradient porous sigmoidal sandwich plates

Analysis of free vibrations of functionally graded (FG) porous sigmoid sandwich plates, is considered in this paper. The plate can have a complex geometric shape and various types of fastening. To solve the problem, we used the variational-structural method (RFM), which combines the theory of R-functions and variational method of Rayleigh-Ritz. The mathematical statement of the problem is carried out within the framework of the deformation theory of plates of the first order (FSDT). Plates are considered, the outer layers of which are made of functionally graded materials (FGM), and the core is isotropic. For different models of porosity distribution (sigmoid uniform and nonuniform), analytical expressions were obtained to calculate the effective properties of FGM. For rectangular plates, a comparison of the obtained results with known results obtained using other approaches is shown. Calculations for plates with a complex shape are presented in the form of tables and graphs. The influence of the volume fraction of ceramics, the different types Of FGM and the coefficient of porosity on the natural frequencies of the plate is analyzed.

Three-dimensional partition-of-unity generalized node method for the simulation of fractured rock mass

A three-dimensional (3D) partition-of-unity (PU) generalized node method (GNM) is developed for the simulation of fractured rock mass. In the 3D PUGNM, generalized nodes with independent deformations are directly defined on the isolated blocks to simplify the construction of PU approximations in 3D problems. The explicitly representing of polyhedral blocks with complex geometric shapes by a proper topological structure, the computational geometric algorithms for block cutting, and the subdivision of integration tetrahedrons adapting to physical boundaries are totally avoided in the present 3D PUGNM, and thus the bottleneck problems encountered in the existing PU methods for three dimensions have been well solved. The present 3D PUGNM has the advantages of simple data structure, strong robustness, and convenient numerical implementation, and paves the way for promising application in various engineering problems. Several numerical examples are tested to demonstrate the accuracy, correctness and robustness of the proposed method.

RESEARCH ON INCREASING THE HARDENING OF A GEAR REDUCER USING PLASMA TECHNOLOGY

Different case hardening methods are used to increase the hardening of machine-building products and their resistance to abrasion, temperature and corrosion. The most modern methods include plasma nitriding technology. This method can be applied for the following parts: crankshaft, gears, piston parts, etc. A common characteristic feature of workpiece that undergo case hardening is that their mechanical processing after hardening is difficult or impossible due to high hardness and complex geometric shape. Plasma nitriding is the process of low-temperature common case hardening for highly loaded gears. When nitriding, a diffusion layer with very hard complex nitride precipitation with a thickness of several microns is formed on the surface of the gear wheel, which greatly increases the technical performance of the part. [1] This article summarizes the state of knowledge in the field of plasma nitriding technology equipments and surface nitriding of gears, provides a overeview of the current state of research in the field of nitrided gears. Keywords: hardening, plasma nitriding, nitriding, gears, mechanical processing, reducer.