Spatial Mathematical Model Research Articles

Abstract B008: Therapy-protective peristromal niches mediate positive ecological interaction between therapy-sensitive and therapy-resistant cells, altering the evolutionary dynamics of acquired targeted therapy resistance in lung cancers

Abstract Pharmacological inhibitors of oncogenic signaling, such as drugs that target ALK kinase (ALKi) in ALK+ lung cancers, can induce strong and durable clinical responses. However, targeted therapies are not curative in advanced cancers and even strong responders eventually develop resistance. While therapy resistance is typically attributed to cell-intrinsic (epi)mutational characteristics of tumor cells, it can also result from interactions of tumor cells with the tumor microenvironment (TME). In contrast to the detailed elucidation of the molecular mediators of therapy resistance, our knowledge of the evolutionary dynamics underlying the resistance emergence, including the impact of TME, remains poorly defined. A key open question in understanding the evolutionary dynamics of therapy resistance is whether relapse results from an expansion of pre-existing therapy-resistant subpopulations or from a bona fide gradual evolutionary process. To elucidate this question, we integrated experimental mouse studies with mathematical modeling, interrogating therapeutic responses of therapy-naïve experimental xenograft ALK+ tumors, spiked-in with differentially labeled resistant cells. We found that ALKi treatment induced a rapid expansion of resistant cells, which drastically reduced the magnitude and duration of remissions. Surprisingly, our in silico analyses pointed to the existence of a strong positive ecological interaction between therapy-resistant and therapy-sensitive competitors. Using a combination of spatial analyses, experimental studies, and mathematical modeling, we found that this interaction was mediated by peristromal niches that protected therapy-sensitive tumor cells. Specifically, by limiting tumor regression, the therapy- induced expansion of resistant cells limited the loss of protective peristromal niches, while the subsequent resumption of tumor growth created new peristromal niches capable of supporting the survival and proliferation of therapy-sensitive cells. While this niche-mediated interaction had only a marginal impact on the transition from remission to relapse, enhanced survival of therapy-sensitive cells potentiated their ability to adapt to ALKi, leading to a higher diversity of resistance phenotypes. In summary, our study has revealed a new type of indirect, niche-mediated ecological interaction between therapy-resistant and therapy-sensitive cells. The rapid expansion of rare pre-existent resistant cells and fast transition to relapse challenge a common assumption of the pre-existence of therapy resistance. Finally, our results highlight the essentiality of TME considerations in understanding the evolutionary dynamic underlying the development of therapy resistance. Citation Format: Mark Robertson-Tessi, Bina Desai, Tatiana Miti, Pragya Kumar, Sagnik Yarlagadda, Rishi Shah, Robert Vander Velde, Daria Miroshnychenko, David Basanta, Alexander Anderson, Andriy Marusyk. Therapy-protective peristromal niches mediate positive ecological interaction between therapy-sensitive and therapy-resistant cells, altering the evolutionary dynamics of acquired targeted therapy resistance in lung cancers [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Tumor-body Interactions: The Roles of Micro- and Macroenvironment in Cancer; 2024 Nov 17-20; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2024;84(22_Suppl):Abstract nr B008.

INFLUENCE OF DESIGN AND OPERATIONAL FACTORS ON THE STABILITY OF THE CAR WITH TRAILER OF CATEGORY O2 DURING BRAKING MODE

In recent years, enterprises and private manufacturers in Ukraine have mastered the production of a wide range of towed vehicles. Significant attention is given to the issues of road safety for road trains, particularly those of category M1, which have found widespread use not only among state and private enterprises but also among amateur motorists. Ensuring the safety of such road trains is a pressing task. The movement characteristics of a road train fundamentally differ from those of a single vehicle. This difference is explained by the presence of additional forces in the articulated connections of the vehicle components, as well as the forces and moments acting on its individual components, which influence the movement of the vehicle as a whole. This influence is particularly noticeable during the braking of a road train, which can be accompanied by the folding of components and a loss of vehicle stability. Ensuring the safety of such road trains is a pressing task that requires a more detailed analysis of the impact of the distribution of braking forces on the stability of the road train’s movement. Such research was conducted on a spatial mathematical model of the road train. To determine the longitudinal and lateral forces acting on the wheels of a road train during braking, the normal reactions of the support surface on the wheels of the vehicle and trailer were determined. These reactions, along with the specific braking forces, determine the braking forces acting on the wheels of the vehicle and trailer. For example, with a deceleration of 6.0 m/s², the normal reaction of the support surface on the twin axle of the trailer decreases by 25%. In the absence of an anti-lock braking system in the trailer’s brake drive, wheel lockup and loss of road train stability are possible. Therefore, it is advisable to brake the road train with decelerations not exceeding 4.0 m/s². In this case, the initial braking speed that ensures the stability of the road train’s movement is higher than its maximum speed. When changing the trailer’s load while the vehicle’s load remains unchanged at a speed of 25 m/s, the road train remains stable throughout the entire range of the trailer’s total mass variation, whereas at a speed of 30 m/s, the critical mass of the trailer remains at 2500 kg. This is explained by the fact that the trailer’s mass affects the magnitude of the maximum braking force created by the braking system and the braking force that can be realized. The loading of the trailer, particularly the side loading of its wheels, is very important as it can lead to uneven braking forces on the trailer’s axles. It is shown that with the nominal loading of the vehicle and trailer, increasing the unevenness of the braking forces on the trailer’s axles up to 30% reduces the initial braking speed, which still ensures the stability of the road train’s movement, by almost half from 35.3 to 19.7 m/s. Therefore, the unevenness of the braking forces on the trailer’s axles should be limited to 15%. This will ensure the stability of the road train’s movement and the safety of its operation. Keywords: аutomobile, trailer, road train, side and axle load, braking, initial speed, movement stability.

Dissecting the Spatially Restricted Effects of Microenvironment-Mediated Resistance on Targeted Therapy Responses.

The response of tumors to anti-cancer therapies is defined not only by cell-intrinsic therapy sensitivities but also by local interactions with the tumor microenvironment. Fibroblasts that make tumor stroma have been shown to produce paracrine factors that can strongly reduce the sensitivity of tumor cells to many types of targeted therapies. Moreover, a high stroma/tumor ratio is generally associated with poor survival and reduced therapy responses. However, in contrast to advanced knowledge of the molecular mechanisms responsible for stroma-mediated resistance, its effect on the ability of tumors to escape therapeutic eradication remains poorly understood. To a large extent, this gap of knowledge reflects the challenge of accounting for the spatial aspects of microenvironmental resistance, especially over longer time frames. To address this problem, we integrated spatial inferences of proliferation-death dynamics from an experimental animal model of targeted therapy responses with spatial mathematical modeling. With this approach, we dissected the impact of tumor/stroma distribution, magnitude and distance of stromal effects. While all of the tested parameters affected the ability of tumor cells to resist elimination, spatial patterns of stroma distribution within tumor tissue had a particularly strong impact.

Experimental Study of the Regularities of Deformation of the Rubber Cord Shell of a Pneumatic Spring of High-Speed Rolling Stock

Purpose. The aim of this work is to establish the regularities of deformation of the rubber cord shell in the vertical and horizontal directions in the case of changes in the internal pressure in the pneumatic spring by static experimental studies. Methodology. A static test bench was used to establish the regularities of deformation of the rubber cord shell of a pneumatic spring. Changes in the internal pressure in the pneumatic spring were achieved using a compressor, and the deformation of the rubber cord shell was measured directly by high-frequency potentiometric linear displacement sensors. The deformation of the rubber cord shell of a pneumatic spring in both the vertical and horizontal planes was studied under the condition of changing the internal pressure in the spring in the range from 0 to 5 atm. Findings. Using the designed test bench, a methodology for experimental studies of the deformation of a rubber cord shell with increasing internal pressure in a pneumatic spring was developed. The dependences of the deformation value of the rubber cord casing of a pneumatic spring when the internal pressure changes in the range of 0÷5.0 atm were obtained. It is established that the deformation of the rubber cord casing with an increase in the internal pressure in the pneumatic spring in the horizontal plane is more intense compared to the vertical plane. It is found that the maximum values of deformation of the rubber cord shell of a pneumatic spring in the vertical and horizontal directions are observed at the initial stage of air injection in the range of pressure changes from 0 to 0.5 atm. The polynomial equations describing the deformation dependences of the rubber cord shell of a pneumatic spring were obtained. Originality. The regularities of deformation of the rubber cord casing in the vertical and horizontal planes at different values of the internal pressure in the pneumatic spring were determined by experimental static studies. Practical value. The study of the regularities of deformation of the rubber cord shell will contribute to a more accurate modeling of the operation of the pneumatic spring and a reliable determination of its dynamic performance. This will make it possible to use the dynamic performance of the air spring in the spatial mathematical model of the rolling stock at the design stage, as well as to evaluate its dynamic performance and traffic safety indicators.

Simulation of a new process of mixing liquid metal in CCM mold with rotating cooling jacket with vertical ribs

The article proposes a new technology of filling the CCM mold with liquid metal and mixing it. The original patented device consists of a closed bottom nozzle and a rotating jacket. Experimental studies of liquid metal flow in a mold are long, complex and time-consuming, therefore, in the work was used mathematical modeling by numerical method. The objects of research are the hydrodynamic and thermal flows of liquid metal during the new process of steel casting into a CCM mold of rectangular cross-section, and the result is a spatial mathematical model that describes the flows and temperatures of liquid metal in the mold. To simulate the processes occurring during the metal flow in the mold, the authors used a specially crea­ted software package. The theoretical calculations are based on the fundamental equations of hydrodynamics, the equations of mathematical physics (equation of thermal conductivity taking into account mass transfer) and a proven numerical method. The area under study is divided into elements of finite dimensions, for each element a formulated system of equations is written in a difference form. The result is the velocity and temperature fields of the metal flow in the mold volume. According to the developed numerical schemes and algorithms, a calculation program was compiled. The paper considers an example of calculating the steel casting into a mold of rectangular cross-section and flow diagrams of liquid metal over various mold sections. Vector flows of liquid metal in various mold sections are clearly presented for different rotary speed of the rotating jacket. The authors identified the areas of intense turbulence and presented the results of the problem numerical solution in graphical form by diagrams of the velocity fields of liquid metal flows and their temperature over various mold sections.

Studies of oil product pollution in the aeration zone by mathematical modelling

Formulation of the problem. The article presents the results of a study to assess the pollution of the aeration zone due to the leakage of oil products as a result of the destruction of the «Amik» oil depot during the military operations in the town of Borodyanka. The destruction of the tanks resulted in an immediate leakage of light oil products onto the soil of the surrounding area. The result was a technogenic environmental situation that required immediate determination of the mechanisms of accidental penetration of pollutants into the soil and groundwater, determination of the area of contamination and scientifically sound methods of soil remediation of oil products. The article highlights the issues of organising mathematical modeling of various data for solving applied problems using Google Earth data. Materials and methods. In order to assess the contamination area and determine the mechanism of accidental penetration of oil products into the soil and groundwater, the existing models of pollutant penetration in case of accidental oil spill were analysed and mathematical spatial models of geomorphological, hydrogeological, engineering-geological and experimental filtration data were created using interpolation, mathematical approximation and gradient analysis. The latter made it possible to identify the directions of surface and groundwater flow both in the local area of the oil depot and in adjacent areas. Using the investigation and filtration parameters obtained during the field work, hydraulic gradients and soil filtration coefficients were calculated, and a spatial mathematical model of the local subterranean gradient of groundwater flow was created. Results. It was shown that the direction of the underground flow is controlled by a zone of local depression, which is expressed by a decrease in the absolute height of the natural lithological layer with a height difference of about 0.4 m or the maximum values of the height of the contamination lens. The direction of extension of this zone has been determined to be from north to south. This zone can be considered the zone of maximum accumulation of liquid with oil products. Based on the survey results, the thickness of the contamination lens was calculated to be 0.3 m on average. Using this indicator, the area of contamination is 4169 m2, the volume of contamination is 1250.7 m3, which corresponds to the claimed damage. However, taking into account the anisotropy of the filtration properties of the lithological types in different directions within the aeration zone, the presence of dissolved water due to dispersion and the presence of local accumulation depressions in the lithological strata, options with other indicators (0.5 m / 0.1 m) are also acceptable. The calculation of the contamination areas was carried out taking into account the power variations. The approximate total areas of oil product distribution in the aeration zone were plotted with reference to Google Earth imagery. Conclusions. The research enabled practical recommendations to be made for cleaning up the area of oil products and preventing the spread of the pollutant by pumping oil products out of the modelled and actually confirmed pollution lens. In accordance with the recommendations, 140 wells were drilled to a depth of 5.2 m, with a diameter of 0.11‑0.168 m and a total length of 710 m, which made it possible to prevent the spread of the contaminant by pumping out the oil products and reusing them after clean-up.

Computer modeling and software research of car and engine parts

Problem. The development of automotive technology for various purposes and the improvement of existing car models, requires a fast and flexible design process. Spatial models of details and nodes are the starting points for design, and the necessary design documentation is performed on their basis. When manufacturing parts on CNC machines, it is necessary to quickly obtain a control program that will increase the accuracy of the product by ensuring the optimal trajectory of the mutual movement of the part and the tool. Therefore, the creation of a comprehensive methodology for the design of car parts, their basic inspection and obtaining design documentation is an important technical task. Goal. The main goal of the work is to determine the rational sequence and basic principles of computer-aided design, research and manufacturing of car and engine parts, and the development of mathematical spatial models of surfaces in order to optimize control programs for CNC machines. Methodology. The approaches adopted in the work for solving the set goal are based on general design principles. The methods of conducting static and dynamic calculations, as well as spatial mathematical modeling of the processes of manufacturing parts were also used. Results. A comprehensive methodology for designing parts of engines and cars has been developed. The main principles of creating spatial models have been determined in order to achieve their flexibility and simple editing. Methods of automating the development of drawings and design documentation are described. The software options for the primary verification of static strength and frequency analysis are considered. A calculation program has been developed for constructing transient and amplitude-phase-frequency characteristics. The mathematical spatial modeling of typical surfaces of the camshaft is provided with the aim of further research and optimization of the development of a control program for processing on a CNC machine tool. Originality. The defined basic principles of designing parts of engines and cars provide an opportunity to create a flexible spatial model and more fully automate the process of drawing up technical documentation. The developed mathematical spatial models of the supporting and working surfaces of the camshaft make it possible to write a control program with the determination of the optimal trajectory of the mutual movement of the part and the tool. Practical value. The obtained results can be recommended when designing car parts and assemblies.

Математическая модель волновой зубчатой передачи с генератором волн внешнего деформирования

The paper considers a spatial mathematical model of a wave gear with the annular generator of the external deformation waves. Calculation method was based on determination of the elastic interaction between flexible wheel, rigid wheel and wave generator. Numerical studies confirmed the adequacy of the proposed mathematical model. Theoretical studies of the influence of preload in the gearing and initial clearance between the flexible wheel and the deforming washers on the forces acting on the wave generator bearings were conducted. It is shown that a decrease in the specified clearance leads to an increase in loads on the bearings. By calculation, torsional rigidity characteristics of the wave gear with an external deformation generator were obtained for various interference values in the gearing and the clearance.

TO DETERMINE STABILITY OF THE ROAD TRAIN WITH O1-CATEGORY TRAILER

In the work improved system of equation of plane-parallel movement of the road train with single-axle O1-category trailer. Defined lateral reactions on the vehicle and trailer wheels at body roll, wheels slip caused by body roll and also developed road train spatial mathematical model in a transverse plane. This model is used to study the road train course stability with O1-category trailer. It is shown that the spatial model of road train with no vehicle and trailer wheels inclination has the same divergent instability characteristic as the plane road train layout.

Farmland abandonment in the mountainous areas from an ecological restoration perspective: A case study of Chongqing, China

Farmland abandonment reflects the decline of rural areas, resulting in a series of vicious chain reactions, hindering the promotion of the comprehensive rural revitalization strategy. From the perspective of ecological restoration, this paper integrated multi-source data such as Landsat, GF-1, and Google Earth images and household survey data, aiming to reveal the spatiotemporal pattern, attribution, and mechanism of farmland abandonment in typical mountainous areas over the past 20 years by employing spatial analysis and mathematical models and to promote comprehensive management of abandoned farmland. The results are as follows. (1) The scope of abandoned farmland in Chongqing has been expanding, with the abandoned area growing from 142,385.8 hm2 to 345,778.4 hm2 from 2000 to 2020, with the initially abandoned farmland mostly concentrated in the northeastern areas, such as Chengkou, with an abandonment rate of 21.8%, and thereafter, spreading in all directions; In the end, abandoned farmland was concentrated in northeastern and southeastern Chongqing, such as Wuxi and Youyang, with abandonment rates of approximately 25.1% and 20%, respectively. (2) The attribution of farmland abandonment mainly includes wild boar damage, labour shortage, and natural conditions, among which wild boar proliferation has become an important factor under the background of ecological restoration. (3) Ecological restoration has produced a counter-servicing effect of the ecosystem on human beings, forming a vicious circle in the mountainous countryside where ecological restoration continues to aggravate farmland abandonment. The contribution of this study is to investigate the pattern of farmland abandonment from both macroscopic and microscopic perspectives. At the same time, this paper explores the intrinsic mechanism between ecological restoration and farmland abandonment and proposes scientific countermeasures to break the vicious cycle of ecological restoration that continues to exacerbate farmland abandonment in mountainous areas.

Expected position and attitude adjustment control method of coal mine roadway support robot

AbstractThis paper proposes an expected position‐attitude adjustment control method of coal mine roadway support robot (CMRSR) based on a real‐time position‐attitude detection system. Taking advantage of lateral adjustment mechanism and control method, the CMRSR has flexible maneuverability and high dynamic expected position‐attitude adjustment performance. It can guarantee stability and safety of the relative position‐attitude in time‐varying roadway environment in underground coal mines. First, the structural characteristics, hydraulic system characteristics, and kinematic characteristics of the CMRSR are considered, and the spatial mathematical relationship model on position‐attitude parameters and sensor data information, roadway environment dimensions, and CMRSR structural dimensions are established. In addition, the real‐time position‐attitude of the CMRSR with respect to the roadway is recognized by the position‐attitude detection system. Then, according to real‐time roadway environment and relative position‐attitude, the expected position‐attitude parameters are set, and the adjustment parameters and types of each lateral hydraulic cylinder are selected based on different deviated position‐attitude conditions. A position‐attitude adjustment controller is designed based on the sliding mode variable structure control algorithm to achieve precise position‐attitude adjustment of the CMRSR. In addition, the position‐attitude detection system is used to provide feedback control to maintain the relative position‐attitude of the CMRSR. Finally, the practical performance illustrates high effectiveness and feasibility of the proposed control method. The average error of distance can be controlled within ±30 mm, the average error of angle can be controlled within ±0.5°, and the adjustment time can be controlled within 20 s.

Analysis of the construction of a port-storm mathematical model of a articulated two-link road train regarding the vertical storage

The article considers possible ways of development and improvement of a flat mathematical model of the movement of an articulated two-link road train considering the track and bringing this model to a spatial model that could consider the change in vertical loads and the subsequent change in the lateral deflection forces, which affect the indicators of turning and controllability of the articulated vehicle. This article proposes constructing a spatial mathematical model of a two-link road train considering the vertical component. The authors consider the problems associated with the movement of a two-track train over uneven terrain and height differences that may occur on the track. They consider the gravitational force's influence on the train's movement and develop a mathematical model that describes this process. The article presents mathematical equations describing the direction of a two-track train in three-dimensional space. They consider the mass of the train, traction forces, air resistance, gravitational force, and reactions from the ground. The authors use numerical methods to solve these equations and conduct computer simulations to study train motion under various conditions. The results of the study demonstrate that the vertical component significantly impacts the movement of a two-track train. It can affect the train's speed, energy efficiency, and stability. The authors conclude with the need to consider the vertical component when building mathematical models of double-track road trains. This paper is essential for researchers and engineers developing and designing road trains. Considering the vertical part will help improve the accuracy of mathematical models and increase the efficiency of two-track road trains in actual operating conditions. The obtained results are essential for developing and improving control systems for two-track road trains, particularly in transport, logistics, and mobile robots. The proposed model can be used to optimize the traffic trajectory and improve the efficiency and safety of the operation of road trains in natural conditions. The proposed model is designed for circular stationary and transient modes of movement of an articulated road train with the possibility of conducting a comparative analysis with a full-scale experiment. Keywords: spatial mathematical model, circular modes, vertical oscillations, articulated train.

Nonlinear resonant phenomena in the secondary suspension system of the vehicle cab research

The issue of creating a methodology for analyzing nonlinear phenomena in the occurrence of spatial resonances in the truck cab suspension system is solved in research. The study purpose is the creating of spatial vibrations mathematical model of the cab on the suspension with regard to the car frame and changing the differential equations of the model dynamics to a form that allows visually analyze the nonlinear resonant phenomena arising in the system to research oscillations instability in resonance conditions. The transformation of the oscillation equations to a quasi-linear form is performed using the replacement of the trigonometric functions of Euler angles by the first two terms of their power series expansions. Because of the research, unfavorable frequency ratios for external and internal resonances in the cab suspension system were obtained. Guides are given to reduce the cab on the suspension rocking amplitudes when spatial nonlinear resonances occur. Keywords: nonlinear resonance, secondary suspension system, car cab suspension, mathematical model, quasi-linear view, vibration stability

Research of the Solutions Proximity of Linearized and Nonlinear Problems of the Biogeochemical Process Dynamics in Coastal Systems

The article considers a non-stationary three-dimensional spatial mathematical model of biological kinetics and geochemical processes with nonlinear coefficients and source functions. Often, the step of analytical study in models of this kind is skipped. The purpose of this work is to fill this gap, which will allow for the application of numerical modeling methods to a model of biogeochemical cycles and a computational experiment that adequately reflects reality. For this model, an initial-boundary value problem is posed and its linearization is carried out; for all the desired functions, their final spatial distributions for the previous time step are used. As a result, a chain of initial-boundary value problems is obtained, connected by initial–final data at each step of the time grid. To obtain inequalities that guarantee the convergence of solutions of a chain of linearized problems to the solution of the original nonlinear problems, the energy method, Gauss’s theorem, Green’s formula, and Poincaré’s inequality are used. The scientific novelty of this work lies in the proof of the convergence of solutions of a chain of linearized problems to the solution of the original nonlinear problems in the norm of the Hilbert space L2 as the time step τ tends to zero at the rate O(τ).

МОДЕЛИРОВАНИЕ ЗАДАЧИ О СВОБОДНОМ РАСТЕКАНИИ ПЛАСТИЧЕСКОГО СЛОЯ, СОСТОЯЩЕГО ИЗ РАЗНЫХ СРЕД, В ПОСТАНОВКЕ МОДЕЛИ «ИДЕАЛЬНОЙ ЖИДКОСТИ»

The approach under study is important for practical application, since is the basis of many basic plastic deformation operations associated with plastic flow in a thin layer of material deformed by rolls (longitudinal rolling, rolling) or dies (volumetric and sheet stamping), which are described by spatial mathematical models with a variety of parameters that determine the rheology of the material. Pressures are created on the contact surfaces of the processing material with the tool, which exceed the shear characteristics of the material by an order of magnitude, so that, in the initial approximation, it is possible to use the model of a hydrodynamic fluid to describe the properties of the material of the plastic layer [1, 2, 3]. As was shown earlier, sliding is observed almost along the entire contact surface, in which the contact surfaces coincide with the sliding surfaces, and the specific friction forces on them are maximum [4] and equal to the shear yield strength of the material [5, 6]. It should be noted another feature of the course of these processes, which determines the requirements for the accuracy of the final forging. It is clear that high contact pressures cause normal elastic displacements of the working surfaces of the tool, commensurate with the thickness of the plastic layer [7, 8]. We consider a plastic layer in the wedge-shaped region, composed of materials with different mechanical characteristics. the layer spreads freely between the rigid rough slabs converging in parallel. The layer under the action in the direction of the thickness of the distributed load from the side of the tool flows freely in the direction of the radii.

EXPERIMENTAL AND CALCULATION STUDY OF PRESSURE PULSATIONS IN THE RADIALAXIAL HYDROTURBINE

The force interaction of the vortex swirls in the draft tube of the hydraulic turbine RO with the elements of the flow path can lead to serious accidents. Reducing low-frequency pressure pulsations is an urgent task, as it helps to increase the reliability and increase the power of hydraulic units. For this, special devices are sometimes used. The aim this of the work was to compare modern methods for calculating low-frequency bundle pressure pulsations in a draft tube with experiment. Experimental studies of pressure pulsations in the flow part and the impeller blade of the RO115 hydraulic turbine were carried out in a wide range of operating modes. Numerous experiments were carried out to determine the bundle pressure fluctuations using a spatial mathematical model according to the method of NTU ''KhPI''. In addition, calculations of pressure fluctuations were performed based on a modern hydrodynamic software package that solves problems of continuum mechanics and uses the Reynolds equation. The process of solving problems in this case is carried out by means of the CFD application package, which includes the following steps: creating a three-dimensional model of the object under consideration using the CAD system; construction of the computational grid; choice of mathematical model of turbulence; problems of limiting conditions. A comparison of the experimental and calculated results indicates their good agreement. Prediction of pressure fluctuations using the above methods when designing hydraulic turbines makes it possible in the future to choose the best flow path with lower pressure fluctuations (with lower losses) and with higher energy-cavitation performance. In the first case, the task requires insignificant resources of computer time, and the error in calculating the amplitudes of pressure fluctuations is up to 15 % compared with the experimental data, in the second case it is 10 % with a much longer calculation time. In the future, the results of calculations of bundled pressure pulsations are used in strength calculations of elements of the flow path of a hydraulic turbine with large margins in terms of strength factors, so it is possible to use mathematical models of varying complexity in predictive calculations of bundled pressure fluctuations in a draft tube.

Методика расчетных исследований усиления предварительно напряженной базальтокомпозитной арматурой стен камер шлюзов с учетом фактических данных об их эксплуатационном состоянии

Introduction. Calculation studies have shown that due to the long-term operation of hydraulic structures of the sluice, opening of horizontal and vertical construction joints, as well as corrosion of reinforcement at the rear edge of the reinforced concrete wall of the sluice in the areas of horizontal construction joints, the bearing capacity of the structure as a whole is reduced. In this regard, it is necessary to strengthen the structure, the methodology of which is given in this study. Materials and methods. The analysis of scientific and technical documentation has been made, instrumental examination of the state of structures has been carried out, a spatial mathematical model has been developed on the basis of the finite-element method. Multivariant calculated researches of the actual stressed-strained state (SSS) of structures have been made. Calculation studies of the SSS structures were performed taking into account the reinforcement of prestressed basalt composite reinforcement (BCR). Results. Visual and instrumental inspection showed a presence of cracking on the front face of the reinforced concrete wall of the sluice chamber. Modeling of the actual state of SSS structures is performed, according to the results of calculations, a scheme for strengthening structures of prestressed BCR is proposed and justified. Conclusions. As a result of the calculated studies of the deflected stresses, the occurrence of cracks and opening of horizontal and vertical construction joints in the reinforced concrete structure of the sluice chamber wall was confirmed. At the same time, taking into account corrosion of reinforcement at the rear edge of the sluice’s reinforced concrete wall in the areas of horizontal construction joints, stresses in it reach the design resistance of the reinforcement of class A-II. In order to ensure further safe operation of the structures, the scheme of strengthening the structures with prestressed BCR has been proposed and substantiated.

Building a model of dressing the working surfaces of wheels during the two-side grinding of round end faces at CNC machines

This paper reports the spatial mathematical modeling of the process of dressing the working surface of grinding wheels for implementing the double-sided grinding of the ends of cylindrical components. Parts with high-precision end surfaces that are commonly used include bearing rollers, piston fingers, crosspieces of cardan shafts, and others. The geometric accuracy of surfaces is ensured by simultaneously grinding the ends at two-sided end-grinding machines with crossed axes of the part and wheels that operate under a self-blunting mode. Before starting the machining, the wheels are dressed in a working position. Moreover, the total orientation angle of the tools is selected subject to the condition of uniform distribution of allowance along the rough sections of wheels. Dressing involves a single-crystal diamond tool with a variable feed. That ensures different development of the surface of abrasive tools, which prolongs their operating time between dressings and improves overall stability. The constant size of micro irregularities at the calibration site enhances the quality of machining. The calibration site is made in the form of a straight line belonging to the plane that passes through the axis of rotation of the wheel and is perpendicular to the plane of the machined part. Based on the spatial mathematical models of the processes of removal of allowance and shape formation when dressing the wheel, the surface of the grinding wheel was investigated. Mathematical models for shaping the ends of parts when grinding with wheels with conical calibration sites have been proposed; it is shown that when applying the proposed machining scheme, there is no geometric error in the size of the part. In addition, due to the uniform distribution of the allowance along the rough area of the wheel, the quality of the surface layer of the ends of parts increases. The devised method for dressing the working surface of wheels could be used to grind the ends of non-circular components.

Matematičko modeliranje tečenja i pronosa nanosa - primjer brane na rijeci Tisi

High flow velocities downstream of the Tisa Dam at Novi Bečej (Serbia), produced by the large difference between water levels in the upstream and downstream reaches, cause bank erosion by the right bank immediately downstream of the emergency spillway, threatening stability of the dam itself. Due to complex interaction between the parameters of flow and sediment transport at the given location, an approach involving a spatial (3D) mathematical model of flow and sediment transport, aimed at solving such complex processes, is investigated in this paper. An optimum solution meeting all requirements for the stability of structures in question has been reached by the model, through comparison of the results generated by the existing conditions with the result provided by the measures proposed to fix the problems.

Creation and verification of spatial mathematical model of vibrating machine with two self-synchronizing unbalanced exciters

Vibration technological machines with self-synchronized unbalanced vibration exciters (vibrating conveyors, vibrating screens, vibrating crushers, etc.) are widely used in modern industry. Despite drive construction simplicity throughout exploitation of such machines a number of nonlinear dynamics effects can be observed. Most of such effects are related to machine drive and elastic suspension interaction and appear while passing through resonant frequencies. Nowadays the idea of resonant vibrating machines creation got a second breathe. The distinctive feature of such machines is the automated system for maintaining resonant mode of machine. Creation of such automated systems requires accurate mathematical models of vibrating machines that can reflect its most important features. The aim of this work is to create a spatial mathematical model and determine the dynamic system unknown parameters of a vibrating screen experimental sample with two self-synchronizing unbalanced vibration exciters that can create the working body spatial motion. The mathematical model motion equations are derived using the Lagrange equations of the second kind. Using the obtained experimental data (natural frequencies and logarithmic damping decrement), the mathematical model mass-geometric parameters and the damping parameters values were calculated. The investigation result is a verified mathematical model of a vibrating screen sample with two self-synchronizing unbalanced vibration exciters.