Introduction. The study of the motion of a rigid body carrying moving masses greatly simplifies the design of capsule robots that can move inside aggressive environments and perform the required operations. The following cases have been studied quite well: movement during interaction of a solid body with a reference plane and in aggressive environments; vibratory displacement of bulk media and solids on a vibrating base; optimization of rigid body motion; variation of average speed and acceleration at different intervals of motion; dependence of average speed on task parameters; control of the motion speed of the internal mass for the fastest possible rotation of a rigid body. However, at present, insufficient attention has been paid in the literature to the problems of studying the motion of a heavy flat body along a horizontal plane under the action of a harmonic force directed at an angle to the horizon, specifically, in terms of taking into account all possible driving modes and their features. This does not allow determining the optimal parameters of the problem. Therefore, the objective of this research was to identify the features of all possible modes of motion of a heavy solid body along a horizontal plane under the action of a harmonic force directed at an angle to the horizon.

Materials and Methods. The equations of motion of the mechanical system were used. Both analytical approaches and numerical methods were used to solve the steady-state equations of motion of the system. The dry friction model was adopted as a friction model, which made it possible to obtain accurate solutions for positive and negative values of the slip velocity up to constants. Values of these constants were determined from the docking conditions and the periodicity of the solution.

Results. An analytical solution to the problem for periodic solutions was obtained. Three possible motion modes were identified. Using numerical analysis, the dependences of the average speed of a body motion over the period on the angle of inclination of the force to the horizon were constructed. The optimal direction of force was established.

Discussion and Conclusion. The results of the conducted research allowed us to determine the optimal values of the problem parameters in order to reach the required value of the average velocity of a solid body. In particular, optimal values of the amplitude of the force and its direction can be found to reach the maximum value of the average velocity of motion of a solid.

Introduction. Walking robots are widely used in industry due to their unique capabilities for moving on uneven and complex surfaces. To provide high precision in controlling their movement, it is required to develop mathematical models and algorithms for planning the robot movement along various trajectories. A key aspect of the motion control system of walking robots is the planning of their leg movements. Despite significant advances in the field of modeling the kinematics of quadruped robots, existing scientific publications do not provide a complete kinematic model for robots similar to the Mini Cheetah. This research was aimed at the development of a kinematic model of a quadruped robot based on Mini Cheetah, as well as the formulation of recommendations for optimizing its gait to provide rotation around various axes. The creation of such a model will improve the smoothness and accuracy of the robot movements, which, in turn, will increase its efficiency under real production conditions.

Materials and Methods. The process of constructing a kinematic model of the robot was based on the use of formulas for the geometry of spatial motion of solids. To test the efficiency of the proposed algorithms for moving the robot legs when performing rotational movements of its body, numerical modeling of the robot kinematics was used. Numerical calculations were performed using the Wolfram Mathematica package.

Results. The laws of changing the endpoints of the robot legs during its rotation around the vertical axis were proposed. The conducted numerical modeling of the robot kinematics covered the rotation of the body at the course, roll and pitch angles. Based on the simulation results, it was established that the dependences of the rotation angles of the leg links were periodic functions. The considered rotational movements of the robot platform could take place without the occurrence of singular configurations.

Discussion and Conclusion. The results of numerical modeling of the robot platform rotation movements confirmed the operability of the proposed leg transfer plan, which allowed for smooth movement of the robot body and avoidance of singular configurations. The resulting kinematic model can be used to control the robot motion at the kinematic level when moving along curvilinear trajectories. As a prospect for further research, it is worth highlighting the development of a mathematical model of the dynamics of a four-legged robot, as well as the creation of laws for controlling its movement at a dynamic level. This will significantly expand the functionality of the robot and increase its efficiency under various operating conditions.

Introduction. Thermal performance of materials based on triply periodic minimal surfaces (TPMS) is becoming increasingly important in view of the growing interest in materials with special thermophysical properties and their applications in engineering, energy, and other fields. Since these materials have unique structural and functional characteristics, understanding the relationship between their geometry and thermal parameters plays a key role in optimizing their use. Despite the considerable attention paid to the problem, the study of the relationship between the geometry of porous structures and their thermal characteristics remains incomplete. Existing scientific papers cover only individual options, and a complete understanding of the effect of complex micro- and macrostructure on thermal conductivity requires further study. The current gap in scientific knowledge is the lack of systematization and generalization of existing data, which complicates the development of universal approaches to calculating thermal conductivity in such materials. The objective of this study was to develop simplified formulas for calculating the effective thermal conductivity of porous structures based on S-type TPMC cells proposed by Fisher and Koch. The authors also set the task of analyzing the heat-conducting process in a plate with given porosity parameters. This will improve the understanding of the thermodynamic processes occurring in such systems.

Materials and Methods. To achieve the stated objectives, mathematical modeling was performed, including the solution to the boundary value problem taking into account the identified correlations. A cellular structure made of PETG plastic and having pores consisting of identical repeating elements was considered. These elements formed a three-dimensional minimal surface that corresponded to the Fisher-Koch model. The analysis was performed using two methods: calculations in MathCAD based on the finite difference method, and modeling in ANSYS using the finite element method. In this case, the effect of the geometric parameters of the porous structure on its thermal characteristics was taken into account.

Results. The research results represented a numerical solution to the thermal conductivity problem for a porous plate, taking into account the symmetrical boundary conditions of the first kind, and the presence of internal heat sources that remained constant in time and considered the topological features of the material. In the course of the study, temperature distributions were obtained, both in the spatial coordinate and in time. The change in heat flow depending on variations in the plate porosity coefficient was estimated. The graphs of isotherm distribution and their speed of movement were constructed and analyzed, which allowed for a deeper understanding of the heat transfer dynamics in the system under consideration.

Discussion and Conclusion. The obtained mathematical dependences demonstrate the degree and nature of the effect of porosity on the distribution of heat flux density. It has been found that changes in the porosity of the plate can both increase and decrease the intensity of heat transfer, which provides reaching the required values ​​of thermal resistance of the material. The obtained results are consistent with the findings presented in other studies on similar topics, which opens up opportunities for their application in further research. These results can be useful in designing thermal protection systems for heat-generating equipment, as well as for heat and mass transfer paths of heat-mechanical equipment and other applications. The solutions are presented in an accessible and understandable form, which makes them easy to use for a wide range of researchers and engineers, and does not require expensive software or specialized computing equipment.

Introduction. Modern research aimed at improving the efficiency of the workpart procedures emphasizes the importance of taking into account the effect of periodic disturbances on the cutting dynamics. However, few works consider uncontrolled periodic disturbances, whose sources are spindle units and the supporting system of the machine. These disturbances also have a significant impact on the final quality indicators of the cutting process. Therefore, an urgent task in the mechanical engineering technology is to establish patterns of the effect of uncontrolled disturbances on the dynamics of the cutting process, which is particularly important for the development of systems for the automated selection of operating conditions or vibration diagnostics systems. This research is aimed at determining the mechanism of influence of periodic fluctuations of processing parameters caused by vibration disturbances on the temperature of the front face of the turning cutter, which is the key indicator of the development of diffusion wear of the carbide tool.

Materials and Methods. The study of the effect of periodic disturbances on the temperature of the front face of the tool was performed in two stages. At the first stage, based on a full-scale experiment on finishing longitudinal turning of blanks made of 10GN2MFA steel with cutters with T15K6 hard alloy plates, the parameters of the disturbance model in the system were identified, namely, the oscillatory accelerations of the tool under its wear. The vibration characteristics of the 16K20 universal lathe were measured using a vibration stand assembled on the basis of AP2089–100–3.3–02B vibration transducers, with a signal sampling frequency of 10 kHz. At the second stage, a digital study of the simulated disturbances and their effect on the dynamics of the cutting process was carried out. The results of the experiments were analyzed to compare the calculated maximum temperature of the front face of the tool at the moments when one of the specified output parameters of processing, obtained as a result of digital modeling, reaches an extreme value under the impact of periodic disturbances.

Results. It has been established that fluctuations in the parameters of operating cutting modes caused by periodic disturbances lead to temperature fluctuations in the contact zone of the tool and the blank. The greatest impact on the temperature in the cutting system under study was exerted by the combination of processing parameters at the moments of reaching extreme feed values. However, when fluctuations in cutting depth and speed reached extreme values, no significant changes in contact temperature were observed.

Discussion and Conclusion. The results of the conducted research emphasize the importance of analyzing the effect of periodic disturbances on pulse changes in contact temperature in the processing zone. The presented model of the relationship between tool vibrations and temperature in the cutting zone can be used to optimize turning modes. The criterion of optimality is the minimization of tool wear, which is determined on the basis of an analysis of temperature fluctuations and vibration activity signals of the tool.

Introduction. Vacuum ejectors operating on the Venturi principle are used in various industries and are essential pneumatic devices. An important characteristic of a vacuum ejector is the vacuum depth it creates, where the maximum vacuum value is obtained in a certain range of supply pressure. Failure to comply with the supply pressure affects the performance of the ejector itself and automated vacuum systems in general. One of the options for solving this problem is to establish the recommended range of supply pressure in a fairly narrow pressure range, at which a guaranteed value of vacuum depth is reached without using the maximum capabilities of the ejector. At the same time, the technical literature does not provide the values ​​of the dependence of the vacuum depth on the supply pressure over the entire range of ejector operation, which the authors would like to draw attention to in this work. The research objective was to conduct experimental studies on establishing the true values ​​of the maximum vacuum depth depending on the magnitude of the ejector input pressure.

Materials and Methods. To conduct experimental research, a special stand was designed, manufactured and used, which allowed for the study of vacuum ejectors operating on the basis of the Venturi principle. This stand provided setting the exact vacuum value depending on the input supply pressure for ejectors with a nozzle diameter from 0.1 to 4.0 mm, which completely covered the entire range of ejectors used in real sectors of the economy. Vacuum ejectors of the VEB, VEBL, VED and VEDL families manufactured by Camozzi were investigated in the range of the inlet supply pressure of the ejector from 2.0 to 6.5 bar. The true values of the vacuum depth were determined experimentally depending on the value of the input supply pressure for each ejector, as well as the maximum values of the vacuum depth reached by each ejector at the corresponding value of the input supply pressure.

Results. It was experimentally proved that the recommended values of the input supply pressure given in the catalogs of ejector manufacturers did not always correspond to the true values. It was shown that the character of the obtained graphs also differed. In this regard, it was necessary to adjust the value of the input supply pressure to reach the maximum vacuum depth for each type of ejector.

Discussion and Conclusion. The results of the conducted experimental studies allow for a rational choice of vacuum ejectors depending on the required technological tasks. This will ensure the operability of automated vacuum systems and the performance of the ejector itself. The research results can be used by all ejector manufacturers to adjust their basic catalogs and relevant recommendations for the use of these products.

Introduction. Pneumatic actuators are widely used in industry due to their reliability, simplicity of design, and ability to operate under complex conditions. However, when solving positioning problems, the use of traditional proportional valves is often redundant, which causes an unjustified increase in cost and complexity of the design. The application of simpler discrete distributors faces the problem related to the need to reach a compromise between their switching frequency and positioning accuracy.

Existing studies mainly focus on optimizing individual performance indicators of pneumatic actuators and do not offer effective methods for finding a compromise between conflicting criteria. Using classical methods for constructing a Pareto set for multicriteria optimization requires significant computational resources, which complicates their practical application.

The research objective is to develop a methodology for multicriteria optimization of the parameters of a positioning electropneumatic actuator with discrete distributors based on the construction of a Pareto set using surrogate models, which provides finding the optimal balance between switching frequency and positioning accuracy.

Materials and Methods. The research was conducted on a model of a positioning pneumatic actuator with discrete distributors, implemented in MATLAB Simulink. The Latin hypercube method was used to analyze the parameters, which provided uniform filling of the parameter space. To reduce computational costs, surrogate models, built using neural networks, were used. Sliding control was selected as a control algorithm, which effectively compensated for external disturbances and uncertainties of the system.

Results. The optimization of control parameters has shown the possibility of reaching high positioning accuracy with a minimum frequency of distributor switching. The use of the Latin hypercube method provided a uniform distribution of the calculation points, which made it possible to construct an accurate surrogate model. It has been experimentally proven that the proposed approach reduces computational costs by 48%, while maintaining high accuracy of modeling and analysis.

Discussion and Conclusion. The research results confirm that sliding control is an effective solution for discrete pneumatic drives in the context of multicriteria optimization. The developed approach makes it possible to significantly reduce the frequency of switching distributors without substantial losses in the quality of transients, which helps to extend the service life of equipment and increase the reliability of automated systems. The use of surrogate models and neural network technology opens up new prospects for faster design of complex systems.

Introduction. Controllability analysis is a required stage for the correct formulation and solution of any optimal control problem. This problem becomes specifically relevant in the context of optimizing systems with distributed parameters, which are described by partial difference equations. Such problems include the considered problem of optimization of the shape of the nozzle of a hydrocannon. The optimal nozzle should provide the maximum value of the functional expressed through the average force of the impulse of the jet of a hydrocannon. The relevance of this research is due to the lack of a unified approach to the analysis of controllability of systems with distributed parameters, which complicates the correct formulation and solution of optimization problems. In particular, previous attempts to solve the problem of hydrocannon nozzle optimization using classical variational calculus were unsuccessful due to ignoring aspects of controllability. The objective of this research was to apply a new approach proposed by V.K. Tolstykh to controllability analysis to solve the problem of optimal design of the shape of a hydrocannon nozzle.

Materials and Methods. The research method used was controllability analysis based on the Tikhonov conditional correctness of the inverse problem. This approach allowed us to identify the conditions for the existence of the gradient of the objective functional and construct a regularization of the solution to the inverse problem using adaptive gradient methods. It was of current interest for multiextremal problems, including the problem of the optimum nozzle shape. It was solved by a direct extreme approach in the form of direct maximization of the objective functional based on its gradient. In the process of research, a nonlinear, quasi-one-dimensional mathematical model of isentropic water flow in a hydrocannon nozzle was used. The flow was considered inviscid, compressible, and subsonic.

Results. As part of the research, controllability conditions were obtained that allowed us to radically simplify the problem of optimizing the shape of the hydrocannon nozzle. It was found that in order to correctly determine the gradient of the objective functional, it was required to narrow the solution area of ​​the conjugate problem to a small rectangular area. The use of adaptive gradient methods with satisfactory step factors provided for the regularization of the solution. For the first time, two optimum shapes of the hydrocannon nozzle were found. The first shape provided a local maximum of the objective functional, the second — a global maximum of the functional with a restriction on the expansion of the nozzle.

Discussion and Conclusion. The results obtained show that it is impossible to perform a directed search for an optimal solution using the Frechet derivative without taking into account controllability conditions. The first proposed approach, in combination with the desired adaptive gradient optimization methods, allowed us not only to correctly formulate the optimization problem, but also to find optimal nozzle shapes that provided the maximum average pulse force of the ultrajet. In some cases, for the stability of the solution, it was necessary to introduce expansion limitation of the nozzle beyond the barrel of the hydrocannon. This made it possible to meet the requirements of the controllability theorem and guaranteed the correctness of the results obtained. The theoretical relevance of the research is in the development of controllability analysis methods for systems with distributed parameters, which creates new opportunities for solving similar problems in other areas. The research results can be used to optimize devices operating on the basis of pulsed jets, as well as for further study of more complex models of fluid flow.