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In the realm of engineering the quest for optimization is ceaseless. This article explores the intricate relation-ship between cubic equations and the practical world of production technologies, unearthing the profound connections that underpin mathematical symmetry and its role in engineering. Cubic equations, often arising in the analysis of mechanical systems, electric circuits, and robotics, serve as indispensable tools for under-standing and enhancing real-world applications. This study delves into the methods for finding the roots of cubic equations, shedding light on the vital role of mathematics in engineering and manufacturing technology.

The aim of the research was to assess the influence of additions of different proportions of alumini-um waste chips from the machining technology on the melt quality and final properties of AlSi7Mg0.3 alloy casts. All casts were created using by gravity casting technology into preheated metal mold. The first cast was a pure AlSi7Mg0.3 alloy, followed by other samples with contents of 10, 30, 50, 70 wt.% of aluminum waste chips in the batches. All the samples were subjected to the Brinnel hardness and Vickers microhardness of solid solution of α(Al). Also, Density index was measured. At the end of research, the microstructures of the samples were analyzed using a Laser Confocal Microscope Olympus Lext OLS 5000.

Over the last decades, nickel-based superalloys with TBC coatings have been used as the main material for hot section turbine parts. The next step in the development of engines and increasing the combustion temperature is the use of Ceramic Matrix Composites (CMC). Nevertheless, in the presence of water vapour or molten salts, accelerated degradation of substrate material. This problems can be pre-vented by additional layers or coatings produced on its surface, or combinations of layers and coatings that form Environmental Barrier Coatings (EBCs). The aim of the research was the preparation of sam-ples of a mixture of erbium oxide powders with silicon oxide with the addition of: polyvinyl alcohol, starch and cellulose gum. Then their technological properties were examined. A mixture with the most favourable properties was selected and sprayed using HV-APS method using with various process parameters and investigated. Conducted research showed that energy of HV-APS process is too low for synthesis of erbium disilicate in the resulting coating. The material was only melted, not vaporized. Making powder agglomerates with an average size of 150 μm with the addition of 3% PVA leads to a significant decrease in the surface area of powder grains. This results in a significant increase in flowability and allows it to be used as a charge material for APS plasma spraying.

Laser cladding technology, a novel surface modification technique, is widely employed in tasks such as metal surface strengthening and repair. However, the quality post-cladding often falls short of usage requirements, harbouring defects like cracks and pores. In pursuit of a crack-free cladding method, surface texture technology is integrated with laser cladding technology to establish a multi-field coupled numerical simulation model. This model investigates the temperature, stress, and fluid fields during laser cladding with and without texture, aiming to identify the optimal cladding parameters. The results indicate that the optimal cladding parameters are a laser power of 1200 W, a scanning speed of 7 mm.s^-1, and a spot radius of 2 mm. In comparison with cladding without texture, the minimum temperature has increased by approximately 50 %, while the peak temperature has remained almost unchanged. The maximum residual stress of the cladding layer without texture is 369.46 MPa, whereas that of the cladding layer with pre-set texture is 338.46 MPa, representing a reduction of approximately 8.39 %. The bottom of the cladding layer has decreased by about 29.1 %, effectively enhancing the mechanical properties at the metallurgical bond of the cladding layer. The pre-set texture induces a decreasing trend in the flow velocity inside the molten pool, eliminating the double-vortex effect, and resulting in a more uniform temperature distribution within the molten pool, consequently reducing the residual stress of the cladding layer. This paper employs multi-field coupled numerical simulation technology to monitor the internal state of the molten pool, offering insights for enhancing the quality of the cladding layer in subsequent endeavours.

With the increasing demand for high-quality flange, there is a greater need for high-quality and high-speed machining technology. Aiming at the difficulty of surface roughness in meeting design requirements and poor machining stability of 7075 aluminum alloy, the classical Design of Experiments (DOE) method is employed to optimize the machining parameters and identify eight pertinent factors. By selecting the feed rate and cutting speed as the two significant factors, a  mathematical model of roughness is derived, and the theoretically optimal machining parameters are determined. According to corresponding experimental results, the roughness, the parallelism of the two end faces of the flange, and machining efficiency, in order to further validate the accuracy of the model. The final processing parameters are 0.07 mm.r^-1 feed rate and 1100 m.min^-1 cutting speed, which provide a reference for actual production.

The geometric accuracy of a machine is primarily determined by the accuracy of assembly, manufactur-ing, and overall setup. Standardized procedures for assessing geometric accuracy are established and detailed in delivery protocols for various types of machining machines. To effectively monitor and ana-lyze machining machine errors, the most suitable approach is to construct a comprehensive error balance that accounts for the overall performance of the machine. This error balance methodology, a tool within the realm of system analysis, is utilized for predicting and managing systemic errors. The errors ob-served in machined components are intimately connected to the errors present in the machining ma-chines themselves. These errors are further intertwined with the design and physical properties of indi-vidual machine components, as well as their interactions. In the case of multi-axis machines, they col-lectively determine the overall accuracy of the produced components. The objective of this study is to analyze machining machine errors using the Renishaw XL-80 laser interferometric system. The findings of this study reveal that errors in machining machines can also be the result of the dynamics of the cut-ting process, which may have a significant impact on accuracy.

Composite materials have consistently been applied in areas where a combination of properties such as strength, stiffness, and low weight is crucial. Motorcycle construction is no exception, as these parameters significantly impact riding characteristics, safety, and overall performance. This article focuses on quantifying the torsional and vertical stiffness of a single-sided swingarm made of carbon fiber reinforced polymer (CFRP) using finite element analysis (FEA) and verifying these results through experimental measurements. To enhance the accuracy of the simulations, which involve complex geometries and anisotropic materials, the material properties of selected fabrics used in the prototype production were measured. Specific fixtures were designed for the experimental measurements, enabling the application of torsional moments and vertical forces. Deformation under these loads was evaluated using the TRITOP photogrammetric system, which tracks deformations by monitoring the displacement of reference points under static load conditions and comparing them to a reference, unloaded state. Based on the acquired data, the overall stiffness values and their distribution along the length of the swingarm were calculated. The results showed a significant difference between simulation and reality. For the overall torsional stiffness, the simulated value was 249 N·m/°, while the measured was 270 N·m/°, showing a discrepancy of 7.7%. The vertical stiffness value from simulation was 414 N/mm, compared to 411 N/mm from experimental measurements, with a minimal difference of -0.7%. The stiffness distribution along the length of the swingarm exhibited a correlation, but with notable variation in certain areas. This confirms that accurately simulating CFRP parts with complex geometries is highly challenging, partly due to the sensitivity of the manufacturing process. Therefore, verification through experimental measurement is considered good practice.

The article highlights the promising potential of automating the forging process to enhance the durability of multi-cavity forging tools. Entrepreneurs aim to boost production efficiency by increasing output per unit of time and reducing the degradation of forging dies and punches. The high costs associated with specialized materials and complex manufacturing processes for these tools elevate the final product price. Automation offers a viable alternative, ensuring consistent process parameters and reducing the physical strain on workers. This consistency leads to extended tool durability, even without the use of special manufacturing techniques for their production. The study simulates the durability of multi-cavity dies in automated operations, demonstrating substantial advantages compared to manual forging. Simulation programs for forging processes and tool durability offer significant cost savings by providing insights into potential fatigue cracks, aiding in decision-making, and verifying operational parameters and tool designs. These simulations reduce the need for extensive: real-world tests and modifications of the forging tools.

Unfortunately, in connection with the application of the Actavia anti-plagiarism system, we cannot accurately describe our paper, which deals with the production of non-compact materials based on zinc and tin alloys, which have a higher density than aluminium (ρ = 2700 kg.m^-3 ) and its alloys, such as zinc alloys (ρ = 6980 kg.m^-3 ) or tin (ρ = 7580 kg.m^-3 ). Test samples were prepared from these materials, which were characterized by material non-compactness based on the use of NaCl particles. For this purpose, two different size groups of NaCl particles (3 to 5 mm and 5 to 7 mm) were used. In the production of non-compact metallic materials, it is assumed that half of the volume of the workpiece cavity will be occupied by NaCl particles and half of the volume of the work piece cavity will be filled with a melt of the relevant alloy (ZnAl4Cu1 or Sn89Pb). This is different from our previous experiments [24, 25]. In the case of this paper, the fabrication consisted in the fact that in a spe-cial preparation, the melt of the respective alloy was forced between the NaCl particles. The produced samples of non-compact material were analyzed and their specific gravities were determined. In a standard manner (as may be against the findings of the Actavia system), the microstructure was observed on an electron microscope and EDS analysis was also performed. It is anticipated that the non-compact materials thus produced from these two alloys will be used to produce not only filters but also bodies for liquid hydrogen storage.

This article deals with the influence of the applied solution annealing temperatures in the precipita-tion hardening process on the resulting increase in the mechanical properties of Al-Si-Cu alloy cast-ings with different copper contents in the alloy. AlSi7Cu2 and AlSi7Cu4 alloys were cast by gravity casting in a metal molds. Each of the samples was subjected to the Vickers microhardness measure-ment of a solid solution of α(Al) and Brinnel hardness measurement. Microscopic analysis and evalu-ation of the internal structure of each alloy was carried out in relation to used solution-annealing temperature.

This paper carries out the simulation of abrasive flow for twist drill spiral grooves and the experimental study of abrasive flow polishing. The flow of abrasive in spiral groove in abrasive flow polishing twist drill was analyzed by CFD using FLUENT software. Different inlet speeds and abrasive concentrations were used as parameters for simulation calculations to obtain the state parameters of dynamic pressure and abrasive velocity in the flow channel, and to analyse their effects on the abrasive flow in the spiral groove. The analysis results show that the dynamic pressure in the twist drill spiral groove increases with the increase of inlet speed, and becomes smaller as the abrasive flows along the spiral surface. Under the condition of different abrasive concentrations, the velocity of abrasive decreases with the increase of abrasive concentration. Under the same abrasive concentration condition, the abrasive velocity decreases gradually from inlet to outlet. For actual processing, the abrasive concentration can be selected between 50-60%. Based on the simulation analysis results, the parameters of abrasive flow polishing process were set, the orthogonal test method was adopted, and the test data were analysed by the polar analysis method the results showed that the priority order of the influencing factors of spiral groove polishing was: abrasive type > inlet speed > polishing time. Using SiC abrasive, inlet speed 0.5 m.s^-1, polishing time30 min, the surface roughness of the spiral groove of cemented carbide twist drill after polishing is the minimum, reaching Ra0.189, which is far less than the design requirements.

Parting-off stands as a fundamental method of turning, involving the cutting of the workpiece. The tool is most frequently a replaceable insert secured in a clamping bed. A pivotal set of observable metrics that ascertain the efficacy of a tool and its appropriateness for machining a specific material under defined cutting conditions is its durability. These durability parameters need to be determined for all new tools to ensure optimal performance and application in various machining scenarios. The primary objective of this research was analysis of the wear experienced by replaceable cutting inserts within the realm of parting technology. There were three distinct variants of replaceable cutting in-serts, all produced by esteemed manufacturer Dormer Pramet s.r.o. These cutting inserts were ap-plied in the parting process, consecutively machining two materials: bearing steel 100Cr6 and stainless steel 316L. The study not only encompasses the description of the cutting test procedure but also involves the meticulous execution of measurements and the subsequent analysis of the data procured from experimental activities. In the final phase of study, additional analyses are outlined to uncover the factors contributing to variations in certain obtained results. Those analyses, such as material or tool coatings analysis, provides more information about interplay between replaceable cutting inserts and the specific materials subjected to parting processes.

This paper presents a new method of improving the material removal process in metal cutting. Chip formation plays an important factor in the metal cutting process and increasing its condition has a great impact on cutting machine details. Based on lubricating cooling conditions in the metal cutting process, a novel methodology is proposed to decrease the deformation that emerged in the material removal process while cutting cylindrical details in lathes. Application of stating magnetic field on flowing cutting fluids decreased the shrinkage of the chip in turning operation. Analytical and practical experiments show that the effect of cutting fluid under the influence of a static magnetic field decreased the shrinkage of the chip up to 20 % in comparison to the conventional use of cutting fluids in turning cylindrical pars with HSS tools.

The Male and Cockroft ring compression test is one of the methods used to determine the coefficient of friction in forming. This method can be used to determine the coefficient of friction without the need to measure the force. This paper describes the results of the Male and Cockroft ring compres-sion test for the Hardox 450 material at different strain rates. The experiment was performed on ZD40 hydraulic press and CFA-80 pneumatic die hammer at the Faculty of Mechanical Engineering of Brno University of Technology. The test results were recorded in a calibration diagram. The results show that the strain rate has a significant effect on the coefficient of friction, specifically such that as the strain rate increases, the coefficient of friction decreases.

The impact of thermofriction on surface hardness has been investigated in this study. The metal disk method, which hardens parts' surfaces utilizing a metal disk, creates a hardened layer with the re-quired mechanical characteristics at a precise depth. The surface of treated products is one indica-tion of quality indicators. It has been noted that the thermal conductivity of the workpiece and tool material affects the irregular dispersion of heat in the processing zone. For evaluating the average integral rates of heating and cooling of the layer, the metal dependences have a significant impact on the form and properties of the friction-strengthened layer. It is discovered that several processing mode-dependent parameters affect power and density heat flow during hardening. It was found that when the feed rate increases, the hardened layer's depth decreases. The harder layer's depth increases as disk rotation speed (rpm) increases. when the disk rotation speed is increased to 265 rpm and the hardening depth (h) is 0.2 mm or less, it is said to be at N = (190-250) rpm. After heating the treated surface areas to a temperature between 130°C and 160°C above the critical temperature, the treated surface areas were then cooled applying compressed air to achieve the ideal surface hardness. After the hardening process, the surface hardness of blanks made of steel 1045 reached HRC 60, which is higher than conventional hardening.

The article deals with the experimental measurement of the load on the cervical vertebrae when driving a passenger car over bumps. The measurement was done experimentally. The load on the human spine was measured in the area of the C7 cervical vertebra and also in the area of the top of the head. Vehicle crossings over speed bumps. The measurement was carried out at different crossing speeds and at different heights of speed bumps. Three-axis acceleration sensors were placed on selected parts of the vehicle and on the human body. The proposed measurement methodology was verified by the conducted pilot experiment for the possibility of conducting further experiments. The results of the work showed that the crew of vehicles in road transport is more stressed than previous scientific findings indicate.

The paper deals with the solubility and influence of the melting method of alloying elements (Zr, Mo and Sr) on selected properties and structure of the hypoeutectic aluminum alloy AlSi5Cu2Mg. Alloy-ing elements in the form of master alloys (AlZr20, AlMo10, and AlSr10) were melted in two different methods. The first method consisted in melting the master alloy together with the batch material in an electric resistance furnace, the second method consisted in separately melting the master alloy in an induction electric furnace and then introducing the master alloy into the molten batch. The presence of alloying elements led to an increase in the porosity in all experimental alloys, which negatively affected the resulting physical and mechanical properties.

Natural fibre-reinforced polymer (NFRP) composites can be environmentally friendly and cost-effective alter-natives to synthetic fibre-reinforced composites. Major industries have expressed significant interest in the advancement of new natural fibre-reinforced composite materials. However, these materials perform poorly on their own and require further analysis since accessible information is lacking in the literature. This paper presents the results of previously reported works on natural fibre reinforced polymer composites, with strong attention to the types of fibres employed, the polymers used in the matrix, the treatment of fibres as well as the test parameters. The best proportion of composites is consequently selected. Composite materials are tested using a CNC router machine. Pinewood dust is combined with vinyl ester resin. A hand layup tech-nique is used to prepare the samples. The availability of relevant pinewood dust and the volume of pine wood dust to be used are first determined to continue with the experiment. According to the findings, the impact of machining performance is successfully evaluated by employing the tensile strength test, Charpy impact test, flexural strength test and surface roughness measurement. The findings are derived from the microscopic assessment of the surface roughness of pinewood dust (PWD) fibre reinforced vinyl ester resin.

Today's milling cutting tools are produced in various types and shapes for a wide variety of machining processes. Development continues and offers new technological solutions. The design of replaceable milling heads offers a significant cost reduction, as only the worn-out part is replaced instead of the en-tire tool. The tough connection between the tool and the shank achieves stable performance in roughing and finishing milling. Because of the possibility of using different milling inserts, the number of neces-sary tools will also be reduced and the flexibility of using milling tools will increase. The article exam-ines the cutting forces when machining a milling head produced by additive technology and made of Onyx material, which is reinforced with carbon fibre.

Nowadays, the digitalization of the production process is an indispensable part of the stampings production in the pre-series stage, but also as a subsequent support for series production. Automotive producers are under pressure to comply with the ever decreasing CO2 production standards for cars, which predicates the use of modern material types with an advantageous weight-to-strength ratio. This paper focuses on the use of mathematical modelling in a numerical simulation environment to predict the deformation process and subsequent material spring-back of dual-phase steel DP500. The material data and characteristics are used to define the material computational model in numerical simulation. The results of the numerical simulations are then compared with the stamping obtained by a real pressing process, where their shape comparison and further evaluation of the used material models and selected parameters are performed.

The aim of this article is to approach the measurement of forces and pressures of collaborative robots. In the article, research will be carried out on measuring the forces and pressures of a collaborative robot before putting it into real application. Force and pressure values will be measured using appropriate measuring devices. The measured results will be compared with the ISO/TS 15066:2016 technical specifi-cation and subsequently evaluated.

In this study, the ballistic resistance of multi-layered composite armour is experimentally investigated. The composition of this armour consisted of armour steel Armox 500T, para-aramid fabric Twaron CT 747 and ultra-high molecular weight polyethylene Endumax Shield XF33. To compare the ballistic resistance, the ballistic resistance of the armour with the perforated steel Armox 500T was tested. The rifle cartridges 7.62 x 51 mm FMJ NATO M80 were used to test this resistance. The aim of this experiment was to compare the ballistic resistance of unperforated and perforated steel Armox 500T. As part of the experimental part, the chemical composition and microhardness of the steel Armox 500T was verified. The hardness of the composite materials was also measured for optimal armor configuration. After the projectile impact, the damage mechanism of the steel Armox 500T and the composite materials were investigated by using optical and electron microscopy. It was proved that the ballistic resistance of the perforated steel depends on the used pattern. Based on the performed experiments, the steel Armox with pattern A effectively reduced the weight of the testing configuration and absorbed all the kinetic energy of the projectile 7.62 mm FMJ M80.

This paper investigates the rubber wood honeycomb core by manipulating its cell wall thickness. Rubber wood honeycomb core was fabricated with cell walls range from 1 mm to 3 mm. The impacts of the cell geometrical parameters on the flexural and out-of-plane compression performance are studied. In the case of solid rubber wood without facesheet, the density is much higher than those rubber wood honeycomb composites. The failure can be disastrous without facesheet under bending. Rubber wood honeycomb sandwiches are able to offer the similar specific flexural strength with lower density. With increasing wall thickness from 1 mm to 3 mm, the specific flexural strength increased by 12.32 %. Meanwhile, specific compressive strength improved by 11 % from 1 mm to 2 mm. However, its specific strength dropped by 3.55 % when the wall thickness at 3 mm. Minimum improvement in the compressive strength per density has caused the decrement.

Selective Laser Sintering (SLS) or sintering of polymer powders is one of the most well-known additive technologies for printing 3D components. The properties of individual polymer powder materials have a significant impact on the quality of the manufactured part. Potential deformation and shrinkage can occur during printing if a significant number of parts are piled on top of one another or are oriented incorrectly, accumulating thermal energy in certain areas. The aforementioned research focuses on an experimental study to investigate the impact of the distribution and orientation of printing samples in the build chamber on the accuracy of dimensions and the surface roughness of PA12 prints. The aim of the study was to examine the impact of model settings during production as well as the effect of individual factors on the properties of manufactured parts, with a focus on ensuring that heat rises evenly from each print without accumulating.

Article deals with comparison of cutting forces and surface roughness between materials produced by powder metallurgy M390 and M398 Microclean® from producer, company Böhler. Main interest is the analysis & comparison of the cutting forces and surface roughness after the processing by cutting in-serts with DNMG and WNMG geometry, radius 0.4 and 0.8 mm, after hard turning at the same pro-cess parameters for both materials and all types of cutting inserts. The comparative studies were car-ried out for cutting forces and surface roughness with the aiming to observe the difference between “old generation” M390 and “new generation” M398 PM Steel for future processing in production. The corelation between the cutting forces and surface roughness was investigated with resulting the M398 is necessary to process by higher cutting forces which are linked with higher surface roughness than at M390. It is in relation with higher contain of additive elements and carbides formed by them, even that the material is in delivered condition – soft annealed [1], [2]. These results helped to fulfil the knowledge about both materials in the row of experiments which are provided to increase material properties against abrasion and wear.

This study focuses on the analysis and solution of thread production in thin-walled profiles. It explores three different threading technologies, including cutting, forming, and extrusion. The issue of a screw joint in a thin-walled component is complex due to the stiffness of the joint and the short length of the thread. Hence, the careful choice of a suitable manufacturing process for producing inner threads in thin-walled components holds significant importance. The study entails monitoring the hardening of surface layers of materials after thread production, in conjunction with the acquisition of microstructure images of the experimental material. The outcome is a comparative evaluation of different individual thread production technologies.

Article deals with processing of intermetallic materials produced by powder metallurgy M390 and M398 Microclean® produced by Böhler. Main interest is the analysis & measurement of their surface rough-ness and topography after the processing by DNMG and WNMG geometry of cutting inserts with 0.4 and 0.8 mm radius after hard turning at the same process parameters for both materials and all types of cutting inserts. The comparative studies were carried out for the microgeometrical and chip formation research on the machined surfaces and the technological processes were assessed, including chip dia-grams. Spectral analysis was used to verify the composition of investigated materials by spectral analysis measuring device. In order to examine the surfaces in detail, in addition to the standard roughness measurement, surface topography was performed by the coherent correlation interferometric micro-scope. The results of surface roughness as well as topography show higher wear resistance of M398 ma-terial compared to M390. This was confirmed indirectly by the fact that it is primarily shown by the higher surface roughness of M398 after machining under the same conditions. These properties are ob-tained by a higher content of additive elements, respectively of their carbides. Based on the conclusions of these experiments, additional knowledge and recommendations for the processing of these materials were created.

Traditional assembly sequence solving methods often face problems such as combinatorial explosion and low efficiency in solving complex products with multiple parts. To improve the level of assembly sequence planning (ASP), an interference matrix is established to express the basic assembly information of a product. Taking the stability of the assembly sequence, the number of assembly direction changes, and the number of assembly tool changes as evaluation indicators, a fitness function is constructed. An improved particle swarm optimization (IPSO) approach for ASP is developed based on the peculiarities of the ASP issue. Redefining particle positions, velocities, and their update operations, and introducing mutation operators in genetic algorithm (GA) to improve the ability of PSO algorithms to jump out of local optima. Furthermore, the algorithm's convergence speed is enhanced by adjusting the value of the inertia weight. Finally, an example is provided to demonstrate the IPSO algorithm's usefulness and efficiency.

Aluminum alloys are one of the most used materials today, and therefore great emphasis is placed on their continuous development. Improving the ratio of strength and stiffness to weight, improving plasticity, casting properties or resistance to corrosion are examples of properties of aluminum alloys that are constantly being improved. This work focuses on the evaluation of the corrosion resistance of the Al-Si5Cu2Mg alloy with graded addition of zirconium (0.05; 0.10; 0.15; 0.20 wt.%). Corrosion re-sistance was evaluated based on immersion, exposure and potentiodynamic polarization tests. The addition of Zr to the AlSi5Cu2Mg alloy improved the thermodynamic stability in all evaluations. The application of heat treatment led to even more significant increases in corrosion resistance in almost all evaluations. Microscopic observation of the samples revealed mainly pitting corrosion along with intercrystalline corrosion.

Machining is an important part of the manufacturing process in the engineering field. Turning is one of these areas. At present, almost exclusively exchangeable cutting inserts are used in production machining. The article describes the research in the field of their wear, where the electron microscopy was used to evaluate the results. Electron microscopy is a very important aid in research in many are-as not only of human activity and also is the important aid in the field of mechanical engineering and manufacturing technologies. The results thus obtained can make in a given area it clearer and better document the resulting situation. Within the experiments, selected cutting inserts were used and the given material was machined. The electron microscope Tescan Vega 3, which is available at the workplace where the experiment was conducted, was used to evaluate the resulting wear. In the frame of experiments was also performed the composition analyze of used cutting inserts. Analyzes of the machined material were also performed to confirm the declarations from the supplier.