EUREKA: Physics and Engineering https://journal.eu-jr.eu/engineering <p><strong>EUREKA: Physics and Engineering </strong>scientific journal whose main aim is to publish materials allowed to see&nbsp;<strong><em>new discoveries at the intersection of sciences.</em></strong></p> en-US <p style="text-align: justify;">Our journal abides by the Creative Commons CC BY copyright rights and permissions for open access journals.</p> <p style="text-align: justify;">Authors, who are published in this journal, agree to the following conditions:</p> <p style="text-align: justify;">1. The authors reserve the right to authorship of the work and pass the first publication right of this work to the journal under the terms of a Creative Commons CC BY, which allows others to freely distribute the published research with the obligatory reference to the authors of the original work and the first publication of the work in this journal.</p> <p style="text-align: justify;">&nbsp;2. The authors have the right to conclude separate supplement agreements that relate to non-exclusive work distribution in the form in which it has been published by the journal (for example, to upload the work to the online storage of the journal or publish it as part of a monograph), provided that the reference to the first publication of the work in this journal is included.</p> info@eu-jr.eu (Helen Klimashevska) info@eu-jr.eu (Helen Klimashevska) Fri, 23 Jul 2021 21:31:38 +0300 OJS 3.1.2.2 http://blogs.law.harvard.edu/tech/rss 60 Synthesis of new immobilized N-chloro-sulfonamides and release of active chlorine from them https://journal.eu-jr.eu/engineering/article/view/1929 <p>A method has been developed for the synthesis of granular polymeric materials with immobilized N-chloro-sulfonamide groups. Commercially available resin polymers widely applied for the preparation of ion exchangers have been used as polymer carriers. The elaborated technological conditions make it possible to modify these resins with a high conversion degree, without deteriorating the strength characteristics, and with the possibility of regulating the concentration of active chlorine over a wide range (up to 11&nbsp;%&nbsp;w/w). The structure of the synthesized polymers was confirmed by IR spectroscopy data. To determine the concentration of functional groups, a special method of iodometric titration has been developed. The processes of emission of active chlorine from synthesized polymers into aqueous solutions have been studied. It has been shown that this process significantly depends on the composition of the solution: no release of active chlorine into distilled water is observed, and when using tap water, its concentration is reached 5–8&nbsp;mg/dm<sup>3</sup> and remains up to 30&nbsp;days when the granules are in water. The processes of activation of active chlorine emission by compounds of amine nature have been studied, the corresponding kinetic curves of the dependence between change in the concentration of active chlorine in solution and the used activator are presented. It has been found that the nature of the used activator strongly affects, among other things, the stability of the obtained chlorine-active solutions. Taurine and sulfamic acid are found to be the optimal activators for obtaining stable solutions of active chlorine of high concentration. The composition of the N-chloro-taurin solution obtained in this way has been additionally analyzed by UV spectroscopy. Thus, the synthesized polymers make it possible to quickly <em>in situ</em> obtain high-purity solutions of active chlorine without the use of special electrochemical equipment. The polymers themselves are compact, stable, and can be repeatedly regenerated</p> Bohdan Murashevych, Volodymyr Toropin, Dmytro Stepanskyi, Hanna Maslak, Kostyantyn Burmistrov, Valerii Kotok, Vadym Kovalenko Copyright (c) 2021 Bohdan Murashevych, Volodymyr Toropin, Dmytro Stepanskyi, Hanna Maslak, Kostyantyn Burmistrov, Valerii Kotok, Vadym Kovalenko https://creativecommons.org/licenses/by/4.0 https://journal.eu-jr.eu/engineering/article/view/1929 Fri, 23 Jul 2021 00:00:00 +0300 Adaptive technology for constructing the kinetic equations of reduction reactions under conditions of a priori uncertainty https://journal.eu-jr.eu/engineering/article/view/1959 <p>The object of research is the process of oxide reduction in a reaction system of mass m due to the reaction on a contact surface with an area of S.</p> <p>An adaptive technology is proposed that allows one to construct the kinetic equation of the process in which the oxide is reduced from the initial product under conditions of a priori uncertainty. A priori uncertainty regarding the behavior of a physicochemical system is understood as the fact that the following information is not available to the researcher:</p> <p>–&nbsp;about the change in the mass of the reaction system and the area of the contact surface;</p> <p>–&nbsp;about the rate of accumulation of the finished product;</p> <p>–&nbsp;about the time of withdrawal of the finished product from the system.</p> <p>The proposed adaptive technology includes five sequential stages to eliminate a priori uncertainty. This is ensured through the use of an adaptive algorithm, which allows obtaining the maximum accuracy in estimating the output variable by selecting the optimal parameter of the adaptive algorithm, and the subsequent canonical transformation. The introduced concept "canonical transformation of the kinetic equation" has the following meaning: having received some adequate description of the kinetic equation in a Cartesian coordinate system, a transformation is carried out that allow representing the equation in a new Cartesian coordinate system in such a way that its structure corresponds to the canonical form. The basic postulate of chemical kinetics can be such a canonical type.</p> Dmitriy Demin, Oleh Domin Copyright (c) 2021 Dmitriy Demin, Oleg Domin https://creativecommons.org/licenses/by/4.0 https://journal.eu-jr.eu/engineering/article/view/1959 Fri, 23 Jul 2021 17:17:43 +0300 Development of a method for assessment and forecasting of the radio electronic environment https://journal.eu-jr.eu/engineering/article/view/1940 <p>Decision making support systems (DSS) are actively used in all spheres of human life. The system of the electronic environment analysis is not an exception. However, there are a number of problems in the analysis of the electronic environment, for example: the signals are analyzed in a complex electronic environment against the background of intentional and natural interference. Input signals do not match the standards, and their interpretation depends on the experience of the operator (expert), the completeness of additional information on a particular task (uncertainty condition). The best solution in this situation is found in the integration with the data of the information system analysis of the electronic environment, artificial neural networks and fuzzy cognitive models. Their advantages are also the ability to work in real time and quick adaptation to specific situations. The article develops a method for assessing and forecasting the electronic environment.</p> <p>Improving the efficiency of evaluation information processing is achieved through the use of evolving neuro-fuzzy artificial neural networks; learning not only the synaptic weights of the artificial neural network, the type and parameters of the membership function. The efficiency of information processing is also achieved through training in the architecture of artificial neural networks; taking into account the type of uncertainty of the information that has to be assessed; synthesis of rational structure of fuzzy cognitive model. It reduces the computational complexity of decision-making; has no accumulation of learning error of artificial neural networks as a result of processing the information coming to the input of artificial neural networks. The example of assessing the state of the electronic environment showed an increase in the efficiency of assessment at the level of 15–25&nbsp;% on the efficiency of information processing</p> Oleg Sova, Andrii Shyshatskyi, Olha Salnikova, Oleksandr Zhuk, Oleksandr Trotsko, Yaroslav Hrokholskyi Copyright (c) 2021 Oleg Sova, Andrii Shyshatskyi, Olha Salnikova, Oleksandr Zhuk, Oleksandr Trotsko, Yaroslav Hrokholskyi https://creativecommons.org/licenses/by/4.0 https://journal.eu-jr.eu/engineering/article/view/1940 Fri, 23 Jul 2021 17:17:55 +0300 Comparison between some meteorological elements measured by ECMWF and Earth stations in different regions in Iraq https://journal.eu-jr.eu/engineering/article/view/1941 <p>The aim of this paper is to validate the data of three meteorological elements Air Temperature (Ta) , Relative Humidity (RH), Wind Speed (WS) from the European Center For-Medium Range Weather Forecasting (ECMWF) , against ground stations data using several Models at six stations well distributed in Iraq (Mosul, Kirkuk, Baghdad, Kut, Nasiriya, and Basra).</p> <p>Due to the difficulties which experienced by the ground climate stations in Iraq from a shortage of devices and equipment for measuring the various climatic elements, which led to a huge shortage of data throughout time for political, economic and natural disasters. It is found that researchers can adopt the data of satellite stations to monitor the climate because let’s found that there is a highly significance Correlations between the data of these stations and the data of the ground stations for climate monitoring</p> <p>Five Mathematical Models were used for that [Linear Models, Quadratic Models, Exponential Models, Logarithmic Models, and Power Models]. The performance of these models were evaluated by comparing the calculated (Ta, RH, WS) from earth stations.</p> <p>Those mathematical correlations help to be able to calculate the ground data in state of there is no ground climate stations data.</p> <p>Several statistical tests Correlation Coefficient (<em>R</em>), Coefficient of Determination (<em>R</em><sup>2</sup>), Root Mean Square Error (RMSE), Mean Absolute Error (MAE) were used to control the validation and goodness of these Models.</p> <p>The <em>R</em><sup>2</sup> obtained from these Models were very high in all stations. This means that, there is a highly significance Correlations between (Ta, RH, WS) estimated and [Ta, RH, WS] measured in all station</p> Rajaa A. Basheer, Dr. Waleed I. AL-Rijabo Copyright (c) 2021 Rajaa A. Basheer, Dr. Waleed I. AL-Rijabo https://creativecommons.org/licenses/by/4.0 https://journal.eu-jr.eu/engineering/article/view/1941 Fri, 23 Jul 2021 17:18:03 +0300 Determination of laminar burning velocity of methane/air flames in sub atmospheric environments https://journal.eu-jr.eu/engineering/article/view/1775 <p>The global energy demand enhances the environmental and operational benefits of natural gas as an energy alternative, due to its composition, mainly methane (CH<sub>4</sub>), it has low polluting emissions and benefits in energy and combustion systems. In the present work, the laminar burning velocity of methane was determined numerically and experimentally at two pressure conditions, 0.85&nbsp;atm and 0.98&nbsp;atm, corresponding to the city of Medellín and Caucasia, respectively, located in Colombia. The environmental conditions were 0.85&nbsp;atm, 0.98&nbsp;atm, and 295±1&nbsp;K. The simulations and experimental measurements were carried out for different equivalence relations. Experimental laminar burning velocities were determined using the burner method and spontaneous chemiluminescence technique, flames were generated using burners with contoured rectangular ports to maintain laminar Reynolds numbers for the equivalence ratios under study and to reduce the effects of stretch and curvature in the direction of the burner's axis. In general, the laminar burning velocity fits well with the numerical results. With the results obtained, a correlation is proposed that relates the laminar burning velocity with the effects of pressure, in the form <em>S<sub>L</sub></em>=<em>aP<sup>b</sup></em>, where <em>a</em> and <em>b</em> are model constants. Sensitivity analysis was performed using the GRI-Mech&nbsp;3.0 mechanism which showed that the most sensitive reaction was H+O<sub>2</sub>=O+OH (R38). Additionally, it was found that the reactions H+CH<sub>3</sub> (+M)=CH<sub>4</sub> (+M) (R52), 2CH<sub>3</sub> (+M)=C<sub>2</sub>H<sub>6</sub> (+M) (R158), and O+CH<sub>3</sub>=H+CH<sub>2</sub>O (R10) dominate the consumption of CH<sub>3</sub> which is an important radical in the oxidation of methane, this analysis is carried out for equivalence ratios of 0.8 and 1.0, and&nbsp;atmospheric pressures of 0.85&nbsp;atm and 0.98&nbsp;atm</p> Arley Cardona Vargas, Carlos E. Arrieta, Hernando Alexander Yepes Tumay, Camilo Echeverri-Uribe, Andrés Amell Copyright (c) 2021 Arley Cardona Vargas, Carlos E. Arrieta, Hernando Alexander Yepes Tumay, Camilo Echeverri-Uribe, Andrés Amell https://creativecommons.org/licenses/by/4.0 https://journal.eu-jr.eu/engineering/article/view/1775 Fri, 23 Jul 2021 17:18:10 +0300 Development of a mathematical model of the trolleybus steering system using a rolling rotor switched reluctance motor https://journal.eu-jr.eu/engineering/article/view/1938 <p>An important part of the overall task of social and economic development of many developed countries is the creation of a unique transport infrastructure or improvement of transport services for the population.</p> <p>The cumulative solution to many problems is to improve the quality and reliability of elements and equipment in any vehicle design. This determines its efficient operation and the safety of passengers.</p> <p>A common urban electric transport in megacities is a trolleybus, the reliability of which depends on individual components and assemblies, power supply systems and traffic control.</p> <p>But this type of transport requires modern scientific and technical solutions for the design of individual components and assemblies, for example, steering, which is directly related to the safe and comfortable transportation of passengers.</p> <p>An innovative technical solution has been proposed that will increase the energy efficiency of the trolleybus steering system through the use of an electric power steering based on a rolling rotor electric motor. The analysis of the design is carried out and the principle of control of the rolling rotor motor is determined. Functional diagrams of the components of the trolleybus steering system with an electric power steering based on a rolling rotor motor are developed. The electromagnetic and mechanical connections of the motor with the rolling rotor are determined and mathematically described. Factors affecting the steering system when turning the steered wheels are reasoned. A mathematical model of a trolleybus steering system with an electric booster based on an electric rolling rotor motor has been developed. The mathematical model is based on the differential equations of the electrical and mechanical parts. Algebraic equations were used to characterize the electromagnetic connections of the rolling rotor motor. The proposed solution will allow simulating dynamic processes in the trolleybus steering system and evaluating the results. Determination of the efficiency of the steering system was carried out by comparative analysis of the following factors: the control action created by the driver, the condition of the road surface, dynamic and transient electromechanical processes of the system, and the like</p> Tatyana Pavlenko, Оleksandr Petrenko, Viacheslav Shavkun, Ivan Aharkov Copyright (c) 2021 Tatyana Pavlenko, Оleksandr Petrenko, Viacheslav Shavkun, Ivan Aharkov https://creativecommons.org/licenses/by/4.0 https://journal.eu-jr.eu/engineering/article/view/1938 Fri, 23 Jul 2021 17:18:21 +0300 Implementation of marble waste as aggregate material rigid pavement https://journal.eu-jr.eu/engineering/article/view/1932 <p>The rigid pavement is used for the pavement with soft ground conditions (subgrade). On the other hand, in recent years, marble waste for civil construction has been widely used to substitute conventional materials such as fine and coarse aggregate in concrete. This study aims to optimize marble sand waste as a substitute for river sand aggregates on concrete pavements. This research creates innovation in the production of rigid pavement. The study used an experimental method to test the raw material, namely fine aggregate (river sand and marble sand) and rigid pavement testing, with various variations in the material's composition, including loading, strain, and concrete slab stress tests. The use of marble sand as a substitute for river sand affects the compressive strength of concrete. The maximum compressive strength of 34.67&nbsp;N/mm² occurs at 60&nbsp;% marble sand content. Calculation of the optimum level of marble sand by the regression method yielded 48.90&nbsp;% with an average compressive strength of 32.37&nbsp;N/mm². In terms of strain, rigid pavement concrete slabs with 60&nbsp;% marble sand content showed the best performance among all specimens. The stretch is relatively small so that it is not so fluctuating, the flexibility is relatively small, and the stiffness is the highest. The strain character tends to be compressive so that the dependence on reinforcement will decrease. Dynamically at the shock load, the three concrete slabs are quite good and very far from resonance in both the traffic service load frequency and the large shock load. Rigid pavement concrete slabs with a marble sand content of 40&nbsp;% show the best performance because they are damping faster and have less tension. Statically, rigid pavement concrete slabs with a marble sand content of 60&nbsp;% are the best</p> Candra Aditya, Dafid Irawan, Silviana Silviana Copyright (c) 2021 Candra Aditya, Dafid Irawan, Silviana Silviana https://creativecommons.org/licenses/by/4.0 https://journal.eu-jr.eu/engineering/article/view/1932 Fri, 23 Jul 2021 17:18:29 +0300 Study on multi-objective optimization of X12M steel milling process by reference ideal method https://journal.eu-jr.eu/engineering/article/view/1737 <p>For all machining cutting methods, surface roughness is a parameter that greatly affects the working ability and life of machine elements. Cutting force is a parameter that not only affects the quality of the machining surface but also affects the durability of cutter and the level of energy consumed during machining. Besides, material removal rate (MRR) is a parameter that reflects machining productivity. Workpiece surface machining with small surface roughness, small cutting force and large MRR is desirable of most machining methods. Milling is a popular machining method in the machine building industry. This is considered to be one of the most productive machining methods, capable of machining many different types of surfaces. With the development of the cutting tool and machine tool manufacturing industries, this method is increasingly guaranteed with high precision, sometimes used as the final finishing method. Milling using a face milling cutter is more productive than using a cylindrical cutter because there are multiple cutter s involved at the same time. This article presents a study of multi-objective optimization of milling process using a face milling cutter. The experimental material used in this study is X12M steel. Taguchi method has been applied to design an orthogonal experimental matrix with 27&nbsp;experiments (L27). In which, five parameters have been selected as the input parameters of the experimental process including insert material, tool nose radius, cutting speed, feed rate and cutting depth. The Reference Ideal Method (RIM) is applied to determine the value of input parameters to ensure minimum surface roughness, minimum cutting force and maximum MRR. Influence of the input parameters on output parameters is also discussed in this study</p> Khanh Nguyen Lam Copyright (c) 2021 Khanh Nguyen Lam https://creativecommons.org/licenses/by/4.0 https://journal.eu-jr.eu/engineering/article/view/1737 Fri, 23 Jul 2021 17:34:44 +0300 Research of the problem of optimization and development of a calculation method for two-stage chain drives used in heavy industrial vehicles in conditions of economic efficiency https://journal.eu-jr.eu/engineering/article/view/1930 <p>The article is dedicated to the problem of optimization of chain drives of the drilling unit. At present, increasing the power per machine to the optimal limits, reducing the material and energy consumption per unit capacity of the machine, as well as operating costs are considered topical issues. The machines that are designed and constructed to optimal limits must be very powerful and productive. The machines that are applied to perform drilling works in the oil and gas industry must be easy to operate, reliable and have ability to operate for a long time. When constructing such machines, their being lightweight, economical, as well as their preparation in a short time and at low cost should be taken into account in advance. In order to ensure the reliable operation of drilling rigs, it is more expedient to apply chain drive in their mechanical transmission. First of all, the application of chain drive in drilling units and hoisting mechanisms is considered. Then a calculation method was developed for the chain drives of the drilling unit used in deep exploration wells and the exploitation of wells, and, accordingly, the calculation of the chain drive was carried out. The chain drive consists of drive and driven sprockets and a chain that encompasses the sprockets and engages in their teeth. Chain drives with several driven sprockets are also used. In addition to the basic listed elements, chain drives include tensioners, lubricating device and guards. The chain consists of hinged links that provide mobility or “flexibility” of the chain. Chain drives can be performed in a wide range of parameters. The calculation took into account the quality of the material, the service life and durability of the chain drive construction</p> Sevda Aliyeva, Javida Damirova, Sevinc Abasova Copyright (c) 2021 Sevda Aliyeva, Javida Damirova, Sevinc Abasova https://creativecommons.org/licenses/by/4.0 https://journal.eu-jr.eu/engineering/article/view/1930 Fri, 23 Jul 2021 17:34:52 +0300 Development of surface roughness model in turning process of 3X13 steel using TiAlN coated carbide insert https://journal.eu-jr.eu/engineering/article/view/1937 <p>Surface roughness that is one of the most important parameters is used to evaluate the quality of a machining process. Improving the accuracy of the surface roughness model will contribute to ensure an accurate assessment of the machining quality. This study aims to improve the accuracy of the surface roughness model in a machnining process. In this study, Johnson and Box-Cox transformations were successfully applied to improve the accuracy of surface roughness model when turning 3X13&nbsp;steel using TiAlN insert. Four input parameters that were used in experimental process were cutting velocity, feed rate, depth of cut, and insert-nose radius. The experimental matrix was designed using Central Composite Design (CCD) with 29&nbsp;experiments. By analyzing the experimental data, the influence of input parameters on surface roughness was investigated. A quadratic model was built to explain the relationship of surface roughness and the input parameters. Box-Cox and Johnson transformations were applied to develop two new models of surface roughness. The accuracy of three surface roughness models showed that the surface roughness model using Johnson transformation had the highest accuracy. The second one model of surface roughness is the model using Box-Cox transformation. And surface roughness model without transformation had the smallest accuracy. Using the Johnson transformation, the determination coefficient of surface roughness model increased from 80.43&nbsp;% to 84.09&nbsp;%, and mean absolute error reduced from 19.94&nbsp;% to 16.64&nbsp;%. Johnson and Box-Cox transformations could be applied to improve the acuaracy of the surface roughness prediction in turning process of 3X13&nbsp;steel and can be extended with other materials and other machining processes</p> Nhu-Tung Nguyen, Do Duc Trung Copyright (c) 2021 Nhu-Tung Nguyen, Do Duc Trung https://creativecommons.org/licenses/by/4.0 https://journal.eu-jr.eu/engineering/article/view/1937 Fri, 23 Jul 2021 17:35:01 +0300 Development of a procedure for determination of damage to seeds and cotton fibers in cotton cleaning machines https://journal.eu-jr.eu/engineering/article/view/1944 <p>Studies on the dynamic state of cotton raw materials when introducing working bodies of processing machines into it allow to draw the following proposition. Depending on the rate of penetration of the working body into the cotton medium and the density of the medium, in the formulas used to describe the state of the medium, the exponent у ρ can vary from 1.5 to 3. The exponent for density ρ is a measure of the compression and compaction of raw materials on the surface of the working body. The exponent of ρ is also related to the amount of damage to cotton fibers and seeds. For the first time, a cotton mass is considered as a compressible porous two-component medium consisting of a mixture of cotton fibers and air included in the composition of a porous medium, which is essential in dynamic processing processes, and it must be taken into account when planning technological modes. From experiments on the penetration of a splitter with a peripheral speed <em>u</em>=3.5&nbsp;m/s into a cotton medium with a density of ρ=150–350&nbsp;kg/m<sup>3</sup>, it can be seen that a locally located “air cushion” appears in the close vicinity of the split end. The pressure in it increases by 1.5–2&nbsp;times in comparison with the pressure of statistical compression of cotton fibers alone, without taking into account the influence of the air located in the pores of the system. The forces of compression of cotton fibers from the action of the splitter and the force of volumetric action on the fibers are comparable in the area of the "air cushion".</p> <p>Using the general equations of the mechanics of the compressed medium, as well as experimental data, the fundamental equation of the dynamic state of the mass of raw cotton when the working body of the processing machine is introduced into it, such as the density of the medium, the speed of the working body, its external shape and the degree of surface treatment, is derived. The resulting equation can be used to describe the power stresses in a cotton environment in the technological processes of roller and saw ginning, and during cotton cleaning</p> Fazil Veliev, Esmira Mustafayeva, Anatoliі Mamontov, Vadim Shevtsov, Sergii Zinchenko, Anatoliy Rud Copyright (c) 2021 Fazil Veliev, Esmira Mustafayeva, Anatoliі Mamontov, Vadim Shevtsov, Sergii Zinchenko, Anatoliy Rud https://creativecommons.org/licenses/by/4.0 https://journal.eu-jr.eu/engineering/article/view/1944 Fri, 23 Jul 2021 17:35:08 +0300 Implementation of P-type black silicon with high aspect ratio for optoelectronics applications https://journal.eu-jr.eu/engineering/article/view/1902 <p>Black Silicon (BSi) is a semiconductor with a surface modified to get&nbsp;a very low reflectivity and correspondingly high absorption of visible light. P-type &lt;100&gt; silicon wafers were used to prepare very low reflecting samples. These samples may use as substrates in optoelectronic applications. Electrochemical etching at different etching current, and time were applied. B-silicon is chemically equal to normal silicon, differs in surface treatment that changes a morphology. This special morphology is demanded for absorption enhancement which involves maximum light absorption. Surface roughness is&nbsp;done by texturing or trenching a silicon wafer surface. As these structures are in place, and as they are small enough, incident light will be more absorbed and less reflected, this is what gives black silicon its name. BSi was characterized by (FESEM), structural analysis indicates that BS layers were formed<em>.</em> The porosity was in the range of (10–40)&nbsp;% and it is dependent on etching time and etching current value. Etching density is 0.1073/mm<sup>2</sup>. Reflection analysis shows satisfying minimum reflectivity spectrum with the intensity of peaks decrease and red shifted with increasing the etching current. A peak of the Photoluminescence ranges about 360&nbsp;nm, PL peaks are blue shifted and proportional to etching current. The band gap energy ranged from 2 to 3.4&nbsp;eV, it is affected with porous morphology and directly proportional to etching current values</p> Hussam Muhsin Hwail, Manal Midhat Abdullah Copyright (c) 2021 Hussam Muhsin Hwail, Manal Midhat Abdullah https://creativecommons.org/licenses/by/4.0 https://journal.eu-jr.eu/engineering/article/view/1902 Wed, 23 Jun 2021 00:00:00 +0300 Comparison of closed-form solutions to experimental magnetic force between two cylindrical magnets https://journal.eu-jr.eu/engineering/article/view/1955 <p>The force between permanent magnets implemented in many engineering devices remains an intriguing problem in basic physics. The variation of magnetic force with the distance <em>x</em> between a pair of magnets cannot usually be approximated as<em> x<sup>-4</sup></em> because of the dipole nature and geometry of magnets. In this work, the force between two identical cylindrical magnets is accurately described by a closed-form solution. The analytical model assumes that the magnets are uniformly magnetized along their length. The calculation, based on the magnetic field exerted by one magnet on the other along the direction of their orientation, shows a reduction in the magnetic force with the distance <em>x</em> and a dependence on the size parameters of magnets. To verify the equation, the experiment was set up by placing two cylindrical neodymium iron boron type magnets in a vertical tube. The repulsive force between the identical upper and lower magnets of 2.5&nbsp;cm in diameter and 7.5&nbsp;cm in length was measured from the weight on the top of the upper magnet. The resulting separation between the magnets was recorded as <em>x</em>. The forces measured at <em>x</em>=0.004-0.037&nbsp;m differ from the values calculated using the analytic solution by -0.55&nbsp;% to -13.60&nbsp;%. The calculation also gives rise to a practical remnant magnetic field of 1.206&nbsp;T. When <em>x</em> is much large than the equation of force is approximated as a simple form proportional to 1/<em>x</em><sup>-4</sup>. The finding can be directly used in magnetic levitation as well as applied in calculating magnetic fields and forces in other systems incorporating permanent magnets.</p> Sampart Cheedket, Chitnarong Sirisathitkul Copyright (c) 2021 Sampart Cheedket, Chitnarong Sirisathitkul https://creativecommons.org/licenses/by/4.0 https://journal.eu-jr.eu/engineering/article/view/1955 Fri, 23 Jul 2021 17:35:46 +0300