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This review paper is an homage to Arvid Palmgren’s pioneering paper on rolling bearing service life to highlight its relevance a century later. It follows the evolution of bearing service life theory from Palmgren’s fundamental research to the contemporary international standard ISO 281. Palmgren’s theory, based on the previously published papers of Stribeck and Hertz, laid the basis for the later development of bearing service life assessment methodology. Based on the Weibull theory of probability of damage, Lundberg and Palmgren introduced stochastic elements to explain the effect of reliability on bearing service life prediction. Harris and Ioannides, who made a significant contribution to the revision of the international standard on rolling bearing load rating and rating life are mentioned as well. Zaretsky’s critical analysis also was not neglected in this review, due to a different approach respecting the original influence of material properties and bearing performances. Despite standardization, ongoing research by leading advanced bearing industries and academic institutions continues to refine methodologies for service life assessment. Through a comprehensive review and analysis, this paper offers insight into the current state of bearing service life theory, highlighting the collaborative efforts bringing progress in this field.

The presented research is a part of widely research of the nonlinear dynamic behaviour of rolling bearings, which are the parts of all rotating assemblies and machinery. In accordance with the state-of-the-art requirements for the advanced mechanical design and industrial digitalization, the large experiments and research are performed and the new mathematical model of the dynamic behaviour of rolling bearings with damages is developed. The results obtained for a particular type of deep groove ball bearings are presented, and the possible further research and implementation of the obtained model in digitalized self-monitoring systems is discussed.

In recent decades composite materials have become widely used across various industries, either alongside traditional materials or as complete replacements for conventional materials and technologies. This shift is attributed to several advantages they offer, such as low mass, chemical resistance, significant load-bearing capacity, strength, adaptability to modern construction principles, and utilisation of new technologies as additive manufacturing. The first composite materials were developed and patented in the late 19th and early 20th century. For more than a century, composites have seen significant progress in terms of types, properties, technologies, and various applications. Consequently, the need for standardized practices has emerged that can only be achieved through the establishment of standards and standardization processes. Both the International Organisation for Standardization (ISO) and the American Society for Testing and Materials (ASTM) have dedicated technical committees and subcommittees focused on standards for composite materials. Each of these organisations has published approximately one hundred standards related to composites, covering terminology, properties, test methods, procedures, and more. The paper provides a concise historical overview of the development of composite materials and outlines fundamental types of composites. Additionally, it presents an analysis of the quantity and content of standards related to composites published by aforementioned standardization organisations. Statistical data regarding the publication of these standards over time and by specific area are also presented. Conclusions have been drawn based on these analyses.

The load-carrying capacity of shafts is a critical factor in the design and performance of various technical systems, ranging from industrial machinery to all kinds of transmissions. This paper presents a comprehensive study aimed at understanding and quantifying the influence of key factors, including material durability, shaft diameter, surface roughness, stress concentration and the distance between shaft supports, on the load-carrying capacity of the shaft. The load-carrying capacity criterion is the fatigue safety factor. The paper offers a systematic exploration of the influential factors affecting shaft load-carrying capacity, both individually and in combination. The paper concludes by considering the simultaneous influence of all the aforementioned factors. A composite factor is introduced, representing the cumulative effect of material and geometry parameters. This composite factor allows for a holistic approach to shaft design, enabling engineers to make informed decisions that maximize load-carrying capacity while minimizing material usage and manufacturing costs.

The purpose of this paper is to analyze the lubrication quality of porous sliding bearings, starting from the bearing model and in combination with experimental results aimed at analyzing the lubrication regimes of different working conditions. The separation between the surfaces by the lubricant layer is what determines the regime. The quality and type of lubrication regime are determined by parameters in the mathematical model including typically speed, load, motion, materials, environment, etc., which have an impact on friction. Besides those elements, important parameters such as coefficient of friction (COF) and working temperature are to be measured due to experimental investigations to detect an equilibrium working state. The self-lubrication mechanism in porous metal bearings improves their service life and lubrication processes; however, the COF still varies within a wide interval. This variability can be understood, considering that during bearing operation it operates within a broad range of lubrication regimes. Those findings are explained in the paper by using a combination of calculated parameters according to the bearing model and in combination with our own results of experimental investigations. With the obtained results for particular working conditions, the authors are trying to explain, in the form of a diagram with the limit line as an important outcome of the work, that the lubrication regime for porous metal bearings could arise from boundary lubrication (BL) close to hydrodynamic lubrication (HDL).

Every industrial product should be adapted and harmonized with existing or potential needs in various areas of human activity. Basic sciences are followed by technical sciences, which lead to product development, including engineering design and related activities. After completing the engineering design, the product is manufactured using appropriate production technologies. Art, particularly through industrial design, is more or less included in product development, depending on the type of product. Last, but not least, the state and dynamics of product development are influenced by the social and economic situation, as well as politics, which create an environment for all these activities [1]. Otherwise, realized products significantly impact each of these areas of society and civilization development. A product life-cycle includes the following main stages [1]: 1) Problem/Need/Market and Company Goals/Potential; 2) Product planning; 3) Design/ Development; 4) Parts production/Assembly/Testing; 5) Marketing/Sale; 6) Use/Maintenance and 7) Energy recovery/Recycling/Disposal. The main steps of product design and development are: 1) Task setting; 2) Concept design/Synthesis; 3) Selection of shapes, dimensions and materials; 4) Analysis/Simulation/ Optimisation; 5) Corrections/Modifications and 6) Detailed drawings.In the Architecture, Engineering, and Construction (AEC) industry, there is a concept known as Building Information Modelling (BIM), which has undergone significant development over the past fifteen years. It represents a modern approach to the design, documentation, delivery, and lifecycle management of buildings by utilizing project databases in conjunction with object-based parametric modelling [2]. The primary aim of this work is to propose a comprehensive methodology for Machine Information Modelling (MIM) to the scientific community in the field of machine design. It also seeks to initiate the development of a complex methodology tailored to all aspec

The rapid development of additive manufacturing technologies has opened novel opportunities for producing metal components with a variety of uses. 3D printing of metals provides the capability to produce parts with complex geometry and offers design freedom that cannot be achieved through conventional methods. That is the reason why 3D printed metal parts are increasingly finding applications in areas such as automotive, aerospace, and tool manufacturing. Surface properties of 3D printed metal components are of great importance for the functionality of machine systems, because they often operate under conditions where contact stresses occur. There is just one standard that deals with the measurement and characterization of the surface texture of 3D printed metals – ASTM F3624-23 [1]. Generally, methods for testing surface properties are divided into two groups: non-destructive and destructive methods. The most commonly nondestructive methods for the determination of surface roughness are SEM, EDS, and XRD analysis. Also, all other ultrasonic thermographic, laser, atomic force microscopy (AFM), X-ray, magnetic, and eddy current methods (ETC) can be applied, but their limitations must be taken into account. Usually, post-processing methods are used to reduce the roughness of parts. It has been shown for stainless steel 316L that shot peening can reduce up to 50% of the average surface roughness [2]. Tribological properties are very important in cases where contacting parts is in the relative motion.For determining tribological properties well-known testing methods are adapted for 3D printed metals. The most commonly used are dry erosion, slurry erosion and high-stress abrasion tests on stainless steel 316. Testing procedures of ASTM B611 and ASTM G65 standards are used for determining wear properties of 3D printed cemented carbide, which is not metal, but that procedures can be applied on 3D printed metals [3]. For measuring the hardness of 3D printed metals the Vicke

During the last few decades, the requirements for modern machine elements in terms of size reduction, increasing the energy efficiency, and a higher load capacity of standard and non-standard gears have been very prevalent issues. Within these demands, the main goals are the optimization of the gears’ tooth profiles, as well as the investigation of new tooth profile designs. The presented design idea is based on the optimal solutions inspired by nature. Special attention is paid to the new design of the tooth root zones of spur gears in order to decrease the stress concentration values and increase the tooth root fatigue resistance. The finite element method is used for stress and strain state calculations, and the particular gear pair is modeled and optimized for these purposes. For tooth root strength analysis, the estimations are based on the theory of critical distances and the stress gradients obtained through finite element analysis. The obtained stress gradients have shown important improvements in the stress distribution in the transition zone optimized by biomimetics. An analysis of the material variation influence is also performed. Based on the investigations of a particular gear pair, a significant stress reduction of about 7% for steel gears and about 10.3% for cast iron gears is obtained for tooth roots optimized by bio-inspired design.

This paper investigates the load capacity of bolted flanged joints, which are a common type of mechanical joints used in machinery. Bolted joints offer several advantages, including easy maintenance and disassembly, sealing, reduction of vibrations and noise, and protection against pollution and moisture. However, they are also the weakest element in most structures, and their degradation can reduce the safety and reliability of the machine system. Using an analytical research method, the load capacity of two types shear-loaded bolted joints, fitted and clamped, was compared by varying the nominal thread diameter of the bolts, the number of bolts in a group joint, and the pitch diameter on which the bolts are mounted for torque transmission. The function that enables the reduction of the difference in load capacity between fitted and clamped bolted joints by varying their number and pitch diameter is derived in this paper. The research shows that with certain combinations of geometric characteristics and tightening conditions of clamped joints, the load capacity of clamped bolted joints can be improved. This study aims to provide the constructor with relevant practical data to make an appropriate choice of bolted joint type (fitted or clamped) by combining various influence parameters of group shear-loaded joint, and, at the same time, achieve the same desired load capacity or, in the case of different load capacities, to know the exact ratio of their safety factors.

The modern era of composite materials begins at the end of the 19th century with the production of the first polymer–based artificial resins. Since then, the types and technologies of composite materials have been continuously developed and improved, until today. Their use in modern industry is progressively growing. That is why orderliness and regularity are necessary for the development, production, meeting of market requirements, exploitation and recycling of these materials. It can only be achieved through standards and standardization. Within the technical committee TC 61 of the International Organization for Standardization – ISO, the subcommittee ISO/TC 61/SC 13, which deals with composites and reinforcing fibres, operates. The American Society for Testing and Materials – ASTM International also publishes international standards. The D30 committee for composite materials operates within this organization. ISO/TC 61/SC 13 has existed since 1985, and ASTM/D30 since 1964. In this paper, an analysis of the number, types and dynamics of the publication of standards in the field of composites and related fields was carried out. Based on the analysis carried out, it was concluded that a large number of significant standards have been published, that the number of standards is increasing following the development of new composite materials, as well as that further expansion of the concept of standardization in the field of composites can be expected. The results shown here are the result of research supported by COST action CA21155 – Advanced Composites under HIgh STRAin RaTEs Loading: a route to certification–by–analysis (HISTRATE).

The involute is the most common shape of the gear tooth profile due to a number of its advantages compared to other profiles used in practice. The main advantages are the same type of tool for making both meshed gears, simple geometry of the tool, simple control and measuring of the shape and dimensions of the teeth, as well as that the gear meshing is not sensitive to varying gears' centre distance. Involute gears made with the same cutting tool - toothed rack can mesh correctly, regardless of the number of teeth. This fact, as well as the simple shape of the blade (a straight line), contributed to the establishment of the toothed rack as the basic tool for making involute teeth. In engineering education in the field of machine design and machine elements, it is still important to consider in detail the theory of gear pairs. Students learn about the geometry of gears, the kinematics of gear meshing, the strength, calculation of load carrying capacity, service life and reliability of gear pairs in various applications. Regardless of modern information technologies, modelling and computer simulations, the classic, traditional way of learning (or possibly hybrid, as a combination of conventional and modern approaches) is still the most prevalent in teaching. At the same time, laboratory exercises are of essential importance. The existing design of the laboratory educational device for simulating the generation of gearing using a toothed rack is presented in this paper. Then its design was modelled in the SolidWorks program and an improved variant solution is suggested. Also, a simulation of the involute teeth shaping was performed using AutoCAD.

This paper explores the significance of standardization in the field of additive manufacturing (AM). The rapid growth of AM in modern industries has highlighted the need for standardization to ensure compatibility, quality control, and market opportunities for AM products. The paper emphasizes the flexibility of AM technologies in meeting industrial and ecological requirements, revolutionizing business models, and satisfying customer needs. It provides an overview of the International Organization for Standardization (ISO) and ASTM International (American Society for Testing and Materials), two major organizations involved in developing and publishing international standards for AM. The paper discusses the technical committees, working groups, and collaborations established by ISO and ASTM to address various aspects of AM standardization. Additionally, it highlights the ongoing efforts in Serbian national standardization and proposes future research on analyzing the scopes and contents of AM standards for improved usability. Overall, the paper emphasizes the crucial role of standardization in supporting the continued advancement of additive manufacturing.

Bolted joints are the most common and primary form of joints in most machines. The directions of research in this area mostly relate to strength, stiffness, load-carrying capacity, causes of failure, temperature influences etc. Fitted and clamped group bolted joints shear-loaded with torque are analyzed in this paper. A comparative analysis of their load-carrying capacity was performed. When the factor of safety (FOS) ratio of fitted and clamped bolts was determined, the geometric characteristics were varied so that this ratio was reduced, i.e. their load-carrying capacities became close. The carried-out research aims to provide the constructor with relevant data for the selection and application of the appropriate type of bolted joint. Using an analytical research method, the nominal thread diameter of the bolts, the number of bolts in a group joint, and the pitch diameter on which the bolts are mounted were varied. Useful practical results have been obtained, based on which the designer can make a choice of the appropriate type of shear-loaded bolted joint (fitted or clamped) and combine different influence parameters of the group joint (number of bolts and pitch diameter) to achieve the same load-carrying capacity or, in the case of different load-carrying capacity, to know in what relation would be their FOS.

Contact stress and deformations in the thrust ball bearing with a contact angle of 90 ° are onsidered in this paper. Ideally, an external axial load of this kind of bearings should be centric, but in reality, this force may act eccentrically. As a result, the load distribution between balls is inequal. The most unfavourable case is when the axial force intersects the radius vector of one of the balls. The load, contact stress and contact deformation of this ball are greater than the load of all rest of the balls and greater in the case of equal load distribution. It limits the load-carrying capacity of a real bearing, compared to the theoretical static load rating. Analyzes have shown that considered thrust ball bearings do not lose operational ability at low speeds, even if there is some load eccentricity when an external axial load is not more than 30- 40% of static bearing capacity. Otherwise, additional bearing capacity analyzes are required.

The function of shear-loaded bolted joints is the prevention of joint members’ slip. This can be achieved in two ways, depending on the construction, i.e. relative dimensions of bolts and holes in connected parts. There are two types of shear-loaded bolted joints, clamped (friction) and fitted bolted joints. In both cases, a connection between joint members is shear-loaded, but the bolts have different stress and strain states. In clamped bolted joints the actual load is tensile stress, while fitted bolts are loaded with shear and contact pressure. In this paper, a comparative analysis of the load capacity (safety factors) of clamped and fitted bolts, under the same geometrical and operational conditions was performed. The analysis showed multiple higher load-carrying capacity of fitted bolts that go up to 60 times(!).

The service life of a rolling bearing is calculated using a standardized formula, based on the bearing’s dynamic load rate, equivalent load, and the appropriate exponent, depending on the rolling elements’ shape. Deep groove ball (DGB) bearings are supplied to the market with radial internal clearance. Clearance ranges are classified into several size groups, with values depending on the bearing bore diameter. Radial clearance causes the presence of axial clearance. DGB bearing is a bearing with initial radial contact between balls and raceways (zero contact angle). This type of bearing can be loaded with pure radial load or universally loaded with combined radial and axial load. When a radial bearing is loaded only with a radial load or a combined load with a negligibly small axial component, the contact angle retains the zero value. When the axial component of the load is significantly large, there is an axial relative displacement of the rings for the value of the axial clearance. Then the radial bearing becomes a bearing with angular contact. In the standard calculation method, the expression of the service life does not explicitly take into account the internal clearance. However, the influence of the clearance is calculated indirectly, through the corresponding values of the equivalent dynamic load’s parameters. These parameters depend on the contact angle, and the contact angle depends on the internal clearance. Theoretical quantitative analysis of the internal clearance influence on the service life of a universally loaded DGB bearing is presented in this paper.

Планетарни преносници спадају у групу механичких зупчастих преносника, који су широко заступљени за трансформацију и пренос снаге првенствено због компактности конструкције, високе поузданости и степена искоришћења. Полазећи од функције, коју треба да испуни у оквиру неке конструкције, као и све строжих захтева у погледу перформанси преносника, предмет истраживања ове докторске дисертације је развој вишекритеријумског оптимизационог модела планетарног преносника. Развијени модели који задовољавају низ строгих захтева у погледу: компактности конструкције, минимизације губитака у преносу снаге, равномерности расподеле оптерећења, као и поузданости у различитим експлоатационим условима. За постављени проблем вишекритеријумске оптимизације планетарног преносника формиране су одговарајуће критеријумске функције и дефинисан је низ функционалних ограничења, као и одговарајући домени примене свих релевантних величина зупчастих парова са спољашњим и унутрашњим озубљењем и планетарног преносника као сложеног система, у циљу несметане монтаже, поузданог рада и спрезања зупчастих парова. У оквиру докторске дисертације, развијен је одговарајући механички модел за одређивање степена искоришћења истовремено спрегнутих зупчастих парова, у зависности од њихових геометријских параметара, као и од услова подмазивања. Критеријумске функције формираног вишекритеријумског оптимизационог проблема су нелинеарне и неконвексне па се глобално оптимално решење не може нумерички одредити конвенционалним методама оптимизације. Према томе, у циљу решавања овог комплексног оптимизационог проблема потребно је применити метахеуристичке оптимизационе алгоритме. Дакле, постоји стална потреба за побољшањем постојећих и развојем нових метахеуристичких алгоритама и то развојем адаптивних техника за подешавање управљачких параметара и хибридизацијом алгоритама. У складу са тим, у оквиру докторске дисертације детаљно су разматрани метахеуристички алгоритми, који припадају групи еволутивних алгоритама, као, Planetary gearboxes have a wide application in the field of transformation and transmission of power from the drive to the working machine, due to the compact structure, high reliability and efficiency. Due to the increasingly stringent performance requirements, which planetary gearboxes must satisfy, the research in this dissertation is focused on the problem of multi-objective non-linear optimization of planetary gearbox based on hybrid metaheuristic algorithm, which satisfies a number of strict requirements, such as: compact construction, minimization of power loss, load distribution and reliability in different operating conditions. In this work the formulations of the objective functions for the considered multiobjective optimization problem of planetary gearbox have been outlined along with the appropriate constraints. The formulated constraints have been analyzed and appropriate domains of practical applications of internal and external gear pairs have been formulated, with the aim to ensure proper working, mounting and meshing of considered gears. Furthermore, the theoretical formulation and numerical procedure for the calculation of the planetary gearbox power efficiency has been developed in this work. However, the objective functions and developed constraints of the considered Multiobjective planetary gearbox optimization problem are nonlinear and multimodal functions, and therefore the global optimal solution cannot be obtained using the conventional optimization methods. Therefore, in order to solve this multiobjective and complex optimization problem, the research in this dissertation is focused on metaheuristic optimization algorithms, which belong to the group of evolutionary algorithms, including: differential evolution algorithm and genetic algorithm, as well as the algorithms inspired by the biological systems, such as particle swarm optimization algorithm. To overcome difficulties in solving complex optimization problems, in this thesis the consi

Additional manufacturing (AM), commonly known as 3D printing, exists for 40 years, still evolving and improving. AM has gained great popularity in modern industries due to many advantages concerning conventional manufacturing technologies. Consequently, AM is one of nine pillars of the currently dominating industry trend – Industry 4.0. Initially, AM was mostly used for making models. Now, objects made by AM technologies, often are physical parts ready to be used as final products or to be installed as parts of assemblies in more complex systems. Because of that, in more applications, the mechanical properties of these parts have to be known for the purpose to determine load carrying capacity essential for their functionality. Mechanical properties are being tested using appropriate methods, specimens, and equipment. In order to obtain comparable and evaluable test results, the test procedures and means should be standardized. Therefore, there was a need to develop standards for testing materials used for AM. International standardization in the field of AM started 10 years ago. The international body for standardization ISO developed and published a certain number of standards, but this is just beginning. This paper discusses aspects of AM standardization in the field of testing the mechanical properties of materials for 3D printing using fused deposition modelling (FDM). As an illustration of the standard application, specimens were prepared for testing the tensile properties of plastic materials widely used in AM: PLA, PETG and ABS+.

Sadržaj monografije je rezultat višegodišnjih istraživanja autora, zasnovanih na praćenju, prikupljanju i analizi publikovanih materijala na temu radnog veka kotrljajnih ležaja. Monografija je pregledni rad, tako da obuhvata već objavljene sadržaje, ali sada svedene na suštinu predmeta istraživanja i prezentovane na prijemčiviji način, ali sa kritičkim osvrtom. Rezultati i saznanja iz dostupnih naučnih i stručnih radova, prema mišljenju autora najznačajnijih za ovu oblast istraživanja, su sistematizovani tematski i/ili hronološk, pogodno prikazani i tumačeni, tako da budu razumljivi široj stručnoj čitalačkoj publici. Monografija sadrži i deo rezultata sopstvenih istraživačkih aktivnosti autora, sprovedenih u okviru projekata tehnološkog razvoja, finansiranih od strane nadležnog Ministarstva.

Self-lubricating sliding bearings are widely used in numerous industrial applications, primarily regarding their specific lubrication mechanism. This lubrication mechanism is the main advantage compared with classical sliding bearings because their production is not complex and makes lower prices. According to the bearing material and type of exploitation, self-lubricating sliding bearings could operate with oil (grease) in their material structure or even without any amount of lubricant. This paper is dealing with the load capacity of the bearing, as probably the most important parameter in the aim to make a proper bearing choice for a particular application and corresponding operating conditions

The study investigates the influence of the load distribution on lubricant film thickness between the rolling elements and raceways of the deep groove ball bearing using the conventional theory of elastohydrodynamic lubrication (EHL) with an applied original mathematical model of load distribution between the rolling elements developed by the authors. A presented mathematical model takes into account the influence of bearing operational load and internal geometry (number of balls and radial internal clearance) on lubricant film thickness between balls and raceways. The analyses show that the lubricant film thickness between the balls and raceways decreases with the decrease of the number of balls, a decrease of bearing load and increase of radial internal clearance, due to the increase of inequality of load distribution. The obtained analytical results can be useful for bearing design development as well as in analyses of lubrication conditions of rolling elements bearings in general.

Planetarni prenosnici spadaju u grupu mehaničkih zupčastih prenosnika, koji su široko zastupljeni za transformaciju i prenos snage prvenstveno zbog kompaktnosti konstrukcije, visoke pouzdanosti i stepena iskorišćenja. Polazeći od funkcije, koju treba da ispuni u okviru neke konstrukcije, kao i sve strožih zahteva u pogledu performansi prenosnika, predmet istraživanja ove doktorske disertacije je razvoj višekriterijumskog optimizacionog modela planetarnog prenosnika. Razvijeni modeli koji zadovoljavaju niz strogih zahteva u pogledu: kompaktnosti konstrukcije, minimizacije gubitaka u prenosu snage, ravnomernosti raspodele opterećenja, kao i pouzdanosti u različitim eksploatacionim uslovima. Za postavljeni problem višekriterijumske optimizacije planetarnog prenosnika formirane su odgovarajuće kriterijumske funkcije i definisan je niz funkcionalnih ograničenja, kao i odgovarajući domeni primene svih relevantnih veličina zupčastih parova sa spoljašnjim i unutrašnjim ozubljenjem i planetarnog prenosnika kao složenog sistema, u cilju nesmetane montaže, pouzdanog rada i sprezanja zupčastih parova. U okviru doktorske disertacije, razvijen je odgovarajući mehanički model za određivanje stepena iskorišćenja istovremeno spregnutih zupčastih parova, u zavisnosti od njihovih geometrijskih parametara, kao i od uslova podmazivanja. Kriterijumske funkcije formiranog višekriterijumskog optimizacionog problema su nelinearne i nekonveksne pa se globalno optimalno rešenje ne može numerički odrediti konvencionalnim metodama optimizacije. Prema tome, u cilju rešavanja ovog kompleksnog optimizacionog problema potrebno je primeniti metaheurističke optimizacione algoritme. Dakle, postoji stalna potreba za poboljšanjem postojećih i razvojem novih metaheurističkih algoritama i to razvojem adaptivnih tehnika za podešavanje upravljačkih parametara i hibridizacijom algoritama. U skladu sa tim, u okviru doktorske disertacije detaljno su razmatrani metaheuristički algoritmi, koji pripadaju grupi ev, Planetary gearboxes have a wide application in the field of transformation and transmission of power from the drive to the working machine, due to the compact structure, high reliability and efficiency. Due to the increasingly stringent performance requirements, which planetary gearboxes must satisfy, the research in this dissertation is focused on the problem of multi-objective non-linear optimization of planetary gearbox based on hybrid metaheuristic algorithm, which satisfies a number of strict requirements, such as: compact construction, minimization of power loss, load distribution and reliability in different operating conditions. In this work the formulations of the objective functions for the considered multiobjective optimization problem of planetary gearbox have been outlined along with the appropriate constraints. The formulated constraints have been analyzed and appropriate domains of practical applications of internal and external gear pairs have been formulated, with the aim to ensure proper working, mounting and meshing of considered gears. Furthermore, the theoretical formulation and numerical procedure for the calculation of the planetary gearbox power efficiency has been developed in this work. However, the objective functions and developed constraints of the considered Multiobjective planetary gearbox optimization problem are nonlinear and multimodal functions, and therefore the global optimal solution cannot be obtained using the conventional optimization methods. Therefore, in order to solve this multiobjective and complex optimization problem, the research in this dissertation is focused on metaheuristic optimization algorithms, which belong to the group of evolutionary algorithms, including: differential evolution algorithm and genetic algorithm, as well as the algorithms inspired by the biological systems, such as particle swarm optimization algorithm. To overcome difficulties in solving complex optimization problems, in this thesis the consi

The operational ability of a rolling bearing selected for a specific application is assessed based on service life. The basic formula for bearing rating life was established more than 70 years ago by A. Palmgren. The first standard presenting a basic mathematical model for rating life calculation was published in 1962 (ISO/R281). The content of this standard has been revised and the next version was published in 1977 (ISO 281-1). The novelty was the introduction of adjustment factors for reliability other than 90%. This standard was replaced by the ISO 281 standard in 1990, which introduced additional adjustment factors for special bearing properties and operating conditions. The latest version of the ISO 281 standard was published in 2007. This standard provides a procedure for calculating the modified service life by taking into account the additional impacts of lubrication condition, lubricant contamination and limit fatigue load. Furthermore, the document ISO/TS 16281 was published in 2008 introducing the influence of bearing internal clearance and misalignment in the rating life calculation. An overview of the development of a standardized formula for bearing rating life is given in this paper, on the example of deep groove ball bearing under radial operational loading.

The aim of this paper is to determine deformations and stresses in the statically loaded thrust ball bearing subjected to a centric external axial load. In this case, all balls in the bearing are equally engaged in the transmission of the operational load. The influence of the load on the stresses and deformations in the bearings of different series has been analysed. The obtained results are the basis for further research of the load distribution in an eccentrically loaded axial ball bearing in order to determine the reduction of the static load bearing capacity in relation to the values determined in appropriate standard and also to the values prescribed by manufacturers' catalogues.

Информације из стручне литературе, као и искуствени подаци, показују да велики проценат енергетских губитака термоелектрана потиче од система тракастих транспортера и њихових кључних компоненти – транспортних (носећих) ваљака. Зато су управо ови склопови, чија је функција да пренесу оптерећење услед масе транспортне траке и транспортованог терета на носећи рам, изабрани за објекат истраживања дисертације. Са циљем повећања поузданости, и смањења финансијских и енергетских губитака узрокованих непланираним отказима, развијене су нове и унапређене постојеће експерименталне процедуре за испитивање кључних карактеристика транспортних ваљака – обједињене у комплексну експерименталну методологију испитивања. Међу развијеним процедурама, по значају се посебно истиче процедура за испитивање радних карактеристика котрљајних лежаја (критичних компоненти транспортних ваљака) – под дејством контаминирајућих честица са површинских копова угља. Научне хипотезе представљене дисертације се односе управо на ову процедуру, односно, напредним статистичким методама (применом софтверских пакета најновије генерације) је позитивно одговорено на питање да ли постоје статистички значајне зависности између посматраних радних карактеристика вештачки контаминираних котрљајних лежаја – вибрација, температура и времена рада. Утврђене статистичке корелације су потом имплементиране у постојећу једначину за прорачун радијалног зазора котрљајних лежаја. Према развијеној експерименталној методологији је испитан велики број узорака транспортних ваљака, различитог типа, произведених од различитих произвођача. Након анализе и дискусије добијених резултата, поређењем са искуственим подацима из праксе и резултатима до сада реализованих истраживања у предметној области, развијена методологија је успешно верификована, па се може даље примењивати за процену квалитета транспортних ваљака и њихових котрљајних лежаја., Relevant literature, as well as practical experience, has shown that large percentage of thermal power plant energy losses is caused by overland conveyor systems and their key components – conveyor idlers (rollers). That’s the main reason why this assemblies, with function to transfer the load from the conveyor belt and transported material to the supporting frame, are chosen as an object of research presented in this dissertation. In order to improve reliability and decrease financial and energy losses due to unplanned maintenance, a new conveyor idlers testing procedures were developed (some of existing were improved) – and joined in complex experimental testing methodology. Among developed testing procedures, experimental procedure for conveyor idler’s rolling bearings testing is the most important – because it provides the information about the influence of exploitation contamination particles (from the open pit coal mines) on rolling bearing’s operational characteristics. Scientific hypothesis presented in this dissertation are related primarily to this experimental procedure. It was confirmed that statistically significant correlations between artificially contaminated rolling bearing’s vibrations, temperatures and time in operation could be established. One of generated correlation was afterward implemented in existing equation for rolling.

Spur gear load carrying capacity and mass are primarily dependent of the tooth root stress. Geometric and kinematic parameters of gear teeth pairs produce multiple effects on the tooth root stress: through tooth root critical section location and root fillet radius, tooth profile shape and load leading point location on tooth profile, as well as through tooth stiffness. In the conventional calculation procedure, according to ISO standard, the influence of geometric and kinematic parameters of the gear pair on the tooth root stress is considered through the "contact ratio factor" Y-epsilon , whose values are determined using the approximate expressions. To view the real effects of geometric and kinematic parameters of the gear pair on the tooth root stress analytical model is developed, defining non-dimensional relative stress factor. The analysis comprises two groups of cylindrical gear pairs with different gear ratios and different coefficients of addendum modification. The results obtained are compared with the results of standard calculation procedure according to ISO standard. In addition, the developed analytical model is used to explain the assumptions, physicality and boundary conditions of the "contact ratio factor" Y-epsilon.

Informacije iz stručne literature, kao i iskustveni podaci, pokazuju da veliki procenat energetskih gubitaka termoelektrana potiče od sistema trakastih transportera i njihovih ključnih komponenti – transportnih (nosećih) valjaka. Zato su upravo ovi sklopovi, čija je funkcija da prenesu opterećenje usled mase transportne trake i transportovanog tereta na noseći ram, izabrani za objekat istraživanja disertacije. Sa ciljem povećanja pouzdanosti, i smanjenja finansijskih i energetskih gubitaka uzrokovanih neplaniranim otkazima, razvijene su nove i unapređene postojeće eksperimentalne procedure za ispitivanje ključnih karakteristika transportnih valjaka – objedinjene u kompleksnu eksperimentalnu metodologiju ispitivanja. Među razvijenim procedurama, po značaju se posebno ističe procedura za ispitivanje radnih karakteristika kotrljajnih ležaja (kritičnih komponenti transportnih valjaka) – pod dejstvom kontaminirajućih čestica sa površinskih kopova uglja. Naučne hipoteze predstavljene disertacije se odnose upravo na ovu proceduru, odnosno, naprednim statističkim metodama (primenom softverskih paketa najnovije generacije) je pozitivno odgovoreno na pitanje da li postoje statistički značajne zavisnosti između posmatranih radnih karakteristika veštački kontaminiranih kotrljajnih ležaja – vibracija, temperatura i vremena rada. Utvrđene statističke korelacije su potom implementirane u postojeću jednačinu za proračun radijalnog zazora kotrljajnih ležaja. Prema razvijenoj eksperimentalnoj metodologiji je ispitan veliki broj uzoraka transportnih valjaka, različitog tipa, proizvedenih od različitih proizvođača. Nakon analize i diskusije dobijenih rezultata, poređenjem sa iskustvenim podacima iz prakse i rezultatima do sada realizovanih istraživanja u predmetnoj oblasti, razvijena metodologija je uspešno verifikovana, pa se može dalje primenjivati za procenu kvaliteta transportnih valjaka i njihovih kotrljajnih ležaja., Relevant literature, as well as practical experience, has shown that large percentage of thermal power plant energy losses is caused by overland conveyor systems and their key components – conveyor idlers (rollers). That’s the main reason why this assemblies, with function to transfer the load from the conveyor belt and transported material to the supporting frame, are chosen as an object of research presented in this dissertation. In order to improve reliability and decrease financial and energy losses due to unplanned maintenance, a new conveyor idlers testing procedures were developed (some of existing were improved) – and joined in complex experimental testing methodology. Among developed testing procedures, experimental procedure for conveyor idler’s rolling bearings testing is the most important – because it provides the information about the influence of exploitation contamination particles (from the open pit coal mines) on rolling bearing’s operational characteristics. Scientific hypothesis presented in this dissertation are related primarily to this experimental procedure. It was confirmed that statistically significant correlations between artificially contaminated rolling bearing’s vibrations, temperatures and time in operation could be established. One of generated correlation was afterward implemented in existing equation for rolling.

Thrust ball bearings with extremely large size and capacity, are not standardized and could not be found in catalogues. In aim to investigate possible failure causes of thrust ball bearings in heavy machinery excavators, this paper presents stress and deformations calculation supported with FME analysis in balls-raceway interfaces because of carrying whole upper construction and allow rotation movement. In this paper it was performed numerical calculations and their comparison for two, conceptually different types of large size thrust bearings. First one is classical pivot, such as load distribution in modified new bearing solution. Contact stress calculation of those bearings and FME analysis show that stress and deformation values for ball are near to the limit of static load capacity. Presented study supported by images of balls and raceways damage appearance, with or without grease as a lubricant, could be very useful in the bearing failure analysis.

Planetary gears take a very significant place among the gear transmissions, and they are widely used in military and civil industry applications such as marine vehicles, aircraft engines, helicopters and heavy machinery. Planetary gears are complex mechanisms which can be decomposed into external and internal gears with the corresponding interaction, which requires geometrical conditions in order to perform the mounting and an appropriate meshing of the gears during their work. Planetary gears have a number of advantages as compared to the transmission with fixed shafts such as a compact design, with co-axial shafts, high power density and higher efficiency, which is achieved by reducing gear weight using thin-rimed gears. The purpose of this paper is to present the optimization model for the planetary gears, where the objective function is the weight of gears, and functional constraints imposed upon their respective structural design. Hence, the objective is to minimize rim thickness of the gear in order to achieve high-performance power transmission and minimize weight. This paper presents the results of an investigation with finite element analysis (FEM) into the effects of thin-rimmed gear geometry on the root fillet stress distribution.

Self-lubricating sliding bearings are widely used in numerous industrial applications, primary regarding their specific lubrication mechanism. This lubrication mechanism is a main advantage compared with classical sliding bearings, where their production is not so complicate and makes lower price. This kind of bearing could be simple to assembly and in operating produce less noise and vibrations. According to their material and type of operating, self-lubricating sliding bearings could operate with oil (grease) in its own material structure or even without any amount of lubricant. Besides numerical analysis and calculations, at Faculty of Mechanical Engineering, University of Belgrade numerous experimental investigations of those bearings have been conducted, regarding own laboratory with test rig. This paper presents only selected results of those experiments, where portable DAQ acquisition with LabVIEW software tool was applied.

U monografiji je prezentovan razvijen originalni matematički model raspodele opterećenja na kotrljajna tela kugličnog kotrljajnog ležaja sa radijalnim dodirom, koji je primenjen za matematičko modeliranje abrazivnog habanja kugličnih kotrljajnih ležaja. U monografiji su prikazani i rezultati eksperimentalne verifikacije razvijenog matematičkog modela.

A prediction of crack propagation is subject of research of many scientists. Understanding crack occurrence and propagation could save lives (i.e. in airplane industry), or at least reduce the costs occurred by unexpected failures and stoppages. In this paper it is provided a brief theoretical background of the crack propagation regarding to stress intensity factor, and simulation of crack propagation through a planar plate made of steel with the middle positioned cylindrical hole, by means of Abaqus software. In addition, it is performed calculation of stress intensity factors with MORFEO, software that could be implemented onto Abaqus.

The reparatory hardfacing of damaged contact surfaces is the most reliable method of renewing the tooth shape, dimensions and operating characteristics of failed gears. Proper selection of method suitable for reparatory hardfacing implies knowledge about the mechanisms of contact surfaces wear. The regeneration itself is a complex process made up of a greater number of technological operations, with a very important and strictly determined arrangement. The comparative tribological characteristics of the gears regenerated by hardfacing and newly made ones are considered at the occurrence of initial pits on the teeth surfaces i.e. at the occurrence of primary pitting on the gear tooth flanks. The speed of destructive pitting development in regenerated and newly made gears is also compared in this paper.

This paper contains the results of experimental analysis of fatigue endurance of used steel teeth regenerated by hard facing. The cylindrical spur gears were tested and compared with the newly made ones, oiler being regenerated by hard facing with subsequent cementation and quenching. The fatigue testing wider variable amplitude loading was used to determine the duration of operational life through measurement of wear. The obtained results demonstrated the impact of hard facing methods on gear endurance in operation. In the test on regenerated gears it was discovered that initial pits appeared almost simultaneously for different facing materials and a bit earlier than in tests on newly made ones, despite their considerably higher pitting rate. Apart from that, the tested operational lives of regenerated and newly-made gears were approximately equal and much longer than predicted.

The impact of load distribution in meshed teeth, teeth geometry and manufacturing accuracy on wear of the spur gear tooth flanks is studied in this paper. The original geometry of teeth is impaired wearing. Due to that, the load distribution is uneven, dynamic forces are increased, and energy efficiency is decreased. The aim of the theoretical and experimental studies, carried out in this paper, is to reach more accurate model for the analysis of tooth flanks load carrying capacity, taking into account a larger number of impacts on the tooth flanks stress state. A mathematical model for the contact stress during contact period is developed, depending on the value and sign of base pitch difference of meshed teeth. The impact of pitch point's position during the meshed teeth contact period was observed. In order to establish a correlation between the tooth flank failures and developed mathematical model, the appropriate experimental studies were carried out. The cemented spur gear pairs were examined on back-to-back gear test rig under conditions of maximum operational load. The results are presented in this paper.

Tribology phenomena are obviously present and have significant importance in most of human activities, processes and actions. This paper presents an attempt in this direction dealing with study of tribology aspects in ballroom dancing. Analysing a couple of Standard and Latin ballroom dances, idea is to make approximate calculation of friction forces and torques and their influence on foot floor interface. Authors take Viennese waltz with couple of other typical dances, where the concept and methodology of friction calculation has been performed. Besides the approximate calculation of friction, this paper attends to measure and analyse complete energy consumption during the dance as a human activity. This has been done by making several experiments where total energy loss in ballroom dance used to be measured. In combination with friction loss calculations, those experiments reach some conclusions, among others that impact of friction losses in total energy consumption is not dominant for quick dances. This topic could be interesting for some further investigations such also for floors and shoes manufacturers aimed to make an optimum product for requested activity. Clear objective is to reduce energy consumption from the one side, but also to prevent possible undesirable slips from the other.

Self lubricated sliding bearings production and investigations are still in great expansion because of their very practical maintenance and very long operating life. This is probably the main reason for their common use in most of modern micromechanics, automotive and household machines, where they are taking a leader position. The best example is porous metal bearing, which is been made by sintering process as a product of powder metallurgy. Experimental investigations are very important for this kind of bearings because is represents the best way for friction and wear process determination in their operating life. The aim of the paper is to present a way of experiments realization using own projected test rig with modern portable DAQ equipment. In addition here are been presented some results of experimental investigations of porous metal bearings following by their analysis with conclusions and recommendations for their further use and exploitation.