Analysis of the influence of internal radial clearance on the static load rating of the rolling bearing

Pri konstruisanju uležištenja vratila i osovina mehanizama i mašina, najrelevantnija eksploatadona karakteristika na osnovu koje se vrši izbor kotrljajnih ležaja je nosivost. Jedan od najvažnijih faktora koji utiče na raspodelu opterećenja na kotrljajna tela, a time i na nosivost ležaja je unutrašnji radijalni zazor. U cilju egzaktnijeg određivanja statičke nosivosti kotrljajnog ležaja u odgovarajuće standardne izraze uvedena je, na novi način definisana veličina - faktor raspodele opterećenja na kotrljajna te/a ležaja, čija vrednost zavisi od veličine unutrašnjeg radijalnog zazora. Na osnovu korigovanih standardnih izraza, razmatran je uticaj veličine unutrašnjeg zazora na statičku nosivost kugličnog kotrljajnog ležaja sa radijalnim dodirom. Pri tome je izvršena i uporedna analiza statičke nosivosti ležaja određene na osnovu ISO preporuka i stvarne nosivosti sa aspekta uticaja unutrašnjeg radijalnog zazora i utvrđen stepen aproksimacije.In the design of the bearing arrangements, load rating is the most relevant exploitational characteristic to be taken into consideration in selection of bearing. One of the most important factors effecting the load distribution between rolling elements, and thereby the load rating of the bearing - is the internal radial clearance. In this paper it was investigated how internal radial clearance influences on the static load rating of the deep groove ball bearing. This effort included a comparative analysis of the static load rating determined under the ISO recommendations, on the one side, and the real load rating, on the other, from the standpoint of the influence of internal radial clearance.

Analysis of the influence of internal radial clearance on the static load rating of the rolling bearing

Pri konstruisanju uležištenja vratila i osovina mehanizama i mašina, najrelevantnija eksploatadona karakteristika na osnovu koje se vrši izbor kotrljajnih ležaja je nosivost. Jedan od najvažnijih faktora koji utiče na raspodelu opterećenja na kotrljajna tela, a time i na nosivost ležaja je unutrašnji radijalni zazor. U cilju egzaktnijeg određivanja statičke nosivosti kotrljajnog ležaja u odgovarajuće standardne izraze uvedena je, na novi način definisana veličina - faktor raspodele opterećenja na kotrljajna te/a ležaja, čija vrednost zavisi od veličine unutrašnjeg radijalnog zazora. Na osnovu korigovanih standardnih izraza, razmatran je uticaj veličine unutrašnjeg zazora na statičku nosivost kugličnog kotrljajnog ležaja sa radijalnim dodirom. Pri tome je izvršena i uporedna analiza statičke nosivosti ležaja određene na osnovu ISO preporuka i stvarne nosivosti sa aspekta uticaja unutrašnjeg radijalnog zazora i utvrđen stepen aproksimacije.In the design of the bearing arrangements, load rating is the most relevant exploitational characteristic to be taken into consideration in selection of bearing. One of the most important factors effecting the load distribution between rolling elements, and thereby the load rating of the bearing - is the internal radial clearance. In this paper it was investigated how internal radial clearance influences on the static load rating of the deep groove ball bearing. This effort included a comparative analysis of the static load rating determined under the ISO recommendations, on the one side, and the real load rating, on the other, from the standpoint of the influence of internal radial clearance.

Influence of wear on deep groove ball bearing service life

Habanje kotrljajnog ležaja je uslovljeno proklizavanjem koje prati kotrljanje kotrljajnih tela duž staza kotrljanja. Usled habanja spregnutih delova ležaja povećava se unutrašnji radijalni zazor. Sa povećanjem unutrašnjeg radijalnog zazora neravnomernost raspodele opterećenja na kotrljajna tela ležaja se povećava, što je uzrok smanjenja radnog veka ležaja. U ovom radu je izvršena analiza uticaja habanja na radni vek ležaja na osnovu klasične teorije radnog veka ležaja i originalnog matematičkog modela raspodele opterećenja na kotrljajna tela ležaja.Frictional sliding which follows rolling of balls along rings raceways causes rolling bearing wear. Internal radial clearance of rolling bearing becomes larger due to wear of rolling elements and raceways. With increasing internal radial clearance, load distribution between rolling elements becomes more unequal. It is cause of decreasing rolling bearing life. Functional dependence of deep groove ball bearing life on wear is presented in this paper. Development of this function is based on classical expressions of bearing life theories and an original mathematical model of load distribution between rolling elements

Influence of wear on deep groove ball bearing service life

Habanje kotrljajnog ležaja je uslovljeno proklizavanjem koje prati kotrljanje kotrljajnih tela duž staza kotrljanja. Usled habanja spregnutih delova ležaja povećava se unutrašnji radijalni zazor. Sa povećanjem unutrašnjeg radijalnog zazora neravnomernost raspodele opterećenja na kotrljajna tela ležaja se povećava, što je uzrok smanjenja radnog veka ležaja. U ovom radu je izvršena analiza uticaja habanja na radni vek ležaja na osnovu klasične teorije radnog veka ležaja i originalnog matematičkog modela raspodele opterećenja na kotrljajna tela ležaja.Frictional sliding which follows rolling of balls along rings raceways causes rolling bearing wear. Internal radial clearance of rolling bearing becomes larger due to wear of rolling elements and raceways. With increasing internal radial clearance, load distribution between rolling elements becomes more unequal. It is cause of decreasing rolling bearing life. Functional dependence of deep groove ball bearing life on wear is presented in this paper. Development of this function is based on classical expressions of bearing life theories and an original mathematical model of load distribution between rolling elements

A new methodology for prediction of high-cycle contact fatigue for spur gears

High-cycle contact fatigue is a localized phenomenon that occurs in highly stressed grains of the material on or under the contact region. The contact zones of tooth flanks for meshed gears are subjected to contact fatigue damages that causes pitting and leads to gears failure. The objective of this paper is to give a new viewpoint in contact fatigue prediction in the case of high-cycle fatigue. The main aim of the presented research is to make the methodology for direct calculation of fatigue crack initiation in contact zones. This methodology is developed for spur gears and used up-to-date methods and multidisciplinary approach. Two methods are built in the new methodology: the Theory of Critical Distances (TCD) and the Finite Element Method (FEM). In this paper the comparative analysis of standard and new methodology for prediction of fatigue crack initiation on tooth flanks is presented. The advantages of methods and procedures used in the new methodology are presented through a case study of particular gear pair. The Finite Element Analysis on 3D gear contact model is used for stress and strain calculation and prediction of the maximum stress location in contact zones along the gear face width. The stress gradient curves from the contact zone are made for a pinion tooth in different cross sections along gear facewidth. The Theory of Critical Distances used these stress gradients and material characteristics for fatigue crack initiation prediction. The benefits of presented methodology are shown by the detail analysis of the obtained results

Mathematical model of load distribution in rolling bearing

Spoljašnje opterećenje kotrljajnog ležaja se sa jednog prstena na drugi prenosi preko kotrljajnih tela. Pri tome je raspodela opterećenja na kotrljajna tela neravnomerna. Stepen neravnomernosti raspodele opterećenja zavisi od unutrašnje geometrije ležaja i intenziteta spoljašnjeg opterećenja. U ovom radu su definisana i razmatrana dva granična slučaja raspodele opterećenja kod kugličnog kotrljajnog ležaja opterećenog spoljašnjim radijalnim opterećenjem. To su idealno ravnomerna i izrazito neravnomerna raspodela opterećenja. Stvarna raspodela opterećenja je između ova dva granična slučaja. Novi matematički model raspodele opterećenja je razvijen na osnovu klasične teorije kotrljajnih ležaja i uvođenjem nove originalne veličine, definisane kao faktor raspodele opterećenja. Razvijeni matematički model obuhvata sve pomenute relevantne uticaje na raspodelu opterećenja u kotrljajnom ležaju (broj kotrljajnih tela u ležaju, unutrašnji radijalni zazor i spoljašnje opterećenje).External load of rolling bearing is transferred from one ring to the other one through the rolling elements. Load distribution between rolling elements is unequal. Degree of load distribution unequality depends on internal geometry of bearing and magnitude of external load. Two boundary load distributions in radially loaded ball bearing were defined and discussed in this paper. These are ideally equal and extremely unequal load distribution. Real load distribution is between these boundary cases. The new mathematical model of load distribution is developed respecting classic rolling bearing theory and by introduction of new, original value defined as load distribution factor. Developed mathematical model includes all main influences on load distribution in rolling bearing (number of rolling elements, internal radial clearance and external load)

Mathematical model of load distribution in rolling bearing

Spoljašnje opterećenje kotrljajnog ležaja se sa jednog prstena na drugi prenosi preko kotrljajnih tela. Pri tome je raspodela opterećenja na kotrljajna tela neravnomerna. Stepen neravnomernosti raspodele opterećenja zavisi od unutrašnje geometrije ležaja i intenziteta spoljašnjeg opterećenja. U ovom radu su definisana i razmatrana dva granična slučaja raspodele opterećenja kod kugličnog kotrljajnog ležaja opterećenog spoljašnjim radijalnim opterećenjem. To su idealno ravnomerna i izrazito neravnomerna raspodela opterećenja. Stvarna raspodela opterećenja je između ova dva granična slučaja. Novi matematički model raspodele opterećenja je razvijen na osnovu klasične teorije kotrljajnih ležaja i uvođenjem nove originalne veličine, definisane kao faktor raspodele opterećenja. Razvijeni matematički model obuhvata sve pomenute relevantne uticaje na raspodelu opterećenja u kotrljajnom ležaju (broj kotrljajnih tela u ležaju, unutrašnji radijalni zazor i spoljašnje opterećenje).External load of rolling bearing is transferred from one ring to the other one through the rolling elements. Load distribution between rolling elements is unequal. Degree of load distribution unequality depends on internal geometry of bearing and magnitude of external load. Two boundary load distributions in radially loaded ball bearing were defined and discussed in this paper. These are ideally equal and extremely unequal load distribution. Real load distribution is between these boundary cases. The new mathematical model of load distribution is developed respecting classic rolling bearing theory and by introduction of new, original value defined as load distribution factor. Developed mathematical model includes all main influences on load distribution in rolling bearing (number of rolling elements, internal radial clearance and external load)

Analysis of grease contamination influence on the internal radial clearance of ball bearings by thermographic inspection

One of the most important factors influencing ball bearings service life is its internal radial clearance. However, this parameter is also very complex because it depends on applied radial load and ball bearings dimensions, surface finish, and manufacturing materials. Thermal condition of ball bearings also significantly affects internal radial clearance. Despite many researches performed in order to find out relevant facts about different aspects of ball bearings thermal behaviour, only few of them are dealing with the real working conditions, where high concentration of solid contaminant particles is present. That is why the main goal of research presented in this paper was to establish statistically significant correlation between ball bearings temperatures, their working time, and concentration of contaminant particles in their grease. Because of especially difficult working conditions, the typical conveyor idlers bearings were selected as representative test samples and appropriate solid particles from open pit coal mines were used as artificial contaminants. Applied experimental methodology included thermographic inspection, as well as usage of custom designed test rig for ball bearings service life testing. Finally, by obtained experimental data processing in advanced software, statistically significant mathematical correlation between mentioned bearings characteristics was determined and applied in commonly used internal radial clearance equation. That is the most important contribution of performed research the new equation and methodology for ball bearings internal clearance determination which could be used for eventual improvement of existing bearings service life equations

Industry 4.0 - renaissance of engineering first edition

The main purpose of this Monograph is to provide students, engineers and researchers with the latest knowledge about Industry 4.0 from the following aspects: (a) what Industry 4.0 is and how it came about, what it is and what the National Industry 4.0 Programs cover. What is the National Program of Serbia for this model, (b) what are its basic elements and how do they work in this model, (c) what engineering knowledge is needed for this concept, and what is our research in this area, (d) what this model means for other industries and how to apply it, and (e) what is the vision of this model in the next decade, until 2030, and in which direction this model will develop. The authors has been intensively involved in this field since 2015, so this Monograph presents a systematization of their knowledge of Industry 4.0 from the following aspects: (a) prepared and held five International Conferences on Industry 4.0 at the Faculty of Mechanical Engineering in Belgrade, thousand participants from the country and the world, (b) held 35 Panels on Industry 4.0 in our country, (c) published 42 papers at international conferences, domestic and foreign journals, or chapters in domestic and foreign monographs, (e) held more than 20 invited lectures in the country and the world on the topic of Industry 4.0, and (f) realized dozens of projects for domestic factories, through research tasks related to business organization and preparation for the application of elements of Industry 4.0 in their environment

Industry 4.0 - renaissance of engineering first edition

The main purpose of this Monograph is to provide students, engineers and researchers with the latest knowledge about Industry 4.0 from the following aspects: (a) what Industry 4.0 is and how it came about, what it is and what the National Industry 4.0 Programs cover. What is the National Program of Serbia for this model, (b) what are its basic elements and how do they work in this model, (c) what engineering knowledge is needed for this concept, and what is our research in this area, (d) what this model means for other industries and how to apply it, and (e) what is the vision of this model in the next decade, until 2030, and in which direction this model will develop. The authors has been intensively involved in this field since 2015, so this Monograph presents a systematization of their knowledge of Industry 4.0 from the following aspects: (a) prepared and held five International Conferences on Industry 4.0 at the Faculty of Mechanical Engineering in Belgrade, thousand participants from the country and the world, (b) held 35 Panels on Industry 4.0 in our country, (c) published 42 papers at international conferences, domestic and foreign journals, or chapters in domestic and foreign monographs, (e) held more than 20 invited lectures in the country and the world on the topic of Industry 4.0, and (f) realized dozens of projects for domestic factories, through research tasks related to business organization and preparation for the application of elements of Industry 4.0 in their environment