Influence of internal radial clearance of rolling bearing on load distribution between rolling elements

Pri prenošenju spoljašnjeg radijalnog opterećenja sa obrtnih delova vratila (zupčanika, lančanika, kaišnika...) na kućište prenosnika, učešće kotrljajnih tela ležaja u prenošenju opterećenja je neravnomerno. Stepen učešća kotrljajnih tela u prenošenju opterećenja pre svega zavisi od unutrašnje geometrije ležaja (ukupan broj kotrljajnih tela, unutrašnji radijalni zazor, oblik staza kotrljanja i kotrljajnih tela) i karaktera spoljašnjeg opterećenja. U ovom radu je razmatran uticaj veličine unutrašnjeg radijalnog zazora na raspodelu opterećenja na kotrljajna tela ležaja. Istovremeno je pokazano da uticaj zazora zavisi od ukupnog broja kotrljajnih tla. Analize su izvršene na osnovu matematičkog modela raspodele opterećenja u koji je uvedena na novi način definisana veličina - faktor raspodele opterećenja na kotrljajna tela ležaja. Sprovedena istraživanja se mogu upotrebiti za precizniju analizu nosivosti i veka ležaja, kao i za optimizaciju unutrašnje geometrije ležaja.In the transmission of external radial force from rotating members on the shaft to housing, through rolling bearing, the engagement of rolling elements is unequal. The engagement degree of every single rolling body in radial load distribution depends on the internal bearing geometry (number of rolling elements, internal radial clearance, form of raceways), as well as an intensity of applied external load. The analysis of influence of internal radial clearance on the load distribution in rolling bearing is carried out in this paper. Also, the variations of the influence of internal radial clearance on load distribution between rolling elements with the variations of external load and number of rolling bodies are shown. The analysis is based on modified conventional mathematical model of load distribution. The new defined value - load distribution factor is introduced in this mathematical model Conducted research can be used for more precise static load capacity and hearing life analysis, as well as for optimization of the bearing internal construction

Influence of internal radial clearance of rolling bearing on load distribution between rolling elements

Pri prenošenju spoljašnjeg radijalnog opterećenja sa obrtnih delova vratila (zupčanika, lančanika, kaišnika...) na kućište prenosnika, učešće kotrljajnih tela ležaja u prenošenju opterećenja je neravnomerno. Stepen učešća kotrljajnih tela u prenošenju opterećenja pre svega zavisi od unutrašnje geometrije ležaja (ukupan broj kotrljajnih tela, unutrašnji radijalni zazor, oblik staza kotrljanja i kotrljajnih tela) i karaktera spoljašnjeg opterećenja. U ovom radu je razmatran uticaj veličine unutrašnjeg radijalnog zazora na raspodelu opterećenja na kotrljajna tela ležaja. Istovremeno je pokazano da uticaj zazora zavisi od ukupnog broja kotrljajnih tla. Analize su izvršene na osnovu matematičkog modela raspodele opterećenja u koji je uvedena na novi način definisana veličina - faktor raspodele opterećenja na kotrljajna tela ležaja. Sprovedena istraživanja se mogu upotrebiti za precizniju analizu nosivosti i veka ležaja, kao i za optimizaciju unutrašnje geometrije ležaja.In the transmission of external radial force from rotating members on the shaft to housing, through rolling bearing, the engagement of rolling elements is unequal. The engagement degree of every single rolling body in radial load distribution depends on the internal bearing geometry (number of rolling elements, internal radial clearance, form of raceways), as well as an intensity of applied external load. The analysis of influence of internal radial clearance on the load distribution in rolling bearing is carried out in this paper. Also, the variations of the influence of internal radial clearance on load distribution between rolling elements with the variations of external load and number of rolling bodies are shown. The analysis is based on modified conventional mathematical model of load distribution. The new defined value - load distribution factor is introduced in this mathematical model Conducted research can be used for more precise static load capacity and hearing life analysis, as well as for optimization of the bearing internal construction

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

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)

Contact stresses and deformations in thrust ball bearing

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

Stiffness as a criterion of dynamic load carrying capacity of tension-loaded bolted joints

The influence of the bolt size and the width of the joint members/bolt diameter ratio (relative clamped length) on the stiffness coefficient of the bolt and joint members, as well as on the ratio of these stiffness coefficients are discussed in this paper. The individual stiffness coefficients of the bolt and the joint members decrease with the increase of the relative clamped length and the decrease of the bolt size. However, the stiffness ratio of the joint members and the bolt increases with the increase of the relative clamped length. Of the considered bolts M6... M24, the bolted joint with the M6 bolt has the highest stiffness ratio of the joint members and the bolt, and the bolted joint with the M12 bolt has the lowest stiffness ratio. When a bolted joint is loaded with a variable working load, then the dynamic safety factor (DSF) is used for evaluating the joint load capacity. The DSF increases with a decrease in the stiffness of the bolted joint, ie by increasing the relative clamped length of the bolted joint. For the same conditions analyzed, the bolted joint with M6 bolt has the largest DSF, and the bolted joint with M12 bolt has the smallest DSF. The obtained result can be used by engineers to evaluate the load-carrying capacity of dynamically tension-loaded bolted joints

Construction variation of packing machine in food processing

U radu je prikazano varijantno konstrukciono rešenje mašine za pakovanje prehrambenih proizvoda. Na osnovu tehno-ekonomske analize pokazano je da originalno i varijantno konstrukciono rešenje imaju približno istu tehničku vrednost, s tim što varijantna konstrukcija ima veću ekonomsku vrednost opravdanost. Ekonomska opravdanost postignuta je pogodnim konstrukcionim rešenjem i primenom domaćih komponenti i tehnologije izrade.The construction variation of packing machine in food processing is shown in this paper. By the techno-economic analyses it is shown that original and new construction has the same construction value, but the new construction has a better economic value – validity. Better economic value has achieved with new construction and engaging domestic components and production technology

Construction variation of packing machine in food processing

U radu je prikazano varijantno konstrukciono rešenje mašine za pakovanje prehrambenih proizvoda. Na osnovu tehno-ekonomske analize pokazano je da originalno i varijantno konstrukciono rešenje imaju približno istu tehničku vrednost, s tim što varijantna konstrukcija ima veću ekonomsku vrednost opravdanost. Ekonomska opravdanost postignuta je pogodnim konstrukcionim rešenjem i primenom domaćih komponenti i tehnologije izrade.The construction variation of packing machine in food processing is shown in this paper. By the techno-economic analyses it is shown that original and new construction has the same construction value, but the new construction has a better economic value – validity. Better economic value has achieved with new construction and engaging domestic components and production technology