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)

Influence of the geometry parameters of cardan joint rolling parts on the load distribution

Kardanove spojnice se široko primenjuju u mašinstvu zbog mogućnosti prenošenja opterećenja i obrtnog kretanja sa jednog vratila na drugo, čije se ose međusobno seku pod promenljivim uglom. Vitalni delovi ovih spojnica imaju ograničeni radni vek zbog nedovoljne površinske čvrstoće kontaktnih površina spregnutih delova. Raspodela opterećenja spregnutih delova Kardanove spojnice ima veliki uticaj na nosivost i njihov radni vek. U tom cilju, u ovom radu, detaljno je analizirana raspodela opterećenja duž linije dodira rukavca Kardanovog krsta i kotrljajnih tela - iglica. Razvijeni su odgovarajući analitički i numerički modeli. Na osnovu razvijenih modela, moguće je izvršiti optimizaciju geometrijskih veličina sa aspekta ravnomernosti raspodele opterećenja spregnutih delova Kardanove spojnice.Cardan joints have a wide range of applications in mechanical engineering because of the capability of transferring the load and motion from one shaft to another with different joint angle. The vital parts of these joints have a limited life due to insufficient surface strength in the area of rolling parts contact. Load distribution of Cardan joints composite parts have a major impact on their capacity and service life. Therefore, a detailed analysis of load distribution along the line of contact between Cardan Cross pins and rolling parts - needles, was carried out in this paper. Appropriate analytical and numerical models are developed. Based on the developed models, it is possible to optimize the geometrical parameters in terms of uniformity of load distribution of Cardan joints component in contact

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

Influence of the geometry parameters of cardan joint rolling parts on the load distribution

Kardanove spojnice se široko primenjuju u mašinstvu zbog mogućnosti prenošenja opterećenja i obrtnog kretanja sa jednog vratila na drugo, čije se ose međusobno seku pod promenljivim uglom. Vitalni delovi ovih spojnica imaju ograničeni radni vek zbog nedovoljne površinske čvrstoće kontaktnih površina spregnutih delova. Raspodela opterećenja spregnutih delova Kardanove spojnice ima veliki uticaj na nosivost i njihov radni vek. U tom cilju, u ovom radu, detaljno je analizirana raspodela opterećenja duž linije dodira rukavca Kardanovog krsta i kotrljajnih tela - iglica. Razvijeni su odgovarajući analitički i numerički modeli. Na osnovu razvijenih modela, moguće je izvršiti optimizaciju geometrijskih veličina sa aspekta ravnomernosti raspodele opterećenja spregnutih delova Kardanove spojnice.Cardan joints have a wide range of applications in mechanical engineering because of the capability of transferring the load and motion from one shaft to another with different joint angle. The vital parts of these joints have a limited life due to insufficient surface strength in the area of rolling parts contact. Load distribution of Cardan joints composite parts have a major impact on their capacity and service life. Therefore, a detailed analysis of load distribution along the line of contact between Cardan Cross pins and rolling parts - needles, was carried out in this paper. Appropriate analytical and numerical models are developed. Based on the developed models, it is possible to optimize the geometrical parameters in terms of uniformity of load distribution of Cardan joints component in contact

Mathematical model of energy efficiency in internal spur gears

The impact of geometric parameters of teeth and lubricating oils to the efficiency of involute internal spur gears, when the transverse contact ratio is 2 lt epsilon(alpha) lt = 3, has been analyzed in this paper. The mathematical model and computer program for determining the current and the effective value of the efficiency have been developed. The influence of the character of load distribution and energy losses due to heating effects during the meshing period is included in the factor of load distribution. The results of computer simulation are given in the form of a diagram of the current values of the efficiency during the meshing period. Also, the values of effective efficiency for the considered cylindrical gear pairs have been calculated

Mathematical model of energy efficiency in internal spur gears

The impact of geometric parameters of teeth and lubricating oils to the efficiency of involute internal spur gears, when the transverse contact ratio is 2 lt epsilon(alpha) lt = 3, has been analyzed in this paper. The mathematical model and computer program for determining the current and the effective value of the efficiency have been developed. The influence of the character of load distribution and energy losses due to heating effects during the meshing period is included in the factor of load distribution. The results of computer simulation are given in the form of a diagram of the current values of the efficiency during the meshing period. Also, the values of effective efficiency for the considered cylindrical gear pairs have been calculated