Question

QUESTION 2 A shaft is supported in two bearings 2.8 m apart and projects 0.7m beyond the bearings at each end. The shaft carries three pulleys, one at each end and one at the middle of its length. The end pulleys have masses of 95 kg and 60 kg and their centres of mass are at 3,65 and 6 mm respectively from the shaft axis. The centre pulley has a mass of 82 kg and its centre of mass is 6.05 mm from the shaft axis. If the pulleys are arranged so as to give static balance, determine the dynamic forces produced on the bearings when the shaft retates at 350 r/min . [20]

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Answer 1

Given data, N=350rpm A M -> mm 0.7m IC MA=95 kg , RA=0.00365 m .: W21N 27X350 - mc=60 kg ; & c = 0.006 m 36.65 grad 60 60 mg = 82kg ; %8 = 0.00605m -ve R. P tre we dont know mass of bearings. Assume, m = mass of L bearing mass of m beasing. 2.8mm EL = radius of rot of mass 4.2 m For L beasing Sm = radius of roth of mass I have taken for M bearing as plane of reference. Plane Mass Radias Centrifugal | Distance from / couple/ Force (w² plane L m A 95. 10. 00365 0.34675 -0.7 -0.242 EL LCR.P mere o 0 B 82 10.00605 0.496) 1.4 0.6945 M mm rm Mm km C 0.36 3.5 L beasing wa mu 2.8 (2.8mm Em 1.26 0.006 -0.2427 Couple polygon is required to find the dynamic forces. → Here, vector oc is the out of balance couple. Measured d'e 1.47 kg/m² ..out of balance couple = 1.47xw2 = 1974.5 Nm 40.69454 1.26 / 6 cl out of Balanced couple 2.8 Manrem

since static balance is already established, hence dynamic force will only depend on out of balance couple. Dynamic force on each out of balance couple 1974.5 beasing Dist blew bearings 705 N 2.8 Ang

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