UNIT 4 Balancing of Rotating Masses 1.A shaft is supported in bearings 1.8 meter apart and projects 0.45 meter beyond bearings at each end. The shaft carries three pulleys one at each end and one at middle of its length. The mass of end pulleys 48 kg and 20 kg and their centre of gravity are 15 nun and 12.5 mrn respectively from the shaft axis. The centre pulley, has the mass of 56 kg and its centre of gravity is 15 mm from shaft axis. If the pulleys are so arranged as to give static balance, determ ine (i) The relative angular position of the pulleys, (ii) And dynam ic forces produced on the bearings when the shaft rotates at 300 rpm. - (20 Marks) (Jan 2014) Dept of Mechanical Engineering, SJBIT Page 44
2.A shaft carries four masses A,B,C, and D, 200kg, 300kg, 240kg, and 360kg respectively, revolving at radii 90, 70, 100 and 120 mm respectively. The distance from the plane A, other planes are at 270 mm, 420 mm and 720 mm respectively. Angle between the cranks A and B is 45, Band C is 75, C and D is 130. Balancing masses are replaced 120 mm and 100 mm from D and A respectively. The distance between them being 500 mm, Find the balancing masses ant their angular positions if they are placed at a radius of 100 mm. (20 marks) (June 2013) Dept of Mechanical Engineering, SJBIT Page 45
3.Four masses A, B = 10 kg, C = 5 kg, D = 4 kg are placed at radius 100,125,200 and 150mm respectively. The distance between the planes are 600mm. Find the required mass A and the relative angular position of the four masses to achieve complex balance. (14 Marks) (June 2015) Dept of Mechanical Engineering, SJBIT Page 46
4.A shaft carries four masses A, B, C, and D of magnitude 200kg, 300kg, 400kg and 200kg respectively and revolving at radie 80mm, 70mm, 60mm and 80mm in planes measured from A at 300mm, 400mm and 700mm. The angle between the crank measured anticlockwise are A to B 45, B to C 70 and C and D 120 the balancing masses are to be placed in planes X and Y. The distance between the planes A and X is 100mm between X and Y is 400mm and between Yand D is 200mm. If the balancing meanes revolved at a radius of 100mm find their magnitudes and angular position. (20 Marks) (DEC 2013) Dept of Mechanical Engineering, SJBIT Page 47
5.What do you mean by static balancing and dynamic balancing? (05 Marks) (DEC 2014) Static and dynamic balancing: Static balance will be produced if the sum of the moments ofthe weights about the axis of rotation is zero. OR A system of rotating masses is said to be in static balance if the combined mass centre of the system lies on the axis of rotation, i.e., A rotor is said to be statically balanced if the vector sum of centrifugal forces os zero. A system of rotating masses id in dynamic balance when there does not exist any resultant centrifugal force as well as resultant couple. i.e., For dynamic force (i) Sum of the centrifugal forces must be equal to zero and (ii) Slim of the couple must be equal to zero. Dept of Mechanical Engineering, SJBIT Page 48
6.A rotating shaft carries four masses A, B, C and D, which are radiauy attached to it, along the shaft axis. The mass centres are 40 mm, 50 mm, 60 mm and 70 mm respectively from axis of rotation. The masses B, C and Dare 60 kg, 50 kg and 40 kg respectively.lthe angles of the masses C and D with respect to mass Bare 900 and 2100 in same sense, respectively. The planes containing Band Care 0.5m apart. For a complete balanced system, determine i) The mass and angular position of mass A. ii) The position of planes containing masses A and D. (15 Marks) (Dec 2014) Dept of Mechanical Engineering, SJBIT Page 49
Dept of Mechanical Engineering, SJBIT Page 50
Explain the procedure for balancing several masses rotating in the same plane. (5 marks) (June 2014) Static balance: A system of rotating masses is said to be in static balance ifthe combined mass center of the system lies on the axis of rotation. Dynamic balance: A system of rotating masses is said to he in dynamic balance if there exists neither any resultant centrifugal force nor any resultant couple when the system rotates. Consider ant number of masses (say four) of magnitude '"I' m; mj and m4 at distance of r., '2' r3 and'4 from the axis of the routing shift. Let 91,92,9) and 94be the angle of these masses with the horizontal line OX, as shown in Fig. 21.4 (a). Let these masses rotate about an axis through o and perpendicular to the plane of paper. with a constant angular velocity of (i) rad/s. Four masses MI = 100 kg, M2 = 175 kg, M3 = 200 kg and M4 = 125 kg are fixed to the crank of200 mm radius and revolve in planes 1,2,3 and 4 respectively. the angular position of the planes 2.3 and 4 with respect to first mass are 75,135 and 240 taken in the same sense. Determine the magnitude and position of the balancing masses at radius 600 mm in planes 'L' and 'M' located in the middle of 1and 2 and in the middle of 3 and 4 respectively. (15Marks) (June 2014) Dept of Mechanical Engineering, SJBIT Page 51