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QB-Godwin-Unit-II.pdf

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Godwin Pithalis
Godwin Pithalis

This document contains 17 problems related to dynamic balancing of rotating and reciprocating masses in machines like engines and locomotives. The problems involve calculating balancing masses, unbalanced forces and couples for systems with multiple rotating/reciprocating masses at different radii and angular positions along a shaft. Key parameters specified in the problems include mass values, radii, angular spacing between masses, engine speed, piston stroke, connecting rod length etc. The goal is to determine balancing requirements to achieve complete dynamic balance of the machine systems.

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ME8594 - DYNAMICS OF MACHINES UNIT –II (Part –B) Prepared By: N. E. Godwin Pithalis Page 1 1. A shaft carries four rotating masses A, B, C and D in this order along its axis. The mass of B, C and D are 30 kg, 50 kg and 40 kg respectively. The planes containing B and C are 30 cm apart. The angular spacing of the planes containing C and D are 90° and 210° respectively relative to B measured in the same sense. If the shaft and masses are to be in complete dynamic balance, find (i) the mass and the angular position of mass A; and (ii) the position of planes A and D. (DEC-2010) 2. The firing order in a 6 cylinder vertical four stroke engine in-line engine is 1-4-2-6-3-5. The piston stroke is 100 mm and the length of each connecting rod is 200 mm. The pitch distances between the cylinder center lines are 100 mm, 100 mm, 150 mm, 100 mm, and 100 mm respectively. The reciprocating mass per cylinder is 1 kg and the engine runs at 3000 rpm. Determine the out-of-balance primary and secondary forces and couples on this engine, taking a plane midway between the cylinder 3 and 4 as the reference plane. (DEC-2010) 3. Four masses A, B, C and D as 'given below are to be balanced A B C D Mass (kg) - 30 50 50 Radius (mm) 180 240 120 150 The planes containing masses B and C are 300 mm apart. The angle between planes containing B and C is 90o . B and C make angles of 210o and 120o respectively with D in the same sense. Find the magnitude and the angular positions of mass A and the position of planes A and D. (DEC-2011) 4. The cranks and connecting rods of a four cylinder in-line engine running at 1800 rpm are 60 mm and 240 mm each respectively and the cylinders are spaced 150 mm apart. If the cylinders are numbered 1 to 4 in sequence from one end, the cranks appear at intervals of 90o in an end view in the order of 1-4-2-3. The reciprocating mass corresponding to each cylinder is 1.5 kg. Determine the unbalanced primary and secondary forces, if any, and unbalanced primary and secondary couples with reference to central plane of the engine. (MAY, DEC-2011) 5. A, B, C and D are four masses carried by a rotating shaft at radii 100mm,125mm,200mm and 150mm respectively. The planes in which the masses revolve are spaced 600mm apart and the masses of B, C and D are 10kg, 5kg and 4kg respectively. Find the required mass A and the relative angular setting of the four masses so that the shaft shall be in complete balance. (MAY-2014, DEC-2012) 6. A four crank engine has the two outer cranks set at 120o to each other, and their reciprocating masses are each 400 kg. The distance between the planes of rotation of adjacent cranks are 450 mm, 750 mm and 600 mm. If the engine is to be in complete primary balance, find the reciprocating mass and relative angular position for each of the inner cranks.
ME6505 - DYNAMICS OF MACHINES UNIT –II (Part –B) Prepared By: N. E. Godwin Pithalis Page 2 If the length of each crank is 300 mm, the length of each connecting rod is 1.2 m and the speed of rotation is 240 rpm. What is the maximum secondary unbalanced force? (MAY-2014, DEC-2012) 7. The following data refer to an outside cylinder uncoupled locomotive Mass of rotating parts per cylinder =350 kg, mass of reciprocating parts per cylinder =300 kg, Angle between cranks =90o , Crank radius = 0.3 m, Cylinder centers =1.8 m, Radius of balance masses = 0.8 m, wheel centers = 1.5 m. If whole of the rotating and 2/3 rd of the reciprocating parts are to be balanced in planes of the driving wheels, find (i) magnitude and angular positions of balance masses, (ii) speed in Km/hr at which the wheel will lift off the rails when the load on each driving wheels is 30 KN and the diameter of tread driving wheels is 1.8 m and (iii) swaying couple at speed found in (ii) plane. (DEC-2013) 8. The axes of the three cylinder air compressor are at 120o to one another and their connecting rods are coupled to a single crank. The length of each connecting rod is 240 mm and the stroke is 160 mm. The reciprocating parts have a mass of 2.4 kg per cylinder. Determine the primary and secondary forces if the engine runs at 2000 rpm. (DEC-2013) 9. A rotating shaft carries four unbalanced masses A,B,C and D as shown below: A B C D Mass (kg) 18 14 16 12 Radius (mm) 50 60 70 60 The masses B, C, and D revolve in the planes 80 mm ,160 mm and 280 mm respectively from the plane of mass A and are angularly located at 60o , 135 o and 270 o respectively measured clockwise from the masses A located at the end of the shaft. The shaft is dynamically balanced by two masses which are located at 50 mm radii and revolving in planes mid way between those masses A and B and masses C and D respectively. Determine the magnitude and position of balancing masses. (MAY-2008) 10. A twin cylinder locomotive as its cylinder center lines in 0.7 m apart and has a stroke of 0.6 m. The rotating mass per cylinder is equivalent to 150 Kg at the crank pin and the reciprocating mass per cylinder is to 180 Kg. The wheel center lines are 1.5 m apart. The cranks are at right angles. The whole of the rotating and 2/3 of the reciprocating masses are to be balanced by masses Find the fluctuation in rail pressure under one wheel, variation of tractive effort and the magnitude of swaying couple at a crank speed of 300 rpm. (MAY-2008)
ME6505 - DYNAMICS OF MACHINES UNIT –II (Part –B) Prepared By: N. E. Godwin Pithalis Page 3 11. A shaft has three eccentrics, each 75 mm diameter and 25 mm thick, machined in one piece with the shaft. The central planes of the eccentric are 60 mm apart. The distance of the centres from the axis of rotation are 12 mm, 18 mm and 12 mm and their angular positions are 120o apart. The density of metal is 7000 kg/m3. Find the amount of out-of balance force and couple at 600 rpm. If the shaft is balanced by adding two masses at a radius of 75 mm and at a distance of 100 mm from the central plane of the middle eccentric, find the amount of masses and their angular positions. (MAY-2013) 12. The three cranks of a three cylinder locomotive are all on the same axle and are set at 120o . The pitch of the cylinders is 1 metre and the stroke of each piston is 0.6 m. The reciprocating masses are 300 kg for inside cylinder and 260 kg for each outside cylinder and the planes of rotation of the balance masses are 0.8 m from the inside crank. If 40% of the reciprocating parts are to be balanced, find (i) The magnitude and the position of the balancing masses required at a radius of 0.6 m and (ii) The hammer blow per wheel when the axle makes 6 rps. (MAY-2012, 2013) 13. A shaft carries four masses A, B, C and D of magnitude 200 kg, 300kg, 400 kg and 200 kg respectively and revolving at radii 80 mm, 70 mm, 60 mm and 80 mm in planes measured from A at 300 mm, 400 mm and 700 mm. The angles between the cranks measured anticlockwise are A to B 45o B to C 70o and C to D 120o . The balancing masses are to be placed in planes X and Y. The distance between the planes A and X is 100 mm, between X and Y is 400 mm and between Y and D is 200 mm. If the balancing masses revolve at a radius of 100 mm, find their magnitudes and angular positions. (MAY-2011, 2012) 14. A shaft is rotating at a uniform angular speed. Four masses M1, M2, M3and M4 of magnitudes 300kg, 450kg, 360kg, 390kg respectively are attached rigidly to the shaft. The masses are rotating in the same plane. The corresponding radii of rotation are 200mm, 150mm, 250 mm and 300mm respectively. The angle made by these masses with horizontal are 0°.45°, 120°and 255° respectively. If the system is to be balanced by adding two balancing mass. Find,(i) the magnitude of balancing masses and (ii) the position of the balancing mass if its radius of rotation is 200mm. (DEC-2009) 15. (i) Derive the expressions for the following (a) variation in tractive force and (b) Swaying couple. (8) (ii) The following data relate to a single cylinder vertical reciprocating engine, mass of reciprocating parts =40 kg, mass of revolving parts = 30 kg at 180 mm radius, speed = 150 rpm, stroke 350 mm. If 60% of the reciprocating parts and all the revolving parts are to be balanced, determine (a) the balance mass required at a radius of 320 mm (b) the unbalanced force when the crank has turned 45o from the top dead center. (DEC-2009)
ME6505 - DYNAMICS OF MACHINES UNIT –II (Part –B) Prepared By: N. E. Godwin Pithalis Page 4 16. A shaft carries four masses in parallel planes A,B, C and D in this order along its length. The masses at B and C are 18kg and 12.5 kg respectively. And each has an eccentricity of 60 mm. The masses at A and D have an eccentricity of 80 mm. The angle between the masses at B and C is 100o and that between masses B and A is 190 o , both being measured in the same direction. The axial distance between the planes A and B is 100 mm and that between b and C is 200 mm. If the shaft is in complete dynamic balance, determine (i) The magnitude of the masses at A and D (ii) The distance between the planes A and D and (iii) The angular position of the mass at D. (DEC-2014) 17. A five cylinder in-line engine running at 750 rpm has successive cranks 144 o apart, the distance between the cylinder centre lines being 375 mm. The piston stroke is 225 mm and the ration of the connecting rod to the crank is 4. Examine the engine for balance of primary and secondary forces and couples. Find the maximum values of these and the position of the central crank at which these maximum values occur. The reciprocating mass for each cylinder is 15 kg. (DEC-2014)

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QB-Godwin-Unit-II.pdf

  • 1. ME8594 - DYNAMICS OF MACHINES UNIT –II (Part –B) Prepared By: N. E. Godwin Pithalis Page 1 1. A shaft carries four rotating masses A, B, C and D in this order along its axis. The mass of B, C and D are 30 kg, 50 kg and 40 kg respectively. The planes containing B and C are 30 cm apart. The angular spacing of the planes containing C and D are 90° and 210° respectively relative to B measured in the same sense. If the shaft and masses are to be in complete dynamic balance, find (i) the mass and the angular position of mass A; and (ii) the position of planes A and D. (DEC-2010) 2. The firing order in a 6 cylinder vertical four stroke engine in-line engine is 1-4-2-6-3-5. The piston stroke is 100 mm and the length of each connecting rod is 200 mm. The pitch distances between the cylinder center lines are 100 mm, 100 mm, 150 mm, 100 mm, and 100 mm respectively. The reciprocating mass per cylinder is 1 kg and the engine runs at 3000 rpm. Determine the out-of-balance primary and secondary forces and couples on this engine, taking a plane midway between the cylinder 3 and 4 as the reference plane. (DEC-2010) 3. Four masses A, B, C and D as 'given below are to be balanced A B C D Mass (kg) - 30 50 50 Radius (mm) 180 240 120 150 The planes containing masses B and C are 300 mm apart. The angle between planes containing B and C is 90o . B and C make angles of 210o and 120o respectively with D in the same sense. Find the magnitude and the angular positions of mass A and the position of planes A and D. (DEC-2011) 4. The cranks and connecting rods of a four cylinder in-line engine running at 1800 rpm are 60 mm and 240 mm each respectively and the cylinders are spaced 150 mm apart. If the cylinders are numbered 1 to 4 in sequence from one end, the cranks appear at intervals of 90o in an end view in the order of 1-4-2-3. The reciprocating mass corresponding to each cylinder is 1.5 kg. Determine the unbalanced primary and secondary forces, if any, and unbalanced primary and secondary couples with reference to central plane of the engine. (MAY, DEC-2011) 5. A, B, C and D are four masses carried by a rotating shaft at radii 100mm,125mm,200mm and 150mm respectively. The planes in which the masses revolve are spaced 600mm apart and the masses of B, C and D are 10kg, 5kg and 4kg respectively. Find the required mass A and the relative angular setting of the four masses so that the shaft shall be in complete balance. (MAY-2014, DEC-2012) 6. A four crank engine has the two outer cranks set at 120o to each other, and their reciprocating masses are each 400 kg. The distance between the planes of rotation of adjacent cranks are 450 mm, 750 mm and 600 mm. If the engine is to be in complete primary balance, find the reciprocating mass and relative angular position for each of the inner cranks.
  • 2. ME6505 - DYNAMICS OF MACHINES UNIT –II (Part –B) Prepared By: N. E. Godwin Pithalis Page 2 If the length of each crank is 300 mm, the length of each connecting rod is 1.2 m and the speed of rotation is 240 rpm. What is the maximum secondary unbalanced force? (MAY-2014, DEC-2012) 7. The following data refer to an outside cylinder uncoupled locomotive Mass of rotating parts per cylinder =350 kg, mass of reciprocating parts per cylinder =300 kg, Angle between cranks =90o , Crank radius = 0.3 m, Cylinder centers =1.8 m, Radius of balance masses = 0.8 m, wheel centers = 1.5 m. If whole of the rotating and 2/3 rd of the reciprocating parts are to be balanced in planes of the driving wheels, find (i) magnitude and angular positions of balance masses, (ii) speed in Km/hr at which the wheel will lift off the rails when the load on each driving wheels is 30 KN and the diameter of tread driving wheels is 1.8 m and (iii) swaying couple at speed found in (ii) plane. (DEC-2013) 8. The axes of the three cylinder air compressor are at 120o to one another and their connecting rods are coupled to a single crank. The length of each connecting rod is 240 mm and the stroke is 160 mm. The reciprocating parts have a mass of 2.4 kg per cylinder. Determine the primary and secondary forces if the engine runs at 2000 rpm. (DEC-2013) 9. A rotating shaft carries four unbalanced masses A,B,C and D as shown below: A B C D Mass (kg) 18 14 16 12 Radius (mm) 50 60 70 60 The masses B, C, and D revolve in the planes 80 mm ,160 mm and 280 mm respectively from the plane of mass A and are angularly located at 60o , 135 o and 270 o respectively measured clockwise from the masses A located at the end of the shaft. The shaft is dynamically balanced by two masses which are located at 50 mm radii and revolving in planes mid way between those masses A and B and masses C and D respectively. Determine the magnitude and position of balancing masses. (MAY-2008) 10. A twin cylinder locomotive as its cylinder center lines in 0.7 m apart and has a stroke of 0.6 m. The rotating mass per cylinder is equivalent to 150 Kg at the crank pin and the reciprocating mass per cylinder is to 180 Kg. The wheel center lines are 1.5 m apart. The cranks are at right angles. The whole of the rotating and 2/3 of the reciprocating masses are to be balanced by masses Find the fluctuation in rail pressure under one wheel, variation of tractive effort and the magnitude of swaying couple at a crank speed of 300 rpm. (MAY-2008)
  • 3. ME6505 - DYNAMICS OF MACHINES UNIT –II (Part –B) Prepared By: N. E. Godwin Pithalis Page 3 11. A shaft has three eccentrics, each 75 mm diameter and 25 mm thick, machined in one piece with the shaft. The central planes of the eccentric are 60 mm apart. The distance of the centres from the axis of rotation are 12 mm, 18 mm and 12 mm and their angular positions are 120o apart. The density of metal is 7000 kg/m3. Find the amount of out-of balance force and couple at 600 rpm. If the shaft is balanced by adding two masses at a radius of 75 mm and at a distance of 100 mm from the central plane of the middle eccentric, find the amount of masses and their angular positions. (MAY-2013) 12. The three cranks of a three cylinder locomotive are all on the same axle and are set at 120o . The pitch of the cylinders is 1 metre and the stroke of each piston is 0.6 m. The reciprocating masses are 300 kg for inside cylinder and 260 kg for each outside cylinder and the planes of rotation of the balance masses are 0.8 m from the inside crank. If 40% of the reciprocating parts are to be balanced, find (i) The magnitude and the position of the balancing masses required at a radius of 0.6 m and (ii) The hammer blow per wheel when the axle makes 6 rps. (MAY-2012, 2013) 13. A shaft carries four masses A, B, C and D of magnitude 200 kg, 300kg, 400 kg and 200 kg respectively and revolving at radii 80 mm, 70 mm, 60 mm and 80 mm in planes measured from A at 300 mm, 400 mm and 700 mm. The angles between the cranks measured anticlockwise are A to B 45o B to C 70o and C to D 120o . The balancing masses are to be placed in planes X and Y. The distance between the planes A and X is 100 mm, between X and Y is 400 mm and between Y and D is 200 mm. If the balancing masses revolve at a radius of 100 mm, find their magnitudes and angular positions. (MAY-2011, 2012) 14. A shaft is rotating at a uniform angular speed. Four masses M1, M2, M3and M4 of magnitudes 300kg, 450kg, 360kg, 390kg respectively are attached rigidly to the shaft. The masses are rotating in the same plane. The corresponding radii of rotation are 200mm, 150mm, 250 mm and 300mm respectively. The angle made by these masses with horizontal are 0°.45°, 120°and 255° respectively. If the system is to be balanced by adding two balancing mass. Find,(i) the magnitude of balancing masses and (ii) the position of the balancing mass if its radius of rotation is 200mm. (DEC-2009) 15. (i) Derive the expressions for the following (a) variation in tractive force and (b) Swaying couple. (8) (ii) The following data relate to a single cylinder vertical reciprocating engine, mass of reciprocating parts =40 kg, mass of revolving parts = 30 kg at 180 mm radius, speed = 150 rpm, stroke 350 mm. If 60% of the reciprocating parts and all the revolving parts are to be balanced, determine (a) the balance mass required at a radius of 320 mm (b) the unbalanced force when the crank has turned 45o from the top dead center. (DEC-2009)
  • 4. ME6505 - DYNAMICS OF MACHINES UNIT –II (Part –B) Prepared By: N. E. Godwin Pithalis Page 4 16. A shaft carries four masses in parallel planes A,B, C and D in this order along its length. The masses at B and C are 18kg and 12.5 kg respectively. And each has an eccentricity of 60 mm. The masses at A and D have an eccentricity of 80 mm. The angle between the masses at B and C is 100o and that between masses B and A is 190 o , both being measured in the same direction. The axial distance between the planes A and B is 100 mm and that between b and C is 200 mm. If the shaft is in complete dynamic balance, determine (i) The magnitude of the masses at A and D (ii) The distance between the planes A and D and (iii) The angular position of the mass at D. (DEC-2014) 17. A five cylinder in-line engine running at 750 rpm has successive cranks 144 o apart, the distance between the cylinder centre lines being 375 mm. The piston stroke is 225 mm and the ration of the connecting rod to the crank is 4. Examine the engine for balance of primary and secondary forces and couples. Find the maximum values of these and the position of the central crank at which these maximum values occur. The reciprocating mass for each cylinder is 15 kg. (DEC-2014)