際際滷

際際滷Share a Scribd company logo

QB-Godwin-Unit-I.pdf

Godwin Pithalis
Godwin Pithalis

This document contains 19 problems related to dynamics of machines. The problems cover topics like determining reaction forces, torque, power, acceleration, and speed fluctuation in engines and machines given parameters like crank angle, torque diagrams, flywheel properties, engine speed, pressure, and dimensions. Solutions require applying equations of motion and dynamics concepts to reciprocating parts in engines.

1 of 3
Download to read offline
ME8594 - DYNAMICS OF MACHINES UNIT I (Part B) Prepared By: N. E. Godwin Pithalis Page 1 1.The lengths of crank and connecting rod of horizontal steam engine are 300 mm and 1.2 m respectively. When the crank has moved 30属 from the inner dead center, the acceleration of piston is 35 m/s2 . The average frictional resistance to the motion of piston is equivalent to a force of 550 N and net effective steam pressure on piston is 500 kN/m2 . The diameter of piston is 0.3 m and mass of reciprocating parts is 160 kg. Determine (i) Reaction on the cross-head guides; (ii) Thrust on the crankshaft bearings; and (iii) Torque on the crank shaft. (DEC-2010) 2. The torque delivered by two-stroke engine is represented by T = (1000 + 300 sin 2慮 500 cos2慮) N.m Where 慮 is the angle turned by the crank from the inner-dead center. The engine speed is 250 rpm. The mass of the flywheel is 400 kg and radius of gyration 400 mm. Determine (i) the power developed; (ii) the total percentage fluctuation of speed; (iii) the angular acceleration of flywheel when the crank has rotated through an angle of 60属 from the inner-dead center; and (iv) the maximum angular acceleration and retardation of the flywheel. (DEC-2010) 3. The crank and connecting rod of a petrol engine, running at 1800 rpm are 50 mm and 200 mm respectively. The diameter of the piston is 80 mm and the mass of the reciprocating parts is 1 kg- at a point during the power stroke, the pressure on the piston is 0.7 N/mm2 , when it has moved 10 mm from the inner dead centre. Determine the net load on the gudgeon pin, thrust on the connecting rod, reaction between the piston and cylinder and the engine speed at which the above values become zero. (DEC-2011) 4. A three cylinder single acting engine has its cranks set equally at 120o and it runs at 600 r.p.m. The torque Vs crank angle diagram for each cycle is a triangle for the power stroke with maximum torque of 90 N-m at 60o from dead centre of corresponding crank. The torque on return stroke is sensibly zero. Determine the power developed, co-efficient of fluctuation of speed, if the mass of the flywheel is 12 kg and a radius gyration of 80 mm, co-efficient fluctuation of energy and maximum angular acceleration of the flywheel. (DEC-2011) 5. Deduce an expression for the inertia force in the reciprocating parts, neglecting the weight of the connecting rod. (DEC-2012) 6. The turning moment curve for an engine is represented by the equation T = (20000 + 9500 sin 2慮 - 5700 cos2慮) N-m Where 慮 is the angle moved by the crank from the inner-dead center. If the resisting torque is constant, find (i) the power developed by the engine (ii) moment of inertia of flywheel in kg-m2 , if the total fluctuation of speed is not exceed 1% of mean speed which is 180 rpm and (iii) the angular acceleration of flywheel when the crank has turned through 45属 from inner-dead center. (DEC-2012) 7. (i) Derive the equation of forces on the reciprocating parts of an engine, neglecting the weight of the connecting rod (12) (ii) What is turning moment diagram and draw its for four stroke IC engine? (4) (DEC-2013) 8. A single cylinder, single acting, four stroke gas engine develops 25 KW at 320 rpm. The work done by the gases during the expansion stroke is three times the work done on the gases during the compression stroke. The work done during the suction and exhaust stroke being negligible. The fluctuation of speed is not to exceed 賊2% of the mean speed. The turning moment diagram during compression and expansion is assumed to be triangular in shape. Find the weight of the flywheel if its radius of gyration is 0.5m. (DEC-2013)
ME6505 - DYNAMICS OF MACHINES UNIT I (Part B) Prepared By: N. E. Godwin Pithalis Page 2 9. A horizontal steam engine running at 120rpm has a bore of 250 mm and a stroke of 400mm. The connecting rod is 0.6 m and mass of the reciprocating parts is 60 kg. When the crank has turned through an angle of 45属 from the Inner Dead Centre, the steam pressure on the cover end side is 550KN/m2 and that on the crank end side is 60KN/m2 . Considering the diameter of the piston rod equal to 50 mm, Determine, (i). Turning moment on the crank shaft (ii). Thrust on the bearing and (iii).Acceleration of the flywheel, if the power of the engine is 20 kW, mass of the flywheel 60 kg and radius of gyration of 0.6m. (MAY-2014) 10. A shaft fitted with a flywheel rotates at 250 rpm and drives a machine. The torque of machine varies in a cyclic manner over a period of 3 revolutions. The torque rises from 750 Nm to 3000 Nm uniformly during 12 revolutions and remains constant for the following revolution. It then falls uniformly to 750 Nm during next 12 revolution and remain constant for one revolution, the cycle being repeated thereafter. Determine the power required to drive the machine and percentage fluctuation in speed, if the driving torque applied to the shaft is constant and the mass of the flywheel is 500 kg with radius of gyration of 600 mm. (MAY-2013, 2014) 11. The piston diameter of an IC engine is 125 mm and the stroke is 220 mm. The connecting rod is 4.5 times the crank length and has a mass of 50 kg. The mass of the reciprocating parts is 30 kg. The center of mass of the connecting rod is 170 mm from the crank pin center and the radius of gyration about an axis through the center of mass is 148 mm. The engine runs at 320 rpm. Determine the magnitude and direction of the inertia force and the corresponding torque on the crank shaft when the angle turned by the crank is 140 degrees from the inner dead center. (MAY-2008) 12. The torque delivered by a two stroke engine is represented by, T= (1000 +300 sin2慮 -500 cos2慮) N.m, where 慮 is the angle turned by the crank from the inner dead centre. The mass of the flywheel is 400 Kg and the radius of gyration 400 mm. Determine (i) The power developed when the engine speed is 250 rpm and (ii) The maximum fluctuations of speed in terms of percentage. (MAY-2008) 13. A horizontal steam engine running at 240rpm has a bore of 300 mm and stroke 600mm. The connecting rod is 1.25 m long and mass of the reciprocating parts is 60 kg. When the crank is 60属 past its Inner Dead Centre, the steam pressure on the cover side of the piston is 1.125 N/mm2 while that on the crank side is 0.125N/mm2 . Neglecting the area of the piston rod, Determine, (i) the force on the piston rod, and (ii).Turning moment on the crank shaft. (MAY-2013) 14. The crank and connecting rod of an engine are 125 mm and 500 mm respectively. The mass of the connecting rod is 60 kg and its center of gravity is 275 mm from the cross head pin center. The radius of gyration about center of gravity being 150 mm. If the engine speed is 600 rpm for a crank position of 45o from the inner dead centre. Determine the acceleration of the piston and the magnitude, position and direction of inertia force due to the mass of the connecting rod. (MAY-2011)
ME6505 - DYNAMICS OF MACHINES UNIT I (Part B) Prepared By: N. E. Godwin Pithalis Page 3 15. A punching press is required to punch 30 mm diameter holes in a plate of 20 mm thickness at the rate of 20 holes/mm. It requires 6 Nm energy /mm2 of sheared area. If punching takes places in 1/10 of a second and the speed of the flywheel varies from 160 to 140 rpm, determine the mass of the flywheel having radius of gyration 1m. (MAY-2011) 16. The turning moment diagram for a multi cylinder engine has been drawn to a scale of 1mm =325 Nm vertically and 1mm = 3o horizontally. The areas above and below the mean torque line are -26, +378, -306, -302, -244, -380, -261 and -225 mm2 the engine is running at a mean speed of 600 rpm. The total fluctuation of speed is not to exceed 賊1.8% of the mean speed. If the radius of flywheel is 0.7m, find the mass of the flywheel. (DEC-2009) 17. The dimensions of a four four-link mechanism are AB=50 mm, BC =66 mm, CD =560 mm, and AD =1000 mm the link AB has an angular velocity of 10.5 rad/s counter-clockwise and an angular retardation of 26 rad/s2 at the instant when it makes an angle of 60o with AD, the fixed link. The mass of the links BC and CD is 4.2 kg/m length. The link AB has a mass of 3.54 kg, the center of which lies at 200 mm from A and a moment of inertia of 88500 kgmm2 neglecting the gravity and friction effects, determine the instantaneous value of the drive torque required to be applied on AB to overcome the inertia forces. (DEC-2009) 18. The equation of the turning moment curve of a three crank engine is (5000+1500sin3慮) N-m, where 慮 is the crank and in radians. The moment of inertia of the flywheel is 1000 kg-m2 and the mean speed is 300 rpm. Calculate (i) Power of the engine and (8) (ii) The maximum fluctuation of the speed of the flywheel in percentage when (a) The resisting torque is constant, and (4) (b) The resisting torque is (5000 + 600sin慮) N-m. (4) (DEC-2014) 19. A certain machine requires a torque of (5000 + 500sin慮) N-m to drive it, where 慮 is the angle of rotation of shaft measured from certain datum. The machine is directly coupled to an engine which produces a torque of (5000 + 600sin2慮) N-m. The flywheel and the other rotating parts attached to the engine have a mass of 500 kg at a radius of gyration of 0.4 m. If the mean speed is 150 rpm, find (i) the fluctuation of energy (ii) the total percentage fluctuation of speed, and (iii) the maximum and minimum angular acceleration of the flywheel and the corresponding shaft position. (DEC-2014)

More Related Content

QB-Godwin-Unit-I.pdf

  • 1. ME8594 - DYNAMICS OF MACHINES UNIT I (Part B) Prepared By: N. E. Godwin Pithalis Page 1 1.The lengths of crank and connecting rod of horizontal steam engine are 300 mm and 1.2 m respectively. When the crank has moved 30属 from the inner dead center, the acceleration of piston is 35 m/s2 . The average frictional resistance to the motion of piston is equivalent to a force of 550 N and net effective steam pressure on piston is 500 kN/m2 . The diameter of piston is 0.3 m and mass of reciprocating parts is 160 kg. Determine (i) Reaction on the cross-head guides; (ii) Thrust on the crankshaft bearings; and (iii) Torque on the crank shaft. (DEC-2010) 2. The torque delivered by two-stroke engine is represented by T = (1000 + 300 sin 2慮 500 cos2慮) N.m Where 慮 is the angle turned by the crank from the inner-dead center. The engine speed is 250 rpm. The mass of the flywheel is 400 kg and radius of gyration 400 mm. Determine (i) the power developed; (ii) the total percentage fluctuation of speed; (iii) the angular acceleration of flywheel when the crank has rotated through an angle of 60属 from the inner-dead center; and (iv) the maximum angular acceleration and retardation of the flywheel. (DEC-2010) 3. The crank and connecting rod of a petrol engine, running at 1800 rpm are 50 mm and 200 mm respectively. The diameter of the piston is 80 mm and the mass of the reciprocating parts is 1 kg- at a point during the power stroke, the pressure on the piston is 0.7 N/mm2 , when it has moved 10 mm from the inner dead centre. Determine the net load on the gudgeon pin, thrust on the connecting rod, reaction between the piston and cylinder and the engine speed at which the above values become zero. (DEC-2011) 4. A three cylinder single acting engine has its cranks set equally at 120o and it runs at 600 r.p.m. The torque Vs crank angle diagram for each cycle is a triangle for the power stroke with maximum torque of 90 N-m at 60o from dead centre of corresponding crank. The torque on return stroke is sensibly zero. Determine the power developed, co-efficient of fluctuation of speed, if the mass of the flywheel is 12 kg and a radius gyration of 80 mm, co-efficient fluctuation of energy and maximum angular acceleration of the flywheel. (DEC-2011) 5. Deduce an expression for the inertia force in the reciprocating parts, neglecting the weight of the connecting rod. (DEC-2012) 6. The turning moment curve for an engine is represented by the equation T = (20000 + 9500 sin 2慮 - 5700 cos2慮) N-m Where 慮 is the angle moved by the crank from the inner-dead center. If the resisting torque is constant, find (i) the power developed by the engine (ii) moment of inertia of flywheel in kg-m2 , if the total fluctuation of speed is not exceed 1% of mean speed which is 180 rpm and (iii) the angular acceleration of flywheel when the crank has turned through 45属 from inner-dead center. (DEC-2012) 7. (i) Derive the equation of forces on the reciprocating parts of an engine, neglecting the weight of the connecting rod (12) (ii) What is turning moment diagram and draw its for four stroke IC engine? (4) (DEC-2013) 8. A single cylinder, single acting, four stroke gas engine develops 25 KW at 320 rpm. The work done by the gases during the expansion stroke is three times the work done on the gases during the compression stroke. The work done during the suction and exhaust stroke being negligible. The fluctuation of speed is not to exceed 賊2% of the mean speed. The turning moment diagram during compression and expansion is assumed to be triangular in shape. Find the weight of the flywheel if its radius of gyration is 0.5m. (DEC-2013)
  • 2. ME6505 - DYNAMICS OF MACHINES UNIT I (Part B) Prepared By: N. E. Godwin Pithalis Page 2 9. A horizontal steam engine running at 120rpm has a bore of 250 mm and a stroke of 400mm. The connecting rod is 0.6 m and mass of the reciprocating parts is 60 kg. When the crank has turned through an angle of 45属 from the Inner Dead Centre, the steam pressure on the cover end side is 550KN/m2 and that on the crank end side is 60KN/m2 . Considering the diameter of the piston rod equal to 50 mm, Determine, (i). Turning moment on the crank shaft (ii). Thrust on the bearing and (iii).Acceleration of the flywheel, if the power of the engine is 20 kW, mass of the flywheel 60 kg and radius of gyration of 0.6m. (MAY-2014) 10. A shaft fitted with a flywheel rotates at 250 rpm and drives a machine. The torque of machine varies in a cyclic manner over a period of 3 revolutions. The torque rises from 750 Nm to 3000 Nm uniformly during 12 revolutions and remains constant for the following revolution. It then falls uniformly to 750 Nm during next 12 revolution and remain constant for one revolution, the cycle being repeated thereafter. Determine the power required to drive the machine and percentage fluctuation in speed, if the driving torque applied to the shaft is constant and the mass of the flywheel is 500 kg with radius of gyration of 600 mm. (MAY-2013, 2014) 11. The piston diameter of an IC engine is 125 mm and the stroke is 220 mm. The connecting rod is 4.5 times the crank length and has a mass of 50 kg. The mass of the reciprocating parts is 30 kg. The center of mass of the connecting rod is 170 mm from the crank pin center and the radius of gyration about an axis through the center of mass is 148 mm. The engine runs at 320 rpm. Determine the magnitude and direction of the inertia force and the corresponding torque on the crank shaft when the angle turned by the crank is 140 degrees from the inner dead center. (MAY-2008) 12. The torque delivered by a two stroke engine is represented by, T= (1000 +300 sin2慮 -500 cos2慮) N.m, where 慮 is the angle turned by the crank from the inner dead centre. The mass of the flywheel is 400 Kg and the radius of gyration 400 mm. Determine (i) The power developed when the engine speed is 250 rpm and (ii) The maximum fluctuations of speed in terms of percentage. (MAY-2008) 13. A horizontal steam engine running at 240rpm has a bore of 300 mm and stroke 600mm. The connecting rod is 1.25 m long and mass of the reciprocating parts is 60 kg. When the crank is 60属 past its Inner Dead Centre, the steam pressure on the cover side of the piston is 1.125 N/mm2 while that on the crank side is 0.125N/mm2 . Neglecting the area of the piston rod, Determine, (i) the force on the piston rod, and (ii).Turning moment on the crank shaft. (MAY-2013) 14. The crank and connecting rod of an engine are 125 mm and 500 mm respectively. The mass of the connecting rod is 60 kg and its center of gravity is 275 mm from the cross head pin center. The radius of gyration about center of gravity being 150 mm. If the engine speed is 600 rpm for a crank position of 45o from the inner dead centre. Determine the acceleration of the piston and the magnitude, position and direction of inertia force due to the mass of the connecting rod. (MAY-2011)
  • 3. ME6505 - DYNAMICS OF MACHINES UNIT I (Part B) Prepared By: N. E. Godwin Pithalis Page 3 15. A punching press is required to punch 30 mm diameter holes in a plate of 20 mm thickness at the rate of 20 holes/mm. It requires 6 Nm energy /mm2 of sheared area. If punching takes places in 1/10 of a second and the speed of the flywheel varies from 160 to 140 rpm, determine the mass of the flywheel having radius of gyration 1m. (MAY-2011) 16. The turning moment diagram for a multi cylinder engine has been drawn to a scale of 1mm =325 Nm vertically and 1mm = 3o horizontally. The areas above and below the mean torque line are -26, +378, -306, -302, -244, -380, -261 and -225 mm2 the engine is running at a mean speed of 600 rpm. The total fluctuation of speed is not to exceed 賊1.8% of the mean speed. If the radius of flywheel is 0.7m, find the mass of the flywheel. (DEC-2009) 17. The dimensions of a four four-link mechanism are AB=50 mm, BC =66 mm, CD =560 mm, and AD =1000 mm the link AB has an angular velocity of 10.5 rad/s counter-clockwise and an angular retardation of 26 rad/s2 at the instant when it makes an angle of 60o with AD, the fixed link. The mass of the links BC and CD is 4.2 kg/m length. The link AB has a mass of 3.54 kg, the center of which lies at 200 mm from A and a moment of inertia of 88500 kgmm2 neglecting the gravity and friction effects, determine the instantaneous value of the drive torque required to be applied on AB to overcome the inertia forces. (DEC-2009) 18. The equation of the turning moment curve of a three crank engine is (5000+1500sin3慮) N-m, where 慮 is the crank and in radians. The moment of inertia of the flywheel is 1000 kg-m2 and the mean speed is 300 rpm. Calculate (i) Power of the engine and (8) (ii) The maximum fluctuation of the speed of the flywheel in percentage when (a) The resisting torque is constant, and (4) (b) The resisting torque is (5000 + 600sin慮) N-m. (4) (DEC-2014) 19. A certain machine requires a torque of (5000 + 500sin慮) N-m to drive it, where 慮 is the angle of rotation of shaft measured from certain datum. The machine is directly coupled to an engine which produces a torque of (5000 + 600sin2慮) N-m. The flywheel and the other rotating parts attached to the engine have a mass of 500 kg at a radius of gyration of 0.4 m. If the mean speed is 150 rpm, find (i) the fluctuation of energy (ii) the total percentage fluctuation of speed, and (iii) the maximum and minimum angular acceleration of the flywheel and the corresponding shaft position. (DEC-2014)