Dynamics of Machinery

Which of the following statements is correct about the balancing of mechanical system?

Secondary forces in reciprocating mass on engine frame are

Which motion of follower is best for high speed cams?

What is meant by jump phenomenon in cam and follower system?

With usual notations for different parameters involved, the maximum fluctuations of energy for a flywheel is given by

What is meant by pitching of ship?

What is the effect of reactive gyroscopic couple when an aeroplane takes a right turn and propeller rotates in anticlockwise direction?

What is meant by critical damping coefficient?

The factor which affects the critical speed of a shaft is

The ratio of the maximum displacement of the forced vibration to the deflection due to the static force, is known as

Discuss the balancing of a single rotating mass when the plane of the disturbing mass lies in between the planes of the two balancing masses.

Discuss the balancing of a single rotating mass when the plane of the disturbing mass lies on one end of the planes of the balancing masses.

Draw the cam profile for following conditions: Follower type = roller follower, offset to the right of cam axis by 18 mm; lift = 35 mm; base circle radius = 50 mm; roller radius = 14 mm; outstroke with SHM in 0.05 sec; dwell for 0.0125 sec; return stroke with UARM, during 0.125 sec; dwell for the remaining period. During return stroke, acceleration is $ 3/5 $ times the retardation. Determine maximum velocity and acceleration during outstroke and return stroke if the cam rotates at 240 r.p.m.

Draw the displacement, velocity and acceleration diagrams for a follower when it moves with uniform acceleration and retardation. Derive the expression for velocity and acceleration during outstroke and return stroke of the follower.

During forward stroke of the piston of the double acting steam engine, the turning moment has the maximum value of 2000 N-m when the crank makes an angle of $ 80^{\circ} $ with the inner dead centre. During the backward stroke, the maximum turning moment is 1500 N-m when the crank makes an angle of $ 80^{\circ} $ with the outer dead centre. The turning moment diagram for the engine may be assumed for simplicity to be represented by two triangles. If the crank makes 100 r.p.m. and the radius of gyration of the flywheel is 1.75 m, find the coefficient of fluctuation of energy and the mass of the flywheel to keep the speed within $ \pm 0.75\% $ of the mean speed. Also determine the crank angle at which the speed has its minimum and maximum values.

A turbine rotor of a ship has a mass of 3500 kg and rotates at a speed of 2000 r.p.m. The rotor has a radius of gyration of 0.5 m and rotates in clockwise direction when viewed from the stern (rear) end. Determine the magnitude of gyroscopic couple and its direction for the following conditions:
(a) When the ship runs at a speed of 12 knots and steers to the left in a curve of 70 m radius.
(b) When the ship pitches $ 6^{\circ} $ above and $ 6^{\circ} $ below the horizontal position and the bow (front) end is lowered. The pitching motion is simple harmonic with periodic time 30 sec.
(c) When the ship rolls and at a certain instant, it has an angular velocity of 0.05 rad/s clockwise when viewed from the stern. Also find the maximum angular acceleration during pitching.

It is said that to balance a single revolving mass, two masses revolving in different planes are necessary. Explain why.

A two cylinder locomotive has the following specifications: Reciprocating mass per cylinder = 306 kg, Crank radius = 300 mm, Angle between cranks = $ 90^{\circ} $, Driving wheels diameter = 1800 mm, Distance between cylinder centres = 650 mm, Distance between driving wheel planes = 1550 mm. Determine (i) the fraction of reciprocating masses to be balanced, if the hammer blow is not to exceed 46 kN at 96.5 km/hr and (ii) the variation in tractive force.

Define logarithmic decrement. Derive an expression for logarithmic decrement.

A machine mounted on springs and fitted with a dashpot has a mass of 60 kg. There are three springs, each of stiffness 12 N/mm. The amplitude of vibrations reduced from 45 mm to 8 mm in two complete oscillations. Assuming that the damping force varies as the velocity, determine (i) the damping coefficient, (ii) the ratio of frequencies of damped and undamped vibrations and (iii) the periodic time of damped vibrations.

Find the natural frequency of vibration of the system shown in the figure below. [The system consists of a mass m attached to a light rod of length L pivoted at point O. A spring of stiffness K is attached horizontally at a distance 'a' from the pivot O.]

Define the terms vibration isolation and transmissibility. Explain with the help of transmissibility vs. frequency curves at various damping ratios.

Which of the following statements is correct about the balancing of mechanical system?

Secondary forces in reciprocating mass on engine frame are

Which motion of follower is best for high speed cams?

What is meant by jump phenomenon in cam and follower system?

With usual notations for different parameters involved, the maximum fluctuations of energy for a flywheel is given by

What is meant by pitching of ship?

What is the effect of reactive gyroscopic couple when an aeroplane takes a right turn and propeller rotates in anticlockwise direction?

What is meant by critical damping coefficient?

The factor which affects the critical speed of a shaft is

The ratio of the maximum displacement of the forced vibration to the deflection due to the static force, is known as

Discuss the balancing of a single rotating mass when the plane of the disturbing mass lies in between the planes of the two balancing masses.

Discuss the balancing of a single rotating mass when the plane of the disturbing mass lies on one end of the planes of the balancing masses.

Draw the cam profile for following conditions: Follower type = roller follower, offset to the right of cam axis by 18 mm; lift = 35 mm; base circle radius = 50 mm; roller radius = 14 mm; outstroke with SHM in 0.05 sec; dwell for 0.0125 sec; return stroke with UARM, during 0.125 sec; dwell for the remaining period. During return stroke, acceleration is $ 3/5 $ times the retardation. Determine maximum velocity and acceleration during outstroke and return stroke if the cam rotates at 240 r.p.m.

Draw the displacement, velocity and acceleration diagrams for a follower when it moves with uniform acceleration and retardation. Derive the expression for velocity and acceleration during outstroke and return stroke of the follower.

During forward stroke of the piston of the double acting steam engine, the turning moment has the maximum value of 2000 N-m when the crank makes an angle of $ 80^{\circ} $ with the inner dead centre. During the backward stroke, the maximum turning moment is 1500 N-m when the crank makes an angle of $ 80^{\circ} $ with the outer dead centre. The turning moment diagram for the engine may be assumed for simplicity to be represented by two triangles. If the crank makes 100 r.p.m. and the radius of gyration of the flywheel is 1.75 m, find the coefficient of fluctuation of energy and the mass of the flywheel to keep the speed within $ \pm 0.75\% $ of the mean speed. Also determine the crank angle at which the speed has its minimum and maximum values.

A turbine rotor of a ship has a mass of 3500 kg and rotates at a speed of 2000 r.p.m. The rotor has a radius of gyration of 0.5 m and rotates in clockwise direction when viewed from the stern (rear) end. Determine the magnitude of gyroscopic couple and its direction for the following conditions:
(a) When the ship runs at a speed of 12 knots and steers to the left in a curve of 70 m radius.
(b) When the ship pitches $ 6^{\circ} $ above and $ 6^{\circ} $ below the horizontal position and the bow (front) end is lowered. The pitching motion is simple harmonic with periodic time 30 sec.
(c) When the ship rolls and at a certain instant, it has an angular velocity of 0.05 rad/s clockwise when viewed from the stern. Also find the maximum angular acceleration during pitching.

It is said that to balance a single revolving mass, two masses revolving in different planes are necessary. Explain why.

A two cylinder locomotive has the following specifications: Reciprocating mass per cylinder = 306 kg, Crank radius = 300 mm, Angle between cranks = $ 90^{\circ} $, Driving wheels diameter = 1800 mm, Distance between cylinder centres = 650 mm, Distance between driving wheel planes = 1550 mm. Determine (i) the fraction of reciprocating masses to be balanced, if the hammer blow is not to exceed 46 kN at 96.5 km/hr and (ii) the variation in tractive force.

Define logarithmic decrement. Derive an expression for logarithmic decrement.

A machine mounted on springs and fitted with a dashpot has a mass of 60 kg. There are three springs, each of stiffness 12 N/mm. The amplitude of vibrations reduced from 45 mm to 8 mm in two complete oscillations. Assuming that the damping force varies as the velocity, determine (i) the damping coefficient, (ii) the ratio of frequencies of damped and undamped vibrations and (iii) the periodic time of damped vibrations.

Find the natural frequency of vibration of the system shown in the figure below. [The system consists of a mass m attached to a light rod of length L pivoted at point O. A spring of stiffness K is attached horizontally at a distance 'a' from the pivot O.]

Define the terms vibration isolation and transmissibility. Explain with the help of transmissibility vs. frequency curves at various damping ratios.

In a plate cam mechanism with reciprocating roller follower, the follower has a constant acceleration in the case of

The size of the cam depends on

The speed of an engine varies from 210 rad/s to 190 rad/s. During a cycle the change in kinetic energy is found to be 400 Nm. The inertia of the flywheel in $ kgm^2 $ is

A rotating disc of 1 m diameter has two eccentric masses of 0.5 kg each at radii of 50 mm and 60 mm at angular positions of $ 0^{\circ} $ and $ 150^{\circ} $, respectively. A balancing mass of 0.1 kg is to be used to balance the rotor. What is the radial position of the balancing mass?

A system in dynamic balance implies that

When the pitching of a ship is upward, the effect of gyroscopic couple acting on it will be

In a slider-bar mechanism, when does the connecting rod have zero angular velocity?

A mass m attached to a light spring oscillates with a period of 2 sec. If the mass is increased by 2 kg, the period increases by 1 sec. The value of m is

A machine of 250 kg mass is supported on springs of total stiffness 100 kN/m. The machine has an unbalanced rotating force of 350 N at speed of 3600 r.p.m. Assuming a damping factor of 0.15, the value of transmissibility ratio is

In a spring-mass system, the mass is 0.1 kg and the stiffness of the spring is 1 kN/m. By introducing a damper, the frequency of oscillation is found to be 90% of the original value. What is the damping coefficient of the damper?

What is the function of a flywheel? How does it differ from that of a governor?

The turning moment diagram for a multi-cylinder engine is drawn to a vertical scale of 1 mm = 4500 N-m and horizontal scale of 1 mm = $ 2.4^{\circ} $. The intercepted areas above and below the mean torque lines are 342, 23, 245, 303, 115, 232, 227 and 164 $ mm^2 $ when the engine is running at 150 r.p.m. If the mass of flywheel is 1000 kg and the fluctuation of speed does not exceed 3% of the mean speed, find the minimum value of radius of gyration.

A cam, with a minimum radius of 25 mm, rotating clockwise at a uniform speed is to be designed to give a roller follower, at the end of a valve rod, motion described below:
(i) To raise the valve through 50 mm during $ 120^{\circ} $ rotation of the cam
(ii) To keep the valve fully raised through next $ 30^{\circ} $
(iii) To lower the valve during next $ 60^{\circ} $
(iv) To keep the valve closed during rest of the revolution, i.e., $ 150^{\circ} $.
The diameter of the roller is 20 mm and the diameter of the cam shaft is 25 mm. Draw the profile of the cam when (a) the line of stroke of the valve rod passes through the axis of the cam shaft, and (b) the line of the stroke is offset 15 mm from the axis of the cam shaft. The displacement of the valve, while being raised and lowered, is to take place with simple harmonic motion. Determine the maximum acceleration of the valve rod when the cam shaft rotates at 100 r.p.m. Draw the displacement, velocity and acceleration diagrams for one complete revolution of the cam.

Draw the displacement, velocity and acceleration diagrams for a follower when it moves with uniform acceleration and retardation. Derive the expression for velocity and acceleration during out-stroke and return-stroke of the follower.

A cam has straight working faces which are tangential to a base circle of diameter 90 mm. The follower is a roller of diameter 40 mm and the centre of roller moves along a straight line passing through the centre line of the cam shaft. The angle between the tangential faces of the cam is $ 90^{\circ} $ and the faces are joined by a nose circle of 10 mm radius. The speed of rotation of the cam is 120 revolutions per min. Find the acceleration of the roller centre (i) when during the lift, the roller is just about to leave the straight flank and (ii) when the roller is at the outer end of its lift.

What is gyroscopic couple? What is the effect of gyroscopic couple on the stability of a four-wheeler while negotiating a curve?

The wheels of a motorcycle have a moment of inertia $ 68 \, kg m^2 $ and engine parts have a moment of inertia of $ 3.4 \, kg m^2 $. The axis of rotation of the engine crankshaft is parallel to that of the road wheels. If the gear ratio is 5 to 1, the diameter of the road wheels is 65 cm and the motor cycle rounds a curve of 30.5 m radius at 60 km/hour, find the magnitude and direction of the gyroscopic couple.

What are in-line engines? How are they balanced? Is it possible to balance them completely?

A four-cylinder marine oil engine has the cranks arranged at angular intervals of $ 90^{\circ} $. The inner cranks are 1.2 m apart and are placed symmetrically between the outer cranks, which are 3 m apart. Each crank is 45.7 cm long, the engine runs at 90 r.p.m., and the weight of the reciprocating parts for each cylinder is 8006 N. In which order should the cranks be arranged for the best balance of the reciprocating masses, and what will then be the magnitude of the unbalanced primary couple?

A five-cylinder inline engine running at 500 r.p.m. has successive cranks at $ 144^{\circ} $ apart. The distance between the cylinder lines is 300 mm. Piston stroke is 240 mm, length of connecting rod is 480 mm. Examine the engine for balance of primary and secondary forces and couples. Find the maximum value of these and position of central crank at which these maximum values occur. The reciprocating mass for each cylinder is 150 N.

Classify different types of vibration and derive an equation for the transverse vibration of a uniformly loaded shaft.

The following data are given for a vibrating system with viscous damping: Mass = 2.5 kg, Spring constant = 3 N/mm. Amplitude decreases to 0.25 of the initial value after five consecutive cycles. Determine the damping coefficient of the damper in the system.

Derive an expression for the free torsional vibration for a shaft fixed at one end and carrying a heavy disc at the other.

Consider a stepped shaft with two discs as shown in the figure given below. The following shaft dimensions are to be taken: $ l_1 = 0.5 \, m, l_2 = 0.3 \, m, l_3 = 0.2 \, m $, $ d_1 = 0.015 \, m, d_2 = 0.012 \, m, d_3 = 0.01 \, m $. Take the modulus of rigidity of the shaft as $ 0.8 \times 10^{11} N/m^2 $. Discs have polar mass moment of inertia as $ I_{P1} = 0.015 \, kg-m^2 $ and $ I_{P2} = 0.01 \, kg-m^2 $. Obtain natural frequencies, mode shapes, and the location of the node.

In a plate cam mechanism with reciprocating roller follower, the follower has a constant acceleration in the case of

The size of the cam depends on

The speed of an engine varies from 210 rad/s to 190 rad/s. During a cycle the change in kinetic energy is found to be 400 Nm. The inertia of the flywheel in $ kgm^2 $ is

A rotating disc of 1 m diameter has two eccentric masses of 0.5 kg each at radii of 50 mm and 60 mm at angular positions of $ 0^{\circ} $ and $ 150^{\circ} $, respectively. A balancing mass of 0.1 kg is to be used to balance the rotor. What is the radial position of the balancing mass?

A system in dynamic balance implies that

When the pitching of a ship is upward, the effect of gyroscopic couple acting on it will be

In a slider-bar mechanism, when does the connecting rod have zero angular velocity?

A mass m attached to a light spring oscillates with a period of 2 sec. If the mass is increased by 2 kg, the period increases by 1 sec. The value of m is

A machine of 250 kg mass is supported on springs of total stiffness 100 kN/m. The machine has an unbalanced rotating force of 350 N at speed of 3600 r.p.m. Assuming a damping factor of 0.15, the value of transmissibility ratio is

In a spring-mass system, the mass is 0.1 kg and the stiffness of the spring is 1 kN/m. By introducing a damper, the frequency of oscillation is found to be 90% of the original value. What is the damping coefficient of the damper?

What is the function of a flywheel? How does it differ from that of a governor?

The turning moment diagram for a multi-cylinder engine is drawn to a vertical scale of 1 mm = 4500 N-m and horizontal scale of 1 mm = $ 2.4^{\circ} $. The intercepted areas above and below the mean torque lines are 342, 23, 245, 303, 115, 232, 227 and 164 $ mm^2 $ when the engine is running at 150 r.p.m. If the mass of flywheel is 1000 kg and the fluctuation of speed does not exceed 3% of the mean speed, find the minimum value of radius of gyration.

A cam, with a minimum radius of 25 mm, rotating clockwise at a uniform speed is to be designed to give a roller follower, at the end of a valve rod, motion described below:
(i) To raise the valve through 50 mm during $ 120^{\circ} $ rotation of the cam
(ii) To keep the valve fully raised through next $ 30^{\circ} $
(iii) To lower the valve during next $ 60^{\circ} $
(iv) To keep the valve closed during rest of the revolution, i.e., $ 150^{\circ} $.
The diameter of the roller is 20 mm and the diameter of the cam shaft is 25 mm. Draw the profile of the cam when (a) the line of stroke of the valve rod passes through the axis of the cam shaft, and (b) the line of the stroke is offset 15 mm from the axis of the cam shaft. The displacement of the valve, while being raised and lowered, is to take place with simple harmonic motion. Determine the maximum acceleration of the valve rod when the cam shaft rotates at 100 r.p.m. Draw the displacement, velocity and acceleration diagrams for one complete revolution of the cam.

Draw the displacement, velocity and acceleration diagrams for a follower when it moves with uniform acceleration and retardation. Derive the expression for velocity and acceleration during out-stroke and return-stroke of the follower.

A cam has straight working faces which are tangential to a base circle of diameter 90 mm. The follower is a roller of diameter 40 mm and the centre of roller moves along a straight line passing through the centre line of the cam shaft. The angle between the tangential faces of the cam is $ 90^{\circ} $ and the faces are joined by a nose circle of 10 mm radius. The speed of rotation of the cam is 120 revolutions per min. Find the acceleration of the roller centre (i) when during the lift, the roller is just about to leave the straight flank and (ii) when the roller is at the outer end of its lift.

What is gyroscopic couple? What is the effect of gyroscopic couple on the stability of a four-wheeler while negotiating a curve?

The wheels of a motorcycle have a moment of inertia $ 68 \, kg m^2 $ and engine parts have a moment of inertia of $ 3.4 \, kg m^2 $. The axis of rotation of the engine crankshaft is parallel to that of the road wheels. If the gear ratio is 5 to 1, the diameter of the road wheels is 65 cm and the motor cycle rounds a curve of 30.5 m radius at 60 km/hour, find the magnitude and direction of the gyroscopic couple.

What are in-line engines? How are they balanced? Is it possible to balance them completely?

A four-cylinder marine oil engine has the cranks arranged at angular intervals of $ 90^{\circ} $. The inner cranks are 1.2 m apart and are placed symmetrically between the outer cranks, which are 3 m apart. Each crank is 45.7 cm long, the engine runs at 90 r.p.m., and the weight of the reciprocating parts for each cylinder is 8006 N. In which order should the cranks be arranged for the best balance of the reciprocating masses, and what will then be the magnitude of the unbalanced primary couple?

A five-cylinder inline engine running at 500 r.p.m. has successive cranks at $ 144^{\circ} $ apart. The distance between the cylinder lines is 300 mm. Piston stroke is 240 mm, length of connecting rod is 480 mm. Examine the engine for balance of primary and secondary forces and couples. Find the maximum value of these and position of central crank at which these maximum values occur. The reciprocating mass for each cylinder is 150 N.

Classify different types of vibration and derive an equation for the transverse vibration of a uniformly loaded shaft.

The following data are given for a vibrating system with viscous damping: Mass = 2.5 kg, Spring constant = 3 N/mm. Amplitude decreases to 0.25 of the initial value after five consecutive cycles. Determine the damping coefficient of the damper in the system.

Derive an expression for the free torsional vibration for a shaft fixed at one end and carrying a heavy disc at the other.

Consider a stepped shaft with two discs as shown in the figure given below. The following shaft dimensions are to be taken: $ l_1 = 0.5 \, m, l_2 = 0.3 \, m, l_3 = 0.2 \, m $, $ d_1 = 0.015 \, m, d_2 = 0.012 \, m, d_3 = 0.01 \, m $. Take the modulus of rigidity of the shaft as $ 0.8 \times 10^{11} N/m^2 $. Discs have polar mass moment of inertia as $ I_{P1} = 0.015 \, kg-m^2 $ and $ I_{P2} = 0.01 \, kg-m^2 $. Obtain natural frequencies, mode shapes, and the location of the node.

A disc is spinning with an angular velocity $ \omega $ rad/sec about the axis. The couple applied to the disc causing precession will be

When the crank is at the inner dead centre, in a horizontal reciprocating engine, then the velocity of the piston will be

The ratio of the maximum fluctuation of speed to the mean speed is called

The size of a cam depends upon

The cam follower generally used in automobile engine is

The primary unbalanced force is maximum when the angle of inclination of the crank with the line of stroke is

The swaying couple is due to the

When there is a reduction in amplitude over every cycle of vibration, then the body is said to have

When a body is subjected to transverse vibrations, the stress induced in a body will be

A shaft carrying two rotors as its ends will have

A small connecting rod 220 mm long between centers has a mass of 2 kg and moment of inertia of $ 2 \times 10^4 kg-mm^2 $ about its centre of gravity. Centre of gravity is located at a distance of 150 mm from the small end centre. Determine the dynamically two-mass system when one mass is located at the small end centre. If the connecting rod is replaced by two masses located at the two centers, find the correction couple that must be applied for complete dynamical equivalence of the system, when the angular acceleration of the connecting rod is 20000 rad/s² clockwise.

The torque exerted on the crankshaft of a two-stroke engine is given by the equation $ T(Nm) = 7000 + 1000 \sin 2\theta - 2000 \cos 2\theta $ where $ \theta $ is the crank displacement from the inner dead centre. Assuming the resisting torque to be constant, determine- (a) the power developed when the engine speed is 300 r.p.m.; (b) the total fluctuation in speed in percentage; (c) the maximum retardation of the flywheel. The mass of flywheel is 500 kg and its radius of gyration is 750 mm.

A disc cam is to give SHM to a knife edge follower during out stroke of 50 mm. The angle of ascent is $ 120^{\circ} $, dwell $ 60^{\circ} $ and an angle of descent $ 90^{\circ} $. The minimum radius of cam is 50 mm. Draw the profile of the cam when the axis of the follower passes through the axis of the camshaft. Also calculate the maximum velocity and acceleration during ascent and descent when the camshaft revolves at 240 r.p.m.

The following data refers to a circular arc cam working with a flat-faced reciprocating follower. Minimum radius of cam = 30 mm, total angle of cam rotation = $ 120^{\circ} $, radius of circular arc = 80 mm and nose radius = 10 mm. Find (a) the distance of the centre of the nose circle from the cam axis, (b) the angle through which the cam turns when the point of contact moves from the junction of minimum radius arc and circular arc to the junction of nose arc and circular arc and (c) velocity and acceleration of the follower when the cam has turned through an angle of $ 20^{\circ} $. The angular velocity of cam is 10 rad/sec.

The mass of a turbine rotor of a ship is 8000 kg and the radius of gyration is 0.75 m. It rotates at 1800 r.p.m. clockwise when viewed from the stern. Determine the gyroscopic effects in the following cases:
(a) If the ship travelling at 100 km/hr steers to the left along a curve of 80 m radius.
(b) If the ship is pitching and the bow is descending with maximum velocity, the pitching is with simple harmonic motion with periodic time of 20 s and the total angular movement between extreme positions is $ 10^{\circ} $.
(c) If the ship is rolling with an angular velocity of 0.03 rad/sec clockwise when looking from stern, in each case, determine the direction in which the ship tends to move.

The following data refer to an outside cylinder uncoupled locomotive: Rotating mass per cylinder = 300 kg, Reciprocating mass per cylinder = 330 kg, Distance between the wheels = 1.4 m, Distance between the cylinder centers = 0.6 m, Diameter of treads of the driving wheels = 1.8 m, Crank radius = 0.3 m, Radius of centre of the balance mass = 0.6 m, Speed of the locomotive = 45 km/h, Angle between the cylinder cranks = $ 90^{\circ} $, Dead load on each wheel = 40 kN. Determine: (a) the balancing mass required in the planes of driving wheels if the complete revolving and 2/3rd of the reciprocating masses are to be balanced; (b) swaying couple; (c) variation in tractive effort; (d) maximum and minimum pressures on rails; (e) maximum speed of locomotive without lifting the wheels from the rails.

A shaft is simply supported at the ends and is of 20 mm in diameter and 600 mm in length. The shaft carries a load of 19.62 N at its centre. The weight of shaft per meter length is 248.2 N. Find the critical speed of the shaft. (Take Young's modulus = $ 200 GN/m^2 $)

Cam

Dynamically equivalent system

A disc is spinning with an angular velocity $ \omega $ rad/sec about the axis. The couple applied to the disc causing precession will be

When the crank is at the inner dead centre, in a horizontal reciprocating engine, then the velocity of the piston will be

The ratio of the maximum fluctuation of speed to the mean speed is called

The size of a cam depends upon

The cam follower generally used in automobile engine is

The primary unbalanced force is maximum when the angle of inclination of the crank with the line of stroke is

The swaying couple is due to the

When there is a reduction in amplitude over every cycle of vibration, then the body is said to have

When a body is subjected to transverse vibrations, the stress induced in a body will be

A shaft carrying two rotors as its ends will have

A small connecting rod 220 mm long between centers has a mass of 2 kg and moment of inertia of $ 2 \times 10^4 kg-mm^2 $ about its centre of gravity. Centre of gravity is located at a distance of 150 mm from the small end centre. Determine the dynamically two-mass system when one mass is located at the small end centre. If the connecting rod is replaced by two masses located at the two centers, find the correction couple that must be applied for complete dynamical equivalence of the system, when the angular acceleration of the connecting rod is 20000 rad/s² clockwise.

The torque exerted on the crankshaft of a two-stroke engine is given by the equation $ T(Nm) = 7000 + 1000 \sin 2\theta - 2000 \cos 2\theta $ where $ \theta $ is the crank displacement from the inner dead centre. Assuming the resisting torque to be constant, determine- (a) the power developed when the engine speed is 300 r.p.m.; (b) the total fluctuation in speed in percentage; (c) the maximum retardation of the flywheel. The mass of flywheel is 500 kg and its radius of gyration is 750 mm.

A disc cam is to give SHM to a knife edge follower during out stroke of 50 mm. The angle of ascent is $ 120^{\circ} $, dwell $ 60^{\circ} $ and an angle of descent $ 90^{\circ} $. The minimum radius of cam is 50 mm. Draw the profile of the cam when the axis of the follower passes through the axis of the camshaft. Also calculate the maximum velocity and acceleration during ascent and descent when the camshaft revolves at 240 r.p.m.

The following data refers to a circular arc cam working with a flat-faced reciprocating follower. Minimum radius of cam = 30 mm, total angle of cam rotation = $ 120^{\circ} $, radius of circular arc = 80 mm and nose radius = 10 mm. Find (a) the distance of the centre of the nose circle from the cam axis, (b) the angle through which the cam turns when the point of contact moves from the junction of minimum radius arc and circular arc to the junction of nose arc and circular arc and (c) velocity and acceleration of the follower when the cam has turned through an angle of $ 20^{\circ} $. The angular velocity of cam is 10 rad/sec.

The mass of a turbine rotor of a ship is 8000 kg and the radius of gyration is 0.75 m. It rotates at 1800 r.p.m. clockwise when viewed from the stern. Determine the gyroscopic effects in the following cases:
(a) If the ship travelling at 100 km/hr steers to the left along a curve of 80 m radius.
(b) If the ship is pitching and the bow is descending with maximum velocity, the pitching is with simple harmonic motion with periodic time of 20 s and the total angular movement between extreme positions is $ 10^{\circ} $.
(c) If the ship is rolling with an angular velocity of 0.03 rad/sec clockwise when looking from stern, in each case, determine the direction in which the ship tends to move.

The following data refer to an outside cylinder uncoupled locomotive: Rotating mass per cylinder = 300 kg, Reciprocating mass per cylinder = 330 kg, Distance between the wheels = 1.4 m, Distance between the cylinder centers = 0.6 m, Diameter of treads of the driving wheels = 1.8 m, Crank radius = 0.3 m, Radius of centre of the balance mass = 0.6 m, Speed of the locomotive = 45 km/h, Angle between the cylinder cranks = $ 90^{\circ} $, Dead load on each wheel = 40 kN. Determine: (a) the balancing mass required in the planes of driving wheels if the complete revolving and 2/3rd of the reciprocating masses are to be balanced; (b) swaying couple; (c) variation in tractive effort; (d) maximum and minimum pressures on rails; (e) maximum speed of locomotive without lifting the wheels from the rails.

A shaft is simply supported at the ends and is of 20 mm in diameter and 600 mm in length. The shaft carries a load of 19.62 N at its centre. The weight of shaft per meter length is 248.2 N. Find the critical speed of the shaft. (Take Young's modulus = $ 200 GN/m^2 $)

Cam

Dynamically equivalent system

The cam follower used in air-craft engine is a _______ follower:

The size of the cam depends on:

The maximum fluctuation of energy in a flywheel is equal to:

For complete dynamic balance, at least....... mass/masses are necessary:

The Primary unbalanced force is maximum, when the angle of crank with the line of stroke is:

The gyroscopic acceleration is give by:

In free vibration, the acceleration vector leads the displacement vector by:

The frequency of damped vibration is always...... the natural frequency.

A torsional vibratory system having two rotors connected by a shaft has:

The axis of spin, the axis of precession and the axis of gyroscopic torque are in:

Draw the profile of a cam operating a roller reciprocating follower and with the following data: Minimum radius of cam = 25 mm. Lift = 30 mm. Roller diameter 15 mm. The cam lifts the follower for $ 120^{\circ} $ with SHM followed by a dwell period of $ 30^{\circ} $. Then the follower lowers down during $ 150^{\circ} $ of the cam rotation with uniform acceleration and deceleration followed by a dwell period. If the cam rotates at a uniform velocity of 150 rpm, calculate the maximum velocity and acceleration of the follower during the descent period.

Derive the expression for maximum and minimum accelerations for a tangent cam with roller follower, assuming roller follower is in direct contact with the circular flank.

Find a relation for the coefficient of fluctuation speed in terms of maximum fluctuation of energy and the kinetic energy of the flywheel at mean speed.

The turning moment diagram for a spark ignition engine is drawn to a vertical scale of 1 mm = 500 N.m and a horizontal scale of 1 mm = $ 3^{\circ} $. The turning moment diagram repeats itself every half revolution of the crankshaft. The areas above and below the mean torque line are 260, -580, 80, -380, 870, and -250 $ mm^2 $. The rotating parts have a mass of 55 kg and radius of gyration of 2.1 m. If the engine speed is 1600 rpm, determine the coefficient of fluctuation of speed.

Explain the gyroscopic effect on four-wheeled vehicles. What is the effect of gyroscopic couple on the stability of a four wheeler while negotiating a curve?

In a vertical double-acting steam engine, the connecting rod is 4.5 times the crank. The weights of the reciprocating part are 120 kg and the stroke of the piston is 440 mm. The engine runs at 250 rpm. If the net load on the piston due to steam pressure is 25 kN when the crank has turned through an angle of $ 120^{\circ} $ from the top dead centre, determine the following: (a) Thrust in the connecting rod. (b) Pressure on the slide bars. (c) Tangential force on the crank pin. (d) Thrust on the bearings. (e) Turning moment on the crankshaft.

A rotor is completely balanced when masses of 2 kg are added temporarily in planes A and D each at 200 mm radius as shown in figure. The balanced mass in the plane A is along the X-axis whereas in the plane D it is at $ 120^{\circ} $ counter-clockwise. It is desired that the actual balancing is to be done by adding permanent masses in plane B and C, each at 120 mm radius. Determine the magnitude and directions of the masses B and C.

Derive from the first principles, a relation for displacement of mass from equilibrium position of a damped vibrating system with harmonic forcing. Also find graphically the amplitude for the given system.

The following data relate to a shaft held in long bearings: Length of shaft = 1.2 m, Diameter of shaft = 14 mm, Mass of a rotor at midpoint = 16 kg, Eccentricity of mass = 0.4 mm, Modulus of elasticity of shaft material = $ 200 GN/m^2 $, Permissible stress in shaft material = $ 70 MN/m^2 $. Determine the critical speed of the shaft and the range of speed over which it is unsafe to run shaft. Assume the shaft to be massless.

The cam follower used in air-craft engine is a _______ follower:

The size of the cam depends on:

The maximum fluctuation of energy in a flywheel is equal to:

For complete dynamic balance, at least....... mass/masses are necessary:

The Primary unbalanced force is maximum, when the angle of crank with the line of stroke is:

The gyroscopic acceleration is give by:

In free vibration, the acceleration vector leads the displacement vector by:

The frequency of damped vibration is always...... the natural frequency.

A torsional vibratory system having two rotors connected by a shaft has:

The axis of spin, the axis of precession and the axis of gyroscopic torque are in:

Draw the profile of a cam operating a roller reciprocating follower and with the following data: Minimum radius of cam = 25 mm. Lift = 30 mm. Roller diameter 15 mm. The cam lifts the follower for $ 120^{\circ} $ with SHM followed by a dwell period of $ 30^{\circ} $. Then the follower lowers down during $ 150^{\circ} $ of the cam rotation with uniform acceleration and deceleration followed by a dwell period. If the cam rotates at a uniform velocity of 150 rpm, calculate the maximum velocity and acceleration of the follower during the descent period.

Derive the expression for maximum and minimum accelerations for a tangent cam with roller follower, assuming roller follower is in direct contact with the circular flank.

Find a relation for the coefficient of fluctuation speed in terms of maximum fluctuation of energy and the kinetic energy of the flywheel at mean speed.

The turning moment diagram for a spark ignition engine is drawn to a vertical scale of 1 mm = 500 N.m and a horizontal scale of 1 mm = $ 3^{\circ} $. The turning moment diagram repeats itself every half revolution of the crankshaft. The areas above and below the mean torque line are 260, -580, 80, -380, 870, and -250 $ mm^2 $. The rotating parts have a mass of 55 kg and radius of gyration of 2.1 m. If the engine speed is 1600 rpm, determine the coefficient of fluctuation of speed.

Explain the gyroscopic effect on four-wheeled vehicles. What is the effect of gyroscopic couple on the stability of a four wheeler while negotiating a curve?

In a vertical double-acting steam engine, the connecting rod is 4.5 times the crank. The weights of the reciprocating part are 120 kg and the stroke of the piston is 440 mm. The engine runs at 250 rpm. If the net load on the piston due to steam pressure is 25 kN when the crank has turned through an angle of $ 120^{\circ} $ from the top dead centre, determine the following: (a) Thrust in the connecting rod. (b) Pressure on the slide bars. (c) Tangential force on the crank pin. (d) Thrust on the bearings. (e) Turning moment on the crankshaft.

A rotor is completely balanced when masses of 2 kg are added temporarily in planes A and D each at 200 mm radius as shown in figure. The balanced mass in the plane A is along the X-axis whereas in the plane D it is at $ 120^{\circ} $ counter-clockwise. It is desired that the actual balancing is to be done by adding permanent masses in plane B and C, each at 120 mm radius. Determine the magnitude and directions of the masses B and C.

Derive from the first principles, a relation for displacement of mass from equilibrium position of a damped vibrating system with harmonic forcing. Also find graphically the amplitude for the given system.

The following data relate to a shaft held in long bearings: Length of shaft = 1.2 m, Diameter of shaft = 14 mm, Mass of a rotor at midpoint = 16 kg, Eccentricity of mass = 0.4 mm, Modulus of elasticity of shaft material = $ 200 GN/m^2 $, Permissible stress in shaft material = $ 70 MN/m^2 $. Determine the critical speed of the shaft and the range of speed over which it is unsafe to run shaft. Assume the shaft to be massless.