DYNAMICS OF MACHINES QUESTION BANK

 

 

UNIT-I (FORCE ANALYSIS)

PART A

1. What is free body diagram?

2. Define static force analysis.

3. Differentiate between static and dynamic equilibrium.

4. Define applied and constraint forces.

5. Differentiate between static force analysis and dynamic force analysis.

6. Define inertia force.

7. Define inertia torque.

8. State D’Alembert’s principle.

9. State the principle of superposition.

10. Define piston effort.

11. Define crank effort and crank-pin effort.

12. What is meant by turning moment diagram or crank effort diagram?

13. Explain the term maximum fluctuation of energy in fly wheel.

14. Define coefficient of fluctuation of energy.

15. Define coefficient of fluctuation of speed.

PART B

1. For reciprocating engine, derive the expression for

      (i)Velocity and acceleration of the piston

     (ii)Angular velocity and angular acceleration of the connecting rod

 

2. In a reciprocating engine mechanism, if the crank and connecting rod are 300mm and 1m long respectively and the crank rotates at a constant speed of 200r.p.m.Determine analytically,

1. The crank angle at which the maximum velocity occurs and

2. Maximum velocity of piston.

3. Derive the relevant equations.    (16)

 

3. (i)Deduce the expression for the inertia force     in the reciprocating force neglecting the weight

  of the connecting rod.                           (8)

    (ii)A vertical petrol engine with cylinder of 150mm diameter and    200mm strokes has a connecting rod of 350mm long. The mass is 1.6kg and the engine speed is 1800 rpm.  On the expansion    stroke with crank angle 30˚ fromTDC, the gas pressure is 750KPa.Determine the net thrust on the piston.    (8)

 

4. The radius of gyration of a fly wheel is 1meter and fluctuation of speed is not to exceed 1% of the mean speed of the flywheel. If the mass of the flywheel is 3340kg and the steam develops 150KW at 135rpm, then find, 1.Maximum fluctuation of energy 2. Coefficient of fluctuation of energy                    (16)

5.  The  length  of  crank  and  connecting rod  of  a  horizontal  reciprocating engine  are  100mm  and  500mm respectively. The crank is rotating at 400rpm.When the crank has turned 30˚ from the IDC, find analytically

1. Velocity of piston  2. Acceleration of piston 3. Angular velocity of connecting rod  4. Angular acceleration of connecting rod.                                   (16)

6. The length and connecting rod of a horizontal reciprocating engine are 200mm and 1meter respectively. The crank is rotating at 400rpm.When the crank has turned 30˚ from  the inner dead center, the difference of pressure between cover end and piston rod is 0.4 N/mm2. If the mass of the reciprocating parts is 100Kg and a cylinder bore is 0.4meters.Calculate

(i)Inertia force (ii) Force on piston   (iii) Piston effort  (iv) Thrust on the side of the cylinder walls            (v) Thrust in the connecting rod  (vi)Crank effort                                                            (16)

 

7. A horizontal gas engine running at 210rpm has a bore of 220mm and a stroke of 440mm. The connecting rod is 924mm long the reciprocating parts weight 20kg.When the crank has turned through an angle of 30˚ from IDC, the gas pressure on the cover and the crank sides are 500KN/m2 and 60KN/m2 respectively. Diameter of the piston rod is 40mm.Determine,

1. Turning moment on the crank shaft 2.Thrust on bearing 3. Acceleration of the flywheel which has a mass of 8kg and radius of gyration of 600mm  while the power of the engine is 22KW                            (16)

 

8. A single cylinder vertical engine has a bore of 300mm and a stroke of 400mm.The connecting rod is 1000mm long. The mass of the reciprocating parts is 140kg.On the expansion stroke with the crank at 30˚from the top dead center, the gas pressure is 0.7MPa.If the runs at 250rpm, determine;

1. Net force acting on the piston 2 .resultant load on the gudgeon pin 3. Thrust on cylinder walls 4. The speed above which other things remaining same, gudgeon pin loads would be reversed in direction                    (16)

9. A vertical double acting steam engine has a cylinder 300mm diameter and 450mm stroke and runs at 200rpm.The reciprocating parts has a mass of 225kg and the piston rod is 50mm diameter. The connecting rod is 1.2m long. When the crank has turned 125˚ from IDC the steam pressure above the piston is 30KN/m2.calculate, (i) Crank-pin effort (ii) The effective turning moment on the crank shaft.    (16)        

10. The turning moment diagram for a petrol engine is drawn to a scale of 1mm to 6N-9-9m and the horizontal scale of 1mm to 1˚.The turning moment repeat itself after every half revolution of  the engine. The area above and below the mean torque line are 305, 710, 50,350,980and 275mm2. The mass of rotating parts is 40kg at a radius of gyration of 140mm.Clculate the coefficient of fluctuation of speed if the mean speed is 1500rpm.                                   (16)

 

UNIT-II (BALANCING)

PART-A

1. What is meant by balancing of rotating masses?

2. Why rotating masses are to be dynamically balanced?

3. Define static balancing.

4. Define dynamic balancing.

5. State the conditions for static and dynamic balancing.

6. State the conditions for complete balance of several masses revolving in different planes of a shaft. 

7. Why complete balancing is not possible in reciprocating engine?

8. Can a single cylinder engine be fully balanced? Why?

9. Differentiate between the unbalanced force caused due to rotating and reciprocating masses.

10. Why are the cranks of a locomotive, with two cylinders, placed at 90˚ to each other?

11. List the effects of partial balancing of locomotives.

12. Define swaying couple.

13. Define hammer blow with respect to locomotives.

14. What are the effects of hammer blow and swaying couple?

15. Define direct and reverse cranks.

 

PART-B

1. A shaft is rotating at a uniform angular speed. Four masses M1, M2, and 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, 250mmand 300mm respectively. The angle made by these masses with horizontal are 0˚.45˚, 120˚and 255˚respectively.

Find,(i) the magnitude of balancing mass

(ii) the position of balancing mass if its radius of rotation is 200mm.

 

2. Four masses M1, M2, M3, and M4 are 200kg, 300kg, 240kg and 260kg respectively. The corresponding radii of rotation are 0.2m, 0.15m, 0.25m and 0.3m respectively and the angle between successive masses45˚, 75˚, and135˚.Find the position and magnitude of balance mass required if its radius of rotation is 0.25m

 

3. The data for three rotating masses are given below:- M1=4kg                       r1=75mm                           θ1=45

M2=3kg                       r2=85mm                           θ2=135

M3=2.5kg                     r3=50mm                          θ3=240

Determine the amount of counter mass at a radial distance of 65mm required for their static balance

 

 

4. Four masses A, B, C, and D are completely balanced masses C and D makes angles of 90˚ and 195˚respectively with B in the same sense. The rotating masses have the following properties:

mA=25kg           rA=150mm mB=40kg           rB=200mm mC=35kg                       rC=100mm rD=180mm Planes B and C are 250mm apart. Determine (i) the mass A and its angular position

(ii) the position of planes A and D.

 

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 4kgrespectively.Find the required mass A and relative angular setting of the four masses so that the shaft be in complete balance.

 

6. Four masses A, B, C and D revolves at equal radii and equally spaced along a shaft. The mass B is 7kg and the radii of C and D make angle s of 90˚ and 240 ˚respectively with the radius of B.Find the magnitude of masses A,C and D and angular position of A . So that the system may be completely balanced.

 

7. A shaft caries four rotating masses A, B, C and D which are completely balanced. The masses B, C and D are

50kg, 80kg and 70kg respectively. The masses C and D make angles of 90˚ and 195˚ respectively with mass B in the   same   sense.   The   masses   A,B,C   and   D   are   concentrated   at   radius   75mm,100mm,50mm  and 90mmrespectively.The plane of rotation of masses B and C are 250mm apart. Determine

(i) the magnitude of mass A and its angular position

(ii) the position of planes A and D.

 

8. A four cylinder vertical engine has cranks 150mm long. The plane of rotation of the first, second and fourth cranks are 400mm,200mm and 200mm respectively from that of the third crank and their reciprocating masses are 50kg,60kg and 50kg respectively. Find the mass of the reciprocating parts for the third cylinder and relative angular position of the cranks in order that the engine may be in complete balance

9. A four cylinder vertical engine has cranks 300mm long. The plane of rotation of the first, third and fourth cranks are 750mm,1050mm and 1650mm respectively from that of the second crank and their reciprocating masses are 10kg,400kg and 250kg respectively. Find the mass of the reciprocating parts for the second cylinder and relative angular position of the cranks in order that the engine may be in complete balance

 

10.  Derive  the  following  expression  of  effects  of  partial  balancing  in  two  cylinder  locomotive     engine

(i) Variation of tractive force (ii) Swaying couple (iii) Hammer blow

 

UNIT-III (FREE VIBRATION)

PART-A

 

1. What are the causes and effect of vibration?

2. Define frequency, cycle, period and free vibration.

3. What are the different types of vibrations?

4. State different method of finding natural frequency of a system.

5. What is meant by free vibration and forced vibration?

6. Define resonance.

7. What is meant by degrees of freedom in a vibrating system?

8. What is the natural frequency of simple spring mass system?

9. Determine the natural frequency of mass of 10kgsuspended at the bottom of two springs (of stiffness: 5N/mm and 8N/mm) in series.

10. What is the effect of inertia on the shaft in longitudinal and transverse vibrations?

11. State the expression for the frequency of simple pendulum.

12. Give the expression for natural frequency of water, which oscillates in a ‘U’tube manometer?

13. What are the different types of damping?

14. Draw the schematic diagram of a free damped vibration system and write the governing differential equation of the system.

15. Sketch the Time Vs Displacement for under-damped and over-damped systems

 

PART-B (FREE VIBRATION

1. Derive an expression for the natural frequency of the free longitudinal vibration by

(i)Equilibrium method (ii) Energy method   (iii)Rayleigh’s method

 

2. In a single degree of damped vibration system a suspended mass of 8kg makes 30 oscillations in 18 seconds. The amplitude decreases in 18 seconds. The amplitude decreases to 0.25 of the initial value after 5 oscillations. Determine (i) the spring stiffness (ii) logarithmic decrement (iii) damping factor (iv) Damping coefficient

 

3. Determine equation of motion when a liquid column vibrating in a ‘U’tube by

(i) Newton’s method (ii) Energy method and hence find its natural frequency

 

4. (i)Deduce the expression for the free longitudinal vibration in terms of spring stiffness, its inertia effect and suspended mass.                                                                                                                                           

(ii)A spring mass system has spring stiffness ‘s’N/m and has a mass of ‘m’kg.It has the natural frequency of vibration as 12Hz.An extra 2kg mass is coupled to ‘m’ and natural frequency reduces by 2Hz.Find the value of ‘s’ and ‘m

 

5.Avibrating system consists of a mass of 8kg,spring of stiffness 5.6N/m and dashpot of damping coefficient of 40N/m/s.Find, (i)Critical damping coefficient  (ii) the damping factor  (iii)the natural frequency of damped vibration (iv)the logarithmic decrement(v)the ratio of two consecutive amplitude    (vi)the number of cycle after which the original amplitude is reduced to 20 percent.

 

6. An instrument vibrates with a frequency of 1Hz when there is no damping. When the damping is provided, the frequency of damped vibration was observed to be 0.9Hz.

Find, (i) damping factor  (ii) logarithmic decrement

 

7. Find the equation of notion for the spring mass-dashpot system for the cases when

(i) ζ = 2   (ii)ζ = 1 and (iii)ζ = 0.3. The mass ‘m’is displaced by a distance of 30mm and released

 

8. Between a solid mass of 0kg and the floor are kept two slabs of isolates, natural rubber and felt, in series. The natural rubber slab has a stiffness of 3000N/m and equivalent viscous damping coefficient of 100 N-sec/m.The felt has a stiffness of 12000N/m and equivalent viscous damping coefficient of 330N-sec/m.Determine undamped and the damped natural frequencies of the system in vertical direction

 

9. (i) A cantilever shaft 50mm diameter and 300mm long has a disc of mass 100kg at its free end. The young’s modulus for the shaft material is 200GN/m2.SDetermine the frequency of longitudinal and transverse vibration of the shaft.         (10)                                                                                                                                              (ii)Explain the sketches different cases of damped vibrations. (6)

 

10. The barrel of a large gun recoils against a spring on firing. At the end of the firing, a dashpot is engaged that allows the barrel to return to its original position in minimum time without oscillation. Gun barrel mass is 400kg and initial velocity of recoils 1m.Determine spring stuffiness and critical damping coefficient of dashpot

 

UNIT-IV (FORCED VIBRATION)

PART-A

1. Define damping ratio or damping factor.

2. Define logarithmic decrement.

3. Give equation for damping factor ζ and damped frequency ωd.

4. What is meant by harmonic forcing?

5. What is the relationship between frequencies of undamped and damped vibration?

6. What is meant by dynamic magnifier or magnification factor?

7. Define transmissibility.

8. Define transmissibility ratio or isolation factor.

9. What is vibration isolation?

10. Sketch the graph for (ω/ωn) Vs Transmissibility for different values of damping factor.

PART – B

1.A mass of 50kg is supported by an elastic structure of total stiffness 20KN/m.The damping ratio of the system is 0.2.A simple harmonic disturbing force acts on the mass and at any time ‘t seconds, the force is 60sin10t newtons.Find amplitude of the vibration and phase angle caused by the damping.         (16)                              

2. A mass of 50kg is supported by an elastic structure of total stiffness 20KN/m.The damping ratio of the system is 0.25.A simple harmonic disturbing force acts on the mass and at any time ‘t seconds, the force is 75cos12t newtons.Find amplitude of the vibration and phase angle caused by the damping.       (16)     

3. A mass of 10kg is suspended from one end of a helical spring, the other end being fixed. The stiffness of the spring is10N/mm.The viscous damping causes the amplitude to decreases to one-tenth of the initial value in four complete oscillations. If a periodic force of 150cos50t N is applied at the mass in the vertical direction .Find the amplitude of the forced vibrations? What is its value of resonance?                                                              

 

4. A harmonic exiting force of 25N is acting on a machine part which is having a mass of 2Kg and vibrating in viscous medium. The exciting force causes resonant amplitude of 12.5mm with a period of 0.2sec.

 

5. A body having a mass of 15kg is suspended from a spring which deflects 12mm under the weight of the mass. Determine the frequency of the free vibrations. What is the viscous damping force needed to make the motion a periodic at a speed of 1mm/s?If, when damped to this extend a disturbing force having a maximum value of 100N and vibrating at 6Hz is made to act on the body, determine the amplitude of the ultimate motion.                

 

6. A single cylinder vertical petrol engine of total mass of 200kg is mounted upon a steel chassis frame. The vertical static deflection of the frame is 2.4mm due to the weight of the engine .The mass of the reciprocating parts is 18kg and stroke of piston 160mm with S.H.M.If dashpot of damping coefficient of 1N/mm/s used to damped the vibrations, calculate al steady state (i)Amplitude of vibrations at 500rpm engine speed.(ii)The speed of the driving shaft at which resonance will occurs.           

 

7. A vertical single stage air compressor having a mass of   500kg is mounted on spring having stiffness of 1.96X105N/m and dashpot with damping factor of 0.2m.The rotating parts are completely balanced and the equivalent reciprocating parts weight 20kg.The stroke is 0.2m.Determine the dynamic amplitude of vertical motion of the excitation force if the compressor is operate at 200rpm.             

8. A machine 100kg has a 20kg rotor with 0.5mm eccentricity. The mounting spring have s=85x103. The operating speed is 600rpm and the unit is constrained to move vertically. Find (i) Dynamic amplitude of machine   (ii) the force transmitted to the support.        

9.A single cylinder engine has an out of balance force of 500N at an engine speed of 30rpm.The total mass of engine is 150kg and its carried on a set of total stiffness 300N/cm. (i) Find the amplitude of steady motion of the mass and maximum oscillating force transmitted to the foundation. (ii)If a viscous damping is interposed between the mass and the foundation the damping force 1000N at 1m/s of velocity, find the amplitude of force damped oscillation of the mass and its angle of lag with disturbing force.        

10. An industrial machine weighting 445kg is supported on a spring with a statical deflection of 0.5cm.If the machine has  rotating imbalance of  25kg-cm.Determine the  force transmitted at  1200rpm  and  the  dynamic amplitude at the speed

UNIT-V (GOVERNOR AND GYROSCOPE)

PART-A  

1. What is the function of governor?

2. How governors are classified?

3. Differentiate between governor and fly wheel.

4. What is meant by sensitiveness of a governor?

5. What is the effect of friction on the governor?

6. Define coefficient of sensitiveness.

7. What is meant by hunting?

8. What is meant by isochronous conditions governor?

9. Give application of gyroscopic principle.

10. What is gyroscopic torque?

11. What is the effect of gyroscopic couple on rolling of ship? Why?

12. Define gyroscopic couple.

13. Write expression for gyroscopic couple.

PART – B

1. A porter governor has equal arms each 250mm long and pivoted on the axis of rotation. Each ball has a mass of 5kg and mass of the central load on the sleeve is 25kg.The radius of rotation of the ball is 150mm when governor is at maximum speed. Find the maximum and minimum speed and range of speed of the governor.

2. The length of the upper and lower arms of a porter governor are 200mm and 250mm respectively. Both the arms are pivoted on the axis of rotation. The central load is 150N, the weight of the each ball is 20N and the friction of the sleeve together with the resistance of the operating gear is equivalent to a force of 30N at the sleeve. If the limiting inclinations of the upper arms to the vertical are 30˚ and 40˚ taking friction in to account. Find the range of speed of the governor.

 

 

3. Calculate the rage of speed of a porter governor which has equal arms of each 200mm long and pivoted on the axis of rotation .The mass of each ball is 4kg and the central load of the sleeve is 20kg.The radius of rotation of the ball is 100mm when the governor being to lift and 130mm when the governor is at maximum speed.

4. A hartnell governor having a central sleeve spring and two right angled bell crank lever operates between290rpm and 310rpm for a sleeve lift of 15mm.The sleeve and ball arms are 80mm and 120mm repectively.The levers are pivoted at 120mm from the governoraxis and mass of the ball is 2.5kg.The ball arms are parallel at lowest equilibrium speed.Determine (i) load on the spring at maximum and minimum speeds and (ii) Stiffness of the spring

5. A governor of hartnell type has equal balls of mass 3kg, set initially at a radius of 200mm.The arms of the bell- crank lever are 110mm vertically and 150mm horizontally. Find (i) the initial compressive force on the spring at a radius of 200mm at240rpm and (ii) the stiffness of the spring required to permit a sleeve movement of 4mm on a fluctuation of 7.5 percent in the engine speed

6. The controlling force in a spring controlled governor is 1500N when radius of rotation is 200mm and 887.5N when radius of rotation is 130mm.The mass of each ball is 8kg.If the controlling force curve is a straight line, then find (i) Controlling force at 150mm radius of rotation (ii) Speed of the governor at 150mm radius.(iii)Increase in initial tension so that governor is isochronous.(iv) Isochronous speed

7. In a spring controlled governor, the controlling force curve is a straight line. When the balls are 400mm apart, the controlling force is 1200N and when 200mm apart, the controlling force is 450N.Determine the speed at which the governor runs when the balls are 250mm apart. When initial tension on the spring would be required for isochronisms and what would be the speed. Take mass of each ball to be 10kg

8. Calculate the minimum speed of a proell governor, which has equal arms each of 200mm and are provided on the axis of rotation. The mass of each ball is 4kg and the central mass on the sleeve is 20kg.The extension arms of the lower links are each 60mm long and parallel to the axis when the minimum radius of the ball is 100mm.of load.

9. (i) Explain the effect of Gyroscopic couple on a Naval ship during pitching.                                              (8)

 (ii) Explain the effect of Gyroscopic couple on a Aeroplane. (8)                                                                      

10.Each paddle wheel of a steamer have a mass of 1600kg and a radius of gyration of 1.2meters.The steamer turns to port in a circle of 160meters radius at 24Km/hr.The speed of the paddle is 90rpm.Find the magnitude and effect of the gyroscopic couple acting on the steamer