Dynamics of Machines Question Bank: ME6505 - Dynamics of Machines, Lecture notes of Mechanics

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JEPPIAAR ENGINEERING COLLEGE

Jeppiaar Nagar, Rajiv Gandhi Salai – 600 119

DEPARTMENT OF

MECHANICAL ENGINEERING

QUESTION BANK

V SEMESTER

ME6505 – Dynamicsof Machines

Regulation – 2013

JEPPIAAR ENGINEERING COLLEGE

Vision of Institution

To build Jeppiaar Engineering College as an institution of academic excellence in technological and management education to become a world class university. Mission of Institution

 To excel in teaching and learning, research and innovation by promoting the principles of scientific analysis and creative thinking.  To participate in the production, development and dissemination of knowledge and interact with national and international communities.  To equip students with values, ethics and life skills needed to enrich their lives and enable them to meaningfully contribute to the progress of society.  To prepare students for higher studies and lifelong learning, enrich them with the practical and entrepreneurial skills necessary to excel as future professionals and contribute to Nation’s economy.

PO

Engineering knowledge : Apply the knowledge of mathematics, science, engineering fundamentals, and an engineering specialization to the solution of complex engineering problems.

PO

Problem analysis : Identify, formulate, review research literature, and analyze complex engineering problems reaching substantiated conclusions using first principles of mathematics, natural sciences, and engineering sciences.

PO

Design/development of solutions : Design solutions for complex engineering problems and design system components or processes that meet the specified needs with appropriate consideration for the public health and safety, and the cultural, societal, and environmental considerations

PO

Conduct investigations of complex problems : Use research-based knowledge and research methods including design of experiments, analysis and interpretation of data, and synthesis of the information to provide valid conclusions.

PO

Modern tool usage : Create, select, and apply appropriate techniques, resources, and modern engineering and IT tools including prediction and modeling to complex engineering activities with an understanding of the limitations.

PO

The engineer and society : Apply reasoning informed by the contextual knowledge to assess societal, health, safety, legal and cultural issues and the consequent responsibilities relevant to the professional engineering practice.

PO

Environment and sustainability : Understand the impact of the professional engineering solutions in societal and environmental contexts, and demonstrate the knowledge of, and need for sustainable development.

PO Ethics : Apply ethical principles and commit to professional ethics and responsibilities and norms of the engineering practice.

PO Individual and team work : Function effectively as an individual, and as a member or leader in diverse teams, and in multidisciplinary settings.

PO

Communication : Communicate effectively on complex engineering activities with the engineering community and with society at large, such as, being able to comprehend and write effective reports and design documentation, make effective presentations, and give and receive clear instructions.

PO

Project management and finance : Demonstrate knowledge and understanding of the engineering and management principles and apply these to one’s own work, as a member and leader in a team, to manage projects and in multidisciplinary environments.

PO12 Life-long learning independent and life-long learning in the broadest context of technological change.: Recognize the need for, and have the preparation and ability to engage in

ME6505- DYNAMICS OF MACHINES

COURSE OUTCOMES

C305.

Students able to understand the force-motion relationship in components subjected to external forces and analysis of standard mechanisms

C305.

Students able to determine the balanced and unbalanced forces, resulting motions obtained from various mechanisms.

C305.

Students are able to understand and solve the free vibrations occuring at various conditions

C305.4 Students can understand the various methods to determine the forced vibration

C305.

Students can able to understand working principles of various types of governors and applications of gyroscopic mechanism.

ME6505 DYNAMICS OF MACHINES L T P C

UNIT I FORCE ANALYSIS 9

Dynamic force analysis – Inertia force and Inertia torque– D Alembert’s principle – Dynamic Analysis in reciprocating engines – Gas forces – Inertia effect of connecting rod– Bearing loads – Crank shaft torque – Turning moment diagrams – Fly Wheels – Flywheels of punching presses- Dynamics of Cam follower mechanism. UNIT II BALANCING 9 Static and dynamic balancing – Balancing of rotating masses – Balancing a single cylinder engine – Balancing of Multi-cylinder inline, V-engines – Partial balancing in engines – Balancing of linkages – Balancing machines-Field balancing of discs and rotors. UNIT III SINGLE DEGREE FREE VIBRATION 9 Basic features of vibratory systems – Degrees of freedom – single degree of freedom – Free vibration – Equations of motion – Natural frequency – Types of Damping – Damped vibration– Torsional vibration of shaft – Critical speeds of shafts – Torsional vibration – Two and three rotor torsional systems. UNIT IV FORCED VIBRATION 9 Response of one degree freedom systems to periodic forcing – Harmonic disturbances – Disturbance caused by unbalance – Support motion – transmissibility – Vibration isolation vibration measurement. UNIT V MECHANISM FOR CONTROL 9 Governors – Types – Centrifugal governors – Gravity controlled and spring controlled centrifugal governors – Characteristics – Effect of friction – Controlling force curves. Gyroscopes – Gyroscopic forces and torques – Gyroscopic stabilization – Gyroscopic effects in Automobiles, ships and airplanes. TOTAL : 45 PERIODS TEXT BOOK:

1. Uicker, J.J., Pennock G.R and Shigley, J.E., “Theory of Machines and Mechanisms” ,3rd Edition, Oxford University Press, 2009.
2. Rattan, S.S, “Theory of Machines”, 3rd Edition, Tata McGraw-Hill, 2009 REFERENCES:
3. Thomas Bevan, "Theory of Machines", 3rd Edition, CBS Publishers and Distributors,
5. Cleghorn. W. L, “Mechanisms of Machines”, Oxford University Press, 2005
6. Benson H. Tongue, ”Principles of Vibrations”, Oxford University Press, 2nd Edition, 2007
7. Robert L. Norton, "Kinematics and Dynamics of Machinery", Tata McGraw-Hill, 2009.
8. Allen S. Hall Jr., “Kinematics and Linkage Design”, Prentice Hall, 1961
9. Ghosh. A and Mallick, A.K., “Theory of Mechanisms and Machines", Affiliated East-West Pvt. Ltd., New Delhi, 1988.
10. Rao.J.S. and Dukkipati.R.V. "Mechanisms and Machine Theory", Wiley-Eastern Ltd., New Delhi, 1992.
11. John Hannah and Stephens R.C., "Mechanics of Machines", Viva Low-Prices Student Edition, 1999.
12. Grover. G.T., “Mechanical Vibrations”, Nem Chand and Bros., 1996
13. William T. Thomson, Marie Dillon Dahleh, Chandramouli Padmanabhan, “Theory of Vibration with Application”, 5th edition, Pearson Education, 2011
14. V.Ramamurthi, "Mechanics of Machines", Narosa Publishing House, 2002.
15. Khurmi, R.S.,”Theory of Machines”, 14th Edition, S Chand Publications, 2005.

Q.No. Questions BT

Level

Competence PO

(^19) Define 'Coefficient of Fluctuation of Energy'. BTL-1 Remembering PO2, PO (^20) Define 'Coefficient of Fluctuation of Speed'. BTL-1 Remembering PO2, PO (^21) Define Coefficient of Steadiness. BTL-1 Remembering PO2, PO

22 How you will reduce a dynamic analysis problem into an equivalent problem of static equilibrium? BTL-1 Remembering^

PO1, PO

23 What do you mean by Equivalent offset inertia force? BTL-1 Remembering PO2, PO

24 What do you mean by crank effort or turning moment on the crank shaft?

BTL-1 Remembering

PO1, PO

25 What do you understand by the fluctuation of energy in Fly wheel?

BTL-1 Remembering

PO1, PO

26 Define shaking force. BTL-1 Remembering PO2, PO (^27) Differentiate the function of flywheel and governor_._ BTL-4 Analyzing PO1, PO 28 What is meant by piston efforts and crank efforts. BTL-1 Remembering PO1, PO (^29) List out the few machines in which flywheel are used. BTL-1 Remembering PO1, PO 30 What does ‘float’ or jump of a follower? BTL-1 Remembering PO1, PO

31 Why smaller fly wheels are used in multi cylinder engines? BTL-1 Remembering

PO1, PO

32 Why negative loops are formed in turning moment diagrams? BTL-1 Remembering^

PO1, PO

33 What is the function of a fly wheel in engines? BTL-1 Remembering PO1, PO

PART-B&PART-C

A petrol engine has a stroke of 120 mm and connecting rod is 3 times the crank length. The crank rotates at 1500 rpm clockwise direction. Determine 1. Velocity and acceleration of the piston and 2. Angular velocity and angular acceleration of the connecting rod, when the piston has traveled one-fourth of its stroke from I.D.C.

BTL-5 Evaluating^ PO1, PO2, PO

The ratio of the connecting rod length to crank length for a vertical petrol engine is 4:1. The bore/stroke is 80/100 mm and mass of the reciprocating part is 1 kg. The gas pressure on the piston is 0.7 N/mm2 when it has moved 10 mm from TDC on its power stroke. Determine the net load on the gudgeon pin. The engine runs at 1800 rpm at what engine speed will this load be zero.

BTL-5 Evaluating^ PO1, PO2, PO

The turning moment diagram for a four stroke gas engine may be assumed for simplicity to be represented by four triangles, the areas of which from the line of zero pressure are as follows: Expansion stroke = 3550 mm2; Exhaust stroke = 500 mm^2 ; Suction stroke = 350 mm2; and compression stroke = 1400 mm^2. each mm2 represents 3 N-m. Assuming the resisting moment to be uniform, find the mass of the rim of a fly wheel required to keep the mean speed 200 rpm within ±2%. The mean radius of the rim may be taken as 0.75 m. Also determine the crank positions for the maximum and minimum speeds.

BTL-5 Evaluating^ PO1, PO2, PO

During a trail on steam engine it is found that the acceleration of the piston is 36m/s^2 when the crank has moved 30º from the inner dead center position. The net effective steam pressure on the piston is 0.5MPa and the frictional resistance is equivalent to

BTL-1 Remembering PO1, PO2, PO

force of 600 N, the diameter of the piston is 300 mm and the mass of the reciprocating parts is 180 kg. If the length of the crank is 300 mm and the ratio of the connecting rod length is 4. find (i) reaction on the guide bars (ii) thrust on the crank shafts bearings (iii) turning moment on the crank shaft.

A single cylinder double acting steam engine develops 150 kW at mean speed of 80 rpm. The co efficient of fluctuations of energy is 0.1 and the fluctuations of speed are ± 2% of mean speed. If the mean diameter of the flywheel rim is 2m and the hub and spokes provide 5% of the rotational inertia of the flywheel. Find the mass and cross sectional area of the flywheel rim. Assume density of the flywheel material (cast iron) as 7200 kg/ m^3.

BTL-1 Remembering PO1, PO2, PO

(i) Derive the equation of force on the reciprocating parts of an engine, neglecting the weight of the connecting rod (ii) What is turning moment diagram and draw it four stroke IC engine?

BTL-

BTL-

Creating Remembering PO1, PO2, PO

UNIT II BALANCING

Static and dynamic balancing – Balancing of rotating masses – Balancing a single cylinder engine – Balancing of Multi-cylinder inline, V-engines – Partial balancing in engines – Balancing of linkages – Balancing machines- Field balancing of discs and rotors. PART-A

CO Mapping : C305.

Q.No. Questions

BT

Level

Competence PO

(^1) What is meant by balancing? BTL-1 Remembering (^) PO1, PO 2 Write the importance of balancing. BTL-5 Evaluating PO1, PO (^3) Mention any two practical examples of balancing. BTL-1 Remembering PO1, PO (^4) Write different types of balancing BTL-6 Creating PO1, PO (^5) What is static balancing? BTL-1 Remembering PO1, PO (^6) State the condition for static balancing. BTL-1 Remembering PO1, PO (^7) What is dynamic balancing? BTL-1 Remembering PO1, PO (^8) Write the conditions for complete balancing. BTL-1 Remembering PO1, PO

(^9) State the condition for dynamic balancing. BTL-1 Remembering PO1, PO

10 What^ do^ you^ understand^ by^ the^ term^ partial balancing?

BTL-1 Remembering

PO1, PO

11 What is the effect of unbalanced primary force in a twin cylinder locomotive?

BTL-1 Remembering

PO1, PO

(^12) Define Tractive force. BTL-1 Remembering PO1, PO

35 What do you mean by the term 'shaking force' and 'shaking moment'?

BTL-1 Remembering

PO1, PO

PART-B&PART-C

Three masses are attached to a shaft as follows: 10 kg at 90 mm radius, 15 kg at 120 mm radius and 9 kg at 150 mm radius. The masses are to be arranged so that the shaft is in complete balance. Determine the angular position of masses relative to 10 kg mass. All the masses are in the same plane.

BTL-5 Evaluating^ PO1, PO3, PO

A.B, C and D are four masses carried by a rotating shaft at radii 100, 125, 200 and 150mm respectively. The planes in which the masses revolve are spaced 600mm apart and the mass 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 ib complete balance.

BTL-1 Remembering PO1, PO3, PO

A 900 -V engine has two cylinders which are placed symmetrically. The two connecting rods operate a common crank. The length of connecting rods is 320mm each and crank radius of 80mm. the reciprocating mass per cylinder is 12kg. If the engine speed is 600 rpm, then find the resultant primary and resultant secondary forces. Also find the maximum resultant secondary force.

BTL-1 Remembering PO1, PO3, PO

The axes of the three cylinder air compressor are 120 º to one another and their connecting rod are coupled to a single crank. The length of each connecting rod is 240mm 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.

BTL-5 Evaluating PO1, PO3, PO

A shaft has tree 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 centers 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 700 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 75 mm and at distance of 100 mm from the central plane of the middle eccentric, find the amount of the masses and their angular positions.

BTL-1 Remembering PO1, PO3, PO

The cranks of a three-cylinder locomotive are set at 120o. The reciprocating masses are 450 kg for the inside cylinder and 390 kg for each outside cylinder. The pitch of the cylinder is 1.2 m and the stroke of each piston 500 mm. The planes of rotation of the balance masses are 960 mm from the inside cylinder. If 40% of the reciprocating masses are to be balanced, determine 1. The magnitude and the position of the balancing masses required at a radial distance of 500 mm; and 2. The hammer blow per wheel when the axle rotates at 350 rpm.

BTL-5 Evaluating^ PO1, PO3, PO

UNIT III SINGLE DEGREE FREE VIBRATION

Basic features of vibratory systems – Degrees of freedom – single degree of freedom – Free vibration – Equations of motion – Natural frequency – Types of Damping – Damped vibration– Torsional vibration of shaft – Critical speeds of shafts – Torsional vibration – Two and three rotor torsional systems. PART-A

CO Mapping : C305.

Q.No. Questions

BT

Level

Competence PO

1 Define vibration. (^) BTL-1 Remembering (^) PO1, PO (^2) Vibration can have desirable effects – justify BTL-5 Evaluating PO1, PO

3 How do you classify vibration? (or) What are the different types of vibrations?

BTL-1 Remembering

PO1, PO

(^4) What is meant by free vibration? BTL-1 Remembering PO1, PO

5 What^ do^ you^ meant^ by^ damping^ and^ damped vibration?

BTL-1 Remembering

PO1, PO

(^6) Define followings. BTL-1 Remembering PO1, PO (^7) Define followings. BTL-1 Remembering PO1, PO

8 What^ do^ you^ mean^ by^ a^ degree^ of^ freedom^ or movability?

BTL-1 Remembering

PO1, PO

9 Define steady state and transient state vibrations. BTL-1 Remembering PO1, PO

10 What do you mean by the term^ –^ Equivalent spring stiffness?

BTL-1 Remembering^

PO1, PO2, PO

List out the various methods of finding the natural frequency of free longitudinal vibrations. BTL-1 Remembering

PO1, PO3, PO

12 Distinguish^ between^ critical^ damping^ and^ large damping.

BTL-4 Analyzing^

PO1, PO

13 When^ do^ you^ say^ a^ vibrating^ system^ is^ under damped?

BTL-1 Remembering^

PO1, PO

14 Write the expression for the estimation of the natural frequency of free torsional vibration of a shaft.

BTL-5 Evaluating

PO1, PO

(^15) Define Vibration Isolation. BTL-1 Remembering PO1, PO

16 What is the principle of Rayleigh’s method of finding naturalfrequencyofvibrations?

BTL-1 Remembering^

PO1, PO4, PO

Define critical or whirling or whipping speed of a shaft. BTL-1 Remembering

PO1, PO

18 What are the factors that affect the critical speed of a shaft?

BTL-1 Remembering

PO1, PO

(^19) What are the causes of critical speed? BTL-1 Remembering PO1, PO (^20) Define Damping ratio. BTL-1 Remembering PO1, PO (^21) Define logarithmic decrement. BTL-1 Remembering PO1, PO

22 What do you know about inertia effect of the mass of spring in longitudinal vibration?

BTL-1 Remembering^

PO1, PO

23 In a geared system, what assumptions to be made before replacing it with an equivalent system.

BTL-4 Analyzing^

PO1, PO

(^24) What is the condition of a system to vibrate? BTL-1 Remembering PO1, PO (^25) What is harmonic forcing? BTL-1 Remembering PO1, PO (^26) What is meant by periodic forcing? BTL-1 Remembering PO1, PO

N/mm/s. the system is initially at rest and a velocity of 120 mm/s is imported to the mass. Determine (i) the displacement and velocity of mass as a function of time, and the displacement velocity after 0.4 sec (ii) Describe the types of vibrations with simple sketch.

UNIT IV FORCED VIBRATION

Response of one degree freedom systems to periodic forcing – Harmonic disturbances – Disturbance caused by

unbalance – Support motion – transmissibility – Vibration isolation vibration measurement.

PART-A

CO Mapping : C305.

Q.No. Questions

BT

Level

Competence PO

What is meant by Forced vibrations? BTL-1 Remembering

PO1, PO

(^2) Define Torsional vibration BTL-1 Remembering PO1, PO

3 Differentiate between transverse and torsional vibration. BTL-4 Analyzing

PO1, PO

4 What^ is^ meant^ by^ dynamic^ magnifier^ or magnification factor? BTL-1 Remembering

PO1, PO

(^5) Define torsional equivalent shaft. BTL-1 Remembering PO1, PO 6 Define transmissibility ratio or isolation factor. BTL-1 Remembering PO1, PO 7 Briefly explain elastic suspension. BTL-2 Understanding PO1, PO 8 What are the methods of isolating the vibration? BTL-1 Remembering PO1, PO

9 Specify any two^ industrial^ application^ where^ the transmissibility effects of vibration are important. BTL-1 Remembering

PO1, PO

(^10) Define node in torsional vibration. BTL-1 Remembering PO1, PO

11 What is free torsional vibration of a single rotor system? BTL-1 Remembering

PO1, PO

(^12) What do you know by multifilar systems? BTL-1 Remembering PO1, PO 13 What is bifilar suspension? BTL-1 Remembering PO1, PO (^14) What is Trifilar suspension? BTL-1 Remembering PO1, PO

15 Explain briefly about free torsional vibrations in a Two – Rotor system. BTL-2 Understanding

PO1, PO

Explain briefly about free torsional vibrations in a Three – Rotor system. BTL-2 Understanding

PO1, PO

17 What do you understand by two – node frequency? BTL-1 Remembering PO1, PO (^18) What do you understand by single – node frequency? BTL-1 Remembering PO1, PO

19 How will you find the frequency of rotors are fixed to a shaft of various diameters at different sections? BTL-1 Remembering PO1, PO

20 Write down the assumptions in the geared system to be replaced by an equivalent shaft system? BTL-1 Remembering

PO1, PO

Q.No. Questions

BT

Level

Competence PO

21 What^ is^ meant^ by^ dynamic^ magnifier^ or magnification factor? BTL-1 Remembering

PO1, PO

(^22) What is meant by “Transmissibility? BTL-1 Remembering PO1, PO

A vibrating system consist of a mass of 7Kg and a spring stiffness 50N/cm and damper of damping coefficient 0.36Ncm-1sec. Find damping factor.

BTL-1 Remembering

PO1, PO

(^24) Briefly explain elastic suspension. BTL-2 Understanding PO1, PO 25 Specify the importance of vibration isolation? BTL-5 Evaluating PO1, PO 26 What are the methods of isolating the vibration? BTL-1 Remembering PO1, PO 27 Define frequency response curve. (^) BTL-1 Remembering PO1, PO (^28) Define Damping ratio. BTL-1 Remembering PO1, PO 29 Define Whirling speed.^ BTL-1 Remembering PO1, PO

30 Differentiate between transverse and torsional vibration. BTL-^ Analyzing PO1, PO

What are the conditions to be satisfied for an equivalent system to that of geared system in torsional vibrations?

BTL-1 Remembering

PO1, PO

PART-B& PART-C

A single cylinder vertical petrol engine has a mass of 200 kg and is mounted upon a steel chassis frame. The vertical static deflection of the frame is 2.4 mm due to the weight of the engine. The reciprocating part of the engine has a mass of 9 kg and move through a vertical stroke of 160 mm with simple harmonic motion. A dashpot with a damping co efficient of 1N/mm/s is also used to dampen the vibrations considering that the steady state of vibration is reached, determine (i) Amplitude of the forced vibration if the driving shaft rotates at 500 rpm (ii) The speed of the driving shaft at which resonance will occur

BTL-5 Evaluating

PO1, PO3, PO

(i)Derive the relation for the displacement of mass from the equilibrium position of a damped vibration system with harmonic forcing (ii)Define the term vibrating isolation.

BTL-

BTL-

Creating Remembering

PO1, PO3, PO

(i) Discuss the forcing due to support motion. (ii) What is mean by magnification factor in case of forced vibrations?

BTL-

BTL-

Creating Remembering

PO1, PO3, PO

A shaft supported freely at the ends has a mass of 120 kg placed 250 mm from one end. Determine the frequency of the natural transverse vibrations if the length of the shaft is 700 mm, E = 200 GN/m2 and shaft diameter is 40 mm.

BTL-5 Evaluating

PO1, PO3, PO

A shaft 40 mm diameter and 2.5 m long has a mass of 15 kg per meter length. It is simply supported at the ends and carries three masses 90 kg, 140 kg and 60 kg at 0.8 m, 1.5 m and 2 m respectively from the left support. Taking E = 200 GN/m2, find the frequency of the transverse vibrations.

BTL-1 Remembering

PO1, PO3, PO

6 The following data relate to a shaft held in long BTL-5 Evaluating PO1, PO3, PO

characteristics. Justify.

26

Mention any two advantages of using spring loaded governors in the place of gravity controlled governors.

BTL-1 Remembering

PO1, PO

When the engine is the above case rotates in clockwise then what is the effect of reactive gyroscopic couple?

BTL-1 Remembering

PO1, PO

28 Explain the principle of gyroscope. BTL-2 Understanding PO1, PO

29

When the aeroplane in the above case runs right, with other conditions kept same then what is the effect of reactive gyroscopic couple?

BTL-1 Remembering

PO1, PO

30 What is the effect of gyroscope on rolling of ship?^ BTL-1 Remembering PO1, PO 31 Write short notes on stability of an automobile. (^) BTL-1 Remembering PO1, PO 32 State the conditions for stability of a two wheeler. BTL-1 Remembering PO1, PO 33 What are the types of Automatic control of systems? BTL-1 Remembering PO1, PO

34 What are the terminologies used in Automatic control of systems? BTL-1^ Remembering^

PO1, PO

35 What is the effect of friction on the governors? BTL-1 Remembering PO1, PO PART-B& PART-C

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

BTL-5 Evaluating

PO1, PO3, PO

The turbine rotor of a ship has a mass of 3500 kg. it has a radius of gyration of 0.45 m and a speed of 3000 rpm clockwise when looking from stern. Determine the gyroscopic couple and its effect upon the ship: (i) When the ship is steering to the left on a curve of 100m radius at a speed of 36kmph (ii) When the ship is pitching in a simple harmonic motion the bow falling with its maximum velocity the period of pitching is 40 sec and the total angular displacement between the two extreme positions of pitching is 12º

BTL-5 Evaluating

PO1, PO3, PO

(i) Explain the functions of a proell governor with the help of a neat sketch. Derive the relationship among the various forces acting on the ling (ii) What are the centrifugal governors? How do they differ from inertia governors?

BTL-

BTL-

Understanding Remembering

PO1, PO3, PO

Q.No. Questions BT

Level

Competence PO

Each arm of a Porter governor is 250 mm long. The upper and lower arms are pivoted to links of 40 mm and 50 mm respectively from the axis of rotation. Each ball has a mass of 5 kg and the sleeve mass is 50 kg. The force of friction on the sleeve of the mechanism is 40 N. Determine the range of speed of the governor for extreme radii of rotation of 125 mm and 150 mm.

BTL-5 Evaluating

PO1, PO3, PO

The mass of each ball of a Proell governor is 7.5 kg and the load on the sleeve is 80 kg. Each of the arms is 300 mm long. The upper arms are pivoted on the axis of rotation whereas the lower arms are pivoted to links of 40 mm from the axis of rotation. The extensions of the lower arms to which the balls are attached are 100 mm long and are parallel to the governor axis at the minimum radius. Determine the equilibrium speeds corresponding to extreme radii of 180 mm and 240 mm.

BTL-5 Evaluating

PO1, PO3, PO

In a spring loaded Hartnell type of governor, the mass of each ball is 4 kg and the lift of the sleeve is 40 mm. The governor begins to float at 200 rpm when the radius of the ball path is 90 mm. The mean working speed of the governor is 16 times the range of speed when friction is neglected. The lengths of the ball and roller arms of the bell-crank lever are 100 mm and 80 mm respectively. The pivot centre and the axis of governor are 115 mm apart. Determine the initial compression of the spring, taking into account the obliquity of arms. Assuming the friction at the sleeve to be equivalent to a force of 15 N, determine the total alteration in speed before the sleeve begins to move from the mid- position

BTL-5 Evaluating

PO1, PO3, PO

UNIT I FORCE ANALYSIS

Dynamic force analysis – Inertia force and Inertia torque– D Alembert’s principle – Dynamic Analysis in reciprocating engines – Gas forces – Inertia effect of connecting rod– Bearing loads – Crank shaft torque – Turning moment diagrams – Fly Wheels – Flywheels of punching presses- Dynamics of Cam follower mechanism. PART-A

1. Define free body diagram (AU Jun 2009, May 2005) A free body diagram is a sketch of the isolated or free body which shows all the pertinent weight forces, the externally applied loads, and the reaction from its supports and connections acting upon it by the removed elements. 2.What are the conditions for a body to be in static and dynamic equilibrium? (AU Jun 2006) Necessary conditions for static and dynamic equilibrium are i) Vector sum of all forces acting on a body is zero. ii) The vector sum of the moments of all forces acting about any arbitrary point or axis is zero.

3.Define static force analysis. (AU May 2012, 2013) If components of a machine accelerate, inertia is produced due to their masses. However, the magnitudes of these forces are small compared to the externally applied loads. Hence inertia effects due to masses are neglected. Such an analysis is known as static force analysis.

4.Define Dynamic force analysis. (AU May 2012) If components of a machine accelerate by the applied forces (F), inertia force (-ma) is produced due to their masses. Even though the magnitudes of these forces are small as compared to the externally applied loads, if we do force analysis of machine considering the inertia forces in addition to all applied forces, then the force analysis is called Dynamic force analysis. 5.When will the two force member is in equilibrium? (AU May 2014) The member under the action of two force will be in equilibrium if i) The two forces are of same magnitude. ii) The forces act along the same line. iii) The forces are in opposite direction. 6.Give any three advantages of free body diagrams.

system dynamically equivalent a couple should be applied. This couple is called correction couple. The value of correction couple is always positive and its direction will be the same as that of angular acceleration ‘α’. 17.Explain the term Maximum Fluctuation of Energy. (AU Dec 2003)

The difference between the maximum and minimum energies is known as the maximum fluctuation of energy. 18.Define 'Inertia Torque'. The inertia torque is an imaginary torque, which when applied upon the rigid body, brings it in an equilibrium position. It is equal to the accelerating couple in magnitude but opposite in direction. 19.Define 'Coefficient of Fluctuation of Energy'. (AU Dec 2015, May 2014) It is defined as the ratio between the maximum fluctuation of energy (ΔE) and the work done per cycle. CE = ΔE / Work done per cycle

20.Define 'Coefficient of Fluctuation of Speed'. (AU May 2014) It is defined as the ratio of maximum fluctuation speed to the mean speed. CS = (N 1 - N 2 ) / N where, N 1 & N 2 - Maximum & Minimum speed in rpm N - Mean Speed in rpm - (N 1 + N 2 )/

21.Define Coefficient of Steadiness. The reciprocal of the coefficient of fluctuation of speed is known as Coefficient of steadiness. m = 1 / CS 22.How you will reduce a dynamic analysis problem into an equivalent problem of static equilibrium? By applying D’Alembert’s principle (Σ F + (-ma) = 0, Σ T + (-Iα) = 0 ) to a dynamic analysis problem, we can reduce into an equivalent problem of static equilibrium. 23.What do you mean by Equivalent offset inertia force? Equivalent offset inertia force is the force which can replace both inertia force and inertia torque. 24.What do you mean by crank effort or turning moment on the crank shaft? It is the product of the crank-pin effort (FT ) and crank pin radius (r). T = FT * r 25.What do you understand by the fluctuation of energy in Fly wheel? The difference between the maximum and the minimum energies in Turning moment diagram is known as Fluctuation of energy. 26.Define shaking force. (AU Nov 2013) A net unbalanced force acting on the frame of machine or mechanism is know as shaking force 27.Differentiate the function of flywheel and governor****. (AU Dec 2012,2011)

S.No Flywheel Governor 1 Flywheel used is to reduce the fluctuation of speed during a cycle above and below the mean value for constant load from prime mover

Governor is used to control the mean speed over a period for output load variations

2 Flywheel works continuously from cycle to cycle

Governor works intermittently, i.e. only when there is change in the load. 3 Flywheel has no influence on mean speed of the prime move

Governor has no influence over cycle speed fluctuations.

28.What is meant by piston efforts and crank efforts.(AU Dec 2012,2013, May 2016) Piston effort: it is the net force applied on the piston along the line of stroke. Crank effort: it is the net force applied on the crank pin perpendicular to the crank which gives the required turning moment on the crank shafts. 29.List out the few machines in which flywheel are used. 1.Punching machines 2.Shearing machines 3.Riveting machines 4.Crushing machines.

30.What does ‘float’ or jump of a follower? The stored energy in a camshaft due to windup phenomenon which occurs because of variations in torque gets released at the end of follower rise. This results in undue variation of velocity and acceleration of the follower. This phenomenon is called ‘Jump’ or ‘Float’ 31.Why smaller fly wheels are used in multi cylinder engines? In multi cylinder engine more than one power stroke is produced per second. So the need to store energy in flywheel is lesser than single cylinder engines. This leads to smaller flywheel for multi cylinder engines. 32.Why negative loops are formed in turning moment diagrams? During strokes other than power stroke, flywheel losses energy, negative loops are formed in turning moment diagram. This indicates more energy than produced is being taken from flywheel to do work absorbing processes. 33.What is the function of a fly wheel in engines? (AU Dec 2011, 2012, 2014) Fly wheel acts as a reservoir. It absorbs some portion of energy while power stroke and delivers it in all other strokes in an Engine. PART-B

1. A petrol engine has a stroke of 120 mm and connecting rod is 3 times the crank length. The crank rotates at 1500 rpm clockwise direction. Determine 1. Velocity and acceleration of the piston and 2. Angular velocity and angular acceleration of the connecting rod, when the piston has traveled one-fourth of its stroke from I.D.C. (Dec 2003)

Refer: “Khurmi, R.S.,”Theory of Machines”, 14th Edition, S Chand Publications, 2005. Page No:

2The ratio of the connecting rod length to crank length for a vertical petrol engine is 4:1. The bore/stroke is 80/100 mm and mass of the reciprocating part is 1 kg. The gas pressure on the piston is 0.7 N/mm when it has moved 10 mm from TDC on its power stroke. Determine the net load on the gudgeon pin. The engine runs at 1800 rpm at what engine speed will this load be zero. (Nov 2007) Refer: “Khurmi, R.S.,”Theory of Machines”, 14th Edition, S Chand Publications, 2005. Page No: 537 3The turning moment diagram for a four stroke gas engine may be assumed for simplicity to be

represented by four triangles, the areas of which from the line of zero pressure are as follows: Expansion

stroke = 3550 mm2; Exhaust stroke = 500 mm2; Suction stroke = 350 mm2; and compression stroke = 1400

mm2. each mm2 represents 3 N-m. Assuming the resisting moment to be uniform, find the mass of the

rim of a fly wheel required to keep the mean speed 200 rpm within ±2%. The mean radius of the rim may

be taken as 0.75 m. Also determine the crank positions for the maximum and minimum speeds. (Dec 2010)

Refer: “Khurmi, R.S.,”Theory of Machines”, 14th Edition, S Chand Publications, 2005. Page No: 584