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Sr. No.

Particulars

Page Number

1 Scheme 2

2 Syllabus 3

3 Lecture Plan 6

4 List of Books 8

5 Tutorial Sheets -

6 Assignments 10

7 MID Question Papers 26

8 Model Question Paper 27

9 Gtu Question Paper 28

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Course of Study and Scheme of Examination for Batch starting from December 2018

B.E-6th Semester (AUTOMOBILE ENGINEERING )

Teaching Scheme Credit Examination Marks

Total Marks L T P C

Theory Marks Practical Marks ESE(E) PA(M) ESE(V) PA(I) PA ALA ESE OEP

3 0 2 5 70 20 10 20 10 20 150

4

SSYYLLLLAABBUUSS

UNIT-I

Balancing of Rotating Masses

Concept of static and dynamic balancing, Analysis of effect of unbalanced masses in single and multiple planes in rotating elements, Bearing reactions. Approaches and equipment for measurement of unbalanced masses.

UNIT-II

Dynamics of Reciprocating Engines

Single Cylinder Engine: Slider – Crank kinematics (Analytical), Gas force and torque; static and dynamic equivalence of models (for masses); Inertia, shaking force and shaking torque, Analysis of pin forces, balancing. Multi Cylinder Engines: Configurations; Inline Engines: Effect of phase angles, firing order and number of strokes; Shaking forces and moments, inertia torques and determination best configuration / unbalanced mass. Analysis of V and radial engine configurations. Graphical methods may be demonstrated but emphasis should be on analytical approach.

UNIT-III

1. Introduction to Mechanical Vibrations

Elements of simple harmonic motion, concept of natural frequency, types of vibrations, Basic elements and lumping parameters of a vibratory system, lumping of physical systems, Concept of Degrees of Freedom (DOF).

2. Single Degrees of Freedom System (Linear and Torsional)

Undamped free vibrations, equivalent stiffness, equivalent systems, determination of natural frequency; Coulomb and Viscous damping, Types of dampers, Damping coefficient, damping effects: under, over and critically damped system, Damping factor, damped natural frequency and logarithmic decay; Analytical solution of Forced vibrations with harmonic excitation system and vector representation, Dependence of Magnification Factor, Phase difference and Transmissibility on frequency of 10 20% excitation for various damping factors, Concept of vibration isolation, effect of base excitation.

3. Two Degrees of Freedom System

Equation of motion and principal mode of vibration, torsional vibrations of two and three rotor system, torsionally equivalent shaft, geared system.

Category of Course

Course Title Course Code Theory Paper L T P

AUTOMOBILE Dynamics of Machinery 2161901 3 0 2 70

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4. Multi degree freedom systems and analysis (Free vibrations)

Concepts of normal mode vibrations, natural frequencies, mode shapes, nodes, correct definition of natural frequency.

5. Vibrations of Continuous Systems (Free Vibrations)

Longitudinal vibrations of bar or rod: Equation of motion and solution, Lateral vibrations of beam: Equation of motion, initial and boundary conditions, solution

6. Rotating unbalance

Whirling of shafts, Critical speed and its practical importance in the design of shafts, Application of Dunkerley’s method and Rayleigh’s method for estimating the critical speed of shafts.

7. Vibration Measurement

Introduction to vibration measurement and analysis devices: Vibrometer, velocity pickup, accelerometer, FFT analyser

UNIT – IV

Cam Dynamics

Dynamic analysis of force-closed cam follower: Undamped and Damped response, Jump phenomenon: concept, effect of spring force and dead weights.

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LECTURE PLAN

Lecture Topics to be covered Teaching hours

1 Concept of static and dynamic balancing, Analysis of effect of Single unbalanced masses in single Plane

1

2 Analysis of effect of Single unbalanced masses in Different Plane 1

3 Analysis of effect of Several unbalanced masses in Single Plane – Analytical Method and Graphical Method, Numerical

2

4 Analysis of effect of Several unbalanced masses in Several Plane – Analytical Method and Graphical Method, Numerical

3

5 Single Cylinder Engine: Slider – Crank kinematics (Analytical), Gas force and torque;

6 static and dynamic equivalence of models (for masses); Inertia, shaking force and shaking torque

1

7 Analysis of pin forces, balancing 1

8 Multi Cylinder Engines: Configurations 1

9 Inline Engines: Effect of phase angles, firing order and number of strokes

1

10 Shaking forces and moments, inertia torques and determination best configuration / unbalanced mass

1

11 Inline Engines Numerical 1

12 Analysis of V and radial engine configurations - Numerical 3

13 Elements of simple harmonic motion, concept of natural frequency,

1

14 types of vibrations, Basic elements and lumping parameters of a vibratory system

1

15 Lumping of physical systems, Concept of Degrees of Freedom (DOF).

1

16 Undamped free vibrations, equivalent stiffness, equivalent systems, determination of natural frequency; Coulomb and Viscous damping,

1

17 Types of dampers, Damping coefficient, damping effects:

1

18 Under damped system 1

19 over damped system 1

20 critically damped system 1

21 Damping factor 1

22 Damped natural frequency, logarithmic decay 1

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23 Analytical solution of Forced vibrations with harmonic excitation system and vector representation

1

23 Phase difference and Transmissibility on frequency of excitation for various damping factors

1

24 Concept of vibration isolation, 1

25 effect of base Excitation. 1

26 Equation of motion and principal mode of vibration

1

27 torsional vibrations of two rotor system 1

28 torsional vibrations of three rotor system 1

29 torsionally equivalent shaft 1

30 Geared system 1

31 Example on shaft and gear system 1

32 Concepts of normal mode vibrations, natural frequencies 1

33 mode shapes, nodes, Correct definition of natural frequency. 1

34 Longitudinal vibrations of bar or rod: 1

35 Equation of motion and solution, Lateral vibrations of beam 1

36 Equation of motion, initial and boundary conditions, solution. 1

37 Whirling of shafts 1

38 Critical speed and its practical importance in the design of shafts 1

39 Rayleigh’s method for estimating speed of the shaft 1

40 Rayleigh’s method Example 1

41 Introduction to vibration measurement - Vibrometer 1

42 Introduction to vibration measurement - velocity pickup, accelerometer 1

43 Introduction to vibration measurement - FFT analyser 1

44 Dynamic analysis of force-closed cam follower: Undamped response 1

45 Dynamic analysis of force-closed cam follower: Damped response 1

46 Jump phenomenon: concept 1

47 Jump phenomenon: effect of spring force and dead weights 1

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REFERENCE BOOK

S. No. TITLE AUTHOR PUBLISHER / EDITION

1 Theory of Machines R S KHURMI S. Chand

2 Theory of Machines S. S. RATAN McGraw Hill

3 Mechanical Vibrations G. K. Groover Nem Chad and Bros.

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ASSIGNMENT TOPICS

S. No. TOPIC

1 Balancing of Rotating Masses

2 Dynamics of Reciprocating Engines

3A Introduction to Mechanical Vibrations

3B Single Degrees of Freedom System (Linear and Torsional)

3C Two Degrees of Freedom System 3D Multi degree freedom systems and analysis (Free vibrations) 3E Vibrations of Continuous Systems (Free Vibrations): 3F Rotating unbalance 3G Vibration Measurement 4 Cam Dynamics

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ASSIGNMENT -1 Balancing of rotating masses

1 Describe the function of a pivoted-cradle balancing machine with the help of a neat sketch. Show that it is possible to make only four test runs to obtain the balance masses in such a machine.

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A rotating shaft carries four unbalanced masses A=20 kg, B=15kg, C=18kg and D=12kg. The mass centers are 50, 60, 70 and 60 mm respectively from the axis of the shaft. The second, third and fourth masses rotates in planes 100, 150 and 300 mm respectively measured from the plane of first mass and at angular locations of 60º, 120º, and 280º respectively, measured clockwise from the first mass. The shaft is dynamically balanced by two masses, both located at 50mm radii and revolving in planes midway between those of first and second masses and midway between those of third and fourth masses. Determine the balancing masses and their angular positions.

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The four masses m1, m2 m3 and m4 having their radii of rotation as 200 mm, 150 mm, 250 mm and 300 mm are 200 kg, 300 kg, 240 kg and 260 kg in magnitude respectively. The angles between the successive masses are 45˚, 75˚ and 135˚ respectively. Find the position and magnitude of the balance mass required, if its radius of rotation is 200 mm. Use analytical method

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Four masses 150 kg, 200 kg, 100 kg and 250 kg are attached to a shaft revolving at radii 150mm, 200 mm, 100 mm and 250 mm ; in planes A, B, C and D respectively. The planes B, C and D are at distances 350 mm, 500 mm and 800 mm from plane A. The masses in planes B, C and D are at an angle 105o , 200o and 300o measured anticlockwise from mass in plane A. It is required to balance the system by placing the balancing masses in the planes P and Q which are midway between the planes A and B, and between C and D respectively. If the balancing masses revolve at radius 180 mm, find the magnitude and angular positions of the balance masses.

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Four masses 150 kg, 200 kg, 100 kg and 250 kg are attached to a shaft revolving at radii 150 mm, 200 mm, 100 mm and 250 mm ; in planes A, B, C and D respectively. The planes B, C and D are at distances 350 mm, 500 mm and 800 mm from plane A. The masses in planes B, C and D are at an angle 105° , 200° and 300° measured anticlockwise from mass in plane A. It is required to balance the system by placing the balancing masses in the planes P and Q which are midway between the planes A and B, and between C and D respectively. If the balancing masses revolve at radius 180 mm, find the magnitude and angular positions of the balance masses

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A, B, C and D are four masses carried by a rotating shaft at radii 0.1 m, 0.15 m, 0.15 m and 0.2 m respectively. The planes in which the masses rotate are spaced at 500 mm apart and the magnitude of the masses B, C and D are 9 kg, 5 kg and 4 kg respectively. Find the required mass A; and the relative angular settings of the four masses so that the shaft shall be in complete balance

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Four masses A, B, C and D are completely balanced. Masses C and D make angles of 90o and 195o respectively with B in the same sense. The rotating masses have following properties. mb =25 kg, mc =40 kg, md =35 kg, ra =150 mm, rb =200 mm, rc =100, rd =180 mm, Planes B and C are 250 mm apart. Determine 1. The mass A and its angular position 2. The position of planes A and D.

10

A rotating shaft carries four masses A, B, C and D which are radially attached to it. The mass centers are 30 mm, 40 mm, 35 mm and 38 mm respectively from the axis of rotation. The masses A, C and D are 7.5 kg, 5 kg and 4 kg respectively. The axial distances between the planes of rotation of A and B is 400 mm and between B and C is 500 mm. The masses A and C are at right angles to each other. Find for a complete balance, (i) the angles between the masses B and D from mass A, (ii) the axial distance between the planes of rotation of C and D, and (iii) the magnitude of mass B

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Four masses P, Q, R and S are carried by a rotating shaft at radii 100 mm, 125 mm, 200 mm and 150 mm respectively. The planes in which the masses revolve are spaced 600 mm apart and the masses Q, R and S are 10 kg, 5 kg and 4 kg respectively. Determine the required mass P and the relative angular positions of four masses so that the shaft shall be in complete balance.

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ASSIGNMENT -2 Dynamics of reciprocating Engines

1 Explain why the reciprocating masses are partially balanced. 2 Derive the expressions for primary and secondary unbalanced forces in a V -Engine

3 Q) Explain concept of Direct and Reverse Crank Q) Explain the procedure for balancing multi-cylinder radial engines by direct and reverse cranksmethod.

4 Explain Primary and Secondary Unbalanced Force Due to ReciprocatingMasses

5 A statically balanced system need not to be dynamically balanced always. Justify the statement.

6 Explain Balancing of 4 Cylinder Inline Engine Analytically and Graphically

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The cranks and connecting rods of a four cylinder in-line engine running at 2000 rpm are 50mm and 200mm each respectively. The cylinders are spaced 0.2m apart. If the cylinders are numbered 1 to 4 in sequence from one end, the cranks appear at intervals of 90º in an end view in the order 1-4-2-3.The reciprocating mass for each cylinder is 2kg. Determine (i) unbalanced primary and secondary forces, (ii) unbalanced primary and secondary couples with reference to central plane of the engine

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A V-twin engine has the cylinder axes at right angles and connecting rod operate a common crank. The reciprocating mass per cylinder is 10 Kg and crank radius is 80mm.The length of connecting rod is 0.4m. Show that the engine may be balanced for primary forces by means of a revolving balance mass. If the engine speed is 600 rpm, what is the value of maximum resultant secondary force?

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The reciprocating mass per cylinder in a 60˚ V- twin engine is 1.5 kg. The stroke is10 cm for each cylinder. If the engine runs at 1800 rpm, determine the maximumand minimum value of the primary forces and out the corresponding crankposition.

10

The cranks and connecting rods of a 4-cylinder in-line engine running at1800 r.p.m. are 60 mm and 240 mm each respectively and the cylindersare spaced 150 mm apart. The reciprocating mass corresponding to eachcylinder is 10kg. If the cylinders are numbered 1 to 4 in sequence fromone end, the cranks appear at intervals of 90° in an end view in the order1-4-2-3. Determine: (I) Unbalanced primary and secondary forces, if any,and (ii) Unbalanced primary and secondary couples with reference tocentral plane of the engine.

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For a twin V-engine the cylinder centerlines are set at 90o. The mass ofreciprocating parts per cylinder is 2.5 kg. Length of crank is 100 mm andlength of connecting rod is 400 mm. determine the primary andsecondary unbalanced forces when the crank bisects the lines of cylinder center-lines. The engine runs at 1000 rpm.

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A four cylinder engine has the two outer cranks at 1200 to each other and their reciprocating masses are each 400 kg. The distance between the planes of rotation of adjacent cranks are 0.4 m, 0.7 m and 0.5 m. Find the reciprocating mass and the relative angular position for each of the inner cranks, if the engine is to be in complete primary balance. Also find the maximum unbalanced secondary force, if the length of each crank is 350 mm, the length of each connecting rod 1.7m and the engine speed is 500 r.p.m.

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The cylinder axes of a V-engine are at right angles to each other. The weight of each piston is 2 kg and of each connecting rod is 2.8 kg. The weight of the rotating parts like crank webs and the crank pin is 1.8 kg. The connecting rod is 0.4 m long and its centre of mass is 0.1 m from the crank pin centre. The stroke of the piston is 160 mm. Show that the engine can be balanced for the revolving and the primary force by a revolving counter mass. Also, find the magnitude and the position if its centre of mass from the crankshaft centre is 100 mm. What is the value of the resultant secondary force if the speed is 840 rpm?

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A five cylinder in-line engine running at 750 rpm has successive cranks 144° apart, the distance between the cylinder centre lines being 375 mm. The piston stroke is 225 mm and the ratio of the connecting rod to the crank is 4. Examine the engine for balance of primary and secondary forces and couples. Find the maximum values of these and the position of the central crank at which these maximum values occur. The reciprocating mass for each cylinder is 15 kg

15

The cranks and connecting rods of a 4-cylinder in-line engine running at 1800 r.p.m. are 60 mm and 240 mm each respectively and the cylinders are spaced 150 mm apart. If the cylinders are numbered 1 to 4 in sequence from one end, the cranks appear at intervals of 90° in an end view in the order 1-4-2-3. The reciprocating mass corresponding to each cylinder is 1.5 kg. Determine : (i)Unbalanced primary and secondary forces, if any, and (ii) Unbalanced primary and secondary couples with reference to central plane of the engine

16

A twin V-engine has the cylinder center lines at 90o and the connecting rods operate a common crank. The mass of reciprocating parts per cylinder is 10 kg and the crank radius is 75 mm. The length of connecting rod is 300 mm. Show that the engine may be balanced for primary forces by means of a revolving balance mass. If the engine speed is 500 rpm, what is the value of maximum resultant secondary force?

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ASSIGNMENT -3 Introduction to Mechanical Vibration

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ASSIGNMENT -4 Undamped Free Vibration

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ASSIGNMENT -5 Vibration of single Degree of Freedom

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ASSIGNMENT -6 Vibration isolation & Transmissibility

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ASSIGNMENT -7 Whirling of Shaft

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ASSIGNMENT -8 Vibration of torsionally equivalent shaft and gear system

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ASSIGNMENT -9 Vibration of Continuous System

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Laxmi Institute of Technology , Sarigam Approved by AICTE, New Delhi; Affiliated to Gujarat Technological

University, Ahmedabad Academic Year 2018-19

Centre Code: 086 Examination : Mid Sem-I Branch: Automobile Semester: VI Sub Code: 2161901 Sub: DYNAMICS OF MACHINERY Date: 01/02/2019

Time: 9:00 am to 10:00 am Marks: 20

Q.1

A) Derive an expression for natural frequency of cantilever beam subjected to point load at the end. B) List different types of dampings. Explain any one in detail.

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Q-2 A vertical spring mass system has a mass of 0.5 kg and an initial deflection of 0.2 cm. find the spring stiffness and the natural frequency of the system. Also Define springs in series and parallel.

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OR Q-2 The mass 'm' is hanging from a chord attached to the circular homogeneous disc of mass 'M'

and radius 'R' as shown in Figure-1. The disc is restrained from rotating by a spring attached at radius 'r' from the centre. If the mass is displaced downwards from rest position, determine the frequency of oscillations.

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Q-3 In case of dynamic balancing system, minimum two balancing masses are required for the balancing of the system. Justify

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Q-3 Discuss how a single revolving mass is balanced by two masses revolving in different planes. Any one case.

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Q-4 A shaft carries five masses P, Q, R, S and T which revolve at the same radius in planes which are equidistant from one another. The magnitude of the masses in planes P, R and S are 50 kg, 40 kg and 80 kg respectively. The angle between P and R is 90° and that between P and S is 225°. Determine the magnitude of the masses in planes Q and T and their positions to put the shaft in complete rotating balance.

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