Contents i SYLLABUS osmania university UNIT - I CHAPTER - 1 : STATIC TIC FORCE ANALYSIS Force Analysis of Four-Bar and Slider Crank Mechanisms. CHAPTER - 2 : DYNAMIC FORCE ANALYSIS Force Analysis of Four-Bar and Slider Crank Mechanisms, Study of Dynamically Equivalent System, Inertia Forces on Connecting Rod. CHAPTER - 3 : GYROSCOPE Gyroscopic Couple, Gyroscopic Effects in Vehicles. UNIT - II CHAPTER - 4 : GOVERNORS Classification of Governors, Watt, Porter, Hartnell and Hartung Governors, Controlling Force, Stability, Isochronism, Sensitivity, Power and Effort of Governors. CHAPTER - 5 : FLYWHEELS Functions, Differences between Flywheel and Governor, Turning Moment Diagrams, Flywheel Analysis for I.C. Engines and Presses. UNIT - III CHAPTER - 6 : FORCES Forces on Bearings Due to Rotating Shaft Carrying Several Masses in Several Planes, Determination of Balance Masses from the Forces on the Bearings, Shaking Forces in Single Cylinder Engine, Partial Balancing of Reciprocating Engine, Balancing of Two cylinder Locomotive Engine, Balancing of Multi Cylinder In-line Engines, Balancing of Radial Engines by Direct and Reverse Cranks Method.
ii Contents UNIT - IV CHAPTER - 7 : VIBRATIONS Vibrations of Single Degree Freedom System (Axial, Transverse and Torsional), Equivalent System of Combination of Springs, Stepped Shaft, Whirling Speed of Shafts. CHAPTER - 8 : DAMPED VIBRATIONS Types of Damping, Vibrations With Viscous Damping. CHAPTER - 9 : FORCED VIBRATIONS Vibrations Wtih Harmonically Applied Force With Viscous Dampling, Dynamic Magnifier, Resonance, Vibration Isolation and Transmissibility. UNIT - V CHAPTER - 10 : TORSION Torsional Vibrations of Two rotor, Three Rotor and Geared Systems, Natural Frequencies of Two Degree Freedom Systems, Modes of Vibration, Approximate Methods for Determining Natural Frequencies, Dunkerley s Method, Rayleigh s Method and Holzer s Method for Multi Rotor System.
Contents iii dynamics of machines FOR b.e. (o.u) Iii year i semester (COMMON TO MECHANICAL / PRODUCTION ENGINEERING) CONTENTS UNIT - I [CH.. - 1] ] [ST STATIC TIC FORCE ANALYSIS YSIS]... 1.1-1.24 1.1 MECHANISMS... 1.2 1.1.1 Machine... 1.2 1.1.2 Theory of Machines... 1.2 1.1.3 Branches of Theory of Machines... 1.3 1.1.4 Scope of Theory of Machines... 1.4 1.1.5 Structure... 1.4 1.1.5.1 Difference between Structure and Machine... 1.4 1.1.6 Element... 1.5 1.1.7 Link and Classification s s... 1.5 1.2 FORCES... 1.6 1.2.1 Types of Forces... 1.6 1.2.2 Static Force Analysis... 1.6 1.2.3 Static Equilibrium... 1.6 1.2.4 Equilibrium of Forces... 1.7 1.2.5 Force Convention... 1.9 1.2.6 Free Body Diagram and Principle of Superposition... 1.9 1.2.7 Principle of Virtual Work... 1.11 1.2.7.1 Illustrated Problems on Principle of Virtual Work... 1.12
iv Contents 1.3 STATIC TIC FORCE ANALYSIS OF FOUR-BAR MECHANISM... 1.16 1.3.1 Types of Forces in Four our-bar Mechanism... 1.16 1.3.1.1 One Known Force... 1.17 1.3.1.2 Two Known Force orce... 1.18 1.4 STATIC TIC FORCE ANALYSIS OF SLIDER CRANK MECHANISM... 1.20 1.4.1 Types of Forces in Slider-Crank Mechanism... 1.21 1.4.1.1 One Known Force... 1.21 1.4.1.2 Two Known Force orce... 1.22 UNIT - I [CH.. - 2] ] [DYNAMIC FORCE ANALYSIS YSIS]... 1.25-1.40 2.1 DYNAMIC FORCE ANALYSIS... 1.26 2.2 D ALEMBERTS PRINCIPLE... 1.26 2.3 DYNAMIC FORCE ANALYSIS FOR FOUR-BAR MECHANISM... 1.27 2.4 DYNAMIC FORCE ANALYSIS FOR SLIDER CRANK MECHANISM... 1.32 2.5 DYNAMICALLY Y EQUIVALENT SYSTEM / KINEMATICALL TICALLY EQUIVALENT SYSTEM... 1.34 2.5.1 Illustrated Problem on Dynamically Equivalent system... 1.36 2.6 INERTIA FORCES ON CONNECTING ROD... 1.37 UNIT - I [CH. - 3] ] [GYROSCOPE GYROSCOPE]... 1.41-1.104 3.1 INTRODUCTION TO O GYROSCOPE... 1.42 3.1.1 Defintions of Gyroscope... 1.42 3.2 GYROSCOPIC COUPLE... 1.43 3.3 GYROSCOPIC EFFECT IN VEHICLES... 1.44 3.3.1 Aeroplanes... 1.44 3.3.1.1 Illustrated Problems on Gyroscopic Effect on Aeroplanes... 1.49 3.3.2 Naval Ships... 1.55 3.3.2.1 Illustrated Problems on Naval Ships... 1.62
Contents v 3.3.3 Two wo-wheeler Wheeler s... 1.72 3.3.3.1 Illustrated Problems on Two wo-wheeler... 1.77 3.3.4 Stability of Automobile/Four our-wheeler Wheeler s... 1.79 3.4 STABILITY OF A FOUR WHEEL DRIVE MOVING IN A CURVED PATH (COMBINED GYROSCOPIC EFFECT FOR BOTH WHEEL AND ENGINE)... 1.84 3.5 ILLUSTRA USTRATED TED PROBLEMS ON FOUR-WHEEL VEHICLES... 1.88 Short Questions and Answers... 1.102-1.104 UNIT - II [CH. H. - 4] ] [GOVERNORS GOVERNORS]... 2.1-2.48 4.1 GOVERNOR S... 2.2 4.2 CLASSIFICATION OF GOVERNORS... 2.2 4.2.1 Centrifugal Governor... 2.3 4.2.1.1 Pendulum Type Simple Watt att Governor/Concial Governor... 2.4 4.2.1.1.1 Illustrated Problems on Watt att Governor... 2.6 4.2.1.2 Loaded Governor... 2.7 4.2.1.3 Porter Governor... 2.8 4.2.1.3.1 Illustrated Problems on Porter Governor... 2.10 4.2.1.4 Proell Governor... 2.14 4.2.1.4.1 Illustrated Problems on Proell Governor... 2.16 4.2.1.5 Hartnell Governor... 2.18 4.2.1.5.1 Illustrated Problems on Hartnell Governor... 2.21 4.2.1.6 Wilson-Hartnell Governor / Radial Spring Governor... 2.27 4.2.1.6.1 Illustrated Problems on Wilson-Hartnell Governor... 2.30 4.2.1.7 Governor with Gravity and Spring Control... 2.31 4.2.1.7.1 Illustrated Problems on Gravity and Spring Control Governor... 2.32
vi Contents 4.2.1.8 Hartung Governor... 2.34 4.2.1.8.1 Illustrated Problems on Hartung Governor... 2.35 4.2.1.9 Pickering Governor... 2.38 4.2.1.9.1 Illustrated Problems on Pickering Governor... 2.40 4.2.2 Inertia Governor... 2.41 4.3 CONTROLLING FORCE... 2.42 4.3.1 Controlling Force Diagram for Hartnell Governor (or) Condition For Stability of Spring Controlled Governor... 2.43 4.4 HUNTING... 2.44 4.5 ISOCHRONISM... 2.44 4.6 SENSITIVITY... 2.45 4.7 POWER AND EFFORT OF GOVERNOR S... 2.45 4.7.1 Effort and Power of Porter Governor... 2.46 4.8 STABILITY... 2.48 4.9 Quality of a Governor... 2.48 UNIT - II [CH.. - 5] ] [FL FLYWHEELS YWHEELS]... 2.49-2.88 5.1 FLYWHEEL YWHEEL S S... 2.50 5.1.1 Function unction s s of Flywheel s... 2.50 5.1.2 Types of Flywheels... 2.50 5.1.3 Size of Flywheels / Hoop Stress Developed in a Flywheel... 2.52 5.1.4 Difference between Flywheel and Governor... 2.54 5.2 TURNING MOMENT DIAGRAM (TMD) / CRANK-EFFOR -EFFORT DIAGRAM... 2.55 5.2.1 Flywheel Analysis for IC Engines... 2.56 5.2.1.1 Turning Moment Diagram for Single Cylinder Double Acting Steam Engine... 2.56 5.2.1.2 Turning Moment Diagram for Four-Stroke Cycle / Internal Combustion Engine... 2.57
Contents vii 5.2.1.3 Turning Moment Diagram for Multi-Cylinder Engine... 2.58 5.2.1.4 Fluctuation of Energy and Fluctuation of Speed... 2.59 5.2.1.4.1 Co-Efficient of Fluctuation of Energy... 2.60 5.2.1.4.2 Co-Efficient of Fluctuation of Speed... 2.61 5.2.1.4.3 Energy Stored in Flywheel... 2.62 5.2.2 Illustrated Problems on Turning Moment Diagram (TMD) and Internal Combustion (IC) Engines... 2.64 5.3 FLYWHEEL ANALYSIS FOR PRESSES (PUNCHING PRESS)... 2.79 5.3.1 Illustrated Problems on Presses (Punching Press)... 2.81 Short Questions and Answers... 2.85-2.88 UNIT - III [CH. - 6] ] [FORCES FORCES]... 3.1-3.80 6.1 FORCES... 3.2 6.2 CONCEPT OF BALANCING... 3.2 6.2.1 Need for Balancing... 3.2 6.2.2 Static Balancing... 3.2 6.2.3 Dynamic Balancing... 3.3 6.3 BALANCING OF ROTATING TING MASSES... 3.3 6.3.1 Determination of Balance Masses From Forces on Bearing s... 3.3 6.3.1.1 Balancing as Well ell as Distributing Mass Rotating in the Same Plane... 3.3 6.3.1.2 Balancing as Well as Distributing Mass Rotating in the Different Plane... 3.4 6.3.2 Balancing of Several Rotating Masses... 3.7 6.3.2.1 Balancing of Several Rotating Masses in Same Plane... 3.7 6.3.2.1.1 Graphical Method... 3.8 6.3.2.1.2 Analytical Method... 3.8
viii Contents 6.3.2.2 Forces on Bearings Due to Rotating Shaft Carrying Several Masses in Several Planes / Dalby s Method... 3.9 6.3.3 Illustrated Problems on Balancing of Rotating Mass... 3.11 6.4 BALANCING OF RECIPROCATING MASSES... 3.26 6.4.1 Partial Balancing of Unbalanced Primary Force in a Reciprocating Engine... 3.28 6.4.2 Shaking Forces in Single Cylinder Engine... 3.30 6.4.3 Illustrated Problems on Partial Balancing of Reciprocating Engine... 3.30 6.5 BALANCING OF TWO-CYLINDER LOCOMOTIVE ENGINES... 3.35 6.5.1 Effects of Partial Balancing in Locomotives... 3.36 6.5.1.1 Variation of Tractive Force orce... 3.36 6.5.1.2 Swaying Couple... 3.38 6.5.1.3 Hammer Blow... 3.39 6.5.1.4 Illustrated Problems on Balancing of Locomotive Engines... 3.40 6.6 SECONDARY BALANCING... 3.46 6.7 BALANCING OF MULTI- TI-CYLINDER IN-LINE ENGINES... 3.47 6.7.1 In-Line Two wo-cylinder Engine... 3.48 6.7.2 In-Line Four-Stroke Four-cylinder Engine... 3.49 6.7.3 Illustrated Problems on Balancing of In-line Engines... 3.50 6.8 BALANCING OF RADIAL ENGINES/BALANCING OF V-ENGINES... 3.58 6.8.1 Illustrated Problems on Radial / V-Engines... 3.60 6.8.2 Balancing of Radial Engines by Direct and Reverse Crank Method... 3.66 6.8.2.1 Illustrated Problems on Direct and Reverse Crank Method... 3.68 Short Questions and Answers... 3.77-3.80
Contents ix UNIT - IV [CH. H. - 7 [VIBRATIONS VIBRATIONS]... 4.1-4.28 7.1 VIBRATIONS... 4.2 7.1.1 Basic Definitions... 4.2 7.1.2 Causes of Vibrations... 4.3 7.1.3 Harmul Effects of Vibrations... 4.3 7.2 DEGREE OF FREEDOM... 4.4 7.2.1 Single Degree of Freedom... 4.4 7.2.2 Two wo-degree Of Freedom... 4.4 7.3 CLASSIFICATION OF VIBRATIONS... 4.5 7.3.1 Vibrations According to Actuating Force on Body... 4.5 7.3.1.1 Free / Natural Vibrations (According Actuating Force)... 4.5 7.3.1.1.1 Damped Vibrations... 4.6 7.3.1.1.2 Undamped Vibrations... 4.6 7.3.1.2 Forced Vibrations (According to Actuating Force)... 4.6 7.3.2 Vibration s s of Single Degree Freedom System (Axial, Transverse and Torsional) / Vibrations According to Stresses in Supporting Medium / According to Motion Withrespect to the Axis... 4.6 7.3.2.1 Longitudinal Vibrations / Axial Vibrations... 4.6 7.3.2.2 Transverse Vibrations... 4.7 7.3.2.3 Torsional Vibrations... 4.8 7.4 NATURAL FREQUENCY OF VIBRATIONS... 4.8 7.4.1 Natural Frequency of Free Longitudinal Vibrations / Equilibrium Method... 4.8 7.4.1.1 Natural Frequency of Free Transverse Vibrations... 4.10 7.4.1.2 Equivalent System of Combination of Springs... 4.12 7.4.1.2.1 Springs in Series... 4.12 7.4.1.2.2 Springs in Parallel arallel... 4.13 7.4.1.3 Illustrated Problems on Natural Frequency of Vibrations... 4.14
x Contents 7.4.2 Energy Method... 4.20 7.4.3 Rayleigh ayleigh s Method... 4.21 7.5 INERTIA EFFECT OF MASS OF SPRING... 4.21 7.6 STEPPED SHAFT... 4.23 7.7 WHIRLING SPEED OF SHAFTS... 4.24 7.7.1 Illustrated Problems on Whirling / Critical Speed of Shafts... 4.26 UNIT - IV [CH. H. - 8] ] [DAMPED VIBRATIONS]... 4.29-4.62 8.1 DAMPED VIBRATIONS... 4.30 8.2 TYPES / CLASSIFICATION OF DAMPING... 4.30 8.2.1 Viscous Damping... 4.30 8.2.1.1 Energy Dissipation in Viscous Damping... 4.32 8.2.1.2 Eddy Current Damping... 4.33 8.2.2 Coulomb Damping... 4.34 8.2.3 Structural Damping... 4.36 8.2.4 Non-Linear,, Slip / Interfacial Damping... 4.38 8.3 DIFFERENTIAL EQUATIONS OF DAMPED VIBRATIONS... 4.38 8.3.1 Vibrations With Viscous Damping / Single Degree of Freedom With ith Viscous Damping... 4.38 8.3.2 Critical Damping Constant and Damping Ratio... 4.40 8.3.2.1 Over Damped System... 4.41 8.3.2.2 Critically Damped System... 4.43 8.3.2.3 Under Damped System... 4.44 8.3.2.4 Use of Critical Damped System... 4.46 8.4 LOGARITHMIC DECREMENT... 4.46 8.4.1 Vibrational Energy and Logarithmic Decrement... 4.48 8.5 ILLUSTRA USTRATED TED PROBLEMS ON DAMPED VIBRATIONS TIONS... 4.49
Contents xi UNIT - IV [CH. H. - 9] ] [FORCED VIBRATIONS]... 4.63-4.96 9.1 FORCED VIBRATIONS... 4.64 9.2 VIBRATIONS WITH HARMONICALLY APPLIED FORCE WITH VISCOUS DAMPING / HARMONIC FORCE... 4.64 9.2.1 Total Response... 4.68 9.2.2 Characteristic Curves... 4.68 9.2.3 Variation of Frequency Ratio ω/ω 4.69 ω/ω n... 4.69 9.3 SUPPORT MOTION TION... 4.71 9.3.1 Absolute Motion... 4.71 9.3.2 Relative Motion... 4.75 9.4 DYNAMIC MAGNIFIER (OR) MAGNIFICA GNIFICATION FACT CTOR OR : RESONANCE... 4.76 9.5 VIBRATION ISOLATION AND TRANSMISSIBILITY... 4.78 9.6 ILLUSTRA USTRATED TED PROBLEMS ON FORCED VIBRATIONS... 4.80 Short Questions and Answers... 4.92-4.96 UNIT - V [CH. - 10] ] [TORSION TORSION]... 5.1-5.44 10.1 TWO-DEGREE OF FREEDOM... 5.2 10.2 FREE TORSIONAL VIBRATIONS OF SINGLE-RO -ROTOR OR SYSTEM... 5.2 10.2.1 Inertia Effect of Mass of Shaft on Torsional Vibrations... 5.4 10.3 TORSIONAL VARIABLES... 5.5 10.3.1 Free Torsional Vibrations of Two wo-r -Rotor System... 5.5 10.3.2 Free Torsional Vibrations of Three-R -Rotor System... 5.7 10.3.2.1 Torsionally Equivalent Shaft... 5.9 10.3.3 Free Torsional Vibrations of Geared System... 5.12 10.3.4 Illustrated Problems on Free Torsional Vibrations of One, Two, Three Rotor and Geared System... 5.14
xii Contents 10.4 MODES OF VIBRATION... 5.22 10.4.1 Principle Mode of Vibration... 5.22 10.4.1.1 Illustrated Problems on Modes of Vibrations... 5.28 10.4.2 Combined Rectilinear and Angular Modes... 5.32 10.4.2.1 Illustrated Problems on Combined and Angular Modes... 5.34 10.5 APPROXIMA XIMATE METHODS FOR DETERMINING NATURAL Frequencies for Multi-rotor System... 5.35 10.5.1 Dunkerley s Method... 5.35 10.5.2 Rayleigh ayleigh s s Method... 5.37 10.5.2.1 Illustrated Problems on Rayleigh ayleigh s s Method... 5.39 10.5.3 Holzer s s Method... 5.40 Short Questions and Answers... 5.43-5.44 LATEST UNIVERSITY QUESTION PAPER WITH SOLUTIONS [Nov./Dec. - 2012] [Main]... QP.1 - QP.12 [June - 2012] [Supplementary]... QP.13 - QP.26 PREVIOUS UNIVERSITY QUESTION PAPERS [December - 2011] [Main]... QP.27 - QP.28 [June/July - 2011] [Supplementary]... QP.29 - QP.31 [December - 2010] [Main]... QP.32 - QP.34 [July - 2010] [Supplementary]... QP.35 - QP.36 [November/December - 2009] [Main]... QP.37 - QP.38 [May/June - 2009] [Supplementary]... QP.39 - QP.40 [November/December - 2008] [Main]... QP.41 - QP.42