DYNAMICS OF MACHINERY

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GUJARAT TECHNOLOGICAL UNIVERSITY

MECHANICAL ENGINEERING

B.E. 6TH Semester

Subject Code: 2161901

DYNAMICS OF MACHINERY

  1. 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.
  2. Dynamics of Reciprocating Engines: (I) 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. (II) Multi cylinder Engine: Configuration; (III) Inline engines: Effect of phase angles, firing order and number of strokes; Shaking force and moments, inertia torque 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.
  3. Introduction to Mechanical Vibrations: Elements of simple harmonic motion, concept of natural frequency, type of vibrations, Basic elements and lumping parameters of a vibratory system, lumping of physical systems, Concept of Degree of Freedom (DOF). (I) Single Degree 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 excitation for various damping factors, Concept of vibration isolation, effect of base excitation. (II) Two Degree of Freedom System: Equation of motion and principal mode of vibration, torsional vibrations of two and three rotor system, torsionally equivalent shaft, geared system. (III) Multi degree of freedom systems and analysis (free vibrations): Concepts of normal mode vibrations, natural frequencies, mode shapes, nodes, Correct definition of natural frequency. (IV) Vibrations of Continuous System (free vibrations): Longitudinal vibrations of bar and rod: Equation of motion and solution, Lateral vibrations of beam: Equation of motion, initial and boundary conditions, solution. (V) Rotating unbalance: Whirling of shafts, Critical speed and its practical importance in design of shaft, Application of Dunkerley’s method and Rayleigh’s method for estimating the critical speed of shafts. (VI) Vibration Measurement: Introduction to vibration measurement and analysis devices: Vibrometer, velocity pickup, accelerometer, FFT analyzer.
  4. Cam Dynamics: Dynamic analysis of force-closed cam follower: Undamped and Damped response, Jump phenomenon: concept, effect of spring force and dead weights.

 

 

Balancing of Rotating Masses

1
Introduction to Balancing
2
Static and Dynamic Balancing
3
Study of Balancing
4
Balancing of Rotating Masses
5
Balancing of Masses Rotating in Single Plane
6
Balancing of Several Masses Rotating in Different Planes

Dynamics of Reciprocating Engines

1
Introduction and Definitions
2
D’Alembert’s Principle
3
Simple Harmonic Motion (S.H.M)
4
Radius of Gyration of Rigid Bodies (Compound Pendulum)
5
Dynamically & Kinematically Equivalent System
6
Correction Couple
7
Force Analysis in IC Engine Mechanism
8
Balancing of Reciprocating Masses
9
Balancing of Reciprocating Masses in Single Cylinder Engines
10
Balancing of Reciprocating Masses in Multicylinder Inline Engines
11
Concept of Direct and Reverse Cranks

Balancing of Locomotive and V Engines

1
Partial Balancing of Locomotive
2
Balancing of V-Engines
3
Balancing Machines

Introduction to Mechanical Vibrations

1
Introduction to Vibrations
2
Terminology and Basic Concepts
3
Elements of Vibratory System
4
Modeling of System
5
Equivalent Springs
6
Equivalent Dampers
7
Types of Vibrations

Undamped Free Vibrations

1
Introduction
2
Determination of Natural Frequency
3
Undamped Free Transverse Vibrations
4
Undamped Free Torsional Vibrations

Damped Free Vibrations

1
Introduction and types of Damping
2
Damped Free Vibrations with Viscous Damping
3
Logarithmic Decrement
4
Damped Free Torsional Vibrations
5
Free Vibrations with Coulomb or Dry Friction Damping

Forced Damped Vibrations

1
Introduction to Forced Vibration
2
Forced Damped Vibrations with Constant Harmonic Excitation

Forced Vibration with Rotating and Reciprocating Unbalance

1
Forced Vibration Due to Rotating Unbalance
2
Forced Vibrations Due to Reciprocating Unbalance
3
Forced Vibrations Due to Excitation of Support Instead of Mass

Vibration isolation and Transmissibility

1
Vibration Isolation
2
Vibration Transmissibility

Critical Speed of Shafts

1
Introduction to Two Degree of Freedom Systems
2
Free Undamped Longitudinal Vibrations of Two Degree of Freedom System
3
Other Example of Two Degree of Freedom System

Multi-degree Freedom Systems and Analysis

1
Multi-Degree of Freedom Systems
2
Equation of Motion (By using Newton’s Second Law)
3
Flexibility Influence Coefficient
4
Stiffness Influence Coefficient
5
Generalized Co-ordinates
6
Matrix Method
7
Eigen Values and Eigen Vectors
8
Langrange’s Equations
9
Approximate Methods
10
Holtzer’s Method
11
Stodola’s Method
12
Natural Frequency of Shaft Carrying Multiple Rotors

Vibration Analysis of Continuous System

1
Introduction
2
Boundary Conditions in Beams
3
Transverse Vibration of Strings (Wave Equations)
4
Solution of Wave Equation
5
Longitudinal Vibration of Beam
6
Torsional Vibration of Beam (Shafts)
7
Transverse Vibration of Beam
8
Approximate Solution Methods (Rayleigh’s Method)

Rotating Unbalance

1
Introduction
2
Critical Speed of Shaft Carrying Single Rotor (Without Damping)
3
Critical Speed of Shaft Carrying Single Rotor (With Damping)
4
Secondary Critical Speed
5
Critical Speed of Shaft Carrying Mutiple Rotors

Vibration Measurements

1
Introduction to Vibration Measurements
2
Vibration Measurements Process
3
Classification of Vibration Measuring Instruments
4
Vibrometers (Amplitude Measuring Instruments)
5
Velocity Pick-Ups (Velometers)
6
Acceleration Pick-Ups (Accelerometers)
7
Frequency Measuring Instruments
8
Measurement of Damping
9
Vibration Exciters
10
Introduction to FFT Spectrum Analyzer
11
Introduction to Vibration Monitoring (Condition Monitoring and Diagnosis) of Machines

Cams Dynamics

1
Introduction
2
Response of Undamped Cam Mechanisms (Analytical Method)
3
Cam–follower Response (Numerical Method)
4
Cam Synthesis (Numerical Method)
5
Jump and Cross-Over Shock
6
Spring Surge-Unbalance and Windup
5
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