Machine Dynamics

Syllabus

1. Engine Force Analysis (2 hours)
   1. Analytical method for velocity and acceleration of the piston and the connecting rod
   2. Forces on the reciprocating parts of an engine
   3. Equivalent dynamical system
   4. Analytical method for inertia torque
2. Turning Moment Diagram and Flywheel (2 hours)
   1. Turning moment diagram
   2. Fluctuation of energy and coefficient of fluctuation of energy
   3. Flywheel
   4. Coefficient of fluctuation of speed
   5. Energy stored in a flywheel and flywheel sizing
3. Gyroscopic Couple (4 hours)
   1. Precessional angular motion
   2. Gyroscopic couple
   3. Effect of gyroscopic couple on aeroplane
   4. Effect of gyroscopic couple on naval ship
   5. Stability of four wheel and two wheel vehicles
   6. Effect of gyroscopic couple on a disc fixed rigidly at a certain angle to a rotating shaft
4. Governors (4 hours)
   1. Function of a governor
   2. Terms used in governor
   3. Types of governors: Watt, Porter, Proell, Hartnell and Pickering governors
   4. Sensitiveness and stability of governors
5. Vibration of Single Degree of Freedom Systems (10 hours)
   1. Definition and effects of vibration, terms used in vibration, vibration analysis procedure
   2. Elements of a vibrating system
   3. Undamped vibration of single degree of freedom system
   4. Damped vibration of single degree of freedom system
   5. Forced harmonic response of single degree of freedom system with viscous damping
   6. Rotating unbalance
   7. Whirling of rotor-shaft systems
   8. Vibration isolation and force transmissibility
   9. Response to an external motion
   10. Response to multi-frequency and general periodic excitations
6. Vibration of Two Degree of Freedom Systems (6 hours)
   1. Undamped vibration of two degrees of freedom system, natural frequencies and mode shapes
   2. Damped vibration of two degrees of freedom system
   3. Forced harmonic vibration of two degrees of freedom system
   4. Tuned vibration absorber
7. Vibration of Multi Degree of Freedom Systems (6 hours)
   1. Equations of motion in matrix form
   2. Flexibility and stiffness matrices, reciprocity theorem
   3. Eigenvalues and eigenvectors, orthogonal properties of eigenvectors
   4. Modal analysis
8. Vibrations of Continuous Systems (4 hours)
   1. Differences between discrete and continuous systems
   2. Transverse vibration of strings
   3. Longitudinal vibration in bars
   4. Torsional vibration in circular shafts
   5. Transverse vibration in beams
9. Approximate Numerical Methods (3 hours)
   1. Rayleigh method for discrete and continuous system
   2. Dunkerley method
   3. Matrix iteration methods
10. Vibration Measurement and Condition Monitoring (4 hours)
    1. Vibration measurement instruments
    2. Accelerometers and sensors
    3. FFT basics
    4. Spectrum analysis
    5. Active vibration control
    6. Condition monitoring and fault diagnosis using vibration analysis

Practicals

1. Response of governors
2. Measurement of couple on motorized gyroscope during precession
3. Response of a spring mass system
4. Whirling of a rotating shaft and determination of critical speed
5. Measurement and analysis of machine vibration using an accelerometer

Evaluation

Final exam questions cover all chapters. Approximate marks distribution (total 60 marks over 45 hours):

1. Engine Force Analysis and Turning Moment Diagram and Flywheel: 5 marks
2. Gyroscopic Couple: 5 marks
3. Governors: 5 marks
4. Vibration of Single Degree of Freedom Systems: 12 marks
5. Vibration of Two Degree of Freedom Systems: 8 marks
6. Vibration of Multi Degree of Freedom Systems: 10 marks
7. Vibrations of Continuous Systems: 5 marks
8. Approximate Numerical Methods: 5 marks
9. Vibration Measurement and Condition Monitoring: 5 marks