Fall, Even Years

Credit Hours: 3-0-3
Prerequisites: Graduate standing in engineering or related discipline
Catalog Description: Analysis and design of shafts for rotating machinery. Torsional vibration, synchronous and nonsynchronous whirl, stability, gyroscopic effects, hydrodynamic bearings, hysteresis, squeeze film dampers, and balancing.
Textbooks: J. S. Rao, Rotor Dynamics, 2nd Edition, Khaza, 1992.
Instructors: Itzhak Green
References: J. S. Rao, Rotor Dynamics, Wiley, 1991
F. M. Dimentberg, Flexural Vibrations of Rotating Shafts, Butterworths, 1961
R. N. Arnold and L. Maunder, Gyrodynamics and Its Engineering Applications, Academic Press, 1961
Goals: Rotating shafts are employed in industrial machines such as steam and gas turbines, turbogenerators, internal combustion engines, reciprocating and centrifugal compressors for power transmission. On account of the ever increasing demand for power and high speed transportation, the rotors of these machines are made extremely flexible, which makes the study of vibratory motion an essential part of design. The shafting of these machine installations is subjected to torsional and bending vibration and possibly unstable operation. This course is concerned with the dynamic analysis of rotors in rotating and reciprocating machinery.
Prerequisites by topics: Undergraduate fluid mechanics, solid mechanics, math, computing
  • Introduction to Gyroscopic Motion
  • Torsional Vibration Analysis
    • Undamped and damped natural frequencies
    • Forced response for steady and unsteady excitation
    • Numerical computation (finite elements, transfer matrix)
  • Bending Critical Speeds of Simple Shafts
    • Whirling of an unbalanced simple elastic rotor
    • Simple shafts with several disks
    • Transfer matrix analysis for bending critical speeds
  • Gyroscopic Effects
    • Gyroscopics of a spinning disk
    • Synchronous whirl of an overhung rotor
    • Nonsynchronous whirl
  • Fluid Film Bearings
    • Steady state characteristics of plain cylindrical hydrodynamic bearings
    • Stiffness and damping coefficients of a journal bearings
  • Rotors Mounted on Fluid Film Bearings
    • A simple rotor in fluid film bearings
    • Transfer matrix analysis of rotors in fluid film bearings
  • Instability Due to Fluid Film Forces and Hysteresis
    • Instability of rotors mounted on fluid film bearings
    • Rigid rotor instability
    • Instability of a flexible rotor
    • Internal hysteresis of shafts
  • Rotor Balancing
    • Concepts and principles
    • Single-plane balancing
    • Two-plane balancing
    • Flexible rotor balancing
    • Shaft runout
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