Dynamics of machines-3
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This document discusses free vibration in mechanical systems. It defines free vibration as the vibrations of a system that is initially disturbed and then left to vibrate on its own without external forces. Key topics covered include degrees of freedom, natural frequency, types of damping, critical speeds of shafts, and causes of vibration such as unbalance and misalignment. Both undesirable effects and potential useful applications of vibrations are mentioned.
Dynamics of machines-3
- 2. Basic features of vibratory systems Degrees of freedom – single degree of freedom Free vibration– Equations of motion – Natural frequency – Types of Damping – Damped vibration Torsional vibration of shaft – Critical speeds of shafts – Torsional vibration – Two and three rotor torsional systems.
- 3. Is a branch of mechanics of machines which deals with the forces and their effects while acting upon the machine parts in motion (i.e) system changes with time. Machine Machine is a device using mechanical power and have several parts, each with a definite function and together performing a particular task.
- 4. Any motion which repeats itself after an interval of time is called vibration or oscillation or periodic motion. Free Vibration When a system is subjected to an initial disturbance and then left free to vibrate on its own, the resulting vibrations are referred to as free vibrations
- 5. Unbalance : The uneven distribution of mass in a rotating body contributes to the unbalance. Misalignment This is other major cause of vibration particularly in machines that are driven by motors or any other prime movers. Bent Shaft: A rotating shaft that is bent also produces the vibrating effect since it loses its rotation capability about its center.
- 6. Gears in the machine The gears in the machine always tend to produce vibration, mainly due to their meshing. Wind: Wind may cause the vibration in certain systems such as transmission and telephone lines under certain conditions Earthquakes: Is also cause vibrations and are greatly responsible for the failure of dams, buildings etc
- 7. a)Bad Effects: The presence of vibration in any mechanical system produces unwanted noise, high stresses, poor reliability, wear and premature failure of parts. Vibrations are a great source of human discomfort in the form of physical and mental strains. (b)Good Effects: A vibration does useful work in musical instruments, vibrating screens, relive pain in physiotherapy
- 8. Unbalance is its main cause, so balancing of parts is necessary. using shock absorbers. By removing the causes of vibration By resting the machinery on proper type of isolators using dynamic vibration absorbers. providing the screens (if noise is to be reduced)
- 9. (a)Time period (or)period of vibration: Tp It is the time taken by a vibrating body to repeat the motion itself. Time period is usually expressed in seconds. (b) Cycle: It is the motion completed in one time period. (c) Periodic motion: A motion which repeats itself after equal interval of time. (d)Amplitude (X) The maximum displacement of a vibrating body from the mean position. It is usually expressed in millimeter. (e) Frequency (f) The number of cycles completed in one second is called frequency
- 10. Vibrations may be classified according to (a) the actual force on the body (b) the stresses in the supporting medium (a) the actual force on the body 1.Free or natural vibration 2. Forced vibration Damped Undamped Damped Undamped
- 11. (b) according to the stresses in the supporting medium Longitudinal Transverse Torsional
- 13. When the particles of the shaft or disc moves parallel to the axis of the shaft, then the vibrations known as longitudinal vibrations. Transverse vibrations When the particles of the shaft or disc move approximately perpendicular to the axis of the shaft Torsional Vibrations When the particles of the shaft or disc move in a circle about the axis of the shaft, then the vibrations are known as torsional vibrations.
- 14. The minimum number of independent coordinates required to specify the motion of a system at any instant is known as D.O.F of the system. Zero degrees of freedom When a body is at rest, then no coordinate are required to specify the motion of the system. In other words, the body at rest is said to have zero degree of freedom
- 18. Infinite number of coordinates are required to specify the motion.
- 19. If a body moves or vibrates about a mean position such that its acceleration is always proportional to its distance from the mean position and is directed towards the mean position or equilibrium position.
- 20. Damping is the resistance to the motion of a vibrating body. The vibrations associated with this resistance are known as damped vibrations. Types of damping: (1) Viscous damping (2) Dry friction or coulomb damping (3) Solid damping or structural damping (4) Slip or interfacial damping.
- 21. The damping force per unit velocity is known as damping coefficient Damping factor: Damping factor can be defined as the ratio of actual damping coefficient to critical damping coefficient.
- 22. The speed at which resonance occurs is called critical speed of the shaft. In other words, the speed at which the shaft runs so that the additional deflection of the shaft from the axis of rotation becomes infinite is known as critical speed. The critical speed essentially depends on a) The eccentricity of the C.G of the rotating masses from the axis of rotation of the shaft b)Diameter of the disc c)Span (length) of the shaft d)Type of supports connections at its ends Causes of critical speed: a) Eccentric mountings. b) Bending due to self weight c) Non-Uniform distribution of rotor material