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Note for Machine Dynamics - MD By Ravichandran Rao

  • Machine Dynamics - MD
  • Note
  • West Bengal University of technology - WBUT
  • Mechanical Engineering
  • 4 Topics
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1. INTRODUCTION Everyone in the course of our daily life encounters the phenomenon of vl 'bration. The effect of vibration is not only physically unpleasant but may also weaken the structure. It must therefore be regarded as a most undesirable condition, which must be eliminated for both comfort and safety. On the contrary, the vibration is often useful and may be essential in some application. Occasionally, for example vibration can be used to unmix things; as in sieves and other sorting devices, for conveying grain from one place to another, concrete will flow far -more readily into the furthermost recesses when it is poured into shuttering if it is suitably vibrated. Also vibration has got application in medical practice. For instance, it is used to massage away patients unwanted bulges and for removal of kidney stones. Large sums of money are spent nowadays on the study of various forms of vibration. The subject of vibration has acquired considerable importance, with the increasing pace of industrial and technological developments in the world over there has been a phenomenal increase in the speed and power of industrial machines. All devices which have mass and elasticity are capable of vibrating, however, rigid, they might seem. Whether it is desired to use vibration as a tool for failure and maintenance prediction or for using vibration control measure to avoid discomfort and failure, it is necessary to have a proper understanding of the subject. -This course material is concerned with fundamentals of vibration, sources of vibration, measurement of vibration and vibration analysis of rotating machines. 2. FUNDAMENTALS OF VIBRATION 2.0 INTRODUCTION The study of vibration is concerned w' ith oscillatory motions of bodies and the forces associated with them. All bodies possessing mass and elasticity are capable of vibration. Thus most engineering machines and structures experience vibration to some degree. The effects of vibration depend on the magnitude , frequency and duration of the vibration. Also, some times the vibration of a system emits lot of noise, which is harmful from human point of view. 2

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2.1 WHAT IS VIBRATION Vibration is defined as the resp onse of an elastic system to a dynamic disturbance. There are two general classes of vibrations - free and forced. Free vibration takes place when a system oscillates under the action of forces inherent in the system itself, and when external impressed forces are absent. The system under free vibration will vibrate at one or more of its natural frequency, which is a property of dynamic system determined by its mass and stiffness distribution. Vibration that takes place under the excitation of external forces is called forced vibration. The simplest way to show vibration is to follow the motion of a weight suspended at the end of a spring as shown in figure 2. I. This is typical of all machines since, they too have weight and spring-like quality namely elasticity. Until a force is applied to the weight to cause it to move, we have no vibration. By applying an upward force, the weight would move upward, compressing the spring. If we release the weight, it would drop below its neutral position to some bottom limit of travel, where the spring would stop the weight. The weight would travel upward through the neutra position to tie top limit of motion, and then back again through the neutral position. This is vibration! This motion will dampen with time unless force is applied again. 3

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2.2 CHARACTERSTICS OF VIBRATION A lot can be learned about a machine's condition and mechanical problems by simply not'mg its vibration characteristics. Refem'ng to the weight suspended on a spring, we can study the detailed,characteristics of vibration by plotting the movement of the weight against time. This plot is shown in figure 2.2. The simplest form of vibration motion is simple harmonic motion. The motion of the weight from its neutral position, to the top limit of travel back through the neutral position to the bottom limit of travel, and its return to the neutral position, represents one cycle of motion. This one cycle of motion has all the characteristics needed to measure the vibration. Continued motion of the weight will simply be repeating these characteristics. When the instantaneous displacement of the mass is plotted against time, the motion takes sinusoidal form as shown in figure. Fig: 2.2 CHARACTERSICS OF VIBRATION As vibrations are movements of the machines around a rest point, they may be quantified in terms of' displacement, velocity or acceleration. These characteristics of vibration are measured to determine.the amount of severity of the vibration. The displacement, velocity or acceleration of a vibration is often 17eferred to as the 'amplitude' of the vibration. 4

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