FUNDAMENTALS OF VIBRATION 2.0 INTRODUCTION

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2 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.

3 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.

4 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.

5 In terms of the operation of the machine, the vibration amplitude is the indicator used to determine how bad or good the operation of the machine may be. The greater the amplitude, the more severe the vibration DISPLACEMENT (PEAK TO PEAK) The total distance traveled by the vibrating part, from one extreme limit of travel to the other extreme limit of travel is referred to as the 'peak-to-peak displacement'. In Metric units, the peak-to-peak vibration displacement is usually expressed in microns, where one micron equals one-thousandth of a millimeter (0.001-mm). Peak-to-peak vibration displacement is sometimes expressed in mils, where 1 mil equals one thousandth of an inch (0.001 inch) VELOCITY (PEAK) Since the vibrating weight shown in the figure.2.2 is moving, it miist be moving at some speed- However, the speed of the weight is constantly changing. At the top limit of the motion the speed is zero since the weight must come to a stop before it can go in the opposite direction. The speed or velocity is greatest as the weight passes through the neutral position. The velocity of the motion is definitely a characteristic of the vibration but since it is constantly changing throughout the cycle, the highest or 'peak' velocity is selected for measurement. In Metric units, vibration velocity is expressed in millimeters per second peak. Vibration velocity is expressed in terms of inches per second peak for English or imperial units VELOCITY (RMS) The ISO in its work to establish internationally acceptable- units for measurement of machinery vibration decided to adopt VELOCITY (RMS) (root mean square) as the standard unit of measurement. This was decided in an attempt to derive criteria, which would determine an effective value for the varying function of velocity. It should be noted that IRD Mechanalysis instruments may be calibrated to read in -terms of VELOCITY (PEAK) or VELOCITY (RMS) ACCELERATION In discussing vibration velocity, we pointed out tfiat the velocity of the part approaches zero at the extreme limits of travel. Of course, each time that the part comes

6 to a stop at the limit of travel, it must 'accelerate' to pick-up speed as it travels towards the other extreme limit of travel. Vibration acceleration is another important characteristic of vibration. Technically, acceleration is the rate of change of velocity. Referring to the motion plot, figure 2.2, the acceleration of the part is maximum at the extreme limit of travel where the velocity is zero point 'A'. As the velocity of the part increases, the acceleration decreases. At point 'B', (the neutral position) the velocity is maximum and the acceleration is zero. As the part passes through the neutral point, it must now 'decelerate' as it approaches the other extreme limit of travel. At point 'C', acceleration is at peak. Vibration acceleration is normally expressed in "g's" peak, where one is the acceleration produced by the force of gravity at the surface of the C2 earth. By international agreement, the value of cm/se equals C2 C2 inches/se also equals feet/se has been chosen as the standard acceleration due to gravity. 2.3 CONVERSION OF AMPLITUDES The displacement, velocity and acceleration of a vibration are directly related. If the peak-to-peak displacement and frequency of a vibration are known, the velocity of vibration can be found as follows: - V Peak = 52.3D ( F / 1000 ) X Where: - V Peak = vibration velocity (mm/sec) peak D = vibration displacement (microns) peak to peak F = vibration frequency (CPM Further to the above when it is required to calculate vibration acceleration, the following formula can be used. - G (Peak ) = 5.6 D ( F / 1000 ) 2 X.0001 Where: - G (Peak ) D F = Vibration acceleration = Vibration displacement (microns) (peak-to -peak) = Vibration frequency (CPM)

7 It is sometimes necessary to convert Metric measurement to Imperial, or the converse. To convert velocity or displacement measurement from Metric to Imperial: - Velocity (mm/sec) Velocity (inches/sec) = 25.4 Displacement (microns) Displacement (mils) = 25.4 From Imperial to Metric: - Velocity (mm/sec) = Velocity (inches/sec) X 25.4 Displacement (microns) = Displacement (mils) X DISPLACEMENT, VELOCITY OR ACCELERATION WHICH SHOULD WE USE? Since the amplitude of vibration can be measured in terms of displacement, velocity or acceleration, the obvious question is 'Which parameter should we use? Vibration amplitude readings taken for checking overall machinery condition indicate the severity of the vibration. But which is the best indicator of vibration severity: displacement, velocity or acceleration? To answer this question, consider what happens when a wire or piece of sheet metal is bent repeatedly back and forth. Eventually, this repeated bending causes the metal to fai'i by fatigue in the area of the bend. This is similar in many respects to the way a machine or machine component fail from the repeated cycles of flexing caused by excessive vibration. Of course, the time required to fail the wire or sheet metal can be reduced by: - 1. Increasing the amount of the bend (displacement). The further the metal is bent each time, the more likely it is to fail. 2. By, increasing the rate of bending (frequency). Obviously, the more times per minute the metal is flexed, the quicker it will fail. Thus the severity of this bending action is a function of both how far the metal is bent (displacement) and how fast the metal is bent (frequency). Vibration severity then appears to be a function of displacement and frequency.

8 However, since vibration velocity is also a function of displacement and frequency it is reasonable to conclude that a measure of vibration velocity is a direct measure of vibration severity. Through experience we have found this to be basically true. Vibration velocity provides the best overall indicator of machinery condition. Displacement and acceleration readings are sometimes used to measure vibration severity. However, when displacement or acceleration is used, it is also necessary to know the frequency of the vibration. Charts like those shown in figure.2.3 and figure. 2.4 are often used to cross-reference the displacement or acceleration with frequency to determine the level of severity. Note from figure 2.3 that a displacement of 25 microns occurring at a frequency of 1200 CPM is in the 'GOOD' range, however, the same displacement of 25 microns at a frequency of 20,000 CPM is in the 'VERY ROUGH' range. Note also, that the diagonal lines dividing the zones of severity are constant velocity lines. in other words, a velocity of 12.7 mms per second peak is in the 'ROUGH' range regardless of the frequency of the vibration. Referring to the chart, figure 2.4, we can note that an acceleration of 1.0 g at a frequency of 100,000 CPM is in the 'GOOD' region of the chart; however, 1.0 g at a frequency of 18,000 CPM is in the 'SLIGHTLY ROUGH' region. So the real significance of the characteristics of vibration lies in the fact that they are used to detect and describe the unwanted motion of a machine. Each of the characteristics of vibration tells us something significant about the vibration. Therefore, the characteristics might be considered to be symptoms used to diagnose inefficient operation or impending trouble in a machine.

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11 2.5 VIBRATION FREQUENCY Frequency is the number of complete cycle in unit time. From the figure 2.2, the amount of time required to complete one cycle of vibration is the period of If a period of one second is required to complete one cycle of vibration, then during one minute the cycle will be repeated 50 times or 50 cycles per minute (CPM). The measure of the number of cycle for a given interval of time is the frequency of vibration and usually expressed in cycles per second or Hertz (CPS or Hz) or cycles per minute (CPM). 2.6 VIBRATION PHASE Phase is defined as the position of a vibrating part at a given instant with reference to a fixed part or another vibrating part. By measuring the phase we can Compare one vibration with another Determine how one part is vibrating relative to another part Phase readings are normally expressed in degrees (00 to 3600) where one complete cycle of vibration equeals Phase angle of vibrations, like amplitude and frequency, is a useful parameter, for analysis of vibrations. Measurement of phase and its analysis can help in the diagnosis of a machinery problem. Figure 2.5 shows the phase diagram of a vibrating object relative to a fixed reference, which corresponds to the equilibrium position. The phase diagram gives the corresponding to any position 2,3... etc., as shown, as measured from a datum.. Figure.2.6 shows the displacement time diagrams, A and B, of two vibrating par't-s or objects.

12 Fig: 2.6 PHASE DIFFRERANCE BETWEEN TWO VIBRATING PARTS The two reach their peaks or zero values, at different instants. The time difference, being td, phase angle between the two vibrating objects is td X 3600, since the time period corresponds to a full cycle or a phase of 360'. In the case of a rotor, the phase angle gives the location of the rotor at any instant e.g. it defines the location of the heavy spot of the rotor at each measurement point relative to a fixed point and is useful for balancing.

13 The phase may be measured with a stroboscope, as shown in figure 2.7. This is shown for a rotor rotating at same speed. If the frequency of flash of the stroboscope equals the running speed, any mark on the rotor appears stationary and the reading against a fixed reference scale would give the phase difference. 2.7 VIBRATION SEVERITY Since vibration amplitude (displacement, velocity or acceleration) is a measure of the severity of the trouble in a machine, the next question may be; 'how much vibration is too much?' To answer this question, it is important to keep in mind that our objective should be to use vibration checks to detect trouble in its early stages for scheduled correction. The goal is not to find out how much vibration a machine will stand before failure, but to get a fair, warning of impending trouble so it can be eliminated before failure. Absolute vibration tolerance or limits for any given machine are not possi 'ble. That is, it is impossible to select a vibration limit which, if exceeded, wi ill result in immediate machinery failure. The development of mechanical failure is just far too,complex for such limits to exist. However, it would be impossible to effectivel utilise vibration as an indicator of machinery condition y unless some guidelines are available

14 and the years of experience of those familiar with machinery and machinery vibration have provided some realistic guidelines. The vibration velocity provides a direct measure of machinery condition for the, intermediate vibration frequencies (600 to 60,000 CPM). The velocity values in figure 2.3 and figure, 2.4 are offered as a guide for overall unaltered velocity readings. When vibration amplitude is measured in displacement or acceleration, the charts in figure 2.3 and figure 2.4 may be used as guides in selecting acceptable levels of machinery vibration. Displacement and acceleration measurements applied to these charts should be filtered readings only. The guidelines offered in the above figures apply io machinery such as motors, fans, blowers, pumps and general rotating machinery where vibration does not directly influence the quality of a finished product. Amplitude readings should be those taken on the bearings or structure of the machine. Of course, the vibration tolerances suggested in these references will not be applicable to all machines. For example, some machines such as hammer mills or rock and coal crushers will inherently have high levels of vibration. Therefore, the values selected using these guides should be used,' only so long as experience, maintenance records and history proves them to be valid. For machines such as gr' ders and other precision machine tools where vibration can affect the quality of a finished product, refer the 'Guide to Vibration Tolerance For Machine Tools' provided in Table 2.1. Applying vibration tolerances to machine tools is rather easy because they can be based on the machine's ability to produce a certain size or finish tolerance. The values shown in the table are the result of years of experience with vibration analysis of machine tools, and represent the vibration levels for which satisfactory parts have been produced. Of course, these values may vary depending on specific size and finish tolerances required. A comparison of the normal pattern of vibration on the machine and the quality of finish, and size control required would reveal what level of vibration is acceptable. The first time the quality of finish or size control deteriorates, an unacceptable vibration level would be indicated. The initial values selected from Table 2.1 can then be modified to the new, more realistic ones.

15 Another severity standard which is coming into increasing use is ISO 2372 (BS 4675) as given in Table 2.2. This standard differs somewhat to the general severity standards referred to as it seeks to establish classifications of various types of machinery. Annexure-A, which follows the standard, describes the machines covered in the classification. To use ISO 2372 it is first necessary to classify the machine. Next reading across the chart can correlate the severity of the machine condition. The severity of the machine condition is indicated by the letter A 5 B, C or D. Making the decision to correct a condition of vibration is often a very difficult one indeed, especially when it involves downtime of critical machinery. Therefore, when establishing acceptable levels of machinery vibration, e erience and factors such as safety, labour costs downtime costs and the importance of a machine's operation to. the company's profits must be considered. Table-2.1 TENTATIVE GUIDE TO VIBATION TOLERANCES FOR MACHINE TOOLS TYPE OF MACHINE Displacement of vibration as read with pickup on spindle bearing housing in the direction of cut. Grinders Tolerance Range Thread Grinder 0.25 to 1.5 microns Profile of Contour Grinder 0.76 to 2.0 microns Cylindrical Grinder 0.76 to 2.5 microns Surface Grinder (vertical reading) 0.76 to 5.0 microns Gardner or Besly Type 1.3 to 5.0 microns Centreless 1.0 to 2.5 microns Boring Machine 1.5 to 2.5 microns Lathes 5.0 to 25.Omicrons

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