CSU, Chico Spring 2009 Machine Vibration Measurement Hussam AliKhan Mechatronic Engineering Student California State University Chico, CA 95929-0789 April 8, 2009
Machine Vibration Measurement Abstract This paper presents the methods of measuring vibration of systems. During the development stage of machines, many factors are needed to be considered and taken into account and problems that arise due to miss-computation of parts that cause vibration in systems. Measurement is a critical component in machine design. The sole purpose of this measurement analysis is that if it is feasible to lower the risk of machine failures due to vibration. Many measuring fundamentals are used to measure the vibration of systems. The measurements are taken by transducers. Nomenclature A - The radius of the circular orbit traveled C - Damping coefficient F - Centrifugal force f n - Natural frequency in hertz g - Gravitational constant K - Stiffness a property of a solid body M - Mass of body r Radius by the point under examination t - Time in seconds W - Unbalance weight x(t) - Displacement of a point as a function of time ẋ(t) - Velocity of a point as a function of time ẍ(t) - Acceleration of a point as a function of time ω - Angular velocity ω 1 - Rotational speed system. These systems are used in the engineering, medical, or business fields. The continuing trend toward development of powerful machinery that operates at high speeds needs accurate measurement techniques before the deployment of machinery in the fields. Imagine a crawler dozer automobile equipped with a Pipe- Layer that can carry around thousands of pounds, suddenly fails. The damage that will be caused by the crawler dozer might include casualties, cost of repair, and the Introduction In the 21st century, most of the machinery we use is controlled by a unique project may suffer a delay. In order to minimize the risk of these forms of disasters, it is required that, at the development stage 1
every system should undergo some measurement and instrumental analysis. The measuring systems should be replicated under certain dimensions to produce data needed to draw meaningful conclusions (Wowk, [2]). These data can be used to minimize or eliminate the error factor, which is in our case the vibration. Vibration is a known phenomenon. There are obvious yet clear reasons why vibration occurs. The most common source of vibration is unbalance (VSC, [3]). Vibration analysis not only facilitates to pinpoint the machinery defects, it also locates problems as rotor imbalance and misalignment that create a great proportion of mechanical deficiencies (Corvib, [1]). If a control system contains excessive vibration, which will cause damages to the device, and accelerated wear, or even cause disastrous machinery failure. Therefore, it is vital to undergo vibration measurements, and it is important to examine vibration from a fundamental view to determine what is to be measured. Data Acquisition One of the main methods to measure vibration is to use transducers. Transducers are devices that are used in vibration analysis to convert mechanical energy into electrical energy (Wowk, [2]). In addition, these devices are sensors capable of detecting parameters such as displacement, velocity, and acceleration. Machine vibration is a combination of periodic functions that are essentially generated by a repeated disturbances or unbalanced forces (Mitchell, [11]). There are two basic types of unbalances, static and dynamic. Static unbalance is a condition where the only force acting on the object is gravity (VSC, [3]). Dynamic unbalance is a condition where the element rotating at its design speed will cause a centrifugal force that tends to displace the mass center of gravity 2
and results in a vibration (VSC, [3]). Therefore, the relationship between the machines operating speed is proportional to the vibration. The vibration increases, when machines operating speed is increased. Vibration Specialty Corporation states that the increase is many times the amount anticipated; the centrifugal force due to the unbalance varies as the square of the speed increases (VSC, [3]). The mathematical representation of the above statement is given by: FF = WW ωω gg 1 2 rr (1) Every machine has a different weight, radius, and rotation speed. Therefore, the above equation assists to define the centrifugal force acting on the machine. There are several devices that can be used to measure vibration of machines, but each device has its advantages and disadvantages. To determine the appropriate on whether the system is statically or dynamically unbalanced. In addition, frequency related parameters should be considered to accurately detect the vibration. As far as the unbalanced machinery vibration displacement is concerned the motion is time dependent and the displacement can be described by the equation: DDDDDDDDDDDDDDDDDDDDDDDD xx(tt) = AA sin ωωωω (2) In order to generate an accurate vibration measurement, it is vital to use a velocity or a acceleration transducer. Therefore, by taking the derivative of the earlier equation, it gives the velocity of the point as a function of time that can be described by the equation: VVVVVVVVVVVVVVVV ẋ(tt) = AA ω cos ωωωω (3) In the same way, the acceleration is obtained by differentiating the velocity equation, which gives as follows: AAAAAAAAAAAAAAAAAAAAAAAA ẍ(tt) = AA ωω 2 sin ωωωω (4) device to use for measurement is dependent 3
There are some other factors that shape machine vibration, such as stiffness, damping and mass. These factors if they are combined with the above equations, they form the equation of motion, a second-order differential equation that defines dynamic force as a function of time (PH2130 Mathematical, [5]): FF(tt) = KKKK + CCẋẋ + MMẍ (5) The total force generated by the three equations changes with respect to frequency. In addition, to analyze the vibration, it is essential to obtain a frequency chosen amplitude data. The frequency will clearly establish the possible causes and then the amplitude can be used to evaluate the vibration severity (Shreve, [10]). Vibration severity charts are formed by the preceding equation. The chart represents the tolerable levels of vibration in terms of displacement (IRD Mechanalysis, [4]). The chart is diagramed in Fig.1. 4
Fig.1. Vibration Severity Chart of General Machinery. (IRD Mechanalysis,[4]) The above chart characterizes the technique to choose a sensor, and the option of measuring displacement, velocity and acceleration, are both best accomplished by comparing the relative contributions to total force at the specific frequencies of interest (IRD Mechanalysis, [4]). The reason why acceleration is chosen to be measured is because acceleration is a physical characteristic of a 5
system, and the measurement of acceleration is used as an input into some types of control systems. In addition, the control system uses the measured acceleration to frequencies that are greater than the natural frequency of the pickup (Wowk, [2]). The resonance or natural frequency's equation is given by: correct the changing dynamic condition (Accelerometers and How They Work, [9]). ff nn = 1 2ππ kk mm (6) Device Measurement Technique There are many transducers that can measure vibration of machines. In order to precisely measure vibration, it is necessary to choose whether to measure velocity or acceleration of the machine application. If velocity is chosen to be measured, then Velocity pickup can be used, and velocity pickup is a transducer greatly used for monitoring the vibration of rotating machinery (Reliability Direct, [6]). This device converts the physical motion into an electrical signal that can further process along a frequency axis (Wowk, [2]). This device has a low natural frequency and they are designed to measure vibration The importance of the preceding equation is that the weight of the object and the stiffness affects the measuring data of vibration using the velocity pickup transducer. However, if acceleration is chosen to measured, then Accelerometer can be used, and accelerometer is a transducer that measures the acceleration of a device, and it measurers the vibration and acceleration due to gravity (Bob, [7]). When the accelerometer is active, the acceleration of an object is converted into a proportional analog signal (Vibra. [8]). The advantage of using accelerometer over other transducer is that this device can calculate acceleration and measure vibration and shock even if the 6
measuring machine application or building is at an angle. The accuracy of it is sharp enough to measure the smallest vibration caused by a musical instrument (Bob, [7]). [MACHINE VIBRATION MEASUREMENT] April 8, 2009 However, the accelerometer has to be mounted to the device that is being measured to give precise readings or it will not work. The Accelerometer has an advantage over the velocity pickup. Accelerometer is smaller and lighter than the velocity pickup. In addition, it has better sensitivity characteristics, and a wide useful frequency range (Wowk, [2]). The method to attach the accelerometer is critical in order to obtain accurate vibration data. Fig.2 shows one example of how to attach an Accelerometer to eliminate selected measurement errors. Fig.2 Accelerometer attached to Surface to eliminate measurement errors. (Lok Shun,[14]) There are many types of Accelerometers, such as Capacitive, Piezoelectric, Piezoresistive, Hall Effect, Magnetoresistive, Heat Transfer (Accelerometers and How They Work, [9]). There are two major types of accelerometer and they are high and low impedance accelerometer. However, the main difference between them is that the high impedance has a very high output from the charge of the piezoelectric crystal, and the low impedance has a FET circuit built into it in order to detect the charge generated by the piezoelectric crystal (Vibra. [8]). Fig.3 and Fig.4 depicts the High and Low impedance accelerometer. 7
Fig.3 High Impedance Accelerometer. (Vibra,[8]) Fig.5 Endevco Model 22 Accelerometer. (BJ, [16]) These transducers are expensive, and Fig.4 Low Impedance Accelerometer. (Vibra,[8]) In general, measuring data with Accelerometer is accurate as long as the frequency range is within the machines specification. Fig.5 shows a manufacturer accelerometer made by Endevco. there are other methods to analyze the vibration. One of these methods is using FFT Spectrum to generate the frequency on the axis. Fig.6 shows FFT (Fast Fourier Transform) spectrum data analyzed of vibration. 8
Fig.6 FFT Spectrum. (Wowk, [2]) Fig.6 mainly shows a data collected using FFT spectrum. This device does not analyze the data; however, it only generates the frequency that is being inputted to it. Therefore, to accurately measure vibration, it is important to use a transducer. Nonetheless, every machine that can be measured has a standard vibration limit. The vibration limits standard table is provided by Machine Dynamics, INC. This table aids engineers that are using different types of machines to measure vibration; they are capable of using transducers to check if the machine has exceeded the vibration limit. The Vibration limit table is provided in Table 1:
Table.1 Vibration Limits. (Wowk, [2])
Conclusion Machinery vibration is a imperative subject that needs further embracement by physicists and engineers. The measurement of unique systems assists to insure Health societies to be capable of advancing in curing patients. Furthermore, vibration measurement is vital to the development of new buildings and structures. These measurements increase the prevention of potential fatigue failures. Since the turn of the 21st century a revolution in developing machines has brought advancement to improve the way the world revolves around us. Solely given the fact, that machines are used in medical, and engineering fields, if a failure occurs, serious damages can be caused. Therefore, measuring machine application aids in minimizing the risk of causing catastrophic damages. References [1] Corvib, "Predictive Mechanical Maintenance Through Vibration Measurement." Vibration Monitoring. Corvib Precision Measurement Instruments. 6 Apr 2009 [2] Wowk, Victor. "A brief tutorial on machine vibration." Rio Rancho, NM. Machine Dynamics, INC. 6 Apr 2009 [3] Vibration Specialty, Corporation. "Predictive Mechanical Maintenance Through Vibration Measurement." Balance - When and Why. 2001. Vibration Specialty Corporation. 6 Apr 2009 [4] IRD Mechanalysis, INC, "General Machinery Vibration Severity Chart." 1964 International Research and Development Corporation. 5 Apr 2009 [5] Royal Hollywood University of London, "First and Second Order Linear Ordinary Differential Equations with Constant 11
Coefficients." Department of Physics. 6 Apr 2009 [6] Reliability Direct, "Velocity Transducer Installation." Velocity Transducer/Installation. Reliability Direct. 6 Apr 2009 [7] Jonathan, Bob "How does an Accelerometer Work?." How does an Accelerometer Work?. 30 Aug. 2006. EzineArticles.com. 6 Apr 2009 [8] Vibra Metrics, "Accelerometer User's Manual." Accelerometers (Vibration Sensors) and Vibration Monitoring Solutions. MISTRAS GROUP, INC. 6 Apr 2009 [9] Texas Instrument, "Accelerometers and How [11] Mitchell, John. "Vibration Analysis - Its Evolution and use in machinery health monitoring." Vibration Analysis - Its Evolution and use in machinery health monitoring. Endevco. 6 Apr 2009 [12] Tseng, Chyuan-Yow, Ting-Wei Shih, Jun-Tsun Lin, Ting-Wei Shih, and Jun-Tsun Lin. "Dynamic Balancing Scheme for Motor Armatures." Journal of Sound & Vibration, 304.1/2 (2007): 110-123. [13] Lok Shun, CHAN. "Vibration Measurements." Vibration Measurements. City University of Hong Kong. 6 Apr 2009 [14] Furman, BJ. "Accelerometer Specifications." Endevco model 22. 22 NOV 2005. San Jose State University. 6 Apr 2009 They Work,." Texas Instrument. 6 Apr 2009 [10] Shreve, Dennis. "Introduction to Vibration Technology." Introduction to Vibration Technology. NOV 1994. IRD Mechanalysis, INC. 6 Apr 2009 12