By Robert B. McMillan
This e-book brings either a theoretical and functional figuring out of unbalance and misalignment in rotating gear. those stipulations account for the majority of issues of rotating gear encountered within the actual global. you will study the ways that vibration can be utilized to figure out the operational integrity of rotating equipment. you are going to achieve a transparent realizing of the relationships among numerous vibrational features and the linked forces generated in the working equipment whilst stipulations of unbalance and misalignment are current. Resonance and beat frequencies are distinct, besides assets and treatments. additionally coated are right inspection strategies, unmarried and twin aircraft tools of balancing rotating apparatus, the 3 circle approach to balancing gradual pace lovers, the complicated rim and face approach to precision alignment, and the opposite indicator approach to alignment.
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Extra info for Rotating Machinery - Practical Solutions to Unbalance and Misalignment
Sample text
What is the peak-to-peak displacement? If the impeller and shaft weigh 40 pounds, what is the force produced? 15 D = 60000 × . 24 pounds mass. 33 G = 3450 x . 4 × . 19 pounds force. Resonance and Beat Frequencies Chapter Resonance and Beat Frequencies RESONANCE T o have a better grip on operating equipment, it is necessary to understand resonance and beat frequencies. All machines and machine components act like a spring-mass system. They vibrate due to some external force acting upon them. The vibration can either be free vibration or forced vibration.
6) Note: Cycles per second will be expressed in Hertz (Hz) Xmax occurs @ Sin tt) = 1; Sin tt =1 occurs at, //2, 3//2, 5//2, 7// 2… (2n–1) //2 Figure 2-6. 8) Vmax occurs @ Cos (tt) = 1; Cos tt =1 occurs at, /, 2 /, 3 /, 4 /…n/ Where: Vmax = Maximum Velocity, See Figure 2-7. Cos = cosine of the angle t @ time t Rotating Machinery: Practical Solutions Figure 2-7. 34) Or: The use of these equations will transform the three forms of vibration characteristics to one another. 5 Hz. What is the velocity and what is the acceleration?
The frequency of the wave form depends on amplitudes, frequency and phase angle of the contributing sources. A simple beat frequency is shown in Figure 3-8, where two vibrating sources of different frequencies, amplitudes, and phase angles are contributing to the beat wave. Beat frequencies come into and out of phase as the contributing waves add and subtract from one another. Note that the composite wave is not a perfect sine wave as are the contributing sources. The actual frequency of a beat is the sum of two or more vibrating sources adding and subtracting from one another as illustrated in Figure 3-8.
