Centrifugal Pumps Design and Application 2nd ed - Val S. Lobanoff, Robert R. Ross (Butterworth-Heinemann, 1992)

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Vibration and Noise in Pumps 463 cies and mode shapes are generally calculated by the Holzer method or by eigenvalue-eigenvector procedures [401. Either of the methods can give accurate results. A good design practice would be to locate the torsional natural frequencies a minimum margin of 10% from all potential excitation frequencies. An example of the mass-elastic diagram of a torsional system of a 3,600 rpm motor-driven, six-stage pipeline pump is given in Figure 18- 24. The natural frequencies and mode shapes associated with the first four natural frequencies are given in Figure 18-25. The mode shapes can be used to determine the most influential springs and masses in the system. This information is important if a resonance is found near the operating speed and system changes must be made to detune the frequencies. Figure 18-24. Mass-elastic diagram of six-stage pump train.

464 Centrifugal Pumps: Design and Application Parametric variations of the coupling stiffness should be made if changes are necessary, because most torsional problems can be solved by coupling changes. An interference diagram for the six-stage pipeline pump is given in Figure 18-26. In this system, excitation by several orders is possible as the pump is started; however, operation at 3,600 rpm has an adequate margin from the critical speeds. Once the system has been modeled and the natural frequencies have been determined, potential forcing functions should be identified. The forcing functions represent dynamic torques applied at locations in the system that are likely to generate torque varia- Figure 18-25. Torsional resonant mode shapes of six-stage pump train.

464 <strong>Centrifugal</strong> <strong>Pumps</strong>: <strong>Design</strong> <strong>and</strong> <strong>Application</strong><br />

Parametric variations of the coupling stiffness should be made if changes<br />

are necessary, because most torsional problems can be solv<strong>ed</strong> by coupling<br />

changes.<br />

An interference diagram for the six-stage pipeline pump is given in<br />

Figure 18-26. In this system, excitation by several orders is possible as<br />

the pump is start<strong>ed</strong>; however, operation at 3,600 rpm has an adequate<br />

margin from the critical spe<strong>ed</strong>s. Once the system has been model<strong>ed</strong> <strong>and</strong><br />

the natural frequencies have been determin<strong>ed</strong>, potential forcing functions<br />

should be identifi<strong>ed</strong>. The forcing functions represent dynamic torques<br />

appli<strong>ed</strong> at locations in the system that are likely to generate torque varia-<br />

Figure 18-25. Torsional resonant mode shapes of six-stage pump train.

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