How rotordynamics influences pump selection

When purchasing a pump, particularly an “engineered” or “custom” as opposed to “standard” pump, it is important to properly evaluate its rotordynamic behavior, to avoid “turn-key” surprises in the field. OEM’s may be tempted to “trust to luck” with respect to rotordynamics in order to reduce costs, unless the specification requires them to spend appropriate effort.

Below are excerpts from the paper “An end-user’s guide to centrifugal pump rotordynamics” by William Marscher, president and technical director, Mechanical Solutions Inc., presented at the 2016 Turbomachinery Symposium.

Typically, an engineered pump should have the following types of analyses:

 Critical speed and mode shape: What are the natural frequency values, and are they sufficiently  separated from typical “exciting” frequencies, like 1x and 2x running speed, and vane pass? (see API-610, and HI 9.6.8)

 Rotordynamic stability: Is there enough damping for rotor natural frequencies, particularly those below running speed, that they will avoid becoming “self-excited”? (See API-RP-684)

 Forced response: Given the closeness of any natural frequencies to exciting frequencies, and given the amount of damping present versus the amount of allowable or likely excitation force that builds up between overhauls of the pump, will the rotor vibrate beyond its clearances, overload its bearings, or cause fatigue on the driven-end stub shaft?

Preferably, the specification also should require finite element analysis of structural natural frequencies for the following:

 Horizontal pump bearing housings (at least for pumps with drip pockets) and casing/ pedestal assemblies, in each case with the rotor assembly mass and water mass included (not addressed directly in API-610).

 Vertical end-suction or in-line pump motor (if attached “piggy-back”)/ pump casing and bearing pedestal/ pump casing (not directly addressed in API-610)

 Vertical Turbine Pump (VTP) and Vertical Hi-Flow Pump (e.g. flood control) motor/ discharge head or motor/ motor stand, connected to baseplate/ foundation/ column piping/ bowl assembly.

The rotor analysis should use state-of-the-art specialized computer codes such as those available from the Texas A&M TurboLab, and should take into account annular seal (e.g. wear ring and balance device) “Lomakin Effect” rotordynamic coefficients, impeller fluid added mass, and bearing and seal “cross coupling” coefficients that are inherent in bearings, seals, and impeller cavities. The structural analysis should include added mass effects from water inside (and for vertical turbine pumps, outside) the casing, bracketing assumptions concerning piping added stiffness and mass, and bracketing assumptions concerning foundation/ baseplate interface stiffness.

Common bracketing assumptions for piping are that the pipe nozzle are held perfectly rigid in one analysis, and is assumed to be completely free to move in a second analysis. Sometimes the piping is included to at least the first hanger or support, and is then assumed pinned at this location. The only guaranteed accurate analysis is to include all piping and reasonable estimates for support stiffness, but this is usually considered cost-prohibitive. For the foundation, typical bracketing assumptions are that the baseplate edge is simply supported (i.e. like of knife edges, fixed vertically but able to pivot) all around its periphery in one analysis, and fully fixed around the periphery in another analysis. For improved accuracy, at least average flexural properties for the floor and subfloor should be included under or as part of the baseplate.

As with the piping, however, the only guaranteed accurate analysis is to include the entire floor, key other masses on the floor, and all floor pillars and supports, with the assumption of usually a simple support for the outer periphery of the floor, where it meets outside walls of the room or cavity below, such as a sump. Usually, but not always, such floor detail does not substantially change the results and is considered cost-prohibitive. Such detail is particularly important to include, however, when the floor stiffness is less than 10x that of the pump discharge head (horizontal umps) or support pedestal (vertical pumps), or if floor natural frequencies are within +/-30% of running speed.

A counter-intuitive aspect of lateral rotordynamics analysis is how press-fit components (such as possibly coupling hubs, sleeves, and impellers) are treated. For the case of a slip fit/ keyed connection, it is easy to appreciate that only the mass but not the stiffness of these components should be included. However, even if the press-fit is relatively tight, it has been found by researchers (including the author) that the stiffening effect is typically small. Obviously if the press fit is high enough, the parts will behave as a single piece, but typically such a heavy press for is beyond maintenance practicality. Therefore, standard practice in rotordynamic analysis is to ignore the stiffening effect of even press-fitted components, as discussed and recommended in API-RP-684. The author’s approach in such cases typically is to analyze the rotor in a bracketing fashion, i.e. do the analysis with no press fit, and re-do it with the full stiffening of a rigid fit-up, with inspection of the results to assure that no resonances will exist at either extreme, or anywhere in between. In the case of torsional analysis, the rule changes, however. API-RP-684 introduces the concept of penetration stiffness, where the full torsional rigidity of a large diameter shaft attached to a small diameter shaft is not felt until some “penetration length” (per a table in API-RP-684) inside the larger diameter part. Of greater consequence, in most cases in the author’s experience, is the slip between the shaft and fit-up components such as impellers, balancing disks or drums, and sleeves. If the shaft fit is a medium to high level of press-fit, then no slip between the shaft and component is assumed, although the API-684 criteria can be applied for a modest added torsional flexibility. If the shaft fit is a light press and/or loose fit with a key, the shaft is assumed able to twist over a length equal to 1/3 its diameter (API estimates 1/3 the key engagement length, instead), until to key is fully engaged. While this latter procedure is approximate and dependent upon key dimensioning and keyway fit-up, practice has shown that it typically results in an excellent agreement between analysis predictions and torsional critical speed test results.

Although other specifications such as the ANSI/Hydraulic Institute Standards 9.6.4, or ISO 10816-7 (Pumps) provide some guidelines for vibration measurement and acceptance levels, there is not a great deal of guidance in most pump specifications concerning rotordynamic analysis. The new HI 9.6.8 and API-610 11th Edition are exceptions, API-610 discusses lateral analysis in detail in Section 8.2.4 and Annex I. This specification requires that any lateral rotordynamic analysis report include the first three natural frequency values and their mode shapes (plus any other natural frequencies that might be present up to 2.2x running speed), evaluation based on as-new and 2x worn clearances in the seals, mass and stiffness used for the rotor as well as the stationary supports, stiffness and damping used for all bearings and “labyrinth” seals, and any assumptions which needed to be made in the rotor model. It discusses that resonance problems are to evaluated based on damping as well as critical speed/ running speed separationmargin, and provides Figure I.1 to tie the two together (the bottom line is that there is no separation margin concern for any natural frequency with a damping ratio above 0.15, i.e. log dec of 0.94). It also gives criteria for comparison to test stand intentional imbalance test results. It requests test results in terms of a “Bode plot”. This is a plot of log vibration vs. frequency combined with phase angle vs. frequency, as shown by example in Figure 3 of these notes. As will be recalled, this plot identifies and verifies the value of natural frequencies and shows their amplification factor.

One of the more notable novel aspects of API-610 is that it recommends that there are a number of situations for which lateral rotordynamics analysis is over-kill, and therefore its cost can be avoided. These situations are when the new pump is identical or very similar to an existing pump, or if the rotor is “classically stiff”. The basic definition of “classically stiff” is that its first dry critical speed (i.e. assuming Lomakin Stiffness is zero) is at least 20 percent above the maximum continuous running speed (and 30 percent above if the pump might ever actually run dry).

Also, as discussed earlier, in addition to API-610, API also provides a useful “Tutorial on the API Standard Paragraphs Covering Rotordynamics ...”, as API Publication RP-684, which provides some insight and philosophy behind the specifications for pumps, as well as compressors and turbines.