API RP 684:2010 pdf download

API RP 684:2010 pdf download.API Standard Paragraphs Rotordynamic Tutorial: Lateral Critical Speeds, UnbalanceResponse,Stability, Train Torsionals, and Rotor Balancing.
On those occasions when the analyst has difficulty modeling a rotating assembly because the rotor geometry cannot he readily described using rudimentary shaft elements, then an equivalent model can be formulated from more sophisticated analysis. For example, the bending characteristics of a stub shaft bolted to the second stage impeller on an overhung gas pipeline compressor have been determined using a finite element analysis of the shaft and impeller sections. The finite element mesh is displayed in Figure 2-2. Note that the large counter-bored bolt holes dramatically decrease that stub shaft’s lateral bending stiffness. Once the static bending analysis of the component is accomplished, an equivalent lumped parameter beam-type model of the type used in rotordynamics analysis can be formulated that possesses identical bending stiffnesses at the lumped mass and inertia locations.
2.3.3 Addition of External Masses and Inertial Loadings
Sometimes components that arc shrunk on turbomachinery shafts (impellers, sleeves, thrust collars, and so on) affect the bending stillness of the rotating element. The amount of shrink fit determines the amount of contribution to the bending stiffness of the rotor. The model used to predict the unit’s critical speeds may have to be refined according to data collected during mechanical testing of the actual machine if the critical speeds differ by more than 5%.
Components shrunk or fitted onto the shaft affect the mass and inertia characteristics of the rotating assembly, and must be added to the model. This is most often accomplished by adding lumped masses and inertias at the mass centers of the shrunk-on components. It is occasionally necessary, as in the case of motor cores, to generate detailed inertia distributions of the shrunk-on component. Most rotors will include at least several of the following additional masses:
a. Impeller/disks.
b. Couplings.
c. Sleeves.
d. Balance pistons.
e. Thrust collars.
f. Gas seals.
In the rotor lateral model, a station located at the center of gravity of coupling hub should he specified for the coupling associated with the distributed coupling weight and moment of inertia. Coupling vendors provides the location of the center of gravity of each half of the assembled coupling and the weight distribution on the drawings. If the coupling drawing is not available, coupling half weight and moments of inertia can be approximately specified in the rotor model by using information from coupling vendor publications or web sites. When the center of gravity of coupling hub is beyond the shalt end, an equivalent shaft diameter can be estimated from more sophisticated analysis to provide the same bending stiffness. This can also be done by including an element with very low mass and very high modulus of elasticity where the center of gravity can be located.
Particular machines will have specific masses that must be
added. including the following:
a. Armature windings in electric motors.
b. Shrunk-on gear meshes.
c. Wet impeller mass and inertia in pumps.
It is imperative that the rotor model properly account for these masses and any additional rotating masses that may he peculiar to a particular system.
2.3.4 Addition of Stiffening Due to Shrink Fits and Irregular Sections
Most rotating assemblies have non-integral collars, sleeves, impellers, and so forth that are shrunk onto the shaft during rotor assembly. If the amount and length of the shrink fit and the size of the shrunk-on component are sufficiently large. then the shrunk-on component must be modeled as contributing to the shaft stiffness. The vendor must determine the importance of shrink fits for particular cases. Often, this can be accomplished only by experience with units of similar type. A modal test of a vertically hung rotor will give some indication of the stiffening effect of shrunk-on components. hut such measurements will likely exaggerate such effects because the fits will tend to be relieved as a result of centrifugal growth at normal operating speeds.
In some cases, a shaft segment consists of a series of short grooves and steps. Such segments are often found on turbine shafts at main labyrinth packing locations. Since the decrease in the diameter of the shaft segment encompassing the grooves does not affect the rotor critical speeds and the associated mode shapes, the stepping segment is usually simplified as one element using the average shaft diameter to evaluate the mass and bending stiffness of the stepping shaft segment.