Lateral analysis is a critical speed analysis performed on a rotor by modelling its shaft as a series of elements of specific length and diameter, and with constant modulus of elasticity.
The intent of lateral analysis is to calculate the critical speeds (1st, 2nd, and 3rd) of a rotor to find out if there are sufficient margins of separation between those critical speeds and the rotor operating speed. Lateral resonant frequencies can excite the rotor and result in high and damaging rotor vibration.
If the analysis indicated that there were no sufficient margin of separation, a change in the rotor design could be made early on in the design stage to get an acceptable amount of separation. In many application, mostly low energy, a 10% separation is acceptable. Some standards, such as API 610, specify the required minimum amount of separation.
Standard pumps running at standard RPM are presumed to have been designed with no resonant frequencies at their normal running speeds. Hence a lateral analysis is typically required in highly specialized service, such as in high speed application, in critical service, in train arrangement that include another major piece of equipment, such as a turbine, or a gearbox, or in newly designed equipment.
In an undamped analysis (dry critical speed), the damping effects of the process liquid, or the film damping at the bearings, are not included in the analysis. In a damped analysis (wet critical speed), the damping effects are included.
In a typical critical speed analysis, a model drawing of the rotor is made. The static loads consisting of impeller/s, shaft, coupling, and other rotating parts such as wear rings and sleeves, are considered lumped masses located at their respective centerlines. The following calculations are then performed:
Hydrostatic stiffness, of wear parts, which is a function of the rotor rotative speed and the differential pressure across those parts, but independent of the static loading on the shaft.
Hydrodynamic stiffness of bearings which is a function of the bearing load due to static and dynamic reaction forces.
Static and dynamic reaction forces.
Polar mass moment of inertia.
The eigenvalues and resonant frequencies of the rotor.