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ASYMMETRIC/ANISOTROPIC ROTOR, SUPPORT/BEARING EFFECTS AND EXPERIMENTAL VERIFICATIONS
There are many important issues for high-pressure turbocompressors: Rotordynamics, stability, surge, stall, shaft and impeller fatigue strength, asymmetric discharge pressure distribution, rotor thrust load evaluation, rotor system asymmetry/anisotropy and high-pressure seal problems (such as formation of condensates or hydrates at seals).
Anisotropy is the property of being directionally dependent, as opposed to isotropy, which implies identical properties in all directions. Asymmetry/anisotropy of the rotor system can originate from:
• Process flow asymmetries
• Asymmetric/anisotropic bearings or seals
• Asymmetric bearing supports
• Any anisotropy/asymmetric of radial stiffness
• Tangential (cross) stiffness components
• Asymmetric foundation/base/pedestal
• Any asymmetric/anisotropic loadings or asymmetric piping attachments to machinery casing.
Asymmetry/anisotropy can result in closely spaced, coupled pairs of rotor lateral modes and natural frequencies, which are known as split resonances. In a high-pressure turbocompressor, a pair of resonances (1.09×f and 0.91×f) were obtained due to asymmetric/anisotropic effects instead of a natural frequency f calculated by symmetric/ isotropic assumptions. Because of anisotropy/asymmetry, orbits excited in response to a simple unbalance are elliptical.
The presence of anisotropy means that the vibration measurements vary depending on a given angular location. Due to asymmetry, the vibrations measured at various locations would not show a symmetric pattern along the rotor.
In addition, one section of the rotor may show a backward precession (a change in the orientation of the rotational axis of a rotating body) while the other section simultaneously shows a forward behavior. In one example from the field, asymmetry/anisotropy led to the outboard rotor orbits being backward and the inboard vibration (similar to the midspan) showing a forward behavior.
One of the concerns with regards to anisotropy is how to properly identify the unbalance (heavy spot) angular location. The reality is that response phase, vibration amplitudes and Amplification Factors (AF) can vary significantly based on the observation angle and the side of the rotor.
Vibrational data obtained from transducers of any turbocompressor usually indicate some level of system anisotropy and asymmetry. The 1× orbits are generally elliptical in a broad speed range. The 1× Bode and polar plots also display split resonances.
Within certain ranges of a turbocompressor speed, system anisotropy/asymmetry can lead to specific, excited-by-unbalance rotor lateral synchronous vibrations (usually in a form of backward precession). Unbalance-related backward processional motion can often result in damaging rotor reversal stresses.
The speed bands where the backward precession takes place are relatively narrow, and they occur near closely spaced rotor natural frequencies which are usually avoided as operational speeds. With respect to this issue, however, the following recommendations should be considered:
• Careful balancing and shaft straightening are important
• A sufficient amount of damping in the rotor and support system may effectively suppress the backward motion
• Accurate asymmetric/anisotropic analytical models and experimental verifications are necessary.
Bearings and supports
For a turbocompressor, an accurate rotordynamics model is a flexible rotor on bearings installed on flexible supports. The influence of bearings, support structures and other relatively flexible items (down to the machinery foundation) should properly be included in any rotordynamics analysis and in condition monitoring.
Only a dynamic model with properly simulated bearing, accurately modeled rotor assembly and all support structures could show good agreement with experimental (measured) results. The supports should be modeled with a high accuracy and should consider every detail.
The cross-coupling between the vertical and horizontal directions (between the X and Y directions) could affect results. The relative importance of this effect usually depends on the design of the turbocompressor.
Supports are stiffer in the vertical direction compared to the horizontal direction, highlighting the anisotropy of the supports and rotor assembly. The interactions of supports, sometimes known as cross talk (dynamic response in one support to a force applied at another support) can have a considerable impact on dynamic simulation results. This can influence the prediction of the second critical speed as well as machine stability details in some cases.
Field measurements and experimental results confirm that so-called identical supports do not behave identically in spite of having the same design on paper. Reason: Small differences in tolerances and fabrication. On the other hand, many parameters such as bearing properties, support dynamic behaviors and gyroscopic effects are speeddependent.
An active magnetic bearing (AMB) can be employed as an exciter for high-pressure turbocompressor rotordynamics (and stability) in experimental studies and verifications. This AMB exciter makes it possible, independently of the rotor speed, to set the static eccentricity and a superimposed whirl with freely adjustable frequency (non-synchronous), amplitude and direction of precession.
The responses and forces can be measured directly by the magnetic bearing. Both static forces and non-synchronous excitations are important for the stability of a rotor assembly (particularly for high-pressure applications).
For accurate dynamic modeling and verification, two analytical models should be built: One for the original turbocompressor and another with the AMB using the same concepts and parameters. The analytical results of the later should be compared with measured data by the AMB to verify the machinery and the first model.
In addition to pressures at the casing inlet and outlet, measurement is made of static and total pressures directly in many places inside a turbocompressor, such as in front of a seal inlet. This enables the precise determination of complex aerodynamic effects (such as the swirl at the seal inlet), which are important for any turbocompressor, particularly high-pressure models.
Amin Almasi is a Chartered Professional Engineer in Australia and U.K. (M.Sc. and B.Sc. in mechanical engineering). He is a senior consultant specializing in rotating equipment, condition monitoring and reliability.