In recent years it has been discovered that besides non-uniform flow excitation such as from stator wakes; acoustic pressure pulsation can be a concern, especially for high pressure centrifugal compressor impellers. This has been termed “triple coincidence” and explains rare failures and likely a reason, at least partially, for some previous undocumented failures. Bladed disk interaction resonance discovered by the author in the mid 1970’s can be avoided such as for centrifugal impellers as needed, depending on vibratory mode involved, available damping, and potential excitation level. Especially for stages having vanes in the diffuser near impeller tips, concern for high cycle fatigue is very high as certain numbers of vanes combined with number of rotating blades can give correct phase to excite a highly responding mode. Intentional mistuning of disk-dominated modes has potential for reducing response. A similar but more complex interaction is with transverse acoustic modes having a specific number of nodal diameters. In this case acoustic gas modes in cavities at sides of impellers can match rotating acoustic pulsations at BPF (blade passing frequency) and/or harmonics, termed Tyler-Sofrin modes with increased noise. Also acoustic mode matching impeller structural mode can give the triple coincidence causing resonant response of the impeller. The concern for this coincidence is often difficult to evaluate. For some cases, calculations give enough evidence to modify number of vanes or blades to correct a possible cause of a fatigue failure. This coincidence can add to the direct response, e.g. from either upstream wakes or downstream diffuser vane interacting “potential flow” excitation, herein termed “quadruple coincidence resonance”. Dimensions of impeller side cavities are axisymmetric and are set by aerodynamics, so that outer and inner radii define transverse modes with small radial dimensional changes available. Often a minor aerodynamic performance compromise can be used to change designs to avoid serious resonances, e.g. revise numbers of vanes and/or blades, avoid the response of a matching diameter mode or have a different less responsive mode to alleviate concern. Besides turbomachinery e.g. compressors and pumps, some other methods as described could be utilized for any cavity that has diametrical mode shapes, or possibly other patterns for pressure pulsation frequencies. These modification(s), including patent-pending method, PCT/US2018/020880 described herein can alleviate if not eliminate concern for any mechanism having structural vibration excitation and/or environmental noise issues.

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