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The most common form of impeller failure is that of fatigue. Engineers must ensure that their impellers, commissioned for use in compressors and expanders, are designed to handle fluctuations in pressure that give rise to alternating stress conditions. To accomplish this, modern impeller design involves the use of analytical tools such as computational fluid dynamics (CFD) to predict aerodynamic behavior including pressure loading, and finite element analysis (FEA) to predict the stress response to the applied pressure.
There are different levels of fidelity that can be employed to this end. The top level is fluid-structure interaction analysis where the effect of structural deflection on aerodynamics is accounted for. This type of analysis measures aeroelastic response often referred to as flutter. More commonly, the aero problem is solved separately from the structural problem. CFD-predicted steady-state and oscillating pressures are mapped onto the structural model. The stress response is then predicted either with a static or dynamic structural analysis. Fatigue assessments are then made based on the mean and alternating stress state, and a Goodman Diagram for the material.
It is well established that impeller displacement and stress levels are drastically increased under resonant conditions. Therefore,a key objective of the impeller designer should be to avoid resonance to prevent rapid fatigue failure (Figure 1).Engineers have a tool called the interference diagram for assessing the potential for impeller structural resonance. It is also referred to in the literature as the Singh’s Advanced Frequency Evaluation (SAFE) Diagram and the Zigzag Excitation Line in Nodal Diameter vs.Frequency (ZZENF) Diagram.
Figure 1. Fatigue failure at an impeller blade hub fillet[/caption]
Take, for example,a covered (shrouded) impeller designed to operate at 14,700 RPM (Figure 2). The original design incorporated 17 impeller blades, and 19 diffuser vanes in close proximity to the impeller outer diameter.
Figure 2. Shrouded centrifugal compressor impeller[/caption]
Depicted in Figure 3 is the Interference Diagram for this impeller. At this point, the structural analysis has not been performed yet, so there are no natural frequencies plotted. The diagram shows the excitations that are to be avoided to prevent resonance. The excitation frequency (y-axis) must fall on a multiple of vane pass (VP). In this case, two horizontal red lines are drawn: 1X VP (19X running speed) and 2X VP (38X running speed). The x-axis represents the nodal diameter of the mode shape.
For resonance to occur, not only does the frequency have to match, but also the mode shape must exhibit a specific nodal diameter.That is where the zig-zag lines come in. For resonance to take place, the nodal diameter must equal the difference between multiples of the blade number (B) and vane number (V). The locations where the zig-zag line intersect the horizontal vane pass lines are the excitation locations of potential resonance. For this case, natural frequencies at vane pass that exhibit two nodal diameters must be avoided. The same for natural frequencies at 2X VP that exhibit 4 nodal diameters.
The black diamonds (Figure 4) depict natural frequencies predicted by an FEA modal analysis. Unfortunately, in this case, interferences showed up near both excitation points. The two-nodal diameter mode shape which involved both hub and shroud vibration is depicted. Since this analysis was carried out in the design stage,the issue was easy to rectify. Changing the number of vanes to 22 cleared the interference and prevented a costly impeller failure from taking place. The updated Interference Diagram for the new vane count is depicted in Figure 5.
Figure 3. Interference Diagram for B=17 blades, V=19 vanes, and ω=14,700 RPM speed[/caption]
Figure 4. Interference Diagram that includes the results from a modal analysis,
2 ND/ 1X VP mode shape shown on right[/caption]
Figure 5. Modified Interference Diagram[/caption]
Aspects of impeller resonanceare also relevant to bladed disks and blisks. Some other related topics of importance not considered here include blade mistuning, stress stiffening, packetedturbine blades,harmonic forced response, damping techniques and analysis, specific FEA techniques and boundary conditions, and the relationship between wheel resonance and rotordynamics. An impeller or bladed disk designer should be well versed in these topics to prevent wheel fatigue failure.
William Kelly, PE, is Assistant Technical Director at Mechanical Solutions, Inc., which specializes in rotating machinery design, analysis and troubleshooting. For more detailed coverage of how to avoid centrifugal impeller structural resonance, visit https://www.mechsol.com/publications/