Mixed Whirl Modes in Numerical Rotordynamics Analysis

During the design phase of a rotor system, the identification of whirl type carries much significance. Forward whirl (FW) critical speeds reveal themselves by harmonic peaks during spin-up. Backward whirl (BW) modes are dynamically quiet, but produce cyclic stresses and therefore contribute to material fatigue. The realization, that FW and BW can occur simultaneously in so-called mixed whirl (MW) modes, demands greater investigative scrutiny from the design team. While pure FW or BW modes can be identified by one pair of proximity probes at any single rotor location, many measurements along the rotor axis are needed to either rule out or confirm MW. Since there are practical and economic limits to the number of measurement locations and experiments, the purpose of this paper is to deliver guiding analytic insight. The proposed approach is to overcome experimental limitations by using a finite element (FE) model of the rotor system, compute its nodal whirl distributions from each of its complex-valued eigenvectors, and map the resulting whirl quantities back onto all FE grids. This delivers insightful surface and volume diagnostics to augment experimental rotor validation. Exercising this technique on simplified example models reveals unexpected insight in that FW and BW modes influence one another and become mixed across a greater rotor speed range than anticipated. Therefore, MW turns from an elusive phenomenon into a common occurrence throughout the Campbell diagram, to a point where it becomes increasingly challenging to discern pure FW and BW mode shapes — particularly, at higher modal frequencies. The most surprising and truly unexpected conclusion of this work is that all of the FW/BW pairs considered here do not intersect but veer upon closer investigation. And, as FW transforms into BW and vice versa during the veering transition in the Campbell diagram, their stability maps and root loci accentuate this shift by indicating that stability is traded between them. A mode’s ability to transition from one whirl type to another is significant from the practical design and simulation perspectives, in that engineering responsibility is shared between accurate predictions and appropriate design. As shown in this work, both numerical and eigenvector-based tracking algorithms favor intersection over veering at low rotor speed resolution and can produce believable but incorrect answers.