Backward Precessional Whip and Whirl for a Two Point Rubbing Contact Model of a Rigid Rotor Supported by an Elastically Supported Rigid Stator



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The present work investigates the phenomena of whip and whirl for a rigid rotor contacting at two bearing locations. The idea originated from an anemometer consisting of a rotor with an elastically supported stator undergoing the phenomena of dry friction whip and whirl at the two bushing contacts. To analyze the behavior, a mathematical model similar to the anemometer is developed and analyzed assuming two possible solutions, Mode1 (normal reaction forces in phase at two contacts) and Mode 2 (normal reaction forces out of phase at two contacts). Analytical solutions are only possible for the models with same RCl (Radius to Clearance ratio) at the two rub locations. A simulation model is constructed using the Texas A&M University (TAMU) Turbomachinery Laboratory rotordynamics software suite XLTRC? comprised of Timoshenko beam finite elements to form multiple degrees of freedom rotor and stator models. The nonlinear connections at the rub surface are modeled using Hunt and Crossley?s contact model with coulomb friction. Dry friction simulations are performed for three separate models depending on the rotor?s mass disk location with respect to the contact locations. The three models used have (1) Disk at center location (2) Disk at 3/4 location (3) Disk at overhang location. The adequacy of the analytical solution is investigated using the above simulations. Also, cases are explored where the general assumed solution would not solve the mathematical model, e.g. different RCl ratios at the two contacts. Simulations are performed for increasing as well as decreasing running speeds. There is partial agreement between simulation predictions and the analytical solutions for the cases with the mass center at centered and at 3/4 location. First, whirl-to-whip transitions occur at near the combine rotor-stator bounce frequency for both disk at center and disk at 3/4 location. The case with overhang mass disk predicts the two contacts to whip and at different frequencies simultaneously. Neither of the analytical solutions predicts a case where precession occurs at two different frequencies at the two contact points. Predictions for models with different RCl on the Backward Precessional (BP) graph imitate whirling. The BP graph predicts increasing BP frequency with increasing rotor speeds which is a characteristic of whirling, whereas investigation of individual contact velocities suggest that they are slipping at all conditions, one of them slipping more than the other netting a whirling like motion. For the overhang model with different RCl, apart from whipping at different frequency the two contacts also whirl at different frequencies corresponding to the RCl at the respective contacts. Simulations for decreasing rotor speed predict jump down from whirl- to-whip different BP frequency as compared to the jump up from whip-to-whirl for the speed up.