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Abstract
This paper presents a method for modeling gimbaled rotor dynamics under trim conditions in X3D, a next-generation 3-D finite element based rotor structural dynamics solver. The rotor is modeled using a free flap hinge at the hub with a single blade, the motion of which is suppressed at integer multiples of the Nb per rev, where Nb is the number of blades. This is accomplished by introducing harmonics of the joint rotation angle as additional trim variables. Rotor frequencies are examined for a three-bladed gimbaled rotor model and are found to combine the modes of both free flap hinge and fixed flap hinge (cantilevered) one-bladed rotor models, similar to the behavior of a teetering rotor, justifying the gimbal modeling methodology. Gimbal flapping is examined for a proprotor in edgewise flight: successfully suppression of steady and 3/rev flapping indicates the gimbal model is performing as intended. The 6/rev and higher harmonics are negligible to begin with for this case and are left uncontrolled, but the same method can also be applied to suppress them if required. Airloads and blade loads are examined with a free flap hinge blade with the gimbal model, revealing an increase in 3/rev sectional normal aerodynamic force on the blade but a decrease in 3/rev flap and lag bending moment when the gimbal is added. Three-dimensional axial stress distribution at the blade root is examined, revealing only minor differences between the two hub rotor models, primarily in the flexbeam.

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