Acceleration-Based Design Procedure for Sloped Rolling-Type Bearings with an Added Rotational Inerter

This research numerically investigates the mechanical behavior of sloped rolling-type bearings equipped with an inerter. After deriving equations of motion, the mechanical behavior, under harmonic excitation, of a sloped rolling-type bearing with its inherent rotational mass (i.e., considering the inertial and restoring forces generated by the existing roller) and one with an added rotational inerter is numerically analyzed. It is demonstrated that the latter is mechanically different from the former and, more importantly, the latter is more effective at controlling acceleration and displacement responses and practically more feasible. The acceleration control performance designed for sloped rolling-type bearings that ignore the inherent rotational mass can basically be retained when adding a rotational inerter if a suitable inertance-to-mass ratio can first be determined based on a specific acceleration target. Precisely stated, retaining the unique mechanical feature of sloped rolling-type bearings under harmonic excitation (i.e., the maximum transmitted acceleration is irrelevant to the external disturbance) is the optimum design objective in this study. Parametric and numerical analyses show that the peak acceleration responses of sloped rolling-type bearings with an added rotational inerter whose inertance-to-mass ratio is determined based on the optimum objective are less dependent on having a sufficiently large harmonic excitation period (i.e., on having the roller in motion within the sloped rolling range). In addition, the peak displacement responses under harmonic excitation can be effectively reduced compared with sloped rolling-type bearings that only consider the inherent rotational mass (i.e., without an added rotational inerter). Similar tendencies are seen when the sloped rolling-type bearings are subjected to ground motion records including far-field and pulse-like near-fault ones. Regardless of the ground motion considered in this study, the sloped rolling-type bearings with an added rotational inerter designed based on the optimum objective show steady displacement reduction. Finally, a simple, practical, and acceleration-based procedure is proposed for designing sloped rolling-type bearings equipped with added rotational inerters based on observations from the parametric and numerical analyses.