Optimal Control of Vertically Stroking Crew Seats Employing Magnetorheological Energy Absorbers

Nondimensional analyses of vertical stroking crew seats with adaptive nonlinear magnetorheological energy absorbers (MREA) and magnetorheological shock isolation (MRSI) were addressed in this study. Under consideration were single-degree-of-freedom vertically stroking seat systems consisting of a rigid occupant mass falling with prescribed initial impact velocity (sink rate). The governing equations of the vertical stroking crew seats were derived using nondimensional variables such as nondimensional stroke, velocity, acceleration and time constant, as well as nondimensional Bingham number (i.e., the ratio of MR yield force to viscous force). The critical Bingham number was defined as that Bingham number for which the available stroke was fully utilized and the seat reaches zero velocity at the end of stroke. This was done in order to maximize shock mitigation performance. Two cases were studied: (1) the MREA problem, or the case where no spring was employed in the suspension, so that the seat was used for a single shock event, (2) the MRSI problem, or the case where a spring was employed in the suspension, so that after the initial shock event, the suspension could be used for either vibration isolation or mitigation of subsequent shock events. Nondimensional displacement, velocity and acceleration were analyzed for MREA and MRSI vertical stroking crew seats for three different payload masses of 47, 77 and 97 kg corresponding to 5th percentile (%tile) female, 50th %tile and 95th %tile male, respectively, with initial impact velocities of 4, 5 and 6 m/s. An optimal control solution was derived for both the MREA and MRSI cases. The effects of payload mass and initial impact velocity on the optimal responses of the vertical stroking crew seats were analyzed for a feasible range of Bingham number based on a realistically constrained (in diameter and volume) MR damper design.