“…While the field of hydrodynamic lubrication has been studied extensively over the years, with or without magnetic force involvement, the nonlinear nature of the physics governing such systems caused prior efforts to avoid explicit dynamic solutions of the lubrication-layer thickness evolution over time. Therefore, these efforts usually set the lubrication layer as constant ( 60 , 61 ), or consider time not as an independent variable, but, rather, as an input parameter, setting eccentricity and rate of change as constant ( 62 , 63 ), resulting in a static problem governed by an elliptical equation. Others use planar configurations ( 61 , 64 ), focus on experimental and numerical examination ( 61 , 64 , 65 ), or a combination of the above.…”