A bearing system for supporting a shaft, comprising: a bearing including: an inner race about an axis, the inner race having an interior coupled to the shaft; rolling elements about the axis and around the inner race; and an outer race about the axis and around the rolling elements; a housing having a cavity defining an axial location relative to the axis, the bearing received by the cavity; a first axial loading structure in the cavity and operatively connected to the bearing; and a second axial loading structure in the cavity extending axially away from the axial location in a first axial direction, the second loading structure opposing movement of the bearing relative to the axial location in a second axial direction when the bearing loads the second axial loading structure in the second axial direction, the first and second axial loading structures operationally independent from one another.