Electric machine with rotor coolant and lubrication distribution system, and systems and methods of cooling and lubricating an electric machine

An electric machine may include a rotor shaft that has a hollow region configured to receive a coolant. The hollow region is defined by an inner surface which has a slope that increases from a first inner diameter at a first end to a second inner diameter at a second end. Centrifugal force generated when rotating the rotor shaft causes the coolant to flow across the inner surface of the rotor shaft from the first end to the second end at a velocity depending at least in part on the slope of the inner surface of the rotor shaft. A method of cooling an electric machine includes injecting a coolant into a first end of the hollow region of the rotor shaft, rotating the rotor shaft at an operational rate of rotation, with the rotation generating centrifugal force that causes the coolant to flow from the first end to the second end, transferring heat from the rotor shaft to the coolant.