A mill drive system includes a gear unit which is arrangeable below a grinding plate and has at least one planetary and/or spur gear stage, having a vertical shaft position. The mill drive system includes an electric motor, integrated into a housing of the gear unit and having a rotor and a stator which have vertically extending axes. Upper and lower bearing covers each including bearing seats for rotor shaft bearing are mounted on opposite end faces on the rotor and stator and are connected via a stator carrier, which has cooling fins on the outer periphery. A collecting tray for coolant is formed between the lower bearing cover and a base part of the housing. The motor is supported via a flange which is formed on an inner face of the housing and extends radially inward and to which the lower and/or upper bearing covers are connected.