A torque smoothing apparatus is utilized in conjunction with a large square baler (LSB), which includes a bale chamber, a plunger mounted for reciprocation within the bale chamber, and an LSB drive line. In embodiments, the torque smoothing apparatus includes a planetary gear train and a flywheel, which is mechanically coupled to the LSB drive line through the planetary gear train. An auxiliary motor having a motor output is mechanically coupled to the LSB drive line through the planetary gear train, while a controller is operably coupled to the auxiliary motor. The controller commands the auxiliary motor to selectively apply torque to the LSB drive line such that the torque applied by the auxiliary motor, taken in combination with a torque contribution of the flywheel, reduces variations in torque demands placed on a vehicle engine as the plunger reciprocates during LSB bale formation.