An abrasive-band grinding device for rolls and method for grinding rolls in which a motor rotates an abrasive band such that the abrasive band is pressed against the face of the roll to be ground. Guide pulleys are arranged in a loop of the abrasive band and, between the guide pulleys, a rotatable contact pulley is arranged over which the abrasive band is pressed against the face to be ground. The contact pulley is controlled by an actuator, preferably a motor, so that it can be inclined in relation to the roll face to be ground.
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