Abstract: A motor driven cylindrical brush for a cleaning apparatus. The brush has bristles which lie in the zone outside a bearing section provided with a contact surface for a drive belt. Between the bristle filling and the bearing section, the brush member has recessed annular grooves. Via these grooves, it is possible to compensate for length changes of the brush member. These length changes occur when the brush filling is anchored in the brush member. By compensating for these length changes, the brush is very smooth running, and minimum bearing loading occurs.