A polishing or grinding pad with a multilayer reinforcement is provided. In one aspect, a floor polishing or grinding pad assembly employs a flexible pad, at least two reinforcement layers or rings with different characteristics, and multiple floor-contacting tools such as abrasive disks. In another aspect, a workpiece polishing or grinding pad assembly includes a flexible and rotatable pad, a polymeric reinforcement layer coupled to the pad and a metallic reinforcement layer to which are coupled abrasive tools. In yet another aspect, a floor-facing reinforcement is more flexible than a pad-facing reinforcement which is more rigid.