A floor polishing or grinding pad assembly is provided. In one aspect, a polishing or grinding pad assembly employs a flexible pad, a reinforcement layer or ring, and multiple floor-contacting tools such as abrasive disks. In another aspect, the reinforcement layer includes a wavy or undulating internal edge shape. A further aspect includes an inner ring edge having radially extending slots between pairs of radially enlarged tool mounting peaks. Still another aspect includes an insulator or spacer between a head of an abrasive tool and a reinforcement ring.