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Aiming to decrease friction coefficient (μ) during the forming of magnesium alloy sheets, nine (9) tools with different hole geometries in their surface (flat, elliptical, and circular) were manufactured from steel Boehler W400 VMR (as known as DIN 1.2343). Tribological investigations were accomplished on a strip drawing machine at 288 °C without lubricants. When compared with a standard tool (surface flat), on average, tools with circular geometries in their surface showed the smallest friction coefficient, while tools with elliptical geometries shown higher. The friction coefficient also was confronted with the ratio between area occupied by holes in the surface of the tool and the total tool surface (i.e., factor f (%)), hole diameter (Ø), and the distance between circle centers (d(c,c)). Principal Component Analysis (PCA) complemented the experimental approach. In summary, both approaches (experimental and theoretical) indicated that the manufactured tool with circular geometries on its surface presented lower friction coefficient values on the forming processes of the magnesium AZ31 sheets. [ABSTRACT FROM AUTHOR]