Actual kinematics-based identification of tool runout parameters in milling using measurable tooth-level responses

Tool runout alters the actual tool rotational center, which influences both the rotational radius and angular spacing of teeth relative to the spindle center, thereby changing the material removal process and significantly affecting both processing quality and tool lifespan. Traditional techniques for determining tool runout, regardless of whether they rely on static measurements or force analysis, often assume uniform pitch angles around the geometric axis and thus neglect the pitch-angle variations caused by actual rotational kinematics. This study presents a method for identifying tool runout parameters by considering the spindle-centered pitch distribution, utilizing measurable tooth-level responses, including actual tooth rotational kinematics, single tooth milling-based pitch measurements, and maximum rotational radii identified from slot milling tests. A kinematic model is developed to relate the theoretical pitch angle (with respect to the tool center) and the measured pitch angle (relative to the spindle center), along with rotational radii, through a geometric triangular configuration. Based on this model, analytical equations are derived linking the tool’s theoretical radius, maximum rotational radius, and runout offset, resulting in an explicit solution for identifying tool runout parameters. The maximum rotational radius is determined from slot widths measured during slot milling operations, while actual pitch angles are extracted by correlating tooth positions with their corresponding force signals in single-tooth milling tests. Experimental validations in both micro- and conventional-milling processes demonstrate that the identified tool runout parameters exhibit strong consistency with traditional methods. This validates the precision of the proposed approach and highlights its independence from specific cutting force magnitudes, ensuring robustness and applicability across various milling scenarios.