Measurement for the identification of static and quasi-static rotational stiffness

Machine tool calibration can be employed to optimise tool path trajectories through on- and off-line compensation of anticipated deflections, which result from a process plan, and to assess the machine tools capability to comply with the geometric dimensions and tolerances of a process plan. This work presents a measurement for the identification of static and quasi-static rotational stiffness of a rotational joint of 5-axis machining centres. This work shall serve as a basis towards the calibration of translational as well as rotational stiffness of 5-axis machining centres. The novelty of this work lies partly in the measurement procedure for the quasi-static rotational stiffness, which relies on multiple circular trajectories, as well as in the comparison of the static and quasi-static rotational stiffness of machine tools, which is usually identified using finite element approaches. The measurement procedure for the static rotational stiffness consists of inducing a static load directly, from an overhead factory crane, to a single rotational joint and measuring its deflection with both three LVDTsLinear Variable Differential Transformers (LVDTs) as well as three Non-Contact Capacitive Probes (NCCPs). While the measurement for the quasi-static rotational stiffness induces quasi-static loads indirectly from the Loaded Double Ball Bar, with different magnitudes and radii from the axis of rotation, between the tool centre point and the machine tool table. The quasi-static measurement procedure measures the deflection with both three LVDTs as well as three NCCPs while the spindle tracks circular trajectories inscribed by the movement of the rotary axis. The measurement procedures are implemented in two case studies on 5-axis machining centres with significantly different kinematic configurations to be able to highlight and discuss the limitations of the applicability of the method. The presented method works well for machining centres with symmetric and acceptably with asymmetric structures due to the corresponding symmetry of the deflection field. Finally, the manuscript concludes with a contextualisation of the introduced measurement procedure towards fully calibrated machine tool models, i.e. translation and rotation as well as static and dynamic, which together with customised post-processors and process models, might form the future basis of a stiffness volumetric compensation system.