Multi-axis machine tools performance is essential in achieving high positioning accuracy at the desired feed rate and to withstand mechanical loads induced by the process-machine interaction. In this regard evaluation and characterization of multi-axis machine performance in terms of kinematic and static accuracy under variable load operating conditions poses a challenge.The paper aims to investigate and characterize the kinematic and static accuracy of a multi-axis milling centre under loaded conditions. Employing the concept of Elastically Linked System (ELS) for “off-operational” evaluation, the accuracy due to the interaction between the machine’s structure the machining process loads and the control system is assessed. Using the Loaded Double Ball Bar (LDBB) measurement system the cutting process is emulated by inserting an “elastic link” between the tool and the workpiece that closes the force-loop of the system.A set of workspace positions is selected to perform the LDBB measurements. The positions are selected so as to cover an adequate region of the effective machining workspace and at the same time utilizing a combination of linear and rotational axis positions and orientations to allow the investigation of their behavior and the effect of the machine structure. The captured deformations and their variation within the examined workspace region give a comprehensive view of the machine’s kinematic and static accuracy under the effect of the load induced errors and kinematic inaccuracies.

Machine tool testing and accuracy analysis has become increasingly important over the years as it offers machine tool manufacturers and end-users updated information on a machine’s capability. A machine tooĺs capability may be determined by mapping the distribution of deformations and their variation range, in the machine tool workspace, under the cumulative effect of thermal and mechanical loads. This paper proposes a novel procedure for the prediction of machine tool errors under quasi-static and loaded conditions. Geometric errors and spatial variation of static stiffness in the work volume of machines are captured and described through the synthesis of bottom-up and top-down model building approaches. The bottom-up approach, determining individual axis errors using direct measurements, is applied to estimate the geometric errors in unloaded condition utilizing homogeneous transformation matrix theory. The top-down approach, capturing aggregated quasi-static deviations using indirect measurements, estimates through an analytical procedure the resultant deviations under loaded conditions. The study introduces a characterization of the position and direction dependent static stiffness and presents the identification how the quasi-static behavior of the machine tool affects the part accuracy. The methodology was implemented in a case study, identifying a variation of up to 27% in the stiffness response of the machine tool. The prediction results were experimentally validated through cutting tests and the uncertainty of the measurements and the applied methodology was investigated to determine the reliability of the predicted errors.

Stiffness is an important characteristic of production machinery, as it contributes to its ability to precisely maintain the pose between a tool centre point with respect to a workpiece under loads. For machine tools, it directly affects the geometric dimensions and surface properties of the parts, i.e. how closely the parts match their design drawings. This work presents an efficient measurement procedure to measure and identify the full translational stiffness matrices of machine tools. The measurement procedure consists of inducing static loads, which vary in magnitude and direction, at the tool centre point of the machine tool using the Loaded Double Ball Bar and measures the displacement with three Linear Variable Differential Transformers. The main components of the uncertainty budget related to the measurement of the cross compliance are also summarized. The measurement procedure is implemented in a case study on a 5-axis machining centre. Finally, the manuscript concludes with a discussion on the utility value of the translational stiffness matrix for the design and operation of machine tools as well as the possibility to expand the measurement procedure to capture the quasi-static and dynamic compliance.

Stiffness is an important characteristic of production machinery, as it contributes to its ability to precisely maintain the pose between a tool center point with respect to a workpiece under load. For machine tools, it directly affects the geometric dimensions and surface properties of the parts, i.e. how closely the parts match their design drawings. This work presents a novel measurement procedure to measure and identify full translational stiffness matrices of 5-axis machining centers using quasi-static circular trajectories. The measurement procedure consists of inducing quasi-static loads, which vary in magnitude and direction, at the tool center point of the machine tool using the Loaded Double Ball Bar and measuring the displacement with three Linear Variable Differential Transformers while the spindle tracks the circular trajectories inscribed by the movement of the rotary axis. The work outlines and quantifies the main components of the uncertainty budget related to the measurement of the translational stiffness matrices. The measurement procedure is implemented in a case study on a 5-axis machining center. Finally, the manuscript concludes with a discussion on the utility value of the translational stiffness matrix for the design and operation of machine tools as well as the possibility to expand the measurement procedure to a calibration procedure for 5-axis machining centers to analyze the translational and 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.