Machine tool accuracy is greatly influenced by geometric and thermal errors that cause positioning deviations within its working volume. Conventionally, these two error sources are treated separately, with distinct procedures employed for their characterization and correction. This research proposes a unified volumetric error compensation approach in terms of a calibration procedure and error compensation model, which considers geometric and thermal errors as a single error source that exhibits temporal variation primarily due to changes in the machine’s thermal state. Building upon previous works that introduced a fully automated volumetric calibration procedure capable of characterizing the variation in volumetric error over time, this study extends this methodology, incorporating multiple temperature sensors distributed throughout the machine and generating a digital twin based on a volumetric error compensation model capable of predicting and compensating for the volumetric error over time at any point in the workspace, using temperature measurements and axis positions as inputs. This methodology is applied to a medium-sized milling machine tool. The digital twin is trained and validated on volumetric calibration tests, wherein various controlled heat sources are employed to induce thermal variations while measuring the temperatures in the machine.

The measurement and compensation of volumetric error in milling machines of medium and large size is a key aspect to meeting the precision requirements of the most demanding applications. There are several solutions for volumetric error measurement—usually based on laser or in calibrated artifacts—that offer different specifications and lead to a variety of levels of precision, complexity of implementation and automation, cost of equipment, and measurement time, amongst others. Therefore, it is essential to have tools that allow, in each case, analysis as to which is the optimal calibration strategy, providing the criteria for evaluating different measurement equipment and strategies. To respond to this need, several tools have been developed which are able to simulate the entire calibration and compensation process (machine, measurement, model adjustment, etc.) and apply optimization methods to find the best measurement strategy for each application. For a given machine architecture and expected error ranges, the compensation error for each strategy is obtained by propagating measurement uncertainties and expected machine errors through the measurement and compensation model fitting process by Monte Carlo simulations. The use of this tool will be demonstrated through the analysis of the influence of the main design parameters of a measurement strategy for the calibration of a 3-axis machine tool, based on the measurement of tool position with a laser tracker.

The volumetric accuracy of machine tools is significantly impacted by thermal errors, making the evaluation of volumetric accuracy a significant challenge for the manufacturing industry. Several technical solutions have been implemented, both at the industrial and research level, to address this issue. However, considering thermal errors in the volumetric error characterization adds complexity to the process and remains an open topic of research in the field.In this study, a novel volumetric error characterization technique based on simulated Thermal Modal Analysis is proposed for a three-axis machine tool. This approach involves analyzing the impact of thermal modes of the machine tool's structural elements on the volumetric error, providing a characterization that incorporates the physical meaning of the structure. This simulated characterization will serve as a foundation for future experiments that combine it with other techniques to achieve a comprehensive understanding of volumetric errors.

A photogrammetry-based error compensation solution, comprising calibration, positioning compensation and accuracy validation methodologies, is presented to the aerospace sector, able to assist industrial robots in manufacturing new composite materials, offering versatility and reconfigurability at a lower cost than that resulting from the currently used milling machines. Against a ground truth measured by a laser tracker, it has boosted, in real time, the accuracy level from ±0.685 to ±0.203 mm, on average, and from ±1.621 to ±0.498 mm at peak, following the ISO 9283 standard, and from ±0.534 to ±0.080 mm, on average, and from ±1.804 to ±0.456 mm at peak, with a real part in a large volume under industrial operating conditions, taking into account occlusions and showing robustness against the impact of the payload, the waviness, and the backlash.