The accuracy of a three-dimensional (3D) positioning system can ultimately be evaluated via measurement of a 3D vector between command and actual end-effector positions at arbitrary points over the entire workspace. This is a simple, yet challenging, metrological problem. The motion accuracy of a machine tool is traditionally evaluated on an axis-to-axis basis, with every error motion of every axis being independently measured as part of a one-dimensional measurement process in a different setup. Toward the ultimate goal of 3D position measurement over the entire workspace, research efforts have offered several new, practical measurement technologies.

This special issue covers the technical and academic efforts regarding the evaluation of machine tool accuracy. The papers in this special issue clarify the latest research frontiers regarding machine tool accuracy from a metrological viewpoint. In the first paper, by Montavon et al., error calibration technologies and their management are reviewed within the Internet of production concept. Long-term accuracy monitoring and management are clearly among the most crucial technical challenges faced regarding machine tools, and the work by Xing et al. is related to them. Ibaraki et al. presented machining tests to evaluate the thermal distortion of a machine tool. Peukert et al. studied the dynamic interaction between machine tools and their foundations. Various 3D measurement schemes for determining machine error motions have been investigated by many researchers, and some have been implemented in industrial applications. Kenno et al. and Florussen et al. investigated 3D measurement using the R-test for five-axis machines. Miller et al. studied simultaneous measurement of six-degree-of-freedom error motions of a linear axis. Nagao et al. presented an error calibration method for a parallel kinematic machine tool.

The editors appreciate the contributions of all the authors, as well as the work of the reviewers. We are confident that this special issue will further encourage research and engineering work for improving the accuracy and performance of machine tools.

Machine tool calibration and subsequent controller-based compensation are industrially established and research-intensive techniques used to monitor and increase the volumetric performance in high-precision manufacturing. Moreover, a variety of interim performance checks and integrated sensor approaches have been developed to predict volumetric performance degradation and avoid an economically undesirable downtime. However, the fragmentation of data acquisition and management limits the potential for additional insights with respect to the value creation based on existing methods in the field of machine tool calibration. The authors reviewed the former from the perspective of data sources according to the frequency of their contribution to the digital twin of a machine tool, adopting a digital view regarding machine tool calibration within the Internet of Production concept. The latter proposes a semantic separation of cyber physical production systems into four layers: data sources, data access and provisioning, storage and analytics, and user respective agent feedback. To achieve a common representation across different layers, devices, and industrial Internet protocols, a model-based abstraction layer is required, which must be compatible with existing standards within the field, e.g., the ISO 230 series. Utilizing different Internet of Production architectures and platforms, a multitude of parallel analytic applications and an evaluation of complex models are enabled owing to the availability of ample computing resources, among which the machine tool’s numerical controller takes the role of an edge-device injecting the feedback into the production process. A proof-of-concept of a digital approach to machine tool calibration data storage and processing was established based on the software prototype VoluSoft, which implements an ISO 230-1:2012 based abstraction layer in JavaScript Object Notation format, and an evaluation of the kinematic models to estimate the volumetric performance at the functional point. Apart from generating compensation tables, the results are used to project the expected deviation at the tool tip to the computer-aided design-model of a work piece, correlate the error motions using the temperature data acquired by integrated sensors, and estimate the contribution of the volumetric performance limitation to the uncertainty budget of on-machine measurements.

The scale and master ball artefact (SAMBA) method allows estimating the inter- and intra-axis error parameters as well as volumetric errors (VEs) of a five-axis machine tool by using simple ball artefacts and the machine tool’s own touch-trigger probe. The SAMBA method can use two different machine error models named after the number of model parameters, i.e., the “13” and “84” machine error models, to estimate the VEs. In this study, we compare these two machine error models when using VE vector directions and values for monitoring the machine tool condition for three cases of machine malfunctions: 1) a C-axis encoder fault, 2) an induced X-axis linear positioning error, and 3) an induced straightness error simulated fault. The results show that the “13” machine error model produces more focused concentrated VE directions but smaller VE values when compared with the “84” machine error model; furthermore, although both models can recognize the three faults and are effective in monitoring the machine tool condition, the “13” machine error model achieves a better recognition rate of the machine condition. This paper provides guidelines for selecting machine error models for the SAMBA method when using VEs to monitor the machine tool condition.

Thermal deformation is one of the contributors of critical errors of machine tools. ISO 10791-10 describes standardized tests to evaluate a machine tool’s thermal deformation; however, they do not include cutting operations. By repeatedly performing the same machining feature, one can observe the change in geometric accuracy, which is typically caused by the thermal influence of the environment or the heat generated by the machine tool. This paper proposes a simple machining test to evaluate a machine tool’s thermal displacement in the tool’s axial direction (Z-direction). Together with a technical committee of the Japan Machine Tool Builders’ Association, the authors proposed the revision of ISO 10791-10 in ISO/TC39/SC2 to add the present machining tests. This paper presents the test procedures and case studies as well as a comparison with an alternative machining test.

The manufacturing accuracy of modern machine tools strongly depends on the placement of the machine tool structure on the factory’s foundation. Civil engineering knows a variety of foundation types and factory planners must carefully consider local circumstances such as the size and the properties of the regional subsoil as well as the individual requirements of machine tools. Two of the major reasons for the effect of the foundation onto the machining accuracy are the added stiffness and the increased mass from the installation site’s foundation. A change of these characteristics greatly affects the dynamic characteristics of the overall machine tool and therefore also the machining dynamics. Although some general rules and guidelines exist for the design of foundations, their dynamic interaction with the supported precision machine tool structures is not well understood yet. This paper presents a series of measurements on two different types of machine tool foundations and highlights the characteristic differences in their dynamic interaction. It also proposes a novel approach to validate the conclusions with the use of foundation and machine tool scale models. These results can serve factory planners of precision targeting shop floors as a valuable guide for deciding on a suitable foundation for lowering the individual machine tool vibrations and/or reducing the dynamic interaction between closely located machine tools.

While evaluating the accuracy of high-precision machine tools, it is critical to reduce the error factors contributing to the measured results as much as possible. This study aims to evaluate both the error motions and geometric errors of the rotary axis without considering the influence of motion error of the linear axis. In this study, only the rotary axis is moved considering two different settings of a reference sphere, and the linear axes are not moved. The motion accuracy of the rotary axis is measured using the R-test device, both the error motions and geometric errors of the rotary axis are identified from the measurement results. Moreover, the identified geometric errors are verified for correctness via measurement with an intentional angular error. The results clarify that the proposed method can identify the error motions and geometric errors of a rotary axis correctly. The method proposed in this study can thus be effective for evaluating the motion accuracy of the rotary axis and can contribute to further improvement of the accuracy of the rotary table.

A wireless non-contact 3D measuring head is used to determine the accuracy of 5-axis machine tools. The measuring head is inserted in the spindle by the tool exchanger automating the measurement routine used. For checking the linear machine axes, a cross shaped artefact containing 13 precision balls is introduced, named Position Inspector, enabling the determination of positioning and straightness errors of two linear axes in one setup. The squareness error between both axes is also determined in this setup. This artefact can be mounted on a pallet system for automatic loading and is measured in a bi-directional run. This artefact can be measured in different orientations (i.e., horizontal, inclined, vertical) and is pre-calibrated with a CMM. The measurement sequence using this artefact is executed in eight minutes and its design and support system is addressed in this paper. The location errors and orientation errors of the axis average line (or pivot line) of both rotary axes are determined with the Rotary Inspector using the same measuring head with a single precision ball. For this, kinematic tests are used from ISO10791-6, e.g., the BK1 test, BK2 test which apply for trunnion or swivel table machines. Derived parameters can be used for machine correction resulting in a significantly improved machine accuracy. An example is given where this correction is performed automatically by implementing this measurement system in the machine’s controller. Finally the machine tool is tested using the BK4 test. For this test all 5-axes are moved simultaneously and the measured displacements between the machine’s spindle and table in X-, Y-, and Z-directions are compared to tolerance levels. This final test reveals the machine’s overall accuracy and dynamic behavior.

The current standard for machine tool calibration supports the use of quasi-static measurement techniques. When measuring the six degrees of freedom motion errors, the measurements are typically taken consecutively. This introduces uncertainty when comparing the results due to machine deformation during individual measurements. Furthermore, quasi-static measurement techniques are known to be time consuming, a problem that is exacerbated as each degree of freedom must be measured separately. Additionally, the spatial resolution between the selected target positions can have an impact on calibration quality. In the following paper, the benefits of measuring the six motion errors simultaneously while the axis under test is traversing at a nominally constant velocity are presented. Firstly, the motivation for simultaneous continuous capture is presented. Secondly, continuous motion measurements are compared with quasi-static measurements for the six degrees of freedom motion errors showing sub-micrometer and sub-arcsecond correlation. The full effect of a ball screw pitch error is shown which can be missed using traditional quasi-static measurement techniques. Finally, wavelet analysis is performed for further spatial diagnostics along with correlation coefficients calculated to quantify the linear dependency between the six error motions.

This paper proposes a calibration method for a parallel mechanism type machine tool (XMINI, Exechon Enterprises L.L.C.). In this method, the kinematic parameters are calculated using forward kinematics and the least squares method from the results obtained by a coordinate measuring machine. By using an articulated arm coordinate measuring machine (AACMM), we can measure a wide space, and the measuring machine position do not have to be determined strictly. This paper provides a solution for the forward kinematics problem to identify the kinematic parameters. The results from the kinematic parameter calculation are evaluated using the experimental results from an actual machine.

Additive manufacturing (AM) is recognized as a core technology for producing high-value components. The production of complex and individually modified components, as well as prototypes, gives additive manufacturing a substantial advantage over conventional subtractive machining. For most industries, some of the current barriers to implementing AM include the lack of build repeatability and a deficit of quality assurance standards. The mechanical properties of the components depend critically on the density achieved. Therefore, defect/porosity analysis must be carried out to verify the components’ integrity and viability. In parts produced using AM, the detection of unfused powder using computed tomography is challenging because the detection relies on differences in density. This study presents an optimized methodology for differentiating between unfused powder and voids in additive manufactured components, using computed tomography. Detecting the unfused powder requires detecting the cavities between particles. Previous studies have found that the detection of unfused powder requires a voxel size that is as small as 4 μm³. For most applications, scanning using a small voxel size is not reasonable because of the part size, long scan time, and data analysis. In this study, different voxel sizes are used to compare the time required for scanning, and the data analysis showing the impact of voxel size on the detection of micro defects. The powder used was Ti6Al4V, which has a grain size of 45–100 μm, and is typically employed by Arcam electron beam melting (EBM) machines. The artifact consisted of a 6 mm round bar with designed internal features ranging from 50 μm to 1400 μm and containing a mixture of voids and unfused powder. The diameter and depth of the defects were characterized using a focus variation microscope, after which they were scanned using a Nikon XTH225 industrial CT to measure the artifacts and characterize the internal features for defects/pores. To reduce the number of the process variables, the measurement parameters, such as filament current, acceleration voltage, and X-ray filtering material and thickness were kept constant. The VGStudio MAX 3.0 (Volume Graphics, Germany) software package was used for data processing, surface determination, and defects/porosity analysis. The main focus of this study is to explore the optimal methods for enhancing the detection of pores/defects while minimizing the time taken for scanning, data analysis, and determining the effects of noise on the analysis.

In this study, we propose a new algorithm to solve the rectangular strip packing problem (RSPP), a variant of the cutting stock problem in which the mother materials have a common fixed width and infinite length. Based on the column-generation technique with three improvements, the proposed algorithm can solve large-scale problems involving tens of thousands of materials within a reasonable time, considering practical cutting constraints, i.e., the three-stage guillotine cutting constraint and the limitations of slitter blades. The proposed algorithm is evaluated in terms of its packing efficiency and calculation time.

A method to uniquely calculate the tool path and to modify the tool path during air cutting motion to reduce the machining time is proposed. This study presents a contour line model, in which the product model is minutely divided on a plane along an axial direction, and the contour line of the cross-section of the product is superimposed. A method is then proposed to calculate the tool position according to the degree of interference between the product surface and the tool. Furthermore, this study proposes a technique to reduce the machining time by tool path modification during air cutting motion. This is determined by the geometric relationship between the product surface and the tool, and not based on cutting simulations. A cutting experiment was conducted to validate the effectiveness of the proposed method. Based on the results, it was confirmed that the difference in machining time between the tool path with modification and the tool path without modification was large. Moreover, the machining time was significantly reduced by the tool path modification. The results showed that the proposed method has good potential to perform customized manufacturing, and to realize both high productivity and reliability in machining operation.

In this study, the authors investigate improving the precision of a thread by deriving its radial force (thrust force) with a four-component piezoelectric dynamometer and thread cutting by helical interpolation motion using a thread mill. The accuracy of the thread is discussed with respect to changing hardness of the work material. In addition, by recording the position information at the time of thread cutting from the servo guide on the data logger, the relationships among the cutting forces of the four components and the radial force are confirmed by various methods; further, the consistency of these relationships was confirmed.

Achieving high workpiece accuracy is a long-term goal of machine tool designers. Many causes can explain workpiece inaccuracy, with thermal errors being the most dominant. Indirect compensation (using predictive models) is a promising thermal error reduction strategy that does not increase machine tool costs. A modeling approach using transfer functions (i.e., a dynamic method with a physical basis) has the potential to deal with this issue. The method does not require any intervention into the machine tool structure, uses a minimum of additional gauges, and its modeling and calculation speed are suitable for real-time applications that result in as much as 80% thermal error reduction. Compensation models for machine tool thermal errors using transfer functions have been successfully applied to various kinds of single-purpose machines (milling, turning, floor-type, etc.) and have been implemented directly into their control systems. The aim of this research is to describe modern trends in machine tool usage and focuses on the applicability of the modeling approach to describe the multi-functionality of a turning-milling center. A turning-milling center is capable of adequately handling turning, milling, and boring operations. Calibrating a reliable compensation model is a real challenge. Options for reducing modeling and calibration time, an approach to include machine tool multi-functionality in the model structure, model transferability between different machines of the same type, and model verification out of the calibration range are discussed in greater detail.

The presented research shows the time dependent temperature distribution and thermal time constant within a typical industrial X-ray computed tomography (XCT) system used for dimensional metrology. Temperature effects can significantly affect measurement results of XCT scans either by directly changing the dimensions of the measurement object, or by indirectly changing the geometry of XCT scanner. In either case, the effect is not known well enough to be used for correction of measurement results or estimation of measurement uncertainty. In order to determine these effects, traceable temperature measurements were performed with a custom measurement system designed for this application. The influence of temperature fluctuations on length errors was determined by correlation of the measured temperature fluctuations with measurement deviations of a reference standard in repeated CT scans at different X-ray power levels. After experimental determination of X-ray focal spot displacement due to thermal expansion, a simple mathematical model of X-ray source displacement as a function of its temperature was developed and validated for a selected X-ray power level.

In the manufacturing industry, molds are required for mass production operations, and the industry’s recent small lot, multi-product production systems call for such molds to be made by NC machine tools in short periods of time. The tool path point coordinates of NC machine tools are derived by geometric computations, which are used in turn to derive the polyhedron-approximated mold surface and the contact positions of the tool. In the conventional method, however, placing surplus tool path points on the planar section makes it difficult to acquire the boundary position coordinate values in the vicinity of the boundaries of the polyhedrons that constitute the curved surface, resulting in errors in the path point coordinates for the polyhedron-approximated shape of the mold surface. In this study, therefore, we have developed CAM algorithms that can reduce the tool path errors and suppress the number of tool path points by not deriving the path point coordinates in the linearly approximated section. This is done by using the boundary information of the approximate polyhedrons that constitute the concave section of the mold model.

This paper investigates the machining stability in ball-end-milling of curved surface in which the inclination of tool continuously changes. Initially, the influence of inclination angle is geometrically investigated on the parameters such as immersion angle and cutting velocity. Then, the paper presents the stability lobe diagrams of the process. Curved surface milling is simulated by slot milling on a cylindrical workpiece using a ball-end-mill to obtain the cutting force and vibration, which are used for fast-Fourier transform and Hilbert-Huang transform (HHT) analyses. Experimental results show that the cutting force increases, and the stability becomes worse with the inclination angle, while the machining errors decrease with the inclination. The vibration analysis showed that the HHT can detect the transition from stable to unstable during milling of curved surface in the time-frequency plots.

Advance avoidance of machine collision by means of computer simulation is now common in NC machining. However, human errors from the tool shape mounted in the machine tool main shaft not matching the simulation data and the actual tool have become a problem. Therefore, in this research, we have developed a high-speed method of comparing the shape of a tool mounted on a machine tool main shaft and an estimated shape in a simulation. This is done by capturing an image of the tool with a camera and estimating the tool shape from multiple images.