A 2023 CIRP Annals study demonstrated traceable on-machine coordinate measurement on a large machine tool (MT) by combining integrated multilateration — a laser tracker embedded in the spindle measuring four fixed retroreflectors — as a virtual metrology frame (VMF) with the short-displacement data reported by the MT controller, achieving an average expanded uncertainty of about 18 µm in a simulated 3000 × 2000 × 1500 mm working volume and a maximum deviation of 6 µm from calibrated values on a medium-sized workpiece. The method's own uncertainty statement and traceability chain are, however, explicitly incomplete: contributions originating from the measurand (workpiece temperature distribution and thermal expansion, gravity-induced deformation, clamping-induced deformation, surface contamination at probing) were not considered; the initial spatial-referencing (alignment) contribution was excluded on the argument that it is a constant within the transformation matrix, an assumption whose validity and stability were not assessed; and the individual calibration procedures for the laser tracker, the MT controller position reporting, and the probing system were not combined into a documented SI-traceability chain. The problem is to complete and validate this evaluation: quantify the omitted contributors, assess the alignment contribution, document the full traceability chain, and demonstrate the completed method at full industrial scale on large workpieces over large probing point clouds.

Background

High-value large components in the aerospace, energy, and scientific-facility sectors are conventionally inspected off-line, beside the production line, using large bridge coordinate measuring machines (CMMs), articulated arms, or laser trackers, because moving such parts to a dedicated measuring machine is costly and error-prone. Performing the dimensional inspection directly on the machine tool (on-machine, or on-MT, measurement) is attractive but difficult: the structure of a large MT drifts in time and space under varying thermal conditions, so the machine's own scales cannot serve as a stable, traceable reference. Schmitt and Peterek (2015) showed that these thermal influences on the MT structure dominate the achievable measurement uncertainty, and Mutilba et al. (2019) assessed an earlier on-MT measurement uncertainty budget under shop-floor conditions using a calibrated workpiece, following the ISO/TS 15530-3 approach (a technical specification for determining the uncertainty of coordinate measurements by comparison against a calibrated workpiece) — an approach that becomes impractical for large components because a calibrated workpiece similar to the manufactured one would be needed.

A second research line therefore avoids the MT structure as a reference and builds an external, "virtual" metrology frame from distance-measuring instruments. Multilateration is the determination of three-dimensional point coordinates from pure distance measurements to a set of fixed fiducial points, in the same way GPS receivers fix position from satellite ranges; a laser tracker is a portable instrument that tracks a retroreflector with a laser beam and measures the distance to it (here with an absolute distance meter, ADM, which reads the absolute length rather than only changes in length). Mutilba et al. (2018) introduced integrated multilateration, in which a single laser tracker is carried by the MT spindle while wide-angle retroreflectors fixed to the MT table act as fiducials, allowing fully automatic volumetric verification of large MTs; Egaña et al. (2021) assessed the uncertainty of this machine-tool-integrated inverse multilateration (MIIM) for volumetric characterization and thermal-error studies.

Building on this, Mutilba et al. (2023) proposed a complete on-MT coordinate measurement method: at each measurement the MT stops at a positioning point a few millimetres (3–10 mm) from the surface; the embedded laser tracker determines the spindle's position and orientation by multilateration; the MT controller then supplies the short relative displacement to the probing point, where a touch-trigger probe (TTP — a stylus-based tactile sensor that registers contact) triggers the coordinate acquisition. The method assumes the positioning and probing points share the same error vector over that short span, so the probing coordinate is essentially determined by the virtual metrology frame. The uncertainty evaluation followed the GUM (Guide to the Expression of Uncertainty in Measurement, the international standard framework for uncertainty budgets), combining the multilateration contribution — assessed by Monte-Carlo simulation according to JCGM 101 — with the MT controller repeatability and the probing-system repeatability, yielding an average expanded uncertainty (coverage factor k = 2, 95% confidence level) of 18 µm in a simulated 3000 × 2000 × 1500 mm working volume. The simulation and the practical realization (a LEICA AT960 laser tracker integrated into a ZAYER ARION GTM large MT) used the Unified Spatial Metrology Network (USMN) algorithm within the Spatial Analyzer software — a network adjustment that, unlike pure multilateration, also uses angle-derived data. The experimental demonstration on a CMM-calibrated medium-sized prismatic workpiece showed a maximum deviation of 6 µm from the calibrated values, about 3 s per measured coordinate, and an initial spatial-referencing (alignment) process of 10–15 minutes. Traceability to the SI metre was argued through the laser tracker calibration and software compliance with NPL, PTB, and NIST standards.

The authors themselves state, however, what the evaluation omits: the measurand-originating effects (temperature and gravity on the workpiece, clamping of the workpiece on the MT, dirt on the probed surface) were not considered in the budget; the alignment contribution was excluded as constant within the transformation matrix, without assessing that assumption; and the individual calibrations of the MT controller position reporting and of the probing system — and their combination with the laser tracker calibration into a single documented chain to the SI — were left as something that "should also be accomplished". The full-scale characterization on larger workpieces was deferred to future work.

Problem Statement

For the virtual-metrology-frame (VMF) on-machine coordinate measurement method of Mutilba et al. (2023) — integrated multilateration with a spindle-embedded laser tracker and table-fixed retroreflectors, combined with MT controller displacement data — establish a complete, validated, SI-traceable uncertainty evaluation at full industrial scale. The single scientific objective is a complete task-specific uncertainty statement and a documented traceability chain for the method, demonstrated on large workpieces; the requested results jointly serve that objective as follows: (1) quantify the measurand-originating uncertainty contributions omitted from the presented budget — the workpiece temperature distribution and thermal expansion, gravity-induced deformation, clamping-induced deformation, and surface contamination (dirt) at the probing points — and incorporate them into the combined uncertainty; (2) assess the uncertainty and temporal stability of the initial spatial referencing (alignment) process, which was previously excluded as a constant within the transformation matrix, including its contribution over long measurement campaigns; (3) define and demonstrate the individual calibration procedures for the laser tracker, the MT controller position reporting, and the probing system, and their combination into a documented traceability chain to the SI for on-machine measurement campaigns; and (4) perform the complete characterization of the method on larger workpieces and over larger probing point clouds, extending the experimental validation beyond the medium-sized prismatic component used in the original demonstration.

References

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