Coordinate measuring machines (CMMs) can in principle receive the uncertainty of any measurement task from simulation-based 'virtual CMM' models that propagate machine, probe and thermal errors by Monte Carlo simulation. In practice, however, every validated virtual-CMM implementation has been built and experimentally validated for one particular machine and probe configuration; guidance for GUM/JCGM 101-compliant uncertainty evaluation from such simulation-based (virtual instrument) models is still under methodological development, with input-sensitivity and artefact-modeling treatment missing; and workflows for toleranced characteristics built from constructed features require per-trial re-simulation that has not been streamlined. The open problem is to establish and validate a configuration-independent transfer chain that converts routinely available CMM calibration and probe-characterization data into task-specific, standards-compliant measurement uncertainties across machine configurations. No validated cross-configuration transfer chain is known: active partial progress exists — a PTB research program on GUM-compliant virtual experiments, digital-twin metrology frameworks, analytic sensitivity-analysis methods, and machine-learning error identification — while the ISO/TS 15530 guidance remains incomplete; the problem remains open.

Background

A coordinate measuring machine (CMM) is the reference instrument of dimensional metrology: a probe — typically a touch-trigger probe whose stylus deflects on contact — is moved along three or more machine axes to sample points on a workpiece, and geometric characteristics (distances, diameters, form deviations such as flatness or cylindricity, and toleranced features) are computed by fitting geometric elements (planes, cylinders, spheres) to the sampled points. The quality of a coordinate measurement is quantified by its task-specific (task-oriented) measurement uncertainty: the uncertainty of the particular measured characteristic, which depends on the machine, the probe, the sampling strategy, and the fitting and construction operations applied. Routine machine acceptance and reverification tests, standardized in the ISO 10360 series, characterize a CMM only through maximum permissible error (MPE) limits on simple length measurements and probe performance; these global figures do not by themselves determine the uncertainty of an arbitrary task. The Guide to the Expression of Uncertainty in Measurement (GUM) and its Supplement 1 (JCGM 101) define how uncertainties should be evaluated — in JCGM 101 by propagation of distributions, implemented as a Monte Carlo method (repeated random sampling of the input quantities of an explicit measurement model) — but a full coordinate measurement rarely admits a simple explicit model. Two practical routes to task-specific uncertainty exist. Comparative methods (ISO/TS 15530-3) measure a calibrated workpiece and infer the uncertainty of similar tasks; they are trusted but consume calibrated artefacts and many repeated measurements. Simulation-based methods (the 'virtual CMM', outlined in the Technical Specification ISO/TS 15530-4) model the measurement process in software and propagate machine errors by Monte Carlo simulation: the residual geometric and kinematic errors left after the machine's software error compensation, probe errors as a function of stylus deflection angles, and thermal effects are represented as random fields sampled over many simulated measurement trials, and the scatter of the simulated characteristic is the predicted uncertainty. Germany's national metrology institute (PTB) distributes such a virtual CMM (VCMM), and research groups — notably at Cracow University of Technology — have built their own virtual CMMs for specific machines, including five-axis CMMs whose articulated probe heads add rotary-error contributions. Three works underlie the present problem, each acknowledging a different face of the same gap. Gąska et al. (2017) developed a virtual-CMM model for industrial conditions and noted the software-integration burden and the treatment of constructed features — derived geometric elements built from measured features, such as an intersection point or the distance between two fitted axes, which force the simulation to re-execute every construction step for each Monte Carlo trial. Gąska et al. (2019) validated a five-axis virtual-CMM method on a single machine (a Zeiss WMM 850S with PH20 probe head) against a calibrated artefact and stated that virtual models must be created and validated separately for each CMM configuration. Kok, Wübbeler and Elster (2022) showed that uncertainty predictions from virtual instruments are sensitive to how the measured artefact is modeled in simulation, and that GUM-compliant uncertainty evaluation using virtual instruments remains an active and underdeveloped area, with treatment of output sensitivity to inputs missing from guidance. Together these limitations define the question stated below.

Problem Statement

Establish and validate a configuration-independent, task-oriented uncertainty evaluation method for coordinate measurements on CMMs — a transfer chain that starts from machine calibration and probe-characterization data of the kind routinely available for any CMM (ISO 10360 performance-test results, software-compensated error maps, probe qualification data) and produces GUM/JCGM 101-compliant task-specific measurement uncertainties for arbitrary geometric tasks, including toleranced characteristics built from constructed features. Portability and validity must be demonstrated experimentally: the method's task-specific uncertainties must be shown to be statistically consistent with trusted reference methods on at least two distinct machine configurations — differing in kinematics or probe system — and on a task set spanning dimensional, form and constructed-feature characteristics, and porting the method to a new configuration must not require rebuilding and re-validating the model from scratch. The single calibration-to-task chain is constituted by the error and probe model identifiable from routine calibration data, the propagation and constructed-feature machinery, the compliance treatment covering input sensitivities and simulated-artefact modeling, and the cross-configuration experimental validation — each supplies one link of the same chain. Alternatively, the objective is to establish rigorously that configuration-independent transfer is unachievable.

References

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