Robust parallelism evaluation of bearing end-faces via correlation-aware joint Gauss-Helmert model

For bearing end-face parallelism measurement using dual-probe synchronous scanning, this study achieved repeatability ranges of 0.66 and 1.47 arcseconds in two independent experiments. In this task, systematic tilt and dynamic runout of the rotary table are mainly represented as common-mode components, whereas the relative attitude between the inner and outer end-faces is reflected in the differential-mode plane-gradient components. However, conventional robust algorithms are usually based on an independent and identically distributed (i.i.d.) noise assumption and may therefore misclassify synchronous common-mode residual components as local outliers, causing the loss of useful attitude information. To address these coupled geometric and stochastic problems, this paper proposes a correlation-aware joint Gauss–Helmert (GH) framework for bearing end-face parallelism evaluation. First, a symmetric reparameterization strategy is introduced to separate common-mode and differential-mode plane-gradient components within a quantified small-angle range relevant to precision bearing end-face measurement. Second, a joint GH model is constructed to handle full-coordinate observation errors and the nonlinear polar-to-Cartesian transformation, while the estimated scan-wise residual correlation between synchronized dual-probe tracks is incorporated into the stochastic model. On this basis, a Mahalanobis-distance-based IGGIII weighting function is used to down-weight residual pairs that deviate from the estimated dual-track correlation structure while preserving synchronous common-mode residual components. Through correlation-aware joint adjustment, the influence of runout-related synchronous residual components on the differential-mode parallelism estimate is reduced. Experiments show that, compared with least squares (LS), RANSAC, and independent IGGIII, the proposed method achieves the smallest repeatability range, standard deviation, and coefficient of variation under the tested coupled disturbances. Furthermore, a GUM-compatible Monte Carlo uncertainty propagation was performed through the complete robust joint GH algorithm, including nonlinear coordinate transformation, scan-wise correlation estimation, Mahalanobis-distance-based robust weighting, and iterative adjustment. The expanded uncertainties were 0.52 and 0.70 arcseconds (k = 2) in the two independent experiments, supporting the reliability of the proposed framework for high-precision bearing end-face inspection.