Assessing the repeatability of on-machine probing is required to estimate the measurement uncertainty. Currently, standards such as ISO 230–2:2014 and ISO 230–6:2002 include approaches only for a single-axis or a diagonal-path evaluation of the machine repeatability. Also, ISO 230–10:2016 is limited to the evaluation of the probing repeatability at a specific position of the machine for single-point surface measurement as well as for measuring the circle and sphere centre location. In this paper, a general model capable of predicting the measurement repeatability, considered as a covariance matrix, for a five-axis machine in any probing situation is sought from replicate measurements on a spherical artifact at various positions and with different probing directions. Polynomial functions fitted to the X, Y and Z recorded coordinates as well as to the normal (radial) and tangential projection values respectively perpendicular and tangent to the target surface estimate the standard deviations, i.e. the square roots of the diagonal elements of the covariance matrix, of on-machine probing in terms of experimental factors. Separate polynomials were fitted to the covariance quantities obtained between the recorded components as well as the normal and the tangential projections to estimate the off-diagonal elements of the covariance matrix. The factors include the positions of all five machine axes at the target point as well as the measurement direction. The repeatability models are validated by comparing measured and predicted values for a separate validation data set, which shows that a quantitative prediction of the randomness of on-machine measurement is achievable. The potential effects of the probe orientation, the hysteretic behavior of the measurement system, the measurement strategy and the time span on the on-machine probing are also studied through different experiments on a ring gauge. The effect of hysteresis on probing repeatability was found negligible but biases were detected.

需要评估在机探测的可重复性，以估计测量不确定度。当前，诸如ISO 230–2：2014和ISO 230–6：2002之类的标准仅包括对机器重复性进行单轴或对角路径评估的方法。同样，ISO 230–10：2016仅限于在机器的特定位置进行探测重复性的评估，以用于单点表面测量以及测量圆和球的中心位置。在本文中，从对球形工件在不同位置和不同探测方向上的重复测量中寻求了一种通用模型，该模型能够预测在任何探测情况下五轴机床的测量重复性，称为协方差矩阵。拟合X的多项式函数 Y和Z记录的坐标以及分别垂直于目标表面和与目标表面相切的法线（径向）和切向投影值估计机上探测中的标准偏差，即协方差矩阵对角元素的平方根。实验因素方面。将单独的多项式拟合到记录的分量之间以及法线和切向投影之间获得的协方差量，以估计协方差矩阵的非对角线元素。这些因素包括目标位置上所有五个机器轴的位置以及测量方向。通过比较单独的验证数据集的测量值和预测值来验证可重复性模型，这表明可以对机上测量的随机性进行定量预测。还通过环规的不同实验研究了探头方向，测量系统的滞后行为，测量策略和时间跨度对机上探测的潜在影响。发现磁滞对探测重复性的影响可以忽略不计，但检测到偏差。