Prediction of machining errors for free-form surfaces based on an improved grey model (1,

\nAn improved grey model (GM) for predicting free-form surface machining errors was established to address the low measuring efficiencies of coordinate measuring machines (CMMs) and the low prediction accuracy of the GM(1,1) model. A number of points on a free-form surface are measured with a CMM, and machining errors are obtained. Ideas from metabolic methods and the GM(1,N) prediction model were combined. To reduce the impact of random fluctuations of the machining errors, a Markov prediction model was then used to correct the fitted results for the residuals and obtain the predicted results of the machining errors for free-form surfaces, thus improving the prediction accuracy of the model. The predicted results of the metabolic GM(1,1) and metabolic GM(1,N) models were then compared. The experimental results showed that the combination of metabolic theory, a grey model, and Markov theory effectively improved the prediction accuracy.\n