Prediction of machine tool's static translational volumetric error caused by compliance from feed motor torque

Machine tool volumetric compliance quantifies the deflection of the tool tip relative to the workpiece under the effect of a mutual force. Its knowledge can help to virtually monitor tool path errors. This study, conducted under static conditions, aims to establish a model for directly predicting static translational volumetric errors caused by compliance from machine tool CNC feed motor torque outputs without the need to calculate the tool tip disturbance force. Static translational volumetric compliance was measured as proposed in ISO 230-1 in the X, Y and Z directions. The friction torques in each direction were modelled as a function of volumetric errors using Dahl's theory with some adjustments. The friction torque variations were detected. The final model links feed motor torques directly to static translational volumetric errors. With the help of an exponential term, the model proposed has a better performance on capturing the friction variations at the motion starting and movement reversal points. The static translational volumetric compliance models had R²_adj values of 0.999, 0.997, and 0.997 in the X, Y and Z directions, respectively. The RMSE with the best starting estimates on the testing dataset for predicting the static translational volumetric errors directly from the feed motor torques along the X-, Y- and Z-axis were 4.9 μm, 6.6 μm and 2.8 μm under maximum absolute volumetric errors values of 200 μm, 200 μm, and 50 μm, respectively.