Prioritization analysis and compensation of geometric errors for ultra-precision lathe based on the random forest methodology

Geometric errors remarkably affect the dimensional accuracy of parts manufactured by ultra-precision machining. It is vital to consider the workpiece shape for the identification of crucial error types. This research investigates the prioritization analysis of geometric errors for arbitrary curved surfaces by using random forest. By utilizing multi-body system (MBS) theory, a volumetric error model is initially established to calculate tool position errors. An error dataset, which contains information of 21 geometric errors, workpiece shape, and dimensional errors, is then constructed by discretizing the workpiece surface along the tool path. The problem of identifying crucial geometric errors is translated into another problem of feature selection by applying random forest on the error dataset. Moreover, the influence extent of each geometric error on the dimensional accuracy of four typical curved surfaces is analyzed through numerical simulation, and crucial geometric errors are identified based on the proposed method. Then, an iterative method of error compensation is proposed to verify the reasonability of the determined crucial geometric errors by specifically compensating them. Finally, under compensated and uncompensated conditions, two sinusoidal grid surfaces are machined on an ultra-precision lathe to validate the prioritization analysis method. Findings show that the machining accuracy of the sinusoidal grid surface with crucial geometric error compensation is better than that without compensation.