A comprehensive error analysis method for the geometric error of multi-axis machine tool

• A comprehensive method is developed to evaluate the effect of each error parameter.
• The differential transformation is applied to estimate the error distribution.
• An error propagation analysis is proposed by summing the differential movements.
• The Spearman method is introduced to discover the importance of an error parameter.

In this paper, a comprehensive error analysis method is proposed to discover how the geometric error propagation through every motion axis, and to find out which error parameters have greater impact on the tool posture error at the end of the kinematic chain. As the geometric error of a motion axis can be regarded as the differential movement, an error model for a four-axis machine tool is established to calculate the tool posture error with all the geometric error parameters. Then a cumulative process of the differential movements of every axis is proposed to describe the error propagation process when moving the tool to the given position. Moreover, the workspace of the machine tool is discretized into an amount of points with a uniform sampling method on the measured positions of the geometric error. Then, a Spearman rank correlation method is presented to find out how closely linked between a single error parameter and the tool posture error all over the sampling workspace. Hence, the ten key error parameters are selected according to the analysis results in the three-axis and four-axis sampling workspace. Finally, an experiment is conducted on the four-axis machine tool with a three-axis controlled trajectory to verify the effectiveness and correctness of the proposed method using a double ballbar.