A Singular Value Decomposition Approach to Similarity Evaluation Between Servo Loops of CNC Machine Tools

In most cases, the servo loops of computer numerically controlled (CNC) machine tools consist of position controllers, drivers, power transmissions, and tables. In the process of diagnosis, adjustment, and calibration of CNC machine tools, it is crucial to make servo loops’ performances as similar as possible, and ideally identical. This work is motivated by establishing a measure to evaluate the similarities between all coordinated axes. Based on the singular value decomposition (SVD) of time series, this contribution addresses an innovative approach to set up a similarity measure for evaluating the performances of CNC machines. A circular interpolation is carried out to sample the displacements of two involved axes into two independent time series. Then a special matrix called attractor is constructed from the time series and SVD algorithm is adopted to process attractors. As a result, a series of singular values is produced. From these values, the singular value ratio spectrum is formed and the similarity ratio, which numerically represents the similarity between the coordinated axes, is proposed. According to the similarity ratio, the similarity of the two series is compared. Finally, the approach has been validated by experimental measurements. The similarity measure presented in this paper provides an overall index on evaluating the mismatch between coordinated axes of CNC machine tools.