A High-Precision Roundness Error Separation Method Based on Time–Frequency-Domain Transformation for Parameter Optimization

The high-precision metrological measurement of circular profile is crucial for various rotational parts, essential in precision machining, manufacturing, and assembly. The existing roundness error separation methods often suffer from harmonic suppression issues, limiting the range of separable harmonics and reducing accuracy. This article proposes a roundness error separation method based on time-frequency-domain transformation (TFDT) for parameter optimization to overcome these challenges. By establishing the relationship between separation accuracy and rotation angle error and optimizing parameters accordingly, the method balances error separation accuracy with the separable harmonic range. Theoretical simulations and experimental validations confirm the method’s effectiveness. By comparing the separation results under different harmonic separation range requirements with those of the methods currently widely used in the field of roundness metrology, we have validated the effectiveness of this method in balancing separation range and accuracy. When the rotation angle is set to 1.406°, the harmonic suppression-free range expands from [0, 204] undulations per revolution (upr) to [0, 255] upr, representing an increase of approximately 25% compared to single-step rotation error separation technique (SEST). Compared to the SEST method, the deviation of this method from the multistep method is reduced by over 68%, and its standard deviation (STD) is only about 65% of that of the other two methods. This innovative approach provides comprehensive and accurate circular profile data, enabling high-precision roundness error separation across a broad harmonic range. It establishes a robust theoretical basis for advanced measurements in national metrology institutes and key laboratories.