| XIA Fu-jia,TANG Jin-yuan,YANG Duo.Improved Linear Transformation Method for Rough Surface Reconstruction[J],51(10):176-184 |
| Improved Linear Transformation Method for Rough Surface Reconstruction |
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| DOI：10.16490/j.cnki.issn.1001-3660.2022.10.017 |
| KeyWord:surface reconstruction linear transformation probability density function time-frequency iteration height distribution autocorrelation function |
| Author | Institution |
| XIA Fu-jia |
State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha , China |
| TANG Jin-yuan |
State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha , China |
| YANG Duo |
State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha , China |
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| Abstract: |
| The work aims to design an improved method to solve the problems that the linear transformation method can not realize the rough surface reconstruction of arbitrary skewness Ssk and kurtosis Skucombination or guarantee the accuracy of surface height extreme characteristic parameters (maximum height Sz, maximum peak height Sp and maximum pit height Sv). The Johnson transformation in the linear transformation method was replaced by solution of probability density function of surface height. A non-Gaussian sequence conforming to the specified height distribution was constructed and the accuracy of reconstructed surface height parameters was ensured by time-frequency iteration method. All the surface height roughness parameters (if there were several parameters with strong linear correlation or equality relationship, some parameters would be eliminated until the remaining parameters did not meet the above relationship) were used as constraints to construct a nonlinear optimization equation so that the surface height probability density function could be directly solved. In order to avoid the error caused by the linear transformation of the matrices in the linear transformation method on the height roughness parameters, the time-frequency iteration method was further used to iterate the non-Gaussian sequence obtained above and the autocorrelation coefficient matrix satisfying the specified autocorrelation function for several times in time domain and frequency domain, so as to ensure that the accuracy of the final reconstructed surface could meet the requirement. In addition, specific theoretical values of Ssk and Sku were set to prove the advantages of improved method, and the shot peening surface and grinding-shot peening surface which were difficult to be reconstructed by the existing linear transformation method were used as the experimental objects and reconstructed by the improved method. The reconstructed rough surfaces were compared with the corresponding measured surfaces to further verify the accuracy of the improved method. The improved method could reconstruct the rough surfaces of any given combination of Ssk and Sku accurately and guarantee the accuracy of height extreme characteristic parameters, with a maximum error no more than 5%. With the help of time-frequency iteration method, the improved method could effectively avoid the error caused by the linear transformation in linear transformation method, and the reconstructed surfaces had high accuracy and good robustness. The height distributions and autocorrelation functions of shot peening surface and grinding-shot peening surface generated by the improved method were consistent with the measured surfaces, and the maximum error of correlation roughness parameters was less than 5%. Compared with the existing linear transformation method, the improved method can achieve efficient and accurate reconstruction of rough surfaces with arbitrary height distribution and autocorrelation function, guarantee the accuracy of surface roughness parameters Sq, Ssk and Sku and characterize the surface height extreme characteristic parameters well. In addition, the height distribution of shot peening and grinding-shot peening surfaces reconstructed by the improved method is more realistic. |
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