改进的粗糙表面线性变换重构方法

目的 设计一种改进方法，解决线性变换法无法实现任意偏斜度S_sk和峭度S_ku组合的粗糙表面重构，以及无法保证表面高度极值特征参数(包括最大高度S_z、最大峰高S_p和最大谷深S_v)精度的问题。方法 通过求解表面高度概率密度函数，代替线性变换法的Johnson转换，构造符合指定高度分布的非高斯序列，并利用时频迭代法保证重构表面高度参数的精度，在此基础上，设置特定的S_sk和S_ku理论值，以证明所提改进方法的优越性，并将重构喷丸表面和磨削喷丸表面与相应实测表面进行对比，验证改进方法的合理性。结果 改进方法对任意S_sk和S_ku组合的粗糙表面均能准确重构，且可以保证表面高度极值特征参数的精度，最大误差不超过5%。此外，基于时频迭代法，改进方法有效避免了线性变换法中线性变换带来的原理性误差，重构表面的精度高且鲁棒性好，利用改进方法重构的喷丸表面和磨削喷丸表面，其高度分布、自相关函数均与实测表面吻合良好，相关粗...

Improved Linear Transformation Method for Rough Surface Reconstruction

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.