| Summary: | In order to simulate the grinding surface more accurately, a novel modeling method is proposed based on the ubiquitiform theory. Combined with the power spectral density (PSD) analysis of the measured surface, the anisotropic characteristics of the grinding surface are verified. Based on the isotropic fractal Weierstrass–Mandbrot (W-M) function, the expression of the anisotropic fractal surface is derived. Then, the lower bound of scale invariance <i>δ</i><sub>min</sub> is introduced into the anisotropic fractal, and an anisotropic W-M function with ubiquitiformal properties is constructed. After that, the influence law of the <i>δ</i><sub>min</sub> on the roughness parameters is discussed, and the <i>δ</i><sub>min</sub> for modeling the grinding surface is determined to be 10<sup>−8</sup> m. When <i>δ</i><sub>min</sub> = 10<sup>−8</sup> m, the maximum relative errors of <i>Sa</i>, <i>Sq</i>, <i>Ssk,</i> and <i>Sku</i> of the four surfaces are 5.98%, 6.06%, 5.77%, and 4.53%, respectively. In addition, the relative errors of roughness parameters under the fractal method and the ubiquitiformal method are compared. The comparison results show that the relative errors of <i>Sa</i>, <i>Sq</i>, <i>Ssk,</i> and <i>Sku</i> under the ubiquitiformal modeling method are 5.36%, 6.06%, 5.84%, and 4.53%, while the maximum relative errors under the fractal modeling method are 23.21%, 7.03%, 83.10%, and 7.25%. The comparison results verified the accuracy of the modeling method in this paper.
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