The processed surface contour shape is extracted with the finite element simulation software, and the difference value of contour shape change is used as the parameters of balancing surface roughness to construct the infinitesimal element cutting finite element model of supersonic vibration milling in cutting stability domain. The surface roughness trial scheme is designed in the central composite test design method to analyze the surface roughness test result in the response surface

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... . The surface roughness prediction model is established and optimized. Finally, the finite element simulation model and surface roughness prediction model are verified and analyzed through experiment. The research results show that, compared with the experiment results, the maximum error of finite element simulation model and surface roughness prediction model is 30.9% and12.3%, respectively. So, the model in this paper is accurate and will provide the theoretical basis for optimization study of auxiliary milling process of supersonic vibration.