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A good surface texture design can effectively improve the tribological performance of the helical pair within a helical hydraulic rotary actuator(HHRA). However, the optimization design process can be time-consuming due to the multiple design variables involved and the complexity of the mathematical model. This paper proposes a modified efficient global optimization (MEGO) method for solving such demanding surface texture design challenges. The MEGO utilizes a Kriging model with the optimized Latin hypercube sampling (OLHS) for initial sampling and the proposed modified expected improvement (MEI) function for sequential sampling. A comparative study of several global optimization algorithms with the MEGO on the surface texture design is performed. Subsequently, surrogate-based optimization and parameter analysis are carried out, resulting in the identification of an optimal set of texture parameters. The findings reveal the superiority of the MEGO in both model prediction accuracy and refinement of minima. Moreover, compared to the base design, the friction coefficient can be reduced by up to 45.2%.