In order to improve the machining quality of hard-cutting metals in the combined machining of ultrasonic vibration and WEDM,the influence of different amplitudes and frequencies on surface roughness under the combined machining of ultrasonic vibration and WEDM was studied by theoretical analysis,numerical simulation and experimental verification.The physical and mathematical models of WEDM based on ultrasonic vibration were constructed,the heat flux formula of moving Gaussian heat source based on ultrasonic vibration was derived,and the complete temperature field simulation model was established.Through the simulation analysis of temperature field in ANSYS finite element composite machining process,the theoretical calculation model of surface roughness based on temperature field numerical simulation was constructed.Finally,the theoretical calculation model of surface roughness was verified by single factor test.The results show that with the increase of amplitude and frequency,the volume of the eliminated pits decreases and the surface quality increases.The experimental results are in good agreement with the theory and simulation,the minimum deviation is 7.717%,the maximum deviation is 16.708%.