目的 研究超声加工过程中微磨粒对冲击波的影响。方法 建立功率超声振动加工下的空化泡动力学方程，以及空化泡溃灭产生冲击波的数学模型，进而建立冲击波在微磨粒与水混合介质中的传播模型。使用六阶Runge-Kutta方法对数学模型进行求解，得到空化泡半径随时间的变化规律，以及空泡内部压强随空化泡半径变化的规律。结果 当空泡半径被压缩至1 μm左右时，空泡内部压强可达1 000 MPa。通过对距离空泡壁1.5R0处的冲击波压力进行求解发现，冲击波的压力仅需0.07 μs就可从初始的1 000 MPa迅速衰减至80 MPa。通过比较纯水介质与混合介质(SiO2微磨粒与水)中冲击波传播速度的结果发现，加入SiO2微磨粒会使冲击波的最大速度由2 976 m/s降至2 681 m/s，降低率约为10%。通过钛钽合金的功率超声振动加工实验验证了数值结果。对比分析了加入SiO2微磨粒前后钛钽合金表面结构和三维表面形貌，发现微磨粒的加入导致材料表面空化坑的投影面积下降了12.5%。结论 证实微磨粒对冲击波的传播起到了明显的衰减作用，是对材料表面产生作用的主要因素。该研究在超声加工领域具有理论意义和工程价值。

The effect of cavitation shock waves during power ultrasonic vibration machining can be produced. The presence of micro-abrasive particles can enhance the machining efficiency and impact the propagation of shock waves. The work aims to investigate the mechanism of micro-abrasive particles on shock waves during power ultrasonic vibration machining. By utilizing the Gilmore-Akulichev equation, the bubble dynamic equation under power ultrasonic vibration machining and the mathematical model of shock waves generated by the collapse of bubble were established. Subsequently, a propagation model for shock waves in the mixed medium of micro-abrasive particles and water was developed. The mathematical model was solved by the sixth-order Runge-Kutta method, providing insights into the dynamic evolution of bubble radius and the internal pressure of the bubble. The results indicated that a bubble with an initial radius of 8 μm exhibited nonlinear oscillations under the effect of the ultrasonic field. After a series of oscillations, the change in radius gradually diminished over time, indicating a convergence towards equilibrium between the pressure inside the bubble and the surrounding environment. When the bubble radius decreased from 8 μm to 3 μm, the pressure on the bubble wall remained relatively stable. Upon compression approximate to 1 μm, the internal pressure of the bubble could reach 1 000 MPa, surpassing the ambient pressure. Consequently, the cavitation bubble rebounded outward, compressing the surrounding water and generating a shock wave that propagated radially. By solving the shock wave pressure at a distance of 1.5R0 from the cavitation wall, it was found that the shock wave pressure rapidly decreased from the initial 1 000 MPa to 80 MPa within a short time of 0.07 μs, covering a propagation distance of 17 μm. Comparing the shock wave propagation speed in a pure water medium with that in a mixed medium of SiO2 micro-abrasive particles and water, it was discovered that the addition of SiO2 micro-abrasive particles reduced the maximum speed of the shock wave from 2 976 m/s to 2 681 m/s, resulting in a reduction rate of 10%. Subsequently, power ultrasonic vibration processing experiments were conducted on Ti-Ta alloy to validate the aforementioned numerical results. Through a comparative analysis of the surface structure and three-dimensional surface morphology of the Ti-Ta alloy before and after the addition of SiO2 micro-abrasive particles, it was observed that the number of cavitation pits decreased from 34 to 21. This indicated that the addition of SiO2 micro-abrasive particles reduced the occurrence of cavitation pits. The software ImageJ was utilized to measure the projected area of cavitation pits with diameter greater than 1 μm on the Ti-Ta alloy surface. The results showed that the addition of SiO2 micro-abrasive particles led to a decrease in the projected area of cavitation pits from 497.132 μm2 to 434.84 μm2, corresponding to a reduction rate of 12.5%. This reduction rate was in line with the 10% calculated by the model, demonstrating consistency. The observed discrepancy mainly arose from the uneven distribution of SiO2 micro-abrasive particles in the machining area during the machining due to factors such as gravity, resulting in varying obstacles to the shock wave. This study confirms that micro-abrasive particles effectively attenuate the propagation of shock waves and become a key factor affecting the material surface. The findings of this research hold both theoretical significance and practical value in the field of ultrasonic processing.