To obtain a longitudinal‐flexural coupling vibration transformer with large amplitude which met the requirements of gear ultrasonic machining ,a transformer with cascades horn was designed .Based on the Mindlin’s theory ,according to the force and displacement coupling condi‐tions between each part of the horn ,between the horn and gear ,and the boundary conditions , the frequency equation and the displacement amplitude equation were achieved .Then the trans‐former was designed and the amplitude distribution curve was obtained .The dynamic characteris‐tics of the transformer got by mode and harmonic response analysis with the help of ANSYS were consistent with both the theoretical solution and the resonance characteristic experiment . The amplitude at the pitch circle of the gear was 12 μm ,which was larger than that of the ordinary transformer and met the requirements of gear ultrasonic machining .%为了使纵弯谐振变幅器的输出振幅满足齿轮超声加工的要求，设计了一个带有级联变幅杆的变幅器。利用M indlin中厚板理论，根据变幅杆各段的力和位移耦合条件、变幅杆与齿轮的力和位移耦合条件、边界条件，推导出变幅器的频率方程和位移方程，实现了变幅器的设计，并求得变幅器的振幅分布曲线。通过理论求解、有限元软件ANSYS进行模态分析和谐响应分析、变幅器谐振特性试验分析变幅器的动力学特性，得出三者的结果一致，齿轮分度圆处的振幅为12μm ，较常用的变幅器有了较大的提高，满足了齿轮超声加工的需求。
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