This paper presents a non-resonant design approach to design transformer based on kinetic equation, force and displacement coupling, and boundary condition in order to design longitudinal vibration system in gear ultrasonic machining. Therefore, frequency equation was a-chieved in this way. The unknown parameters and mode shape had been theoretically solved under the help of Matalab2011Ra. Furthermore, the modal and harmonic analysis had been implemented in ANSYS12. 0. Transformers in longitudinal vibration for different modulus were designed and machined. The laser vibrometer test system based on C6140 lathe was set up to measure the vibration frequency and displacement of longitudinal vibration system. A harmonious vibration experiment was carried out. Comparisons were made with the frequencies and displacement arising from the presented method, finite elements method, and resonant vibration experiment. The largest error is less than 5%, which can meet the need of engineering application. The non-resonant design method of force and displacement coupling is competent for designing transformer in longitudinal vibration system, which has certain theoretical guidance and engineering application significance to design the vibration system of gear ultrasonic machining.%为了解决齿轮超声加工纵向振动系统设计问题,基于纵向振动动力学方程,利用结合面的力、位移振动耦合与边界条件,提出纵向振动变幅器的非谐振设计方法,推导了频率方程；应用Matlab2011Ra对变幅器未知尺寸、振型分布进行理论数值求解,并利用ANSYS12.0对所设计变幅器进行模态分析与谐响应分析.设计加工了不同模数齿轮的纵向振动变幅器,基于C6140车床搭建了齿轮超声加工纵向振动系统的激光测振仪测试系统,进行谐振实验.变幅器的谐振频率和振幅经理论求解、有限元分析、实验测试对比,各自的最大求解偏差都小于5％,可以满足工程应用需要.研究表明:可应用力、位移耦合非谐振设计方法,完成中小模数齿轮变幅器的纵向振动系统设计,对齿轮超声振动系统设计具有理论指导和工程应用价值.
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