纵向谐振变幅器的非谐振设计理论研究与验证

Research and Verification on the Non-Resonant Design Theory of Longitudinal Vibration Transformer

为了实现齿轮超声加工纵向谐振变幅器的设计,提出了纵向谐振变幅器的非谐振设计理论,将变幅器简化为由变幅杆、齿轮等效圆环、心轴、螺母等效圆柱四部分组成的理论分析模型,根据各部分的动力学方程、各结合面的力、位移耦合条件和两端面的边界条件,建立变幅器的频率方程,实现纵向谐振变幅器的设计。分别设计了变幅杆材料为45钢、齿轮材料为铸造锡青铜以及变幅杆材料为45钢、钛合金、硬铝合金、齿轮材料为45钢的纵向谐振变幅器,通过有限元软件ANSYS模态分析和谐振特性实验研究了变幅器的谐振特性,变幅器的谐振频率与理论设计频率的误差小于5%,在误差允许范围内,表明变幅器的非谐振设计理论对于设计齿轮超声加工纵向谐振变幅器具有很好的通用性,为齿轮超声加工振动系统的设计提供了理论基础。

A new non-resonant design theory was built to design longitudinal vibration transformer in gear ultrasonic machining. The new mathematical model of transformer c^nsists of horn, the equivalent ring of gear,dabber and the equivalent cylinder of nut. Kinetic equations, force and displacement coupling and boundary conditions were utilized to establish the frequency equation of transformer. Some transformers with horn material 45 steel, Ti alloy,hard aluminum alloy and gear material 45 steel, as well as the horn material 45 steel and the gear material bronze, were designed The resonance characteristic of transformer has been achieved by modal analysis with the finite element software ANSYS and resonance experiment. The error is less than 5% and meets the need of engineering application. It is proved that the non-resonant design theory is applied to design longitudinal vibration transformer generally and possesses theoretical guidance significance to design the vibration system of gear ultrasonic machining.