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在超声珩齿加工中,由变幅杆和被加工齿轮组成的变幅器的设计是一项关键技术,探索新型变幅器显得非常重要。基于变截面复合变幅杆纵向振动波动方程和中厚圆环板弯曲振动位移方程,根据复合变幅杆与中厚圆环组成的超声珩齿复合变幅器的非谐振性和边界条件,推导了系统的谐振频率方程,利用数值计算对设计参数、谐振频率、变幅杆及圆环振幅分布等进行研究,同时分析了变幅器几何参数对系统谐振频率的影响。结果表明,有限元分析结果与理论计算结果和实验测试基本一致,系统谐振频率随复合变幅杆各段长度的增加而减小;当复合变幅杆大小端半径比和各段长度保持不变时,系统谐振频率随两端半径成比例地增加而增加;其他参数不变时随圆环厚径比地增加而增加,其结论不仅证实了非谐振理论的正确性,而且为超声珩齿变幅器的设计和应用提供了理论依据。
In ultrasonic honing, the design of a horn that consists of a horn and a machined gear is a key technology and it is important to explore new horns. Based on the equations of longitudinal vibration fluctuation of variable cross section composite horn and the bending vibration displacement equation of the medium thickness annular plate, according to the nonresonance and boundary conditions of ultrasonic honing composite horn consisting of composite horn and medium thick ring The resonant frequency equation of the system is studied. The design parameters, resonant frequency, horn and ring amplitude distribution are studied numerically. At the same time, the influence of the geometrical parameters of the horn on the resonant frequency of the system is analyzed. The results show that the finite element analysis results are in good agreement with the theoretical and experimental results. The resonance frequency of the system decreases with the increase of the lengths of the composite horn. When the radius of the composite horn is constant and the lengths of the segments remain the same , The resonant frequency of the system increases with the increase of the radius of both ends. The other parameters increase with the increase of the thickness-to-diameter ratio while the other parameters are invariant. The conclusion not only confirms the correctness of the non-resonant theory, The design and application of the loudspeaker provide the theoretical basis.