Design Of Ultrasonic Horns Of Sine Compound Type And Their Dynamical Analysis

With the application of glass, ceramic, quartz, diamond and other highhardness, high brittleness materials in many fields, how to machine these hardand brittle materials has become a problem needed to be solved urgently. Theultrasonic machining is not only suitable for machining the materials that aredifficult to machine, but also for ultrasonic cleaning, grinding etc.Generally, ultrasonic machining device mainly consists of ultrasonicgenerator, transducer, vibration transmission rod, ultrasonic horn, tool and anyother parts. Among them, ultrasonic horn plays an important role in amplifyingthe vibration displacement or energy. Stepped horn among the horns that oftenused has more advantage in amplification radio than cone，exponential andcatenary horn, however its smaller form factor and stress concentration causedby the section break limits its application. Therefore, to design a horn thatpreferment more excellent in amplification radio and form factor is an important subject in ultrasonic machining study.Homogeneous transformation method using the unknown function is usedto solve one dimensional wave equation of longitudinal vibration. Thenthe sine horn section function is deduced. Through frequency equation,magnification radio and displacement nodal calculation formula is derived bythe analytical method, it can be indicated that the horn shape and amplificationradio and other properties can be changed flexibly by choosing the differentinitial phases when the area of coefficient N is constant. By using the softwareANSYS, the correctness of the theory is verified and the form factor of the hornis calculated. It is observed that with the initial phase increasing, themagnification radio is increased and the form factor is decreased, and the shapeand properties are gradually approaching the conical rod. Due to its lowermagnification radio，sine horn is not suitable for efficient machining as asingle horn.On this basis, two kinds of composite horn are designed by combining withthe one-dimensional longitudinal vibration theory and ANSYS software:（1）Composite horn of sine type with cylindrical rod at narrow end. By choosing thereasonable initial phase and length of sine section, the compound horn has moreadvantages than stepped horn in amplitude radio and form factor;（2）Steppedhorn with transitional section of ψ=90°sine type. Its working stress is less thanthe conical transition that the lengths and diameters of wide and narrow endare the same with the horn. Finally, taking sine horn of initial phase ψ=90°, it analyzes tool how toinfluence working frequency of horn and amplifying ability. The dynamicanalysis results of the vibration system composed of horn and tool, show that（1）the tool does not transform the output displacement of the horn rigidly as aload of the horn simply, but transmits the ultrasonic wave and enlarges furtherthe output displacement;（2）the natural frequency of vibration system is closeto ultrasonic horn, or the tool. Especially when the natural frequency ofvibration system is equal to the tool, it will appear the phenomenon of "localresonance". However, through the establishment of mechanical model on theresearch of the above phenomenon, the vibration system is doing full resonanceworking at any frequency；（3）the diameter and length of the tool have a largeeffect on the resonance frequency and amplification function of the vibrationsystem.