Research On Flexural Vibration Of Horn And Calculation Of Elliptical Vibration System

In ultrasonic machining,conventional chemical mechanical polishing has not been able to meet the needs of ultra-precision instruments for the processing of hard and brittle materials and deep holes.Ultrasonic vibration assisted machining can reduce the roughness of the surface of the processed material and improve production efficiency and material removal rate.The working principle is mainly to that the transducer generate vibration which is amplified by the horn and then transmitted to the ultrasonic tool bar to continuously assist the impact abrasive to process the surface of the workpiece.Therefore,ultrasonic vibration assisted processing has been widely used in recent years.The simplest construction of an ultrasonic vibration system consists of the transducer,the horn and the tool head.Ultrasonic horn,also known as ultrasonic concentrator,ultrasonic shift lever,is mainly used to aggregate energy amplify and the output amplitude of the transducer.In addition,the ultrasonic horn also acts as the impedance match,making the transfer of energy between the ultrasonic transducer and the acoustic load more efficient.There are many parameters for describing the performance of ultrasonic horns.The most basic ones are:amplification factor,resonance frequency,input force impedanee,form factor,and so on.According to the performance,it can be divided into the single horn,such as cylindrical,conical,exponential,catenary linear etc,and the composite horn,such as stepped-conical,conical-cylinder.When the ultrasonic horn is longitudinally vibrated,it is naturally accompanied by bending vibration,which will affects the stability of the ultrasonic vibration system.However,in actual ultrasonic machining,it is necessary to utilize the bending vibration of the rod.Therefore,the bending vibration law of the ultrasonic horn is studied in this paper.The bending vibration equation of the horn and the Euler-Bernoulli of the cylindrical ultrasonic horn and the stepped ultrasonic horn without considering the shear deformation and moment of inertia are derived.The theory,considering only the influence of shear deformation,only considering the influence of moment of inertia and the bending vibration equation and the resonant frequency equation of the Timoshenko theory considered.The resonant frequency of the first three-order bending vibration of the rod is calculated by programming,and the resonant frequency value of the rod is calculated by using the finite element analysis method.Finally,the correctness of theoretical calculations is proved by experiments.The longitudinal-bend composite ultrasonic elliptical vibration system was designed.And the Ultrasonic elliptical vibration system is analyzed using the finite element method.The specific work is as follows:(1)According to the bending vibration equation of the equal-section ultrasonic horn,The bending vibration equation of a cylindrical ultrasonic horn is derived,only considering the moment of inertia and the first three-order resonant frequency of the rod is programmed.Secondly,the bending vibration equation of the rod is derived,only considering the shear deformation,and the first three frequency values are calculated.Then,The bending vibration equation of the rod is derived without considering the moment of inertia and the shear deformation,which is The Euler-Bernoulli theory.And the first three-order resonant frequency is calculated.Finally,The bending vibration equation of the rod is derived with considering the moment of inertia and the shear deformation,which is the Timoshenko theory.And the first three-order resonant frequency of the rod is calculated.The resonant frequency of the first three-order bending vibration of the cylindrical ultrasonic horn is calculated by finite element software,and the theoretical calculation results are verified by experiments.The results show that the Timoshenko theoretical calculation results are closest to the experimental measurements when the quarter-wavelength of the cylindrical ultrasonic horn vibration is greater than the cross-sectional diameter of the rod.(2)The bending vibration of the stepped ultrasonic horn is required in ultrasonic machining.Using the free boundary conditions at the two ends of the rod and the continuous conditions of the physical quantities at the two joints,the bending vibration equation is derived,which including the Timoshenko theory considering shear deformation and moment of inertia,the Euler-Bernoulli theory without considering shear deformation and moment of inertia,the theory only considering the moment of inertia and the theory only considering shear deformation.The bending vibration frequency equation is derived according to the bending vibration equation,and the resonant frequency of the first three orders of the stepped ultrasonic horn is calculated.The finite element software is used to simulate the first three-order bending vibration resonance frequency of the stepped ultrasonic horn.To demonstrate the results,the frequency was tested with the VibPilot vibration system.The results show that when the cross-sectional diameter of the stepped ultrasonic horn is not negligible compared with the axial length,there is a large error between the resonant frequency value calculated by Euler-Bernoulli theory and the experimental test value,and the results of Timoshenko theory are more Close to the experimental value.The effect of shear deformation is higher than the influence of moment of inertia.(3)The resonant frequency of the bending vibration of the cylindrical ultrasonic horn and the stepped ultrasonic horm was tested.The results show that when the quarter-wavelength of the ultrasonic horn vibration is greater thari the cross-sectional diameter of the rod,the influence of shear deformation and moment of inertia on the bending vibration of the rod can’t be neglected at this time.The Timoshenko theoretical calculation is more accurate.The VibPilot vibration system multi-channel tester developed by m+p company can collect,control and analyze the vibration signal.(4)Ultrasonic elliptical vibration system is the core part of ultrasonic elliptical vibration processing.Ultrasonic elliptical vibration machining refers to the addition of elliptical vibration to a machining tool,and the high-frequency intermittent cutting of the workpiece to be processed is performed by using the elliptical vibration trajectory of the blade tip.Therefore,the ultrasonic elliptical vibration processing has the common advantages of ultrasonic longitudinal vibration processing and ultrasonic bending vibration processing,and the separation effect is obvious,and the complete separation of the cutter,the workpiece and the chip can be realized in the machining process.It can reduce cutting temperature and cutting force,and reduce cutting heat.Ultrasonic elliptical vibration is generally formed by two or more unidirectional vibrations.It can be composed of longitudinal-bending composite,bend-bend composite,longitudinal-twist composite,etc.Different processing requirements require different vibration systems..In this paper,an ultrasonic elliptical vibration system is designed,which is formed by the longitudinal-bending composite of ultrasonic transducer and ultrasonic horn.The frequency of the transducer is set to 20kHz.By calculating the relationship between the frequency and size of the ultrasonic horn,the program is written in Matlab software to draw the resonance curves of the longitudinal vibration and the bending vibration.Finally,the longitudinal calculation can be calculated according to the intersection of the curves.The geometry of the rod when the same frequency is resonated,and finally the desired ultrasonic elliptical vibration system is designed.The finite element software is used to calculate the ultrasonic elliptical vibration system.The results show that at the frequency of 20kHz,the longitudinal vibration and baiding vibration of the ultrasonic vibration system can be basically combined into ultrasonic elliptical vibratioii,which can verify that the theoretical design is correct This theoretical calculation "method provides a basis for the design of ultrasonic elliptical vibration system.