Calculation Model for the Steady-State Vibration Amplitude of a New Type of Cascaded Composite Structure-Based Ultrasonic Transducer

The steady-state vibration amplitude is an important performance indicator of high-frequency ultrasonic transducers for ultrasonically assisted manipulating,machining,and manufacturing.This work aimed to develop a calculation model for the steady-state vibration amplitude of a new type of dual-branch cascaded composite structure-based ultrasonic transducer that can be used in the packaging of microelectronic chips.First,the steady-state vibration amplitude of the piezoelectric vibrator of the transducer was derived from the piezoelectric equation.Second,the vibration transfer matrices of the tapered ultrasonic horns were obtained by combining the vibration equation,the continuous condition of the displacement,and the equilibrium condition of the force.Calculation models for the steady-state vibration amplitude of the two working ends of the transducer were then developed.A series of exciting trials were carried out to test the performance of the models.Comparison between the calculated and measured results for steady-state vibration amplitude showed that the maximum deviation was 0.0221μm,the minimum deviation was 0.0013μm,the average deviation was 0.0097μm,and the standard deviation was 0.0046μm.These values indicated good calculation accuracy,laying a good foundation for the practical application of the proposed transducer.

Experimental and computational investigation of transonic speed

The influence of the wing-tip vortex of leading aircraft on energy savings,quantified by formation aerodynamic force fraction of the following aircraft,is studied at transonic speed for a matrix of leading aircraft’s vortex locations.The research model adopts the hybrid formation of medium and large aircraft.The leading aircraft is scaled by 2.1%,and the following aircraft is scaled by 1.4%.An aerodynamic benefit "map"is developed to determine the optimum location of the following aircraft relative to the leading aircraft wake and to compare with experimental results,thus validating the use of CFD for the formation flight at cruising speed.The response surface model of aerodynamic gain effect relative to formation parameters is established via numerical calculation and wind tunnel test.The optimal formation parameters and the setting criteria of the study model are optimized.Results show that the wing-tip vortex of large aircraft significantly increases lift and reduces drag on the medium-sized aircraft following it.Reduced drag slightly increases with the flow direction position.With the increase of flow direction distance,the peak area moves from 15%of wing-tip overlap to 20%of overlap.In addition,the maximum drag decreases about 16%,and the maximum lift increases about 12%.The lift drag ratio of the optimal position is increased by 27%,which is twice as large as that of the same scale ratio aircraft formation.Results show that the increase of lift is mainly caused by the increase of suction peak and suction range.