Study On Ultrasonic Vibration System Of Spiral Bevel Gear Based On Structural Characteristics

Spiral bevel gear is one of the most complex space gears in mechanical transmission,which has been widely used in many fields,such as machine tools,aerospace and so on.With the development of technology and the emergence of new materials,as a traditional method of gear finishing,gear lapping is being continually improved.A new method is provided by combining traditional lapping with ultrasonic vibration for solving the problem of the gear finishing.However,it is vital to have a better ultrasonic vibration system for the ultrasonic lapping.In this paper,the ultrasonic vibration system with bevel gear is taken as the research object.There are several aspects mainly researched in the following:1 According to the design theory of the longitudinal vibration transducer and ultrasonic horn,and the structural characteristics of spiral bevel gear wheel,the bevel gear is reasonably simplified.Then the composite horn is made up of bevel gear and a cylindrical-conical-cylinder three section horn.And the ultrasonic vibration system is designed.Based on the wave equation of longitudinal vibration of one dimensional variable section pole,the mathematical model of composite horn is established.According to the boundary conditions and the continuity conditions of the force and displacement,the resonance frequency equation of the composite horn is derived.Then the resonant frequency equation is used to calculate the parameters of the composite horn to make it achieve resonance.2 The transducer is designed on the basis of the composite horn.Ultrasonic vibration system composed of composite horn and transducer.The dynamic analysis of the ultrasonic vibration system is carried out in the ANSYS software to verify the correctness of the theoretical calculation of the composite horn.It can be obtained that the variations of the shaft bevel gear parameters have regular influences on the ultrasonic vibration resonant frequency and relative displacement of the gear part,which provide the basis for the design of ultrasonic vibration system with the bevel gear,by changing the gear parameters which contain such as large and small end radius,tooth thickness,the radius and the length of the gear shaft,and several modal analyses.3 Based on the functional expression of the general solution of the onedimensional wave equation and the necessary conditions for the solution of the linearequations,the resonance frequency equation of three kinds of ladder shaped composite horn is derived.The parameters of composite horn can be calculated by MATLAB,then the design of the ladder type composite horn is completed.The amplification coefficient and the maximum stress are obtained from the design.The ultrasonic vibration system is composed of the transducer and the composite horn that is selected the best performance of the composite horn.And the dynamic analysis is carried out to the ultrasonic vibration system by using the simulation software ANSYS.4 According to the design of the ultrasonic vibration system,an object is made.Then its impedance and amplitude are tested,the result is that the resonant frequency of the system is 23.269 KHz,which meets the design requirements,though have some error comparing with the theoretical design and finite element analysis,and meet the design requirements.The two main parameters of the ultrasonic horn are the mechanical quality factor and the electromechanical coupling coefficient.And the test demonstrates that the conversion efficiency of the vibrator and the mechanical energy is relatively high.Meanwhile the amplitude of the small end face of the bevel gear is measured by vibration measurement with laser.The result is 9um,which meets the design requirements.