Theoretical And Expeirmental Research On Inharmonic Design Of Resonance System In Gear Ultrasonic Machining

Gear is the foundation of equipment manufacturing industry and plays animportant role in its development. The future gears are oriented to high-accuracy,high speed, long life, high efficiency, low noise, high-power and minimization.So the research and application of a new gear machining process is verymeaningful. Gear ultrasonic machining process can reduce machining forces androughness of gear surface, improve the life of tool, machining efficiency andmachining accuracy, as well as, machining precision and revolution mark areimproved. Therefore, it is of great significance to study the gear ultrasonicmachining process. The design of resonance system is vital and its resonantvibration character has great influence on the quality of gear ultrasonicmachining. Non-resonant design method is the most commonly used method forthe system of gear ultrasonic machining. However, this method is imperfect andthe output displacement amplitude of the existing vibration system is small,which has a negative impact on the application of gear ultrasonic machining.Based on the non-resonant design method, the design of resonance system and the way to increase the output displacement amplitude were studied in this paper.This dissertation was supported by the Outstanding Innovation Project of ShanxiProvince Foundation for Graduate Student “Research on mechanism andapplication of gear ultrasonic vibration honing”(No.20133042) and the Scienceand Technology Innovation Project of Taiyuan University of Technology forGraduate Student “Research on application of gear ultrasonic vibration honing”(No.2013B095). The following researches on the inharmonic design ofresonance system in gear ultrasonic machining have been studied:(1)The design of longitudinal vibration transformerLongitudinal vibration transformer was designed with theoretical analyticalmethod, equivalent circuit method and transfer matrix method. The advantages,disadvantages and applicable occasions of the above three theoretical designmethods are well-known, which provides a theoretical basis to choiceappropriate method to design longitudinal vibration transformer. When thematerials of horn and gear are different, the new analytical model of transformerconsists of horn, the equivalent ring of gear, dabber and the equivalent cylinderof nut. Kinetic equations, force and displacement coupling and boundaryconditions were utilized to establish the frequency equation of transformer. Theresonance characteristic of transformer has been achieved by presented method,finite elements method and resonant vibration experiment, and the resultcorrelation among the three methods is good. It is proved that the non-resonantdesign theory is viable and this theory is further improved and perfected. (2)The design of new longitudinal vibration transformerBased on non-resonant design theory and whole resonant design theory, anew gear longitudinal vibration transformer, which consists of a couplingvibration unit of gear and cylinder rod, a half-wavelength cone horn weredesigned. The amplitudes of gear and horn were large at the connection site ofthis new system, and the output amplitude of gear was increased as well. Whenthe parameters of cone horn are certain, the diameters of gear and cylinder rodmake no difference to the output amplitude of gear. However, the smaller thesmall diameter of cone horn is, the larger the output amplitude of gear is. Finiteelement analysis and resonant vibration experiment verify the feasibility andeffectiveness of this new design method. The result from this paper provides anew design method for gear longitudinal vibration transformer.(3)The design of transformer with longitudinal and transversal vibrationBased on the non-resonant design method and Mindlin’s theory, conetransformers of which the materials of horn are45steel, Ti alloy, hard aluminumalloy and brass were designed, and the amplitude at the pitch circle of the geardecreases with the decreasing of impedance characteristic of horn’s material. Inorder to increase the displacement amplitude of gear, a transformer withcascades horn was designed. The amplitude at the pitch circle of the gear istwelve micrometers, which is larger than that of the existing transformer.(4)The design of new transformer with longitudinal and transversalvibration Based on non-resonant design method, a new transformer with longitudinaland transversal vibration was designed. Positioning gear at anywhere of whichthe displacement amplitude is large increases the displacement amplitude of gear.The resonance characteristic of transformer has been achieved by theoreticalsolution and finite elements method, and the amplitudes of gear and hornincreases sharply at the connection site. The result from this paper provides anew design method for transformer with longitudinal and transversal vibration.The above theory and experiment enriches and perfects the inharmonicdesign theory of resonance system in gear ultrasonic machining. The outputdisplacement amplitude of resonance system was increased. This paper laids atheoretical and experimental foundation of the application of gear ultrasonicmachining.