Theoretical And Experimental Research On Inbarmonic Design Of Resonance System In Ultrasonic Gear Honing

Modern gear transmissions must be compact, noiseless and stable in performance, so the most primary need is hardened gear with high precision. Gear honing process used in the finial process of quench-hardening gear is a surface finishing machining. However, traditional gear honing was inefficient and poor ability of modification, while honing wheel was jammed usually. Gear honing was restricted within these drawbacks. Ultrasonic vibration can reduce honing forces obviously and ultrasonic cavitations of machining liquid can implement dynamic washing during the machining process, which decreases the jam of honing wheel and increases the honing efficience. So the ultrasonic gear honing has a bright future to apply. Gear resonance system is the core of gear ultrasonic honing system, which has significant effect on gear ultrasonic machining quality. Most of the researchers designed ultrasonic resonance system in resonant way. Otherwise, gear is a inharmnoic unit. The inherent vibration frequency of gear is decided by its own stcture and paremeters according to engineering application. It is reasonable to design gear ultrasonic resonance system in inharmnoic design method rather than resonant design. Therefore, it brought forward a inharmonic design theory of gear amplitude transformer, which can design resonant system of thin plate helical gear in ultrasonic honing. However, the ratio of thickness to reference diameters of most gear in engineering application falls into that of moderate plate. At the same time, there are hub, web, rim, weight reducing holes structures in most gear. It can’t adopt moderate plate theory straightway to design resonance system in ultrasonic gear honing, which restricts the development and application of ultrasonic gear honing. There are no consummate design theories of gear ultrasonic resonance system. It is important to set up design theory system of ultrasonic resonance system composed of inharmonic units. The inharmonic design theory is essential for small and moderate modulus gear with different structure feature in ultrasonic honing.It is compulsory to present design theory of resonant system composed of two inharmonic units such as gear and horn. In ultrasonic gear honing, the gear’s modulus is less than10mm and the reference circle diameter is about300mm. It also laid more emphasis on the distinguish and affiliation of whole-resonance and inharmonic design theories. Through theoretical and experimental view, it proved that the whole-resonance design theory is a special case of the inharmonic design theory, the inharmonic design theory covers the whole-resonance design theory, which is the expansion and deepening of the ultrasonic vibration system design theory. It presented a inharmonic design approach to design transformer in ultrasonic gear honing. Firstly, it brought out a simplified vibration analytical model that was equivalent to the gear, according to gear structure characteristic. Secondly, it set up a united analytical model of vibration system composed of gear and horn. Therefore, frequency equation was achieved in this way based on kinetic equation, force and displacement coupling, and boundary condition. The unknown parameter and mode shape have been solved in the theory with the help of Matalab201IRa.There are three kinds of vibration style such as longitudinal mode, longitudinal-flexural mode, and longitudinal-radial mode in ultrasonic gear honing, according to the coupling vibration style of the two inharmonic units. An analyzed model of gear with wheel hub, web and rim was derived from the Mindlin moderate plate theory. The gear was divided into three annular segments along the locations of the step variations. The natural boundary conditions that traverse displacement, rotation angle, shear force and flexural moment were equal to ensure the continuity along the interface of the wheel hub, web and rim segments. The governing differential equations for harmonic vibration of annular segments were derived to solve the gear vibration problem. Comparisons were made with the frequencies arising from the presented method, finite elements method, and structure modal experiment. The result correlation among these three ways is quite consistent. The model has certain theoretical significance to guide designing a vibration system in ultrasonic gear honing.Mechanical impedance and resonance characteristic are two key guideline to design resonant system in ultrasonic gear honing. Impedance characteristic measure system was set up based on impedance analyzer. Polytec Laser Doppler Vibrometers OFV-505and lathe C6140were used to precisely measure mechanical vibrations amplitude of different location in gear of resonant system, which will be helpful for accurate design and experiment of resonant system.Furthermore it pointed out that these gear parameters range was suit to certain vibration style of resonance system. During the machining process of the gear with middle or small modulus, it could be appropriate for the gear with less than100millimeter diameter of reference circle and the ratio of thickness to radial dimension more than0.3to use the amplitude transformer with longitudinal vibration mode. It also could be appropriate for the gear with more than100millimeter diameter of reference circle and the ratio of thickness to radial dimension less than0.3to use the amplitude transformer with longitudinal and flexural vibration mode. A novel design method was derived from a uniform analyzed model of gear with wheel hub, web and rim based on the Mindlin moderate plate theory. The uniform analytical model of resonant system in longitudinal-lexural vibration was set up based on kinetic equation, force and displacement coupling, and boundary condition of horn and gear. The natural boundary conditions that traverse displacement, rotation angle, shear force and flexural moment were equal to ensure the continuity along the interface of the wheel hub, web and rim segments. Therefore, frequency equation was achieved in this way. Comparisons were made with the frequencies and displacement arised from the presented method, finite elements method, and resonant vibration experiment. The result derived from these three ways is very identical, which validates the design method of transformer in longitudinal-flexural vibration mode. The design method of resonant system composed of two units in gear flexural vibration was brought forward, which can extend the transformer design range from gear including thin annular plate to gear including moderate annular plate. The inharmonic design theory will provided theoretical and technical support for resonant system of helical gear with different structure and parameters.It presented the Ritz method in Energy-variational principle based on three dimensional elasticity kinetics equations. Three vibration modes such as longitudinal, bending and torsional vibration inherent frequencies and mode shapes for conical, exponential and catenary horns could be solved. Analytical solutions based on the three dimensional elastic vibration theories produce more accurate answers than ones that are based on the classical Euler-Bernoulli theory. Axisymmetric free vibration such as transverse flexural and radial vibration inherent frequencies and mode shapes for annular disk with non-uniform thickness cross section could be solved. The present work proposes a new approach to vibrational characteristics analysis of the annular disks with non uniform cross-section. The conclusion has certain theoretical guidance and engineering application significance to design the vibration system of ultrasonic gear machining.The high speed ultrasonic gear honing device was developed with the help of the above design theory, furthermore, the ultrasonic gear honing experimental system in gear honing machine Y4650was established. The contrast experiment of using the longitudinal, longitudinal and transversal amplitude transformer in ultrasonic gear honing to the traditional gear honing was also accomplished. At the same time, surface roughness, revolution mark, honing cutting efficiency and the gear machining precision have been contrastive analyzed. It can achieve better gear roughness and two times cutting efficiency through the ultrasonic honing method than it in the traditional method. At last, the tooth precision through the direction of ultrasonic vibration becomes better, which provides a experimental proof that it is possible to improve gear honing precision and enforce modification possibility by gear ultrasonic vibration.The dissertation was supported by the national natural science foundation project of China (Grant No.50975191) of China and the outstanding innovation project (Grant No.20113027) of Shanxi province foundation for graduate student. The above theory and experiment form the inharmonic design theory of resonant system in ultrasonic gear honing, which enriches and perfects the design theory of ultrasonic machining vibration system. The inharmonic design theory is suitable for resonant system in gear ultrasonic hobbing, shaving and lapping. The experiment about the comparison between the result of ultrasonic honing and that of traditional honing laids a solid theoretical and experimental foundation of the research and application of gear ultrasonic machining.