| The ultrasonic vibration system, composed of transducer, transformer and tool, is the core of ultrasonic machining equipments. According to the half-wavelength-vibration theory, the size of the system's each part must have the same resonance frequency to guarantee the system work as a whole. The length of the tool is only allowed to vary within a very small range, making the ultrasonic machining application limited. To improve this situation, Fan Guoliang et al. studied a novel tool system for ultrasonic machining of deep, small holes and proposed so called "local resonance" in the ultrasonic complex vibration system. Although the phenomenon of "local resonance" has been verified by a number of experiment and application, its mechanism is still under discussion and there is no final conclusion so far. Because a stepped ultrasonic transformer and a local resonance system have the similar structure, i.e. they both have an abrupt change in cross section, a study on the vibration characteristic of the stepped transformer will certainly have realistic meanings for probing the mechanism of "local resonance". Zhang Da'an and others studied the variation law of the resonance frequency, when the cross-section ratio N<4,and the empirical formulas was put forward. However, the cross section's concrete vibration and the condition of N>4 has not been studied. This article relies mainly on FEM, adopt the experiment to measure and theoretic calculate to verify at the same time, analyze and research the vibrate characteristic of the stepped transformer in cross-section (including the resonance frequency, amplification coefficient and amplitude distribution). On this basis, local resonance is studied by FEM, the impact on some parameter to that is sought, and the mechanism and the production condition of local resonance of ultrasonic vibration system is discussed. These works for perfecting the ultrasonic vibration theory and promoting the practical application of have important meaning.In detail, the thesis include several aspects:1 Two groups of the stepped transformer with different cross section are studied, and the resonance frequency, amplification coefficient, vibration characteristics in cross section and location of displacement node are analyzed with FEM software. With thechange of cross section ratio of stepped transformer, the parabola regulation of resonance frequency is found. About lnN2=2.4, when the two parts of transformer is equal, the difference between the value of FEM and that of theory is biggest, and lie in the valley bottom of the curve. About lnN =3.5, when the length of two part of transformer is unequal, the difference is biggest. Finding the move of the frequency minimum value has relationship with the ratio of two parts length. According to the comparative discovery with the value of theory and experiment: When the cross section ratio is smaller than 100, ANSYS artificial displacement amplitude vs the cross-section ratio represents the direct ratio. And this law is not restricted by the condition of formula (the cross section ratio <5), which can be applied to all stepped transformer. When the vibration with ANSYS is simulated, the membrane vibration by traction rather than piston vibration on the boundary of two parts of transformer is discovered, the thin part of transformer is regarded as the traction bar glued at membrane. According to the graph of displacement distribution, the nodal location of displacement is found, and for the first and the third mode of two groups of transformer, the boundary of cross section and the nodal point is very close. It can be regarded that the boundary is the location of nodal point, and the antinodes of the stress. But to the second mode of longitudinal vibration of the transformer with equal parts in length, the boundary of cross section is exactly the amplitude of displacement, the node of the stress.2> The article is while studying Local Resonance, the scheme "from simples to complicated" is adopted, the practical vibration system of Local Resonance is simulated by the vibration of the stepped transformer with unequal parts in length. In this way could make the experiment parameter simplify, but the essence of the local resonance will not be influenced. Four groups of the stepped transformer with unequal parts in length are studied by FEM, combining with the value of experiment and theory, the effect of the cross section ratio and the length of tool to local resonance are found. Theoretic discuss of local resonance is processed by carrying on the further study of the stepped transformer. Local resonance can be regarded as the coupling vibration between the driver system and the tool is verified, the weien chart of local resonance is composed of many mutually crossed and coupling curves, which is caused by the action of the frequency mutual coupling and the influence of many vibrant units. The article simulates the stepped transformer by FEM for probing into the local resonance. When the length ratio of transformer varies, the different in the curve that represent the... |
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