An Analytical Model of Torsional Vibration Isolator Using Negative Stiffness Structure

Abstract

As the recent industrial structure has become more advanced, the technical demands of the industry have been accordingly strengthened. In particular, in the ultra-precision industry, the industry's demands for vibration have become more complicated in the past decades because the vibration applied to machines affects both performance and quality of the product. Thus, vibration problems are a major factor to consider in the design of mechanical systems. Until now, there have been various studies to effectively reduce vibrations. A vibration isolation system is an example of one of several methods, which is a method to disturb the vibration that transmits from the source of vibration to the system. However, the vibration isolation method is only effective when the ratio between the excitation frequency and the system natural frequency is higher than a specific frequency ratio. Therefore, in the past, it was used to reduce the vibration of the desired frequency band by changing the natural frequency of the system, which is affected by the mass and stiffness of the system, and there were limitations in the vibration isolation. Thus, the nonlinear vibration isolation system has been studied as an alternative to overcome the limitation of previous vibration isolators. One of the methods proposed by researchers to construct a nonlinear vibration isolator is an isolation system using the Negative Stiffness Structure (NSS). In this case, “negative” indicates a situation where the displacement occurs in the direction opposite to the force by constructing a specific mechanical design and does not mean that the actual material has negative stiffness. When this NSS is combined with a conventional vibration isolation system, the stiffness of the entire isolation system can depend on the displacement. Therefore, previous studies aimed to make the dynamic stiffness of the system ideally close to zero by selecting the appropriate design value. Ultimately, they attempted to construct an isolation system with vibration isolation performance in a broad frequency region, particularly at low frequencies. Based on previous studies, here, we applied the nonlinear vibration isolation method to the rotational direction instead of focusing on the translational direction vibration. For the vibration that enters a system from a base, the direction of translation is mainly considered, but the rotational vibration such as rolling or yawing should also be considered according to the industry. Therefore, in this thesis, a mechanism that acts like a negative stiffness using links and springs is first constructed, and a Quasi Zero Stiffness (QZS) vibration isolation system is proposed using the above mechanism. To evaluate the performance of the proposed model, we measure the isolation performance against the rotational vibration from a fixed floor to a mass. At this time, a harmonic excitation corresponding to the natural frequency of the system is applied, and the displacement response of the mass according to the excitation is obtained. Then, we compare the resonance peak point change with the results of the previous vibration isolation system without NSS using the frequency response curves. The rotating vibration must be considered to evaluate the performance of the system, particularly in rotating systems. Thus, in this study, we conduct the following numerical example using the proposed model, which confirms that the vibration isolation performance is used as the shaft coupling to connect the drive shaft and the driven shaft. For this numerical example, we derive an approximated 2-DOF equation of motion for a system that rotates differently from the previous numerical example. Then, the isolation effect of the disturbance transmitted from the drive shaft to the driven shaft is analyzed. The result confirms that the proposed model can more effectively isolate the disturbance transmitting from the drive shaft to the driven shaft than the previous vibration isolation system, which only consists of a torsional spring. In addition, we investigate the proper stiffness ratio of the torsional spring and compression springs to improve the isolation effect by analyzing the principal variables. When the proposed model is used as a shaft coupling in the rotating system, the shock isolation ability should be considered as much as the harmonic excitation case. Finally, the results of the isolation performance against the shock pulse of the rotating system are obtained at the end of this study. In summary, the idea of a rotational direction vibration isolation system using NSS is expected to provide a new perspective in constructing a system to effectively isolate the rotational vibration in a broad area.