Modeling, Testing, and Characteristic Analysis of a Planetary Flywheel Inerter

Shock and Vibration, Jan 2018

We propose the planetary flywheel inerter, which is a new type of ball screw inerter. A planetary flywheel consists of several planetary gears mounted on a flywheel bracket. When the flywheel bracket is driven by a screw and rotating, each planetary gear meshing with an outer ring gear generates a compound motion composed of revolution and rotation. Theoretical analysis shows that the output force of the planetary flywheel inerter is proportional to the relative acceleration of one terminal of the inerter to the other. Optimizing the gear ratio of the planetary gears to the ring gear allows the planetary flywheel to be lighter than its traditional counterpart, without any loss on the inertance. According to the structure of the planetary flywheel inerter, nonlinear factors of the inerter are analyzed, and a nonlinear dynamical model of the inerter is established. Then the parameters in the model are identified and the accuracy of the model is validated by experiment. Theoretical analysis and experimental data show that the dynamical characteristics of a planetary flywheel inerter and those of a traditional flywheel inerter are basically the same. It is concluded that a planetary flywheel can completely replace a traditional flywheel, making the inerter lighter.

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Modeling, Testing, and Characteristic Analysis of a Planetary Flywheel Inerter

Modeling, Testing, and Characteristic Analysis of a Planetary Flywheel Inerter Zheng Ge and Weirui Wang College of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China Correspondence should be addressed to Weirui Wang; moc.621@ujzrww Received 21 May 2017; Accepted 27 December 2017; Published 28 January 2018 Academic Editor: Georges Kouroussis Copyright © 2018 Zheng Ge and Weirui Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract We propose the planetary flywheel inerter, which is a new type of ball screw inerter. A planetary flywheel consists of several planetary gears mounted on a flywheel bracket. When the flywheel bracket is driven by a screw and rotating, each planetary gear meshing with an outer ring gear generates a compound motion composed of revolution and rotation. Theoretical analysis shows that the output force of the planetary flywheel inerter is proportional to the relative acceleration of one terminal of the inerter to the other. Optimizing the gear ratio of the planetary gears to the ring gear allows the planetary flywheel to be lighter than its traditional counterpart, without any loss on the inertance. According to the structure of the planetary flywheel inerter, nonlinear factors of the inerter are analyzed, and a nonlinear dynamical model of the inerter is established. Then the parameters in the model are identified and the accuracy of the model is validated by experiment. Theoretical analysis and experimental data show that the dynamical characteristics of a planetary flywheel inerter and those of a traditional flywheel inerter are basically the same. It is concluded that a planetary flywheel can completely replace a traditional flywheel, making the inerter lighter. 1. Introduction Mechanical vibration is widely found in nature as well as construction, vehicles, manufacture process, and other engineering fields. For a long time, researchers have deeply carried out studies on how to control the mechanical vibration. The traditional vibration control system is composed of two basic vibration control elements, spring and damper [1]. In 2002, Smith proposed a new type of two-terminal mechanical device called inerter, whose output force is proportional to the relative acceleration of one of the inerter’s terminals to the other, as sketched in Figure 1. and are the two terminals’ displacement of the inerter. The proportional coefficient in the figure is called the inertance and has units of kilograms [2]. Figure 1: Schematic diagram of an inerter. On the one hand, an inerter has two ends, which cannot be implemented by a mass block. On the other hand, the device can convert a linear motion into the rotational motion of a flywheel, which generates much more equivalent inertial mass than the gravitational mass of the flywheel [3]. For example, if the mass block in a dynamic vibration absorber is replaced by an inerter, the overall weight can be reduced by more than 90% [4]. The two characters of inerters have considerably enriched the design theory of mechanical vibration networks. As the effect of the inerter in the mechanical network is equivalent to that of the capacitor in the electrical network, the theoretical results of the electrical network synthesis can be applied to the mechanical network design. The realization problem of mechanical impedance with inerter was therefore studied in depth [5]. A number of special classes of admittances realization techniques have been applied to vehicle suspension designs [6, 7]. Various types of new passive suspension were proposed [8, 9]. Nowadays, the mechanical network design technology with inerter has also been applied to many fields such as construction [10] and robot [11]. Currently, there are multiple structural variants of inerters, ball screw type [12], rack and pinion type [13], hydraulic motor type [14], fluid type [15, 16], and so on. The ball screw inerter has less friction. And the nut preload of the ball screw inerter helps to reduce the impact of the backlash, gaining a better comprehensive performance [17]. Due to the unique advantages of ball screw inerters, the current theoretical research on them is relatively deep. The ball screw has become the structural basis of many new types of inerters. Papageorgiou and Smith established a dynamical model of a ball screw inerter with backslash and nonlinear elastic force and analyzed the influence of nonlinear factors on the dynamical characteristics of the inerter [18]. Hu et al. built a semiactive inerter by adding an electrically adjusted centrifugal block to a ball screw inerter, which provided a method of changing the inertance dynamically [19]. Pires et al. connected a motor to the end of the screw in an inerter and set up the electrical elements at the motor terminals, formin (...truncated)


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Zheng Ge, Weirui Wang. Modeling, Testing, and Characteristic Analysis of a Planetary Flywheel Inerter, Shock and Vibration, 2018, 2018, DOI: 10.1155/2018/2631539