串联倒摆的空气弹簧隔振器水平动力学分析

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振动与冲击 ›› 2019, Vol. 38 ›› Issue (14) : 176-180.

论文

串联倒摆的空气弹簧隔振器水平动力学分析

喻强1，徐登峰2，朱煜1,2，管高峰1，李强3

作者信息 +

Dynamics analysis on the horizontal isolation effect of an air spring vibration isolator in series with an inverted pendulum

YU Qiang1,XU Dengfeng2,ZHU Yu1,2,GUAN Gaofeng1,LI Qiang3

Author information +

文章历史 +

摘要

串联倒摆的空气弹簧隔振器垂直和水平方向同时实现了低刚度，具有较好的应用前景。以该隔振器为研究对象，考虑以往研究中经常忽略的空气弹簧的影响，通过求解空气弹簧内部压缩空气的压强和水平恢复力的大小，获得了空气弹簧的水平刚度。然后，将空气弹簧等效为一个水平弹簧，再与倒摆串联连接，通过动力学分析建立倒摆转动的运动微分方程，得到了水平方向固有频率表达式，并通过相关实验初步验证了该表达式的计算结果与实验测试结果误差较小。最后，仿真分析表明空气弹簧上活塞半径和负载总质量是影响水平方向固有频率的主要因素。

Abstract

An air spring vibration isolator in series with an inverted pendulum has a good perspective in engineering application, because the stiffnesses in the vertical and horizontal direction can reach very low at the same time.The influence of the airbag horizontal flexibility on the stiffness of the air spring in horizontal direction, which was ignored in previous studies, was investigated by calculating the pressure of compressed air in the airbag and the restoring force of the air spring.The air spring was equivalent to a horizontal spring and then this spring was connected in series with the inverted pendulum.The differential equation of motion of the inverted pendulum was established and the inherent frequency in the horizontal direction of the integrated air spring vibration isolator was obtained.Experimental results validate that the error between the calculated result and the measured one is rather small.In the end, the simulation results show that the radius of the upper piston of the air spring and the mass of the load mainly affect the inherent frequency.

导出引用

喻强1，徐登峰2，朱煜1,2，管高峰1，李强3. 串联倒摆的空气弹簧隔振器水平动力学分析[J]. 振动与冲击, 2019, 38(14): 176-180

YU Qiang1,XU Dengfeng2,ZHU Yu1,2,GUAN Gaofeng1,LI Qiang3. Dynamics analysis on the horizontal isolation effect of an air spring vibration isolator in series with an inverted pendulum[J]. Journal of Vibration and Shock, 2019, 38(14): 176-180

参考文献

[1] BLITZER L. Inverted Pendulum [J]. American Journal of Physics, 1965(33): 1076-1078.
[2] PHELPS F M Ш, HUNTER J H Jr. An Analytical Solution of the Inverted Pendulum [J]. American Journal of Physics, 1965(33): 285-295.
[3] PINOLI M, BLAIR D G, JU L. Tests on a low-frequency inverted pendulum system [J]. Measurement Science and Technology, 1993(4): 995-999.
[4] SAULSON P R, STEBBINS R T, DUMONT F D, et al. The inverted pendulum as a probe of anelasticity [J]. Review of Scientific Instruments, 1994, 65(1): 182-191.
[5] LOSURDO G, BERNARDINI M, BRACCINI S, et al. An inverted pendulum preisolator stage for the VIRGO susoension system [J]. Review of Scientific Instruments, 1999, 70(5): 2507-2515.
[6] YAGMUR L, GULMEZ T, HACIZADE F, et al. A new inverted pendulum to determine anelastic behavior of metals: Design and characterization [J]. Review of Scientific Instruments, 2005, 76(9): 093903-1 -093903-6.
[7] TAKAMORI A, RAFFAI P, MARKA S, et al. Inverted pendulum as low-frequency pre-isolation for advanced gravitational wave detectors [J]. Nuclear Instruments and Methods in Physics Research A, 2007(582): 683-692.
[8] 夏超，谭久彬. 基于复合摆倒摆串联的光学仪器气浮隔振方法研究[J]. 光电子激光，2011，22(10)：1551-1556.
XIA Chao, TAN Jiubin. An air flotation vibration isolation method based on compond pendulum inverted pendulum-series for optical instruments [J]. Journal of Optoelectronics•Laser, 2011, 22(10): 1551-1556.
[9] JOHN L. Car spring: 4965 [P]. United States Patent, 1847.
[10] HARRIS C M. Harris' shock and vibration handbook [M], New York: McGraw-Hill, 2002.
[11] ERIN C, WILSON B, ZAPFE J. An improved model of a pneumatic vibration isolator: theory and experiment [J]. Journal of sound and vibration, 1998, 218(1): 81-101.
[12] PU H, LUO X, CHEN X. Modeling and analysis of dual-chamber pneumatic spring with adjustable damping for precision vibration isolation [J]. Journal of Sound and Vibration, 2011, 330(15): 3578-3590.
[13] WATSON D C, PHILLIPS A H. Vibration isolator with low lateral stiffness: US6953109B2 [P]. United States Patent, 2005.
[14] BUTLER H, AUER F, VAN M, et al. Support Device and Lightographic Apparatus: US7170582B2 [P]. United States Patent, 2007.
[15] 谭久彬，夏朝，王雷，等. 基于球头连杆的气浮式正倒摆串联机构的空气弹簧隔振器: CN102072275 [P]. 2011.
[16] 朱继梅，俞宁长，邹岳华. 倒摆式气动隔振器: CN1487216A [P]. 2004.
[17] 刘亦工，齐豪. 膜片式无磨擦摆动光学平台隔振系统: CN101029853A [P]. 2007.
[18] 蒲华燕. 超精密隔振系统建模与控制方法研究[D]. 武汉：华中科技大学，2012.
[19] 董卡卡, 蒲华燕, 徐振高, 等. 超精密隔振系统的建模与参数辨识[J]. 武汉理工大学学报，2011, 33(1)：125-129.
DONG Kaka, PU Huayan, XU Zhengao, et al. Modeling and Parameter Identification of the Ultra-precision Vibration Isolation System [J]. Journal of Wuhan University of Technology, 2011, 33(1): 125-129
[20] 朱煜，喻强，徐登峰，等. 串联倒摆的空气弹簧隔振器中倒摆的稳定性分析[J]. 振动与冲击，2018, 37(6)：188-194.
ZHU Yu, YU Qiang, XU Dengfeng, et al. Stability analysis of the inverted pendulum in the air spring vibration isolator in series with the inverted pendulum [J]. Journal of vibration and shock, 2018, 37(6): 188-194.