正负刚度并联准零刚度隔振系统的研究

发布时间：2018-05-17 03:16

本文选题：高静低动刚度 + 负刚度　；参考：《哈尔滨工业大学》2015年硕士论文

【摘要】：针对精密超精密加工和测量中低频(频率小于2Hz)干扰的隔振会遇到静变形过大和失稳等问题,使得低频隔振成为隔振系统设计的一大难题。本课题采用正负刚度并联的结构,设计并验证了一种具有高静低动刚度特性的非线性隔振器。建立了高静低动刚度隔振系统的数学模型,对负刚度结构及组合系统的力-位移特性进行了深入分析,求解了系统的准零刚度条件,并将刚度渐硬特性系统、刚度渐软特性系统与该组合系统进行了对比。分析了该系统在简谐激励下的动力学特性,利用谐波平衡法求得了系统的幅频特性方程,分析了系统各参数对幅频特性的影响;由于系统为非线性,系统的幅频特性曲线出现了跳跃现象,为此求解了周期解稳定的条件,并近似计算了在较小激振力下,系统表现出刚度渐硬特性时的向上向下跳跃频率的表达式和跳跃现象消失时的临界阻尼比;设计的系统在较小位移时表现出刚度渐硬的特性,在较大位移时同时表现出刚度渐硬和刚度渐软的特性;通过与其线性系统对比,得出在合适的参数下高静低动刚度系统具更大的隔振区间和更小的力传递率和位移传递率;由于系统在静平衡位置处对载荷变化比较敏感,为此讨论了过载对隔振系统动态特性的影响。使用数值计算的方法得出系统的相图、庞加莱截面图和分岔图,讨论参数变化所引起的分岔和混沌特性。根据最大李雅普诺夫指数的正负判断系统是否处于混沌,利用随机相位和弱周期信号控制的方法,有效消除了系统的混沌。设计了隔振系统的实验平台。在振动台上进行了位移传递率实验,测试了准零刚度系统和线性弹簧的位移传递率。准零刚度隔振系统的实验结果在低频内误差较大,实际到2.5Hz时才有效隔振,但与线性系统对比,仍可得出该非线性系统可以获得较小固有频率,扩大隔振区间,并且在一定频率区间内具有更低的传递率。
[Abstract]:Low frequency (frequency less than 2 Hz) interference in precision ultra-precision machining and measurement will meet the problems of excessive static deformation and instability, which makes low frequency vibration isolation a major problem in the design of vibration isolation system. A nonlinear vibration isolator with low dynamic stiffness of Gao Jing is designed and verified by using a parallel structure with positive and negative stiffness. The mathematical model of Gao Jing vibration isolation system with low dynamic stiffness is established. The force-displacement characteristics of the negative stiffness structure and the composite system are deeply analyzed. The quasi-zero stiffness condition of the system is solved, and the stiffness hardening characteristic system is obtained. The stiffness softening characteristic system is compared with the combined system. The dynamic characteristics of the system under harmonic excitation are analyzed. The amplitude and frequency characteristic equation of the system is obtained by using harmonic balance method, and the influence of system parameters on amplitude frequency characteristic is analyzed. The jump phenomenon appears in the amplitude-frequency characteristic curve of the system. For this reason, the condition of the stability of the periodic solution is solved, and the stability of the periodic solution is approximately calculated under the small excitation force. The expression of the upward and downward jump frequency and the critical damping ratio when the jump phenomenon disappears, and the stiffness hardening characteristic of the designed system when the displacement is smaller, the system shows the expression of the upward and downward jump frequency when the stiffness is gradually hardening, and the critical damping ratio when the jump phenomenon disappears. Compared with the linear system, the Gao Jing low dynamic stiffness system has larger isolation range, smaller force transfer rate and smaller displacement transfer rate under suitable parameters. Since the system is sensitive to the load change at the static equilibrium position, the influence of overload on the dynamic characteristics of the vibration isolation system is discussed. The phase diagram, Poincare section diagram and bifurcation diagram of the system are obtained by numerical calculation, and the bifurcation and chaos characteristics caused by the variation of parameters are discussed. According to the positive and negative judgement of the maximum Lyapunov exponent, the chaos of the system is effectively eliminated by using the method of controlling random phase and weak periodic signal. The experimental platform of vibration isolation system is designed. The displacement transfer rate of the quasi zero stiffness system and the linear spring are tested on the shaking table. The experimental results of the quasi-zero stiffness vibration isolation system have a large error in the low frequency range. In fact, it is only effective to isolate the vibration in 2.5Hz. However, compared with the linear system, the nonlinear system can obtain a smaller natural frequency and expand the isolation range. And the transmission rate is lower in a certain frequency range.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB535.1

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