一种准零刚度系统隔振性能的几何参数优化分析

提出了一种采用菱形连杆组件作为负刚度机构的准零刚度隔振器(下文简称菱形准零刚度隔振器)。通过静力学分析方法,建立了菱形准零刚度隔振器数学模型,并与其他调节变量较少的隔振器模型进行了对比;以被测量曲线在隔振器平衡位置处的曲率作为评价参数,研究了负刚度机构几何参数对系统刚度、阻尼非线性的影响,推导了利用几何参数进行隔振优化的条件;采用谐波平衡法求解系统动力学方程,对隔振器在不同几何参数下的隔振性能进行了分析。结果表明:菱形准零刚度隔振器具有体积相对较小且非线性调节能力较好的特点,可通过调节杆长,或满足相关临界值条件时调节杆长偏差量(下文简称杆长差)对刚度及阻尼非线性特征进行优化;刚度与阻尼的非线性优化方向不同,但通常情况下,刚度非线性因素对隔振优化起主导作用;归一化振动相对位移小于0.1时,由刚度曲线曲率得到的临界值可以较好地作为杆长差参数的隔振优化调节依据。本文提出的非线性评价方法与几何非线性优化临界值计算方法,对于类似隔振器研究和设计具有一定的指导意义。

Analysis of geometric parameters for optimizing vibration isolation performance of a quasi-zero stiffness system

A quasi-zero stiffness vibration isolator with rhombic link assembly as the negative stiffness mechanism(NSM) is proposed(rhombic QZS-VI). The mathematical model of rhombic QZS-VI is established by static analysis and compared with other vibration isolator models of fewer adjusting variables. By taking the curvature of the measured curve at isolator balance position as the evaluation parameter, the influences of NSM geometric parameters on nonlinearity of system stiffness and damping are studied, and the conditions for optimizing the performance of vibration isolation by adjusting geometric parameters are deduced. Then, the system kinetic equation is solved by the Harmonic Balance Method(HBM), and vibration isolation performance under different geometric parameters is analyzed. The results show that the rhombic QZS-VI has characteristics of relatively small volume and better nonlinear regulation ability;stiffness and damping nonlinearity can be optimized by adjusting rod length(RL) or rod length deviation(RLD) when the relevant critical conditions are met;the nonlinearity optimization directions of stiffness and damping are different, but in general, the stiffness nonlinearity plays a dominant role in vibration isolation optimization. When the normalized relative displacement of vibration is less than 0.1, the critical value obtained from curvature of stiffness curve can be used as the basis for vibration isolation optimization adjustment of RLD. The proposed nonlinear evaluation method and geometric nonlinearity optimization critical values calculation method are of importance in the study and design of similar vibration isolator.