考虑设备阻抗的隔振系统特性与主动控制研究

发布时间：2018-05-27 04:36

本文选题：阻抗 + 柔性隔振　；参考：《山东大学》2014年硕士论文

【摘要】：基础的非刚性,隔振器的分布参数特性以及机器在高频下所表现出的弹性特性造成了经典隔振理论与实际隔振效果的高频段差异。柔性隔振理论克服了经典隔振理论的不足,将隔振系统中某子系统以适当弹性模型代替,分析了子系统弹性阻抗特性对高频隔振效果的影响。在隔振系统中,基础的非刚性是造成经典隔振理论差异的主要因素。此外,隔振器是具有一定质量的分布参数系统,当激振频率达到隔振器中弹性波半波长的整数倍时,就有可能在隔振器中产生驻波效应,这是导致高频隔振效果下降的又一因素。除了基础与隔振器所表现出的弹性.特性对隔振效果有影响外,系统中较为薄弱的部件或纵跨比较大的结构在高频下也可能因刚性不足而导致弹性模态被激发。如对于横向尺寸较小的被隔振设备一般刚性较大,可以考虑成绝对刚体,但被隔振设备与隔振器间需通过支撑机脚、支撑框架等连接,这些部件在高频下可能因刚性不足而表现出弹性特性；在双层隔振或浮筏隔振系统中,中间质量弹性模态在高频下也有可能被激发,在高频下其有限阻抗特性都不能被忽略。若不考虑以上部件弹性阻抗特性,也会导致理论预估出现较大偏差。本学位论文着重对系统阻抗特性进行探讨,以功率流为评价指标对系统中部件的弹性特性进行研究,以期为工程实际提供理论指导。为了探讨柔性隔振系统中各子系统弹性特性的影响,建立了Euler-Bernoulli梁、Timoshenko梁、薄板和厚板等模型弯曲振动微分方程,给出了不同边界条件下的振型函数,结合杜哈美积分与正交条件导出了不同模型的导纳函数并通过实例仿真对导纳函数进行了对比。针对单一垂向单层隔振系统,分别以Euler-Bernoulli梁、Timoshenko梁、薄板以及厚板模型为基础,对比探讨了两种梁、板理论模型下的功率流谱。研究表明,在低频下,两种梁、板模型之间无明显差异。但随着激振频的升高或梁长细比减小、板厚度增大,Euler-Bernoulli梁和Timoshenko梁模型之间、薄板和厚板模型之间的差异逐渐增大；隔振器在基础上的安装方式会影响基础模态的激发。对于两端固定梁基础,隔振器对称布置仅激发其奇数阶模态,非对称布置时全部模态都被激发；对于四边简支板基础,隔振器相对x、y轴全部对称布置时,m、n均为奇数的模态被激发,仅相对于x轴(y轴)方向对称时,m为奇数(n为奇数)的模态被激发,若相对与x、y轴都不对称,则所有模态都被激发；为了考察设备有限阻抗特性的影响,在单一垂向柔性隔振系统中,将被隔振设备分为刚性机器与弹性设备支撑两部分。结合Euler-Bernoulli梁、薄板理论,将设备的支撑框架或支撑结构考虑成两端自由Euler-Bernoulli梁或四边自由薄板,为了对设的弹性特性进行探讨,故忽略刚性机器的影响,将其视为振源且输出一常力作用在设备支撑上,以导纳功率流法着重探讨了设备支撑弹性、振源激励点位置以及隔振器安装位置对隔振效果的影响。研究发现,设备中作为振源的机器部分与隔振器都应尽量对称布置,以避免低频段系统横摇模态的出现,此时高频段设备支撑与基础会发生模态丢失现象,由此避免了峰值密集而导致隔振效果变差。考虑设备支撑弹性后功率流谱中会出现向下尖峰模态,这种模态主要由设备支撑的弹性振动引起,其出现频率取决于设备支撑的物理参数与其上激励点位置,与基础及其耦合作用无关。基于Euler-Bernoulli梁理论建立了三向复合激励下的双层主\被动控制系统动力学模型,分析了系统刚体模态,隔振器驻波效应以及基础弹性模态对隔振效果的影响,分析了中间质量有限阻抗特性的影响。对基础功率流最小控制策略进行了详细研究。通过分析得出,在系统对称布置情况下,单一垂向激励会激发系统两阶垂向刚体模态,引起隔振器纵向驻波,使基础奇数阶弯曲振动模态激发。单一横摇力矩会激发系统两阶横摇刚体模态并耦合两阶横向刚体模态,引起隔振器纵向驻波,使基础偶数阶弯曲振动模态激发。单一横向激励会激发两阶横向刚体模态并耦合两阶横摇刚体模态,引起隔振器弯曲驻波,使基础偶数阶弯曲振动模态以及纵向振动模态激发；在中间质量基频以后频段范围其刚体模型不再适用,中间质量弹性模态被激发导致高频隔振效果变差且可能在功率流谱中出现“反共振”峰；对于上层控制双层隔振系统,采用基础功率流最小控制策略后,无约束主动控制力使系统垂向、横摇刚体模态消失,基础弯曲振动模态消失,同时隔振器纵向驻波消失,仅横向刚体模态、隔振器弯曲振动模态和基础纵向振动模态被激发,但二次作动力与一次力相比较大。施加控制约束后整体隔振效果较无约束时有所下降,但在低频段对刚体模态峰值具有很好的衰减,且作动力远小于无约束时作动力,与一次力量级相同,因此约束主动控制更符合工程实际要求。
[Abstract]:In addition , the vibration isolator is a distributed parameter system with a certain mass . In addition , the vibration isolator is a distributed parameter system with a certain mass . In addition , the vibration isolator is a distributed parameter system with a certain mass . In addition , the vibration isolator is an absolute rigid body when the excitation frequency reaches an integral multiple of the half wavelength of the elastic wave in the vibration isolator .
In the double - layer vibration isolation or floating raft vibration isolation system , the intermediate mass elastic mode can be excited at high frequency and its finite impedance characteristic cannot be ignored under high frequency . If the elastic impedance characteristic of the above components is not considered , the theoretical prediction can be greatly deviated . The paper mainly discusses the impedance characteristic of the system , and studies the elastic characteristics of the components in the system with the power flow as the evaluation index , so as to provide theoretical guidance for engineering practice .

In order to discuss the influence of the elastic properties of each subsystem in the flexible vibration isolation system , a differential equation of bending vibration of the model is established , such as Euler - Bernoulli beam , beam , thin plate and thick plate , and the vibration type function under different boundary conditions is given . The admittance function of different models is derived by combining the integration and the orthogonal conditions of Duhamel and the admittance function is compared by example simulation .

For a single vertical single - layer vibration isolation system , the power flow spectrum under the theoretical model of two beams and plates is compared with the Euler - Bernoulli beam , the beam , the thin plate and the slab model .
The vibration isolator is mounted on the foundation , which affects the excitation of the fundamental mode . For the fixed beam foundation at both ends , the symmetric arrangement of the vibration isolator only excites its odd order mode , and all modes are excited when the asymmetric arrangement is arranged .
When the vibration isolator is symmetrically arranged with respect to the x and y axes on the basis of the four - sided simple - supported plate , m and n are all symmetrically arranged with respect to the x - axis and the y - axis . When the vibration isolator is symmetrical only with respect to the x - axis ( y - axis ) direction , m is an odd number ( n is an odd number ) , and if both the x and y axes are not symmetrical , all modes are excited ;
In order to investigate the influence of the finite impedance characteristics of the equipment , the vibration isolation equipment is divided into two parts : a rigid machine and an elastic device in a single vertical flexible vibration isolation system . According to the Euler - Bernoulli beam and the thin plate theory , the supporting frame or the supporting structure of the equipment is considered as a free Euler - Bernoulli beam or a four - sided free thin plate .

Based on the Euler - Bernoulli beam theory , the dynamic model of the double - layer main passive control system under three - directional composite excitation is established , the influence of the rigid mode of the system , the standing wave effect of the vibration isolator and the fundamental elastic mode on the vibration isolation effect are analyzed .
in that frequency band aft the fundamental frequency of the intermediate quality , the rigid body model of the frequency band is no longer applicable , and the elastic mode of the intermediate mass is excite to cause the high - frequency vibration isolation effect to be degraded and the " anti - resonance " peak may appear in the power flow spectrum ;
For the upper - layer control double - layer vibration isolation system , after the minimum control strategy of the basic power flow is adopted , the system vertical , roll rigid body mode disappears , the vibration mode of the basic bending vibration disappears , the longitudinal standing wave of the vibration isolator disappears , and only the transverse rigid body mode , the vibration isolator bending vibration mode and the basic longitudinal vibration mode are excited .
【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB535.1

【参考文献】