新型准零刚度隔振器的设计和特性研究

发布时间：2018-06-04 23:20

本文选题：碟形弹簧 + 准零刚度　；参考：《中国人民解放军军事医学科学院》2015年博士论文

【摘要】：本文在总结国内外准零刚度隔振器理论研究和结构设计的基础上,针对车载精密仪器对其隔振器低频隔振性能的要求和占用空间尺寸的限制,创新设计了两种新型准零刚度隔振器。综合运用非线性振动的近似解析方法和数值方法,对所设计准零刚度隔振器的静力学特性,及其构成的准零刚度隔振系统的动力学特性和隔振性能进行了系统的研究,探索了两自由度准零刚度隔振系统的力传递率特性,设计装配了准零刚度隔振器原理样机,完成了静力实验和振动实验。主要工作和结论如下:(1)基于正负刚度并联隔振原理,采用等厚度碟形弹簧作为负刚度元件与线性正刚度螺旋弹簧并联,设计了一种准零刚度隔振器。首先通过静力学特性研究,分别建立了等厚度碟形弹簧和准零刚度隔振器的回复力和刚度特性表达式;并分别求取了等厚度碟形弹簧具有负刚度,以及隔振器在平衡位置附近具有准零刚度特性的参数条件。研究结果表明,等厚度碟形弹簧在处于压平状态时具有刚度最小值,其最小负刚度值和负刚度区域范围与等效高厚比和支点距离比两个参数有关。通过增大等效高厚比和减小支点距离比,可以使等厚度碟形弹簧的最小负刚度值减小和负刚度区域范围增大。对于准零刚度隔振器,等效高厚比、支点距离比以及等厚度碟形弹簧与线性螺旋弹簧之间的刚度比是影响其准零刚度特性的三个参数。当等效高厚比增大和支点距离比减小时,需要更小的刚度比来保证其在平衡位置处的零刚度。且通过增大等效高厚比和减小支点距离比,可以使准零刚度隔振器在平衡位置附近具有更小的刚度和更大的较小刚度范围,从而具有更大的准零刚度特性位移范围。然后通过动力学特性研究,分别建立了谐波力激励和谐波位移激励条件下准零刚度隔振系统的非线性运动微分方程;采用平均法求解了系统的稳态响应,研究了系统参数和激励幅值对系统频响曲线和隔振性能的影响,并与其等效线性系统进行了比较;采用马蒂厄方程判别法得到了系统稳态响应解的稳定性判定边界条件。研究结果表明,两种谐波激励条件下准零刚度隔振系统的运动微分方程为对称激励条件下的杜芬方程。准零刚度隔振系统为刚度渐硬的非线性系统,且存在不稳定区域和跳跃现象。适当地减小激励幅值和增大阻尼比可以减小系统的不稳定区域和隔振起始频率,且能够使谐波位移激励条件下的系统稳态响应解避免出现无限大值。除此之外,在控制激励幅值的基础上,适当地增大阻尼比,或通过增大等效高厚比和减小支点距离比来减小系统的非线性项,均可以使准零刚度隔振系统相对于其等效线性系统具有更好的低频隔振性能。(2)由于等厚度碟形弹簧的变形量较小,将其作为负刚度元件构建的隔振器具有准零刚度特性的位移范围也相对较小。针对此问题,采用厚度沿径向线性变化的变厚度碟形弹簧作为新的负刚度元件,设计了一种新的准零刚度隔振器。首先通过静力学特性研究,分别建立了变厚度碟形弹簧和准零刚度隔振器的回复力和刚度特性表达式;并分别求取了变厚度碟形弹簧具有负刚度,以及隔振器在平衡位置附近具有准零刚度特性的参数条件;对于分别具有等厚度和变厚度碟形弹簧的两种隔振器,比较分析了相同参数条件下两者的准零刚度特性位移范围;并对具有变厚度碟形弹簧的准零刚度隔振器构造参数进行了优化,得到了其具有最大准零刚度特性位移范围的最优参数取值。研究结果表明,变厚度碟形弹簧和准零刚度隔振器均在变厚度碟形弹簧处于压平状态时具有刚度最小值。相对于采用等厚度碟形弹簧,变厚度碟形弹簧可以使隔振器在相同位移处的刚度减小,且偏离平衡位置的位移和厚度变化规律参数?值越大,刚度减小的越大。因此,具有变厚度碟形弹簧的准零刚度隔振器在平衡位置附近具有更小的刚度和更大的较小刚度范围,从而具有更大的准零刚度特性位移范围。然后考虑实际应用中系统极易出现的过载和欠载情况,通过动力学特性研究,分别建立了谐波力激励和谐波位移激励下过载和欠载系统的非线性运动微分方程;采用谐波平衡法得到了过载系统的稳态响应近似解,并采用四阶龙格库塔法对其进行了数值仿真验证;基于弗洛凯理论,得到了过载系统稳态响应解的稳定性判定边界条件;研究了偏移位移和激励幅值对过载系统频响曲线和隔振性能的影响,并与理想系统和等效线性系统进行了比较;最后探讨了阻尼比对三个系统隔振性能的影响。研究结果表明,两种谐波激励条件下过载和欠载系统的运动微分方程均为霍尔姆兹-杜芬方程,其可以转化为非对称激励条件下的杜芬方程。采用谐波平衡法和四阶龙格库塔法得到的过载系统稳态响应基本吻合,证明了采用谐波平衡法求解的稳态响应近似解具有较强的精确性。不同偏移位移和激励幅值条件下,过载系统的最多稳态响应解数量会出现1个、3个和5个的情况。随着激励幅值的增大,过载系统的刚度特性不断变化,依次表现为线性、渐软、先渐软后渐硬、渐硬。偏移位移和激励幅值越小,过载系统的隔振起始频率越小,隔振频率范围越大。增大阻尼比,可以消除过载系统和理想系统的跳跃现象和不稳定区域,提高其低频隔振性能,但是会影响其在高频段的隔振性能。而当激励幅值较大时,适量的过载可以提高准零刚度隔振系统的隔振性能。但总的来说,减小过载质量、控制激励幅值和适当增大阻尼比,可以使准零刚度隔振系统隔离更低频的振动,具有更好的低频隔振性能。(3)在无阻尼或阻尼较小的情况下,两自由度线性隔振系统第二阶共振频率对应的力传递率最大值较大,导致其在第二阶共振频率附近范围内不能隔振。针对此问题,基于所设计优化的准零刚度隔振器,构建了两自由度准零刚度隔振系统。首先完成了两自由度准零刚度隔振系统及其两自由度等效线性系统的动力学建模,然后采用平均法推导了谐波力激励条件下两个系统的力传递率,最后研究了激励幅值、质量比和阻尼比对其力传递率的影响,并比较分析了两个系统的隔振性能。研究结果表明,两自由度准零刚度隔振系统第二阶共振频率对应的力传递率最大值小于1,意味着其在第二阶共振频率附近范围内仍具有隔振效果,从而克服了其两自由度等效线性系统的缺点。相较于两自由度等效线性系统,两自由度准零刚度隔振系统的隔振起始频率更小,隔振频率范围更大,从而具有更好的低频隔振性能。且激励幅值越小,其低频隔振性能优势越明显。两自由度准零刚度隔振系统在高频段也具有更好的隔振性能。但随着质量比和阻尼比的增大,其在高频段内的隔振性能优势减小。除此之外,通过适当地增大质量比和阻尼比,可以减小两自由度准零刚度隔振系统的隔振起始频率,增大隔振频率范围,提高其低频隔振性能。(4)设计装配了准零刚度隔振器的原理样机,分别搭建实验平台完成了静力实验和振动实验。首先通过静力实验,研究了碟形弹簧、线性螺旋弹簧和准零刚度隔振器的静力学特性;然后通过振动实验,研究了激励幅值对过载系统隔振性能的影响,并与其等效线性系统进行了比较。实验结果表明,所设计碟形弹簧和线性螺旋弹簧的实际与理论力-位移曲线基本吻合。但是由于材料和加工等影响因素的存在,碟形弹簧和线性螺旋弹簧的实际曲线与理论曲线仍存在一定的误差。且实际装配过程中产生的预紧力导致准零刚度隔振器在其碟形弹簧处于压平状态时的回复力大于相同位置处碟形弹簧和线性螺旋弹簧的回复力之和。随着激励幅值的增大,过载系统的共振频率及其对应的传递率最大值均先减小后增大,与理论分析结论相符。但由于原理样机和实验平台存在较大的阻尼,实验获得的实际传递率曲线均表现为线性,并没有出现非线性现象。总的来说,碟形弹簧的负刚度能够抵消线性螺旋弹簧的正刚度,从而有效降低准零刚度隔振器的动态刚度。相对于等效线性系统,过载系统具有更小的隔振起始频率和更大的隔振频率范围,从而具有更好的低频隔振性能。但为了保证过载系统在高频段的隔振性能优势,系统的阻尼不能过大。本文对所设计准零刚度隔振器的理论和实验研究结论,为将来应用于车载精密仪器隔振,保证车载精密仪器的安全性和可靠性具有重要的意义。
[Abstract]:On the basis of summarizing the theoretical research and structural design of the quasi zero stiffness isolator at home and abroad, two new quasi zero stiffness isolators are designed and designed in this paper, aiming at the requirements for the low frequency vibration isolation performance of the vehicle precision instruments and the limitation of the space size of the vibration isolators. The static characteristics of the quasi zero stiffness isolator are designed and the dynamic characteristics and vibration isolation performance of the quasi zero stiffness isolation system are systematically studied. The force transfer rate characteristics of the two degree of freedom quasi zero stiffness isolation system are explored. The prototype of the quasi zero stiffness isolator is designed and assembled, and the static experiment and vibration experiment are completed. The main work and conclusions are as follows: (1) based on the principle of positive and negative stiffness parallel vibration isolation, a quasi zero stiffness isolator is designed with the equal thickness disc spring being parallel to the linear positive stiffness spiral spring as a negative stiffness element. First, the restoring force of the equal thickness disc spring and the quasi zero stiffness isolator is established by the static characteristics. The stiffness characteristic expression and the parameter conditions of the equal thickness disc spring with the negative stiffness and the quasi zero stiffness characteristic near the equilibrium position are obtained respectively. The results show that the minimum stiffness value of the equal thickness disc spring in the flat state, the minimum negative stiffness value and the negative stiffness region range and the equivalent thickness are obtained. The distance between the fulcrum and the fulcrum is related to the two parameters. By increasing the equivalent thickness ratio and reducing the distance ratio of the fulcrum, the minimum negative stiffness value of the equal thickness disc spring and the area of the negative stiffness can be increased. For the quasi zero stiffness isolator, the equivalent height to thickness ratio, the distance ratio of the pivot point and the stiffness between the equal thickness disc spring and the linear spiral spring are the same. The degree ratio is the three parameter that affects its quasi zero stiffness characteristics. When the ratio of the equivalent height to thickness increases and the distance between the pivot points is reduced, a smaller stiffness ratio is needed to ensure the zero stiffness at the equilibrium position. And the quasi zero stiffness isolator can have smaller stiffness near the equilibrium position by increasing the equivalent thickness ratio and reducing the distance ratio of the pivot point. And a larger smaller stiffness range has a larger quasi zero stiffness characteristic displacement range. Then through the study of the dynamic characteristics, the nonlinear differential equations of the quasi zero stiffness isolation system under the harmonic force excitation and the harmonic displacement excitation are established respectively. The steady-state response of the system is solved by means of the mean method, and the system parameters are studied. The effect of the excitation amplitude on the frequency response curve and vibration isolation performance of the system is compared with that of the equivalent linear system. The stability determination boundary condition of the steady-state response solution of the system is obtained by using the Mathieu equation method. The results show that the differential equation of the motion of the quasi zero stiffness isolation system under the two harmonic excitation conditions is symmetric excitation. The quasi zero stiffness isolation system is a nonlinear system with stiffness gradually hardening, and there is an unstable region and jumping phenomenon. Reducing the excitation amplitude and increasing the damping ratio can reduce the unstable region and vibration initiation frequency of the system, and can avoid the steady-state response solution of the system under the harmonic displacement excitation. In addition, on the basis of controlling the excitation amplitude, the damping ratio is properly increased, or the nonlinear term of the system is reduced by increasing the equivalent height to thickness ratio and the distance ratio of the fulcrum, all the quasi zero stiffness isolation system can have better low frequency vibration isolation performance relative to its equivalent linear system. (2) because of the equal thickness disc. The deformation of the shape spring is small, and the displacement range of the isolator, which is constructed by the negative stiffness element, is relatively small. A new quasi zero stiffness isolator is designed by using the variable thickness disc spring with the thickness along the radial line as a new negative stiffness element. The expressions of the restoring force and stiffness characteristic of variable thickness disc spring and quasi zero stiffness isolator are established respectively, and the parameters of the variable thickness disc spring with negative stiffness and the quasi zero stiffness characteristics near the equilibrium position are obtained respectively, and two kinds of separate plates with equal thickness and variable thickness are separated respectively. The displacement range of the quasi zero stiffness characteristic under the same parameters is compared and analyzed, and the structural parameters of the quasi zero stiffness isolator with variable thickness disc spring are optimized and the optimum parameters of the displacement range with the maximum quasi zero stiffness characteristic are obtained. The results show that the variable thickness disc spring and the quasi zero stiffness are obtained. The isolator has the minimum stiffness when the variable thickness disc spring is in the flat state. Compared with the same thickness disc spring, the variable thickness disc spring can reduce the stiffness of the isolator at the same displacement, and deviate from the equilibrium position and the variation of the thickness. The greater the value, the larger the stiffness decreases. Therefore, the thicker is thicker. Therefore, the thicker is thicker. Thus, the thicker is thicker. The quasi zero stiffness isolator of the degree disc spring has a smaller stiffness and a larger smaller stiffness range near the equilibrium position, thus having a larger quasi zero stiffness characteristic displacement range. Then considering the overloading and under load conditions that are very easy to appear in the practical application, the harmonic force excitation harmony is established through the study of the dynamic characteristics. The nonlinear motion differential equations of overload and under load system are excited by wave displacement, and the approximate solution of the steady-state response of the overload system is obtained by using the harmonic balance method. The four order Runge Kutta method is used to verify the numerical simulation. Based on the Floke theory, the stability determination boundary condition of the stability response solution of the overload system is obtained. The effect of displacement and excitation amplitude on the frequency response curve and vibration isolation performance of the overload system, and compared with the ideal system and the equivalent linear system. Finally, the influence of the damping ratio on the vibration isolation performance of the three systems is discussed. The results show that the differential equations of motion of the overload and under load systems under the two harmonic excitation conditions are all Holm This equation can be converted to the duffen equation under asymmetric excitation. The steady-state response of the overload system obtained by the harmonic balance method and the four order Runge Kutta method is basically consistent. It is proved that the approximate solution of the steady-state response by the harmonic balance method is more accurate. With the increase of the excitation amplitude, the stiffness characteristics of the overload system are constantly changing with the increase of the excitation amplitude. In turn, the stiffness characteristics of the overload system are constantly changing, which in turn shows linear, gradually softening, gradually softening and hardening. The smaller the offset displacement and excitation amplitude are, the smaller the starting frequency of the overload system is, the greater the frequency range of the vibration isolation is. The large damping ratio can eliminate the jumping and unstable region of the overload system and the ideal system, and improve its low frequency vibration isolation performance, but it will affect its vibration isolation performance at the high frequency section. When the excitation amplitude is large, a proper amount of overload can improve the vibration isolation performance of the quasi zero stiffness isolation system. But in general, the overload quality and control excitation are reduced. The excitation amplitude and the appropriate increase of damping ratio can make the quasi zero stiffness isolation system isolate the vibration of more low frequency, and have better low frequency vibration isolation performance. (3) the maximum value of the force transfer rate corresponding to the second order resonance frequency of the two degree of freedom linear isolation system is larger in the case of the less damped or less damped, which leads to its vicinity of the second order resonance frequency. In order to solve this problem, a quasi zero stiffness isolation system with two degrees of freedom is constructed based on the quasi zero stiffness isolator designed and optimized. The dynamic modeling of the two degree of freedom quasi zero stiffness isolation system and its two degree of freedom equivalent linear system is completed, and then two systems under the harmonic force excitation are derived by the flat mean method. The effect of the excitation amplitude, mass ratio and damping ratio on the force transfer rate is studied, and the vibration isolation performance of the two systems is compared and analyzed. The results show that the maximum value of the force transfer rate corresponding to the second order resonance frequency of the two degree of freedom quasi zero stiffness isolation system is less than 1, which means that it is near the second order resonance frequency. There is still a vibration isolation effect in the enclosure, thus overcoming the disadvantage of its two degree of freedom equivalent linear system. Compared with the equivalent linear system of two degrees of freedom, the two DOF quasi zero stiffness isolation system has a smaller vibration isolation starting frequency and a larger vibration isolation range, and thus has a better low frequency isolation performance. And the lower the excitation amplitude, the lower the vibration isolation performance. The more obvious advantage. The two degree of freedom quasi zero stiffness isolation system also has better vibration isolation performance at high frequency section. But with the increase of mass ratio and damping ratio, the advantage of vibration isolation performance decreases in the high frequency section. In addition, the vibration isolation of the quasi zero stiffness isolation system of two degrees of freedom can be reduced by increasing the mass ratio and damping ratio appropriately. First frequency, increase the frequency range of vibration isolation and improve its low frequency vibration isolation performance. (4) the prototype of quasi zero stiffness isolator is designed and assembled, and the static experiment and vibration experiment are completed respectively. First, the static characteristics of disc spring, linear spiral spring spring and quasi zero stiffness isolator are studied by static test. The effect of the excitation amplitude on the vibration isolation performance of the overload system is investigated and compared with the equivalent linear system. The experimental results show that the actual force displacement curves of the designed disc spring and the linear spiral spring are basically consistent with the theoretical force displacement curves. But the disc spring and linear screw are the influence factors of the material and processing. There is still some error between the actual curve and the theoretical curve of the rotating spring. And the pre tightening force produced in the actual assembly process leads to the sum of the restoring force of the quasi zero stiffness isolator in the plate spring at which the disk spring and the linear spiral spring are at the same position. With the increase of the excitation amplitude, the overload system is increased. The resonance frequency and its corresponding maximum transfer rate first decrease and then increase, which coincide with the theoretical analysis. However, because of the large damping of the prototype and the experimental platform, the actual transfer rate curves obtained by the experiment are linear and have no nonlinear phenomenon. In general, the negative stiffness of the disc spring can offset the linearity. The positive stiffness of the helical spring can effectively reduce the dynamic stiffness of the quasi zero stiffness isolator. Compared with the equivalent linear system, the overload system has smaller vibration isolation starting frequency and larger vibration isolation frequency range, thus having better low frequency vibration isolation performance. The theoretical and experimental conclusions of the quasi zero stiffness isolator designed in this paper are of great significance for the future application of the vehicle precision instruments to vibration isolation, and to ensure the safety and reliability of the vehicle precision instruments.
【学位授予单位】：中国人民解放军军事医学科学院
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TB535.1

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