本文選題：高靜低動(dòng)剛度 + 負(fù)剛度�。� 參考：《哈爾濱工業(yè)大學(xué)》2015年碩士論文

【摘要】：針對(duì)精密超精密加工和測(cè)量中低頻(頻率小于2Hz)干擾的隔振會(huì)遇到靜變形過(guò)大和失穩(wěn)等問(wèn)題,使得低頻隔振成為隔振系統(tǒng)設(shè)計(jì)的一大難題。本課題采用正負(fù)剛度并聯(lián)的結(jié)構(gòu),設(shè)計(jì)并驗(yàn)證了一種具有高靜低動(dòng)剛度特性的非線(xiàn)性隔振器。建立了高靜低動(dòng)剛度隔振系統(tǒng)的數(shù)學(xué)模型,對(duì)負(fù)剛度結(jié)構(gòu)及組合系統(tǒng)的力-位移特性進(jìn)行了深入分析,求解了系統(tǒng)的準(zhǔn)零剛度條件,并將剛度漸硬特性系統(tǒng)、剛度漸軟特性系統(tǒng)與該組合系統(tǒng)進(jìn)行了對(duì)比。分析了該系統(tǒng)在簡(jiǎn)諧激勵(lì)下的動(dòng)力學(xué)特性,利用諧波平衡法求得了系統(tǒng)的幅頻特性方程,分析了系統(tǒng)各參數(shù)對(duì)幅頻特性的影響;由于系統(tǒng)為非線(xiàn)性,系統(tǒng)的幅頻特性曲線(xiàn)出現(xiàn)了跳躍現(xiàn)象,為此求解了周期解穩(wěn)定的條件,并近似計(jì)算了在較小激振力下,系統(tǒng)表現(xiàn)出剛度漸硬特性時(shí)的向上向下跳躍頻率的表達(dá)式和跳躍現(xiàn)象消失時(shí)的臨界阻尼比;設(shè)計(jì)的系統(tǒng)在較小位移時(shí)表現(xiàn)出剛度漸硬的特性,在較大位移時(shí)同時(shí)表現(xiàn)出剛度漸硬和剛度漸軟的特性;通過(guò)與其線(xiàn)性系統(tǒng)對(duì)比,得出在合適的參數(shù)下高靜低動(dòng)剛度系統(tǒng)具更大的隔振區(qū)間和更小的力傳遞率和位移傳遞率;由于系統(tǒng)在靜平衡位置處對(duì)載荷變化比較敏感,為此討論了過(guò)載對(duì)隔振系統(tǒng)動(dòng)態(tài)特性的影響。使用數(shù)值計(jì)算的方法得出系統(tǒng)的相圖、龐加萊截面圖和分岔圖,討論參數(shù)變化所引起的分岔和混沌特性。根據(jù)最大李雅普諾夫指數(shù)的正負(fù)判斷系統(tǒng)是否處于混沌,利用隨機(jī)相位和弱周期信號(hào)控制的方法,有效消除了系統(tǒng)的混沌。設(shè)計(jì)了隔振系統(tǒng)的實(shí)驗(yàn)平臺(tái)。在振動(dòng)臺(tái)上進(jìn)行了位移傳遞率實(shí)驗(yàn),測(cè)試了準(zhǔn)零剛度系統(tǒng)和線(xiàn)性彈簧的位移傳遞率。準(zhǔn)零剛度隔振系統(tǒng)的實(shí)驗(yàn)結(jié)果在低頻內(nèi)誤差較大,實(shí)際到2.5Hz時(shí)才有效隔振,但與線(xiàn)性系統(tǒng)對(duì)比,仍可得出該非線(xiàn)性系統(tǒng)可以獲得較小固有頻率,擴(kuò)大隔振區(qū)間,并且在一定頻率區(qū)間內(nèi)具有更低的傳遞率。
[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.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：TB535.1

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本文編號(hào)：1899657