【作者】 胡兵；

【导师】 方之楚；

【作者基本信息】 上海交通大学 ， 一般力学与力学基础， 2008， 博士

【摘要】 在现代高速旋转机械中,转子不平衡引起的有害振动造成生产效率的下降、被加工产品精度的降低甚至机器的损坏。转子不平衡造成的严重后果,阻碍和约束下一代工业技术如高速、高精度机加工的实现。由于机械运行中可能存在着时变原始不平衡的瞬态动力特性,成熟的离线不平衡技术已经不能解决这类时变不平衡问题。转子主动平衡控制技术因融合了其它先进技术且提高了机械运转的可靠性,就能解决这类复杂问题并带来显著的经济效益。以前先进的转子主动平衡控制技术仅局限于常转速下使用,现有的自适应主动控制技术也不能处理现代化工业生产中经常出现的变速转子平衡。本文研究的变速转子主动平衡自适应控制技术不仅能有效地适用于一般变速转子,还有效地适用于带作动器时迟或作动器饱和的变速转子。本文对变速转子系统主动平衡自适应控制进行了研究。研究的内容涉及慢变速转子的准稳态条件、变速准稳态转子主动平衡系统的增益调度控制、带作动器时迟的快变速转子主动平衡系统的自适应控制与带作动器饱和的快变速转子主动平衡系统的自适应控制,转子类型包括Jeffcott转子、轴承各向异性的Jeffcott转子、单并置平衡平面(作动器和测量平面几乎在同一个平面)的柔性转子和多并置平衡平面的柔性转子。本文的第一部分研究了常转速和变速转子动力学模型之间的异同点与转化条件。以变速的Jeffcott转子作为基本模型,一方面解析求解瞬态不平衡响应,另一方面离散变转速,以一系列转子常转速全响应来近似表示该瞬态不平衡响应,进而找出后者近似代替前者的定性适用条件,即准稳态条件。第二部分研究了变速准稳态转子主动平衡系统的增益调度控制。在转子系统满足准稳态条件前提下,延伸基于转子稳态平衡的影响系数法到慢变速转子单平面或多平面增益调度控制,分析了影响增益调度控制稳定性的诸因素,以数值模拟证实了增益调度控制能有效地抑制慢变速转子的不平衡振动。本文的第三部分提出了带作动器时迟的快加速转子主动平衡系统自适应控制方法并进行了研究。首先,在转子动力特性的先验知识未知情况下,对一个带作动器时迟的严格正实转子系统建立简单的直接自适应控制律;接着,对原始模型作适当变换,构建一个Lyapunov-Krasovskii函数,推导出该自适应控制律的稳定性条件。然后,以带作动器时迟的快加速Jeffcott转子为研究对象,引入过滤函数,修改这个系统的传递函数使之成为一个严格正实系统,进而可采用前面推导出的满足稳定性条件的自适应控制律。数值模拟表明:满足系统稳定性条件的自适应控制律能有效地抑制该转子原始不平衡产生的振动。接着,还研究了带作动器时迟、轴承各向异性的变速Jeffcott转子系统主动平衡的自适应控制,着重考虑轴承各向异性对作动器时迟的影响。最后,把带作动器时迟的严格正实转子系统的自适应控制策略成功地推广到具有单并置平面的柔性转子及具有多并置平面的柔性转子,一系列数值模拟验证了该控制律对抑制这些转子不平衡振动的有效性。在本文的第四部分中,作者在转子动力学模型未知、转子变速和带作动器饱和的复杂情况下提出能明显抑制转子原始不平衡振动的一种主动平衡自适应控制策略。首先,在带作动器饱和的条件下,对一个严格正实转子系统建立Lyapunov函数,推导出自适应控制律和系统稳定性条件。然后,以带作动器饱和的快加速Jeffcott转子为研究对象,通过引入过滤器,使带主动平衡器饱和的Jeffcott变速转子的传递函数变成严格正实的,可采用上述推导出的自适应控制律和稳定性条件。数值模拟证实,在满足稳定性条件下,该自适应控制策略能明显抑制带作动器饱和的该转子原始不平衡产生的振动。接着,还研究了带作动器饱和的轴承各向异性的Jeffcott变速转子主动平衡的自适应控制,着重探求轴承各向异性对该自适应控制律的影响。最后,把提出的自适应控制策略成功地推广到带作动器饱和、单并置平面的柔性转子和带作动器饱和、多并置平面的柔性转子,一系列数值模拟显示:该控制律能显著减小这些转子原始不平衡引起的振动,作动器的移动能渐近收敛到与原始不平衡相反的目标值。本文的一系列成果对于研究变速转子系统瞬态动力特征、主动平衡及其自适应控制策略的前沿发展具有一定的理论意义和工程应用价值。更多还原

【Abstract】 The harmful effects of unbalanced vibration in the modern high-speed rotating machineries have caused significant drop of productivity efficiency, precision reduction of products machined, even the whole machine damage. Realization of new technology, such as, high-speed and high-precision machining is restricted due to rotor imbalances. Standard off-line rotor balancing techniques can not solve time-varying rotor unbalance problems due to the transient nature of imbalances existed in rotating machinery operation. But, active balancing technology for rotor systems can solve these complicated problems and bring us significant economic benefits through combining other new and advanced technologies and increasing reliability for machinery operation.The rotor active balancing control methods obtained in the past, however, are limited to use for machines with constant rotating speed. Existed adaptive control methods can not be able to deal with speed-varying rotor balancing which often appears in modern industry. The adaptive control methods for speed-varying rotor active balancing systems studied in this dissertation are effectively applicable not only to general speed-varying rotors, but also to the speed-varying rotors with actuator time delay and the ones with actuator saturation. The adaptive controls for speed-varying rotor active balancing systems are systematically and thoroughly studied in this thesis. The contents of this dissertation are involved in studies on quasi steady-state condition of a slow speed-varying rotor system, gain-scheduling control of a quasi steady-state rotor active balancing system, adaptive control of active balancing for a fast speed-varying rotor with actuator time delay and adaptive control of active balancing for a fast speed-varying rotor with actuator saturation. The rotors to be studied include a Jeffcott rotor, a Jeffcott rotor with anisotropic bearings, a flexible rotor with single collocated balancing plane (actuator plane and measuring plane are almost the same one) and a flexible rotor with multiple collocated balancing planes.The differences and their transferring condition between a rotor dynamic model with constant speed and the one with speed-varying are investigated in the first part of this dissertation. With a speed-varying Jeffcott rotor as a fundamental model, on one hand, its transient unbalanced response is analytically solved; on the other hand, discretizing its varying rotating speed, a series of its general responses solved in each time step with a harmonic excitation whose constant frequency is one of those discretized finite rotating speeds are used to indicate approximately its transient responses. An appropriate qualitative condition so called quasi steady-state condition is found so that the latter can approximately replace the former.Gain-scheduling control for a quasi steady-state rotor active balancing system is studied in the second part of this dissertation. Under the premise of a rotor system satisfying the quasi steady-state condition, the influencing coefficient method based on the steady-state rotor balancing is extended to single-plane or multiple-plane gain-scheduling control of a rotor with slowly varying speed and all factors affecting the stability of a gain-scheduling control are analyzed. Numerical simulations verify that the gain scheduling control can effectively suppress imbalance-induced vibration of a rotor with slowly varying speed.Adaptive control techniques of active balancing for a rotor system with fast varying speed and actuator time delay are proposed and investigated in the third part of this dissertation. Firstly, without a prior knowledge of the rotor dynamics, a simple direct adaptive controller is designed for a strictly positive and real rotor system with actuator time delay, a Lyapunov-Krasovskii functional is constructed after an appropriate transformation of the original system model, the stability conditions for the adaptive control system with actuator time delay are derived. Secondly, adding a filter function, the active balancing system for a fast speed-varying Jeffcott rotor with actuator time delay can easily be converted to a strictly positive and real system, and thus it can use the derived adaptive controller satisfying the stability conditions. Numerical simulations show the proposed adaptive controller can effectively suppress the original imbalance-induced vibration of the fast speed-varying Jeffcott rotor with actuator time delay. Then, the adaptive control of active balancing for a speed-varying Jeffcott rotor with anisotropic bearings and actuator time delay is also investigated, and the efforts give emphasis to the effect of bearing anisotropy on actuator time delay. Finally, the adaptive control strategy of active balancing for a strictly positive and real rotor with actuator time delay is successfully extended to a flexible rotor with single collocated plane and a flexible rotor with multiple collocated planes. A series of numerical simulations demonstrate that the proposed controller is valid to suppress the imbalance-induced vibration of these rotor systems.In the fourth part of this dissertation, the adaptive control strategies which can notably reduce imbalance-induced vibration of rotor active balancing systems are proposed under a complicated situation including no prior knowledge of rotor dynamics, rotor with fast varying speed and actuator saturation. At first, a Lyapunov functional is constructed for a strictly positive and real rotor system with actuator saturation, its adaptive controller and the corresponding stability conditions are deduced. Then, a fast speed-varying Jeffcott rotor active balancing system with actuator saturation is considered as a research objective, its transfer function can become strictly positive and real by introducing a filter function so that the adaptive control law and the stability conditions derived above can be applicable to the Jeffcott rotor. Numerical simulations verify that the adaptive control strategy can perfectly suppress the original imbalance-induced vibration of the Jeffcott rotor with actuator saturation. Furthermore, the adaptive control of active balancing for a fast speed-varying Jeffcott rotor with anisotropic bearings and actuator saturation is studied, and the efforts emphasize how bearing anisotropy affects the adaptive control law. Finally, the adaptive control strategy of active balancing for a strictly positive and real rotor with actuator saturation is successfully extended to a flexible rotor with single collocated plane and actuator saturation and a flexible rotor with multiple collocated planes and actuator saturation. A series of numerical simulations show that the proposed adaptive control law can evidently reduce the original imbalance-induced vibration of these rotors and the actuator movement asymptotically approaches to its target value, the opposite of the original imbalance.A series of studying results of this dissertation possess important theoretical meanings and applicable value in engineering for the further front study on the transient dynamics of speed-varying rotors and their adaptive control techniques of active balancing.更多还原