用形状记忆合金对转子系统进行主动控制
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摘要
形状记忆合金是一种新型的功能材料，它具有形状记忆特性、变刚度特性和超弹性特性。利用这些特性可以设计出用于转子系统的可变刚度支承，通过结合主动控制技术，在临界转速附近改变系统刚度，从而降低系统在临界转速时的最大振幅。本文研究利用形状记忆合金对转子系统振动进行主动控制。
1） 运用非线性热弹性耦合理论研究记忆合金材料的力学性能，特别是应力、应变和温度三者之间的耦合关系，改进了原有的线性结果。
2） 运用非线性理论和运动稳定性理论研究带有记忆合金支承的转子系统在非定常状态的非线性动力学行为，指出了软、硬非线性系统的区别。研究了系统的稳定性条件和发生分岔的条件，提出了通过改变参数来提高系统稳定性和抑制振幅的方法；
3） 运用强非线性理论研究了轻型高速转子系统在大扰动条件下的强非线性主共振和1/3亚谐共振的动力学特性，给出在强非线性条件下系统的运动趋势和系统参数对系统动力学特性的影响，并进一步指出强/弱非线性系统、软/硬非线性系统的区别以及强软非线性系统的独有特性。
4） 运用现代非线性动力学分岔与混沌理论研究了系统分岔行为，给出系统在发生混沌时的参数区域，指出了通过改变系统参数避免系统发生混沌的方法。运用数值积分方法结合Floquet理论对滑动轴承-转子系统的大参数范围非线性动力学特性进行了全面的研究，详细地讨论了系统的一次和二次分岔行为；
5） 提出了用形状记忆合金在超弹性状态下的软非线性，结合挤压油膜阻尼器实现系统刚性的非线性可控，降低系统在非定常状态下的最大振幅的构想。建立了形状记忆合金弹簧的热力学模型以及利用记忆合金丝的温度进行振动控制的闭环系统，得到减小系统振幅的刚性优化控制规律，以及最优控制力和控制电流的强度变化规律；
6） 引入模糊控制思想，以转子不平衡力为参考信号对转子系统进行模糊控制。为了解决转子系统变刚度控制中由于参数随时间变化导致的瞬态响应问题，引入时变控制理论结合参数估计中的梯度算法，得到抑制转子瞬态响应所需的控制规律。最后通过仿真验证了控制系统的振动抑制效果。仿真结果表明控制后系统振幅降为控制前的40%。
Shape Memory Alloy (SMA) is a new type of metal material. It has characteristics of shape memory, variable stiffness and super-elasticity. Because of these characteristics, the variable stiffness SMA bearing used in rotor system can be designed, and then the stiffness of system can be varied by active control technology when the rotate speed of system is near the critical rotate speed to reduce the maximum vibration amplitude of rotor system. In the paper, active control to rotor vibration with SMA is studied:
1) The material performance of SMA , especially the coupled relation of strain, stress and temperature, is studied in nonlinear coupled thermoelasticity theory and the linear result is modified;
2) The nonlinear dynamic behavior of rotor system with SMA bearing is studied in the nonlinear theory and the dynamic stability theory and the deference of the soft /hard nonlinear system is pointed out. The stability and bifurcation condition of rotor system are obtained and the way to improve system stability and reduce the vibration amplitude through adjusting system parameters is indicated;
3) The strong nonlinear dynamic characteristic of high-speed rotor system is studied. The movement trend of system and the effect of system parameters to dynamic characteristic are indicated. The deference of the strong/weak nonlinear system and the unique characteristic of the strong soft-nonlinear system are pointed out;
4) The bifurcation behavior of nonlinear rotor system is studied and the parameter region when chaos phenomenon is appeared is obtained in bifurcation and chaos theory. The way to eliminate chaos phenomenon through adjusting system parameters is indicated. The nonlinear dynamic behavior of journal bearing-rotor system in large parameter space is studied in numerical integral method and Floquet theory and the first and second bifurcation behavior of nonlinear rotor system are discussed;
The concept is advanced that realizing the controllable nonlinear stiffness with SFD with the soft-nonlinear of SMA in the super-elasticity state to make the vibration amplitude of system always be in the small solution state to reduce the vibration amplitude of rotor system. The thermomechanics model of SMA
5) spring and the close loop control system to reduce vibration through adjusting SMA temperature are set up. The discipline of optimum stiffness control, the optimum control force and the optimum control electric current are obtained;
6) The concept of fuzzy control and time-varying control are introduced to reduce the vibration of rotor system. Gradient algorithm is introduced to solve the transient response problem caused by parameter varying with time in variable stiffness control of rotor system. The control discipline to eliminate transient response of rotor system is obtained. Finally, the vibration control effect of active control system is proved by emulation. The emulation results show that the active SMA control can reduce the vibration amplitude of system greatly, and the vibration amplitude of improved system is only 30% of the original one.
1） 运用非线性热弹性耦合理论研究记忆合金材料的力学性能，特别是应力、应变和温度三者之间的耦合关系，改进了原有的线性结果。
2） 运用非线性理论和运动稳定性理论研究带有记忆合金支承的转子系统在非定常状态的非线性动力学行为，指出了软、硬非线性系统的区别。研究了系统的稳定性条件和发生分岔的条件，提出了通过改变参数来提高系统稳定性和抑制振幅的方法；
3） 运用强非线性理论研究了轻型高速转子系统在大扰动条件下的强非线性主共振和1/3亚谐共振的动力学特性，给出在强非线性条件下系统的运动趋势和系统参数对系统动力学特性的影响，并进一步指出强/弱非线性系统、软/硬非线性系统的区别以及强软非线性系统的独有特性。
4） 运用现代非线性动力学分岔与混沌理论研究了系统分岔行为，给出系统在发生混沌时的参数区域，指出了通过改变系统参数避免系统发生混沌的方法。运用数值积分方法结合Floquet理论对滑动轴承-转子系统的大参数范围非线性动力学特性进行了全面的研究，详细地讨论了系统的一次和二次分岔行为；
5） 提出了用形状记忆合金在超弹性状态下的软非线性，结合挤压油膜阻尼器实现系统刚性的非线性可控，降低系统在非定常状态下的最大振幅的构想。建立了形状记忆合金弹簧的热力学模型以及利用记忆合金丝的温度进行振动控制的闭环系统，得到减小系统振幅的刚性优化控制规律，以及最优控制力和控制电流的强度变化规律；
6） 引入模糊控制思想，以转子不平衡力为参考信号对转子系统进行模糊控制。为了解决转子系统变刚度控制中由于参数随时间变化导致的瞬态响应问题，引入时变控制理论结合参数估计中的梯度算法，得到抑制转子瞬态响应所需的控制规律。最后通过仿真验证了控制系统的振动抑制效果。仿真结果表明控制后系统振幅降为控制前的40%。
Shape Memory Alloy (SMA) is a new type of metal material. It has characteristics of shape memory, variable stiffness and super-elasticity. Because of these characteristics, the variable stiffness SMA bearing used in rotor system can be designed, and then the stiffness of system can be varied by active control technology when the rotate speed of system is near the critical rotate speed to reduce the maximum vibration amplitude of rotor system. In the paper, active control to rotor vibration with SMA is studied:
1) The material performance of SMA , especially the coupled relation of strain, stress and temperature, is studied in nonlinear coupled thermoelasticity theory and the linear result is modified;
2) The nonlinear dynamic behavior of rotor system with SMA bearing is studied in the nonlinear theory and the dynamic stability theory and the deference of the soft /hard nonlinear system is pointed out. The stability and bifurcation condition of rotor system are obtained and the way to improve system stability and reduce the vibration amplitude through adjusting system parameters is indicated;
3) The strong nonlinear dynamic characteristic of high-speed rotor system is studied. The movement trend of system and the effect of system parameters to dynamic characteristic are indicated. The deference of the strong/weak nonlinear system and the unique characteristic of the strong soft-nonlinear system are pointed out;
4) The bifurcation behavior of nonlinear rotor system is studied and the parameter region when chaos phenomenon is appeared is obtained in bifurcation and chaos theory. The way to eliminate chaos phenomenon through adjusting system parameters is indicated. The nonlinear dynamic behavior of journal bearing-rotor system in large parameter space is studied in numerical integral method and Floquet theory and the first and second bifurcation behavior of nonlinear rotor system are discussed;
The concept is advanced that realizing the controllable nonlinear stiffness with SFD with the soft-nonlinear of SMA in the super-elasticity state to make the vibration amplitude of system always be in the small solution state to reduce the vibration amplitude of rotor system. The thermomechanics model of SMA
5) spring and the close loop control system to reduce vibration through adjusting SMA temperature are set up. The discipline of optimum stiffness control, the optimum control force and the optimum control electric current are obtained;
6) The concept of fuzzy control and time-varying control are introduced to reduce the vibration of rotor system. Gradient algorithm is introduced to solve the transient response problem caused by parameter varying with time in variable stiffness control of rotor system. The control discipline to eliminate transient response of rotor system is obtained. Finally, the vibration control effect of active control system is proved by emulation. The emulation results show that the active SMA control can reduce the vibration amplitude of system greatly, and the vibration amplitude of improved system is only 30% of the original one.
引文
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