主动电磁轴承—裂纹柔性转子系统动力学特性研究
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摘要
与传统的滚动轴承或滑动轴承支承的转子系统相比,主动电磁轴承支承的转子系统中,转子裂纹故障的动力学特性要复杂得多,其中有许多问题需要解决,如：裂纹对电磁轴承控制系统稳定性的影响、裂纹对电磁轴承-转子系统的动力学特性的影响、电磁轴承控制器对裂纹转子故障的动力学特性影响、电磁轴承-转子系统中裂纹故障的诊断方法等。本文以电磁轴承-裂纹柔性转子系统的动力学特性研究为主要目标,分别对电磁轴承的2DOF PID控制器设计、H∞控制器设计、裂纹转子的数学模型、电磁轴承-裂纹柔性转子系统的动力学模型、电磁轴承控制器参数对裂纹转子系统的动力学特性影响等问题开展了研究。
2DOF PID (two-degree-of-freedom PID)控制既有良好的抗外干扰能力,又具有很好的目标值跟踪特点,将其应用于电磁轴承的控制中,建立了2DOF PID控制电磁轴承的数学模型,通过仿真分析,选取了2DOF PID控制的控制参数,并在所建立的电磁轴承-柔性转子系统实验平台上进行实验,实验结果表明,所设计的2DOF PID控制器能使电磁轴承实现稳定悬浮运行,保证柔性转子系统能平稳地通过其一阶弯曲临界转速。
利用H∞控制具有良好的鲁棒性及抑制干扰的特点,设计了电磁轴承的H∞控制器。为克服在采用转子系统的有限元数学模型设计H∞控制器时,选取加权函数W1(s)、W2(s)及W3(s)异常困难的问题,采用集总参数法,将转子系统的物理参数集总到电磁轴承的支承点,选取加权函数设计出了H∞控制器,并在所建立的电磁轴承-柔性转子系统实验平台上进行实验,实验结果表明,该H∞控制器能使电磁轴承实现稳定悬浮运行,保证柔性转子系统能平稳地通过其一阶弯曲临界转速。
根据呼吸裂纹转子的刚度数学模型,采用有限元方法,建立了PD控制的电磁轴承-裂纹柔性转子系统的动力学方程,并进行仿真分析,研究了电磁轴承的控制器参数P增益和D增益对裂纹转子系统动力学特性的影响,对比分析了与传统弹性支承-裂纹转子系统的动力学特性的异同,结合电磁轴承的等效刚度受偏置电流影响的特点,分析了PD控制的电磁轴承偏置电流I0对裂纹柔性转子系统动力学特性的影响。
建立了最优控制的电磁轴承-裂纹柔性转子系统的动力学方程,并进行了仿真分析,研究了最优控制的控制器参数加权矩阵Q和R对裂纹转子系统动力学特性的影响,对比分析了与传统支承-裂纹柔性转子系统的动力学特性的异同,结合电磁轴承的等效刚度受偏置电流影响的特点,分析了最优控制的电磁轴承偏置电流I0对裂纹柔性转子系统的动力学特性的影响。
在电磁轴承-柔性转子系统实验平台上,在不改变转子系统的固定条件的前提下,将柔性转子系统的转轴通过线切割加工出一条横向切槽,在切槽中嵌入铜片并与切槽一侧强力粘接的办法得到与实际裂纹尽可能相似的横向裂纹。当实验平台中的电磁轴承分别采用2DOF PID控制器和H∞控制器时,在控制器参数不变的情况下,在电磁轴承-裂纹柔性转子系统实验平台上进行了裂纹柔性转子的稳态响应实验,不平衡响应实验,加速响应实验和减速响应实验等动力学特性实验,分析了当实验台的电磁轴承采用不同控制器时,转子横向裂纹对电磁轴承-柔性转子系统振动特性的影响,实验结果表明,转子裂纹到一定深度将导致电磁轴承-柔性转子系统失稳,且监测转子的振动是检测电磁轴承-柔性转子系统中转子裂纹故障的有效方法。
Compared to the rotor system supported by the traditional bearing such as ball bearings and plain bearings, dynamics characteristics of a cracked flexible rotor system supported by active magnetic bearings are such more complex. Therefore, many problems need to study, such as, the influence of cracks on the stability of the active magnetic bearing controller, the influence of cracks on the dynamic characteristics of the active magnetic bearing-rotor system, the influence of the active magnetic bearing controller on the dynamic characteristics of the cracked rotor, the diagnostic approach of the crack fault in active magnetic bearing-rotor system.The purpose of this paper is to study the dynamic characteristics of the active magnetic bearing-cracked flexible rotor systems, including designing the2DOF PID controller, H∞controller of the active magnetic bearings, building the mathematical model of cracked flexible rotor systems, the dynamic model of the active magnetic bearing-cracked flexible rotor systems and analysing the influence of the parameters of the bearing controller on the dynamic characteristics of the cracked flexible rotor system.
2DOF PID controller, which has a performance in the optimal tuning for the disturbance response and the one for the set-point response, is used in the control of the active magnetic bearing-rotor systems. The mathematical model of the2DOF PID controller is built. The control parameters are selected by simulation. The experiments on a experimental platform of an active magnetic bearing-flexible rotor systems validate that the designed2DOF PID controller can easily make the rotor system smoothingly pass through the first flexible critical speed.
The H∞controller with good robustness and ability of anti-disturbance is designed. In order to overcome the problem of choosing the weighting functions W1(s)、W2(s) and W3(s), the lumped parameter method is used. The physical parameters of the rotor system are lumped to the position of the active magnetic bearings and the weighting functions W1(s)、W2(s) and W3(s) are chosen and the H∞controller is designed. The experiments on the experimental platform of the active magnetic bearing-flexible rotor systems indicate that the H∞controller can make the rotors smoothingly pass through the first flexible critical speed.
Based on the breathing stiffness model of the cracked rotor and finite element method, the equation of the cracked rotor-active magnetic bearing with PD controller is built. The influence of the parameters P and D of the controller on the dynamic characteristics of the cracked flexible rotor system is analysed, theoretically the differences between the cracked rotor system supported respectively by the traditional bearing and the active magnetic bearing are compared. The influence of the bias current Io of the PD controller on the dynamic characteristics of the cracked rotor system is discussed.
The equation of the ctive magnetic bearing-cracked flexible rotor with optimum control is built and the simulation is conducted. The influence of the weighting matrixes Q and R in the optimum controller on the dynamic characteristics of cracked rotor system is analysed, the differences between the cracked rotor system supported respectively by the traditional bearings and the active magnetic bearing are compared. The influence of the bias current Io of the optimum controller on the dynamic characteristics of the cracked rotor system is discussed.
On the experimental platform of the active magnetic bearing-flexible rotor system. under no changing the fixed conditions of the flexible rotor system, a transverse grooving with the depth of4mm is acquired by wire-electrode cutting. A copper sheet is inset in the transverse grooving and glued one side of the copper sheet to one side of the transverse grooving, so the transverse cracked flexible rotor acquired is similar to a real cracked rotor. Dynamics experiments of cracked flexible rotor that include steady-state response experiments, unbalance response experiments, acceleration response and deceleration response experiments, were done on the active magnetic bearings-cracked flexible rotor systems experimental platform with the unchanged controller parameters of active magnetic bearings used2DOF PID controller and H∞controller. Dynamics characteristics of the tansverse crack of flexible rotor were analyzed when the active magnetic bearings-flexible rotor systems experimental platform used different active magnetic bearings controller. Experimental results show that the depth of crack causes the active magnetic bearings-flexible rotor system instability, and the monitorings of the rotor's vibration are effective manners to detect the rotor crack faults of the active magnetic bearings-flexible rotor system.
2DOF PID (two-degree-of-freedom PID)控制既有良好的抗外干扰能力,又具有很好的目标值跟踪特点,将其应用于电磁轴承的控制中,建立了2DOF PID控制电磁轴承的数学模型,通过仿真分析,选取了2DOF PID控制的控制参数,并在所建立的电磁轴承-柔性转子系统实验平台上进行实验,实验结果表明,所设计的2DOF PID控制器能使电磁轴承实现稳定悬浮运行,保证柔性转子系统能平稳地通过其一阶弯曲临界转速。
利用H∞控制具有良好的鲁棒性及抑制干扰的特点,设计了电磁轴承的H∞控制器。为克服在采用转子系统的有限元数学模型设计H∞控制器时,选取加权函数W1(s)、W2(s)及W3(s)异常困难的问题,采用集总参数法,将转子系统的物理参数集总到电磁轴承的支承点,选取加权函数设计出了H∞控制器,并在所建立的电磁轴承-柔性转子系统实验平台上进行实验,实验结果表明,该H∞控制器能使电磁轴承实现稳定悬浮运行,保证柔性转子系统能平稳地通过其一阶弯曲临界转速。
根据呼吸裂纹转子的刚度数学模型,采用有限元方法,建立了PD控制的电磁轴承-裂纹柔性转子系统的动力学方程,并进行仿真分析,研究了电磁轴承的控制器参数P增益和D增益对裂纹转子系统动力学特性的影响,对比分析了与传统弹性支承-裂纹转子系统的动力学特性的异同,结合电磁轴承的等效刚度受偏置电流影响的特点,分析了PD控制的电磁轴承偏置电流I0对裂纹柔性转子系统动力学特性的影响。
建立了最优控制的电磁轴承-裂纹柔性转子系统的动力学方程,并进行了仿真分析,研究了最优控制的控制器参数加权矩阵Q和R对裂纹转子系统动力学特性的影响,对比分析了与传统支承-裂纹柔性转子系统的动力学特性的异同,结合电磁轴承的等效刚度受偏置电流影响的特点,分析了最优控制的电磁轴承偏置电流I0对裂纹柔性转子系统的动力学特性的影响。
在电磁轴承-柔性转子系统实验平台上,在不改变转子系统的固定条件的前提下,将柔性转子系统的转轴通过线切割加工出一条横向切槽,在切槽中嵌入铜片并与切槽一侧强力粘接的办法得到与实际裂纹尽可能相似的横向裂纹。当实验平台中的电磁轴承分别采用2DOF PID控制器和H∞控制器时,在控制器参数不变的情况下,在电磁轴承-裂纹柔性转子系统实验平台上进行了裂纹柔性转子的稳态响应实验,不平衡响应实验,加速响应实验和减速响应实验等动力学特性实验,分析了当实验台的电磁轴承采用不同控制器时,转子横向裂纹对电磁轴承-柔性转子系统振动特性的影响,实验结果表明,转子裂纹到一定深度将导致电磁轴承-柔性转子系统失稳,且监测转子的振动是检测电磁轴承-柔性转子系统中转子裂纹故障的有效方法。
Compared to the rotor system supported by the traditional bearing such as ball bearings and plain bearings, dynamics characteristics of a cracked flexible rotor system supported by active magnetic bearings are such more complex. Therefore, many problems need to study, such as, the influence of cracks on the stability of the active magnetic bearing controller, the influence of cracks on the dynamic characteristics of the active magnetic bearing-rotor system, the influence of the active magnetic bearing controller on the dynamic characteristics of the cracked rotor, the diagnostic approach of the crack fault in active magnetic bearing-rotor system.The purpose of this paper is to study the dynamic characteristics of the active magnetic bearing-cracked flexible rotor systems, including designing the2DOF PID controller, H∞controller of the active magnetic bearings, building the mathematical model of cracked flexible rotor systems, the dynamic model of the active magnetic bearing-cracked flexible rotor systems and analysing the influence of the parameters of the bearing controller on the dynamic characteristics of the cracked flexible rotor system.
2DOF PID controller, which has a performance in the optimal tuning for the disturbance response and the one for the set-point response, is used in the control of the active magnetic bearing-rotor systems. The mathematical model of the2DOF PID controller is built. The control parameters are selected by simulation. The experiments on a experimental platform of an active magnetic bearing-flexible rotor systems validate that the designed2DOF PID controller can easily make the rotor system smoothingly pass through the first flexible critical speed.
The H∞controller with good robustness and ability of anti-disturbance is designed. In order to overcome the problem of choosing the weighting functions W1(s)、W2(s) and W3(s), the lumped parameter method is used. The physical parameters of the rotor system are lumped to the position of the active magnetic bearings and the weighting functions W1(s)、W2(s) and W3(s) are chosen and the H∞controller is designed. The experiments on the experimental platform of the active magnetic bearing-flexible rotor systems indicate that the H∞controller can make the rotors smoothingly pass through the first flexible critical speed.
Based on the breathing stiffness model of the cracked rotor and finite element method, the equation of the cracked rotor-active magnetic bearing with PD controller is built. The influence of the parameters P and D of the controller on the dynamic characteristics of the cracked flexible rotor system is analysed, theoretically the differences between the cracked rotor system supported respectively by the traditional bearing and the active magnetic bearing are compared. The influence of the bias current Io of the PD controller on the dynamic characteristics of the cracked rotor system is discussed.
The equation of the ctive magnetic bearing-cracked flexible rotor with optimum control is built and the simulation is conducted. The influence of the weighting matrixes Q and R in the optimum controller on the dynamic characteristics of cracked rotor system is analysed, the differences between the cracked rotor system supported respectively by the traditional bearings and the active magnetic bearing are compared. The influence of the bias current Io of the optimum controller on the dynamic characteristics of the cracked rotor system is discussed.
On the experimental platform of the active magnetic bearing-flexible rotor system. under no changing the fixed conditions of the flexible rotor system, a transverse grooving with the depth of4mm is acquired by wire-electrode cutting. A copper sheet is inset in the transverse grooving and glued one side of the copper sheet to one side of the transverse grooving, so the transverse cracked flexible rotor acquired is similar to a real cracked rotor. Dynamics experiments of cracked flexible rotor that include steady-state response experiments, unbalance response experiments, acceleration response and deceleration response experiments, were done on the active magnetic bearings-cracked flexible rotor systems experimental platform with the unchanged controller parameters of active magnetic bearings used2DOF PID controller and H∞controller. Dynamics characteristics of the tansverse crack of flexible rotor were analyzed when the active magnetic bearings-flexible rotor systems experimental platform used different active magnetic bearings controller. Experimental results show that the depth of crack causes the active magnetic bearings-flexible rotor system instability, and the monitorings of the rotor's vibration are effective manners to detect the rotor crack faults of the active magnetic bearings-flexible rotor system.
引文
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