航天器飞轮动力学建模与振动控制研究
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摘要
反作用轮和动量轮（本文中统称为飞轮）是高精度航天器常用的姿态控制和姿态稳定设备，但飞轮工作期间会产生扰动力和扰动力矩，降低高精度航天器载荷的指向精度和指向稳定度，影响有效载荷性能。因此对飞轮系统进行振动控制势在必行。本文从理论分析、数值仿真和地面实验三个方面，系统深入地研究了飞轮动力学建模和振动控制问题，提出并验证了飞轮主、被动振动控制的新方法。本文主要工作如下：
1.建立了航天器飞轮线性动力学模型和非线性动力学模型，分析了飞轮动力学特性，研究了利用弹性支承提高飞轮转速、降低飞轮扰动力的机理。
(1)建立了飞轮线性动力学模型和飞轮扰动因素模型，推导了基于传递矩阵的飞轮动力学方程，分析了扰动因素对飞轮扰动力和扰动力矩的影响。
(2)建立了考虑飞轮轴承刚度非线性的Jeffcott转子模型，分析指出了弹性支承提高飞轮转速、降低飞轮扰动力的基本原理。
2.建立了航天器飞轮被动隔振和主动振动控制模型，提出并分析了利用被动隔振和主动振动控制对飞轮振动进行抑制的方法和技术。
(1)提出了一种基于折臂梁支承的弹性支承飞轮被动隔振方法，建立了弹性支承飞轮动力学模型，推导了基于传递矩阵的弹性支承飞轮动力学方程，分析了弹性支承飞轮隔振性能。结果表明：越过临界转速后，弹性支承可以有效隔离质量不平衡引起的扰动力和扰动力矩。
(2)提出了一种基于折臂梁式的飞轮被动隔振平台设计方法，建立了飞轮与隔振平台系统动力学模型，推导了考虑陀螺效应的飞轮与隔振平台系统动力学方程，分析了陀螺效应对隔振平台隔振性能的影响。结果表明：飞轮与隔振平台系统临界转速与飞轮质量特性有关。当飞轮转子轴向转动惯量大于飞轮系统径向转动惯量时，系统临界转速小于静止时的径向固有频率；反之，系统临界转速大于静止时的径向固有频率。越过临界转速后，隔振平台可以有效隔离质量不平衡引起的扰动力和扰动力矩。
(3)提出了一种弹性支承飞轮主动振动控制方法；建立了弹性支承飞轮主动振动控制模型，推导了基于速度负反馈的飞轮主动振动控制方程，分析了飞轮主动振动控制性能。结果表明：主动振动控制系统可以控制除轴向转动外其余五个自由度的振动，有效抑制飞轮共振转速时的扰动力和扰动力矩。
3.建立了航天器飞轮振动控制实验系统，验证了飞轮振动控制方法的有效性。
(1)建立了高精度、宽频带的飞轮微振动测试系统，该实验系统能够测量3-300Hz范围内毫牛级的扰动力。
(2)测试了刚性支承飞轮扰动力和扰动力矩，测量结果与理论分析结果一致，验证了飞轮动力学模型和扰动因素模型的正确性和有效性。
(3)测试了弹性支承飞轮和飞轮隔振平台静止时的固有频率和非旋转黏性阻尼系数。弹性支承飞轮和飞轮隔振平台固有频率设计值与实验值吻合，验证了弹性支承飞轮、飞轮隔振平台设计方法和理论模型的正确性。
(4)开展了弹性支承飞轮隔振性能实验研究。结果表明弹性支承飞轮具有转速高、扰动低的特点，验证了弹性支承飞轮被动隔振方法的正确性和有效性。
(5)开展了飞轮隔振平台隔振性能实验研究，结果表明系统临界转速发生在2600rev/min，远高于系统静止时第六阶固有频率26.29Hz（1577rev/min），验证了陀螺效应影响飞轮隔振系统隔振性能的现象；隔振平台可以有效隔离飞轮高频扰动，证明了隔振平台对飞轮被动隔振的有效性。
(6)开展了弹性支承飞轮主、被动一体化振动控制实验研究。结果表明主动振动控制可以有效抑制弹性支承飞轮在临界转速的扰动力，验证了飞轮主、被动一体化振动控制方法的正确性和有效性。
Reaction wheel assembly and momentum wheel assembly (named flywheel in thisdissertation) are widely used on high accuracy spacecraft to provide attitude controltorque or maintain stability. However, the microvibrations produced by the flywheel canaffect the pointing accuracy and stability of the spacecraft, and even degrade theperformance of high sensitive instruments. Thus, the vibration control of the flywheel isimperative. This dissertation focuses on investigating the issue of dynamic modelingand vibration control of the flywheel through theoretical analysis, numerical simulationand experimental research. The methods of passive and active vibration control for theflywheel are proposed and verified by experiment; the main research efforts in thisdissertation are summarized as follows.
1. A linear and a nonlinear dynamic model of the flywheel for spacecraft areestablished; the dynamic characteristic of the flywheel is analyzed; and theprinciple that the soft suspension flywheel can increase the rotational speed anddecrease the disturbance is studied.
(1) The dynamic models of the flywheel and the disturbance sources areestablished; the dynamical equation of the flywheel based on transfer matrix isdeveloped; the influence of the vibration sources on the disturbance force and momentproduced by the flywheel is analyzed.
(2) Considering the nonlinear effect of the bearing stiffness, the flywheel issimplified as a Jeffcott rotor model, and the basic principle is analyzed that the softsuspension can effectively increase the maximum rotational speed and decrease thedisturbance force.
2. The passive vibration isolation model and active vibration control modelare established; method and technique of the passive vibration isolation and activevibration control for the flywheel are proposed and analyzed.
(1) A soft suspension flywheel based on folded beams is proposed; the dynamicmodel of the flywheel is established; the dynamic equation of the flywheel is developed,the passive vibration isolation performance of the soft suspension flywheel is analyzed.The analysis results show that the soft suspension structure can effectively isolate thedisturbance force and moment produced by the mass imbalance when the flywheeloperates above the critical speed.
(2) A passive vibration isolation platform for the flywheel (momentum wheelassembly) is proposed; the dynamic model of the flywheel and the platform isestablished; the dynamic equation of the system is developed, which includes thegyroscopic effect term; the influence of the gyroscopic term on the performance ofvibration isolation of the platform is analyzed. The analysis results show that the critical speed of the system consisting of flywheel and platform is affected by the mass propertyof the flywheel; the critical speed occurs before the natural frequencies of the system atrest if the axial moment of inertia of the rotor is larger than the radial moment of inertiaof the flywheel; else, the critical speed occurs after the natural frequencies at rest. Theplatform can effectively isolate the disturbance force and moment produced by massimbalance.
(3) An active vibration control structure for the soft suspension flywheel isproposed; the dynamic model of the active control for the soft suspension flywheel isestablished; the dynamic equation of the active vibration control based on velocityfeedback is developed; the performance of active vibration control for the flywheel isanalyzed. The results show that the active control structure can suppress the vibrationsat all the six degrees of freedom except the axial rotation, and the active vibrationcontrol can effectively suppress the dynamic amplification at critical speed,
3. An experimental system for the vibration control of the flywheel ofspacecraft is established; the effectiveness of the vibration control method for theflywheel is verified.
(1) A high accuracy and broad frequency range microvibration measurementexperimental system for the flywheel is constructed, which can measure themili-Newton force at the frequency range of3-300Hz.
(2) The disturbance produced by the flywheel is tested; the test results areconsistent with the theoretical results, which demonstrates the correctness andeffectiveness of the dynamic model and disturbance sources model of the flywheel.
(3) The natural frequencies and nonrotating damping coefficients of the softsuspension flywheel and the passive vibration isolation platform are studied. The resultsshow that both of the designed natural frequencies are consistent with the experimentalvalues, which verifies the validity of the design method and mathematical model of thesoft suspension flywheel and the platform.
(4) The performance of the soft suspension flywheel is researched by experimentaltest. The results show that the flywheel implements the relatively high rotational speedbut low disturbance force, which verifies that it is correct and valid to isolate thevibration from the flywheel using soft suspension design.
(5) The performance of the passive vibration isolation platform is researched byexperimental test. The results show that the critical speed occurs at2600rev/min, whichis larger than the sixth natural frequency of the system (26.29Hz), which demonstratesthat the gyroscopic effect affects the performance of the platform; the platform caneffectively isolate the high frequency disturbance, which verifies the effectiveness of thepassive vibration isolation of the platform.
(6) An integrated passive and active vibration control strategy for the flywheel isresearched by experimental test. The test results show that the active vibration control strategy can effectively suppress the disturbance force at critical speed, which verifiesthe correctness and effectiveness of the integrated passive and active control strategy.
1.建立了航天器飞轮线性动力学模型和非线性动力学模型，分析了飞轮动力学特性，研究了利用弹性支承提高飞轮转速、降低飞轮扰动力的机理。
(1)建立了飞轮线性动力学模型和飞轮扰动因素模型，推导了基于传递矩阵的飞轮动力学方程，分析了扰动因素对飞轮扰动力和扰动力矩的影响。
(2)建立了考虑飞轮轴承刚度非线性的Jeffcott转子模型，分析指出了弹性支承提高飞轮转速、降低飞轮扰动力的基本原理。
2.建立了航天器飞轮被动隔振和主动振动控制模型，提出并分析了利用被动隔振和主动振动控制对飞轮振动进行抑制的方法和技术。
(1)提出了一种基于折臂梁支承的弹性支承飞轮被动隔振方法，建立了弹性支承飞轮动力学模型，推导了基于传递矩阵的弹性支承飞轮动力学方程，分析了弹性支承飞轮隔振性能。结果表明：越过临界转速后，弹性支承可以有效隔离质量不平衡引起的扰动力和扰动力矩。
(2)提出了一种基于折臂梁式的飞轮被动隔振平台设计方法，建立了飞轮与隔振平台系统动力学模型，推导了考虑陀螺效应的飞轮与隔振平台系统动力学方程，分析了陀螺效应对隔振平台隔振性能的影响。结果表明：飞轮与隔振平台系统临界转速与飞轮质量特性有关。当飞轮转子轴向转动惯量大于飞轮系统径向转动惯量时，系统临界转速小于静止时的径向固有频率；反之，系统临界转速大于静止时的径向固有频率。越过临界转速后，隔振平台可以有效隔离质量不平衡引起的扰动力和扰动力矩。
(3)提出了一种弹性支承飞轮主动振动控制方法；建立了弹性支承飞轮主动振动控制模型，推导了基于速度负反馈的飞轮主动振动控制方程，分析了飞轮主动振动控制性能。结果表明：主动振动控制系统可以控制除轴向转动外其余五个自由度的振动，有效抑制飞轮共振转速时的扰动力和扰动力矩。
3.建立了航天器飞轮振动控制实验系统，验证了飞轮振动控制方法的有效性。
(1)建立了高精度、宽频带的飞轮微振动测试系统，该实验系统能够测量3-300Hz范围内毫牛级的扰动力。
(2)测试了刚性支承飞轮扰动力和扰动力矩，测量结果与理论分析结果一致，验证了飞轮动力学模型和扰动因素模型的正确性和有效性。
(3)测试了弹性支承飞轮和飞轮隔振平台静止时的固有频率和非旋转黏性阻尼系数。弹性支承飞轮和飞轮隔振平台固有频率设计值与实验值吻合，验证了弹性支承飞轮、飞轮隔振平台设计方法和理论模型的正确性。
(4)开展了弹性支承飞轮隔振性能实验研究。结果表明弹性支承飞轮具有转速高、扰动低的特点，验证了弹性支承飞轮被动隔振方法的正确性和有效性。
(5)开展了飞轮隔振平台隔振性能实验研究，结果表明系统临界转速发生在2600rev/min，远高于系统静止时第六阶固有频率26.29Hz（1577rev/min），验证了陀螺效应影响飞轮隔振系统隔振性能的现象；隔振平台可以有效隔离飞轮高频扰动，证明了隔振平台对飞轮被动隔振的有效性。
(6)开展了弹性支承飞轮主、被动一体化振动控制实验研究。结果表明主动振动控制可以有效抑制弹性支承飞轮在临界转速的扰动力，验证了飞轮主、被动一体化振动控制方法的正确性和有效性。
Reaction wheel assembly and momentum wheel assembly (named flywheel in thisdissertation) are widely used on high accuracy spacecraft to provide attitude controltorque or maintain stability. However, the microvibrations produced by the flywheel canaffect the pointing accuracy and stability of the spacecraft, and even degrade theperformance of high sensitive instruments. Thus, the vibration control of the flywheel isimperative. This dissertation focuses on investigating the issue of dynamic modelingand vibration control of the flywheel through theoretical analysis, numerical simulationand experimental research. The methods of passive and active vibration control for theflywheel are proposed and verified by experiment; the main research efforts in thisdissertation are summarized as follows.
1. A linear and a nonlinear dynamic model of the flywheel for spacecraft areestablished; the dynamic characteristic of the flywheel is analyzed; and theprinciple that the soft suspension flywheel can increase the rotational speed anddecrease the disturbance is studied.
(1) The dynamic models of the flywheel and the disturbance sources areestablished; the dynamical equation of the flywheel based on transfer matrix isdeveloped; the influence of the vibration sources on the disturbance force and momentproduced by the flywheel is analyzed.
(2) Considering the nonlinear effect of the bearing stiffness, the flywheel issimplified as a Jeffcott rotor model, and the basic principle is analyzed that the softsuspension can effectively increase the maximum rotational speed and decrease thedisturbance force.
2. The passive vibration isolation model and active vibration control modelare established; method and technique of the passive vibration isolation and activevibration control for the flywheel are proposed and analyzed.
(1) A soft suspension flywheel based on folded beams is proposed; the dynamicmodel of the flywheel is established; the dynamic equation of the flywheel is developed,the passive vibration isolation performance of the soft suspension flywheel is analyzed.The analysis results show that the soft suspension structure can effectively isolate thedisturbance force and moment produced by the mass imbalance when the flywheeloperates above the critical speed.
(2) A passive vibration isolation platform for the flywheel (momentum wheelassembly) is proposed; the dynamic model of the flywheel and the platform isestablished; the dynamic equation of the system is developed, which includes thegyroscopic effect term; the influence of the gyroscopic term on the performance ofvibration isolation of the platform is analyzed. The analysis results show that the critical speed of the system consisting of flywheel and platform is affected by the mass propertyof the flywheel; the critical speed occurs before the natural frequencies of the system atrest if the axial moment of inertia of the rotor is larger than the radial moment of inertiaof the flywheel; else, the critical speed occurs after the natural frequencies at rest. Theplatform can effectively isolate the disturbance force and moment produced by massimbalance.
(3) An active vibration control structure for the soft suspension flywheel isproposed; the dynamic model of the active control for the soft suspension flywheel isestablished; the dynamic equation of the active vibration control based on velocityfeedback is developed; the performance of active vibration control for the flywheel isanalyzed. The results show that the active control structure can suppress the vibrationsat all the six degrees of freedom except the axial rotation, and the active vibrationcontrol can effectively suppress the dynamic amplification at critical speed,
3. An experimental system for the vibration control of the flywheel ofspacecraft is established; the effectiveness of the vibration control method for theflywheel is verified.
(1) A high accuracy and broad frequency range microvibration measurementexperimental system for the flywheel is constructed, which can measure themili-Newton force at the frequency range of3-300Hz.
(2) The disturbance produced by the flywheel is tested; the test results areconsistent with the theoretical results, which demonstrates the correctness andeffectiveness of the dynamic model and disturbance sources model of the flywheel.
(3) The natural frequencies and nonrotating damping coefficients of the softsuspension flywheel and the passive vibration isolation platform are studied. The resultsshow that both of the designed natural frequencies are consistent with the experimentalvalues, which verifies the validity of the design method and mathematical model of thesoft suspension flywheel and the platform.
(4) The performance of the soft suspension flywheel is researched by experimentaltest. The results show that the flywheel implements the relatively high rotational speedbut low disturbance force, which verifies that it is correct and valid to isolate thevibration from the flywheel using soft suspension design.
(5) The performance of the passive vibration isolation platform is researched byexperimental test. The results show that the critical speed occurs at2600rev/min, whichis larger than the sixth natural frequency of the system (26.29Hz), which demonstratesthat the gyroscopic effect affects the performance of the platform; the platform caneffectively isolate the high frequency disturbance, which verifies the effectiveness of thepassive vibration isolation of the platform.
(6) An integrated passive and active vibration control strategy for the flywheel isresearched by experimental test. The test results show that the active vibration control strategy can effectively suppress the disturbance force at critical speed, which verifiesthe correctness and effectiveness of the integrated passive and active control strategy.
引文
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