微型抗磁轴承特性的研究
摘要
微机电系统(Micro Electromechanical System, MEMS)是包含电子元件和其它微型实体(包括机械、热、磁、流体、光学、化学、生物元件等)的集传感器、执行器、信号处理、通信、接口、控制电路以及电源于一体的系统。典型MEMS器件的特征尺寸大约在1μm～1cm之间,这种微型化的特点使得很多在宏观尺度上无法应用的物理原理在微观尺度上找到了实现的可能性,常温无源式抗磁悬浮就是其中之一。
抗磁材料是磁化率为负值的磁性材料,包括金、银、铜、铅,石墨、水、有机化合物等。根据Earnshaw定理,铁磁材料以及顺磁材料之间的作用力不足以独立实现稳定的磁悬浮。若引入抗磁材料,利用其对外磁场轻微的抵制作用,则可实现常温下的无源稳定磁悬浮。抗磁悬浮原理虽然在一些高精密的科学传感器中有应用,但由于抗磁材料的磁性过于微弱,无法提供足够的承载力,在轴承中的应用还尚未涉及。根据电磁力的尺度效应分析可知,永磁体磁场梯度随系统特征尺度的减小而反比增大,由于抗磁效应正比于磁场的梯度,抗磁悬浮得益于MEMS微小化的特点,可为微机械结构提供简单有效的支撑方法。
微型抗磁轴承的研究涉及到电磁理论、材料科学、工程设计、加工工艺等多个学科,具有丰富的内涵,为微机电系统轴承的设计提供了一条新思路。本文以建立微型抗磁轴承基本设计理论体系为目标,主要研究内容包括:
(1)在抗磁悬浮原理微尺度有效性论证的基础上,研究了适应微系统加工工艺的微型抗磁轴承基本设计方案,并根据磁场能量理论的计算结果,研究了轴承设计参数对轴承承载力以及动力学参数的影响,探讨了实现轴承稳定悬浮的条件,提出了微型抗磁轴承优化设计的方案;
(2)抗磁轴承的非接触式结构需要非接触式的阻尼减振方式,可行的方案包括气膜阻尼以及电涡流阻尼。对于电涡流阻尼,本文根据抗磁轴承的结构特性,采用薄板近似模型以及镜像法建立了轴承电涡流的模型,分析了转子轴向、径向以及倾角方向电磁阻尼的特性,探讨了电涡流阻尼对轴承旋转损耗的影响,通过与气膜阻尼的比较,论证了电涡流阻尼器在微型抗磁轴承中应用的可行性。
(3)在对微型抗磁轴承动力学参数分析的基础上,建立了轴承的转子动力学模型,分析了不同工况和设计方案下的轴承动力学特性,提出了改进轴承动态稳定性的方案。
(4)针对非理想加工条件引起的抗磁轴承磁偏心进行了研究,探讨了永磁体的不对称磁化以及抗磁材料磁性不均匀对轴承性能的影响,并分析了轴承的旋转损耗特性。
(5)对抗磁轴承的基本振动特性进行实验研究。
微型抗磁轴承适应于MEMS准平面加工的特性,与传统的轴承方案相比,抗磁轴承充分利用了MEMS微小化的特点,具有方法简单、对工作环境要求低的优点,并可与其它轴承方案结合,拓展了研究的思路。本论文作为抗磁悬浮原理在微机电系统中应用的初步探索,建立了抗磁轴承机械性能的基本理论框架,为这种新型方案的设计、优化、驱动方式的选择以及运行策略的拟定提供了必要的依据。
Micro-Electro-Mechanical Systems (MEMS) is the integration of mechanical elements, sensors, actuators and electronics on a common silicon substrate through the utilization of microfabrication technology. Due to its diminutive dimension, many physical phenomena that are negligible at the macro-scale could find novel application as size shrinks down. One of the winners of miniaturization is diamagnetic levitation.
Diamagnetism is a magnetic property inherent to many materials such as water, protein, silver, bismuth, graphite, etc. Unlike stated in Earnshaw’s theorem, which eliminates the possibility of stable levitation of a ferromagnetic or paramagnetic body in a static magnetic field, diamagnetic materials are repelled by the magnetic field and attracted to the local field minimum due to their characteristic negative magnetic susceptibility. Since local minima can exist in the free space, diamagnets could thus be employed in combination with other magnetic sources, such as permanent magnets (PM), to construct passive and stable levitation at room temperature, with PM providing the lift capacity to counterbalance gravity and diamagnetic materials providing stability to keep levitation within reasonable limit.
Although such mechanism has already proved its worth for several high-precision scientific sensors and the clean room transportation, it is of little use to bearing systems at the macro-scale mainly because the weak diamagnetic effect of materials available currently is not capable of providing enough stability and bearing pressure for most mechanical applications. According to the electromagnetic theory, the magnitude of the magnetic field mapped around a PM remains unchanged after size reduction, while the field gradient scales inversely with characteristic dimensions. This means that for interaction elements involving magnets and soft magnetic materials, for which the volumic force acting on each particle is governed by the relation of B ? B, the force-to-volume ratio improves strongly as scale shrinks down and therefore diamagnetic material could be utilized with PM to construct simple bearing solution for MEMS.
Engineering of diamagnetic bearings requires a complex mix of disciplines, including electromagnetic theory, kinetics, material science, design theory and etc. The objective of this thesis is to study its basic characteristics so as to gain a systematic understanding of such a novel bearing mechanism. The major content includes:
(1) Based on the electromagnetic theory, the micro-scale effectiveness of diamagnetic levitation is demonstrated and the magnetomechanical interaction in terms of load-carrying capacity and the restoring in the axial, lateral and inclination directions are evaluated.
(2) The eddy current effect on the performance of diamagnetic bearing is investigated. Due to the good electrical conductivity of some of diamagnetic materials or the intentionally introduced eddy current damper for vibration control, eddy current could be induced in the diamagnetic bearing with viscous force opposing the relative motion between the rotor and the stator. Such damping mechanism is analyzed with a thin sheet model and the image method and compared with that due to aerodynamic effects so as to give an idea of its significance at the micro-scale.
(3) Based on the derived dynamic coefficients, linear vibration characteristics and nonlinear parametric resonance of the rotor-bearing system are studied. Results obtained indicate that there are two major instability problems for diamagnetic bearings.
(4) Due to the malmanufacturing of the bearing, magnetic asymmetry could occur either on the PM part or the diamagnetic part. The impact of such non-ideal working condition on the performance of the bearing is investigated. The rotational loss induced thereby is also studied to show the acceleration characteristics of the bearing.
(5) Basic vibration characteristics of the bearing are assessed experimentally. Compared to other bearing mechanisms for microsystems, diamagnetic approach has the advantage of being completely passive, hereby eliminating the design and operational cost associated with active electromagnetic or electrostatic approaches; and it is more compact in configuration as compared to air bearings, which require connection to the external source of pressurized gas. This thesis represents a first step towards a systematic understanding of a potentialy interesting application of magnetic bearings, and the findings herein would pave the way for further extensive study.
抗磁材料是磁化率为负值的磁性材料,包括金、银、铜、铅,石墨、水、有机化合物等。根据Earnshaw定理,铁磁材料以及顺磁材料之间的作用力不足以独立实现稳定的磁悬浮。若引入抗磁材料,利用其对外磁场轻微的抵制作用,则可实现常温下的无源稳定磁悬浮。抗磁悬浮原理虽然在一些高精密的科学传感器中有应用,但由于抗磁材料的磁性过于微弱,无法提供足够的承载力,在轴承中的应用还尚未涉及。根据电磁力的尺度效应分析可知,永磁体磁场梯度随系统特征尺度的减小而反比增大,由于抗磁效应正比于磁场的梯度,抗磁悬浮得益于MEMS微小化的特点,可为微机械结构提供简单有效的支撑方法。
微型抗磁轴承的研究涉及到电磁理论、材料科学、工程设计、加工工艺等多个学科,具有丰富的内涵,为微机电系统轴承的设计提供了一条新思路。本文以建立微型抗磁轴承基本设计理论体系为目标,主要研究内容包括:
(1)在抗磁悬浮原理微尺度有效性论证的基础上,研究了适应微系统加工工艺的微型抗磁轴承基本设计方案,并根据磁场能量理论的计算结果,研究了轴承设计参数对轴承承载力以及动力学参数的影响,探讨了实现轴承稳定悬浮的条件,提出了微型抗磁轴承优化设计的方案;
(2)抗磁轴承的非接触式结构需要非接触式的阻尼减振方式,可行的方案包括气膜阻尼以及电涡流阻尼。对于电涡流阻尼,本文根据抗磁轴承的结构特性,采用薄板近似模型以及镜像法建立了轴承电涡流的模型,分析了转子轴向、径向以及倾角方向电磁阻尼的特性,探讨了电涡流阻尼对轴承旋转损耗的影响,通过与气膜阻尼的比较,论证了电涡流阻尼器在微型抗磁轴承中应用的可行性。
(3)在对微型抗磁轴承动力学参数分析的基础上,建立了轴承的转子动力学模型,分析了不同工况和设计方案下的轴承动力学特性,提出了改进轴承动态稳定性的方案。
(4)针对非理想加工条件引起的抗磁轴承磁偏心进行了研究,探讨了永磁体的不对称磁化以及抗磁材料磁性不均匀对轴承性能的影响,并分析了轴承的旋转损耗特性。
(5)对抗磁轴承的基本振动特性进行实验研究。
微型抗磁轴承适应于MEMS准平面加工的特性,与传统的轴承方案相比,抗磁轴承充分利用了MEMS微小化的特点,具有方法简单、对工作环境要求低的优点,并可与其它轴承方案结合,拓展了研究的思路。本论文作为抗磁悬浮原理在微机电系统中应用的初步探索,建立了抗磁轴承机械性能的基本理论框架,为这种新型方案的设计、优化、驱动方式的选择以及运行策略的拟定提供了必要的依据。
Micro-Electro-Mechanical Systems (MEMS) is the integration of mechanical elements, sensors, actuators and electronics on a common silicon substrate through the utilization of microfabrication technology. Due to its diminutive dimension, many physical phenomena that are negligible at the macro-scale could find novel application as size shrinks down. One of the winners of miniaturization is diamagnetic levitation.
Diamagnetism is a magnetic property inherent to many materials such as water, protein, silver, bismuth, graphite, etc. Unlike stated in Earnshaw’s theorem, which eliminates the possibility of stable levitation of a ferromagnetic or paramagnetic body in a static magnetic field, diamagnetic materials are repelled by the magnetic field and attracted to the local field minimum due to their characteristic negative magnetic susceptibility. Since local minima can exist in the free space, diamagnets could thus be employed in combination with other magnetic sources, such as permanent magnets (PM), to construct passive and stable levitation at room temperature, with PM providing the lift capacity to counterbalance gravity and diamagnetic materials providing stability to keep levitation within reasonable limit.
Although such mechanism has already proved its worth for several high-precision scientific sensors and the clean room transportation, it is of little use to bearing systems at the macro-scale mainly because the weak diamagnetic effect of materials available currently is not capable of providing enough stability and bearing pressure for most mechanical applications. According to the electromagnetic theory, the magnitude of the magnetic field mapped around a PM remains unchanged after size reduction, while the field gradient scales inversely with characteristic dimensions. This means that for interaction elements involving magnets and soft magnetic materials, for which the volumic force acting on each particle is governed by the relation of B ? B, the force-to-volume ratio improves strongly as scale shrinks down and therefore diamagnetic material could be utilized with PM to construct simple bearing solution for MEMS.
Engineering of diamagnetic bearings requires a complex mix of disciplines, including electromagnetic theory, kinetics, material science, design theory and etc. The objective of this thesis is to study its basic characteristics so as to gain a systematic understanding of such a novel bearing mechanism. The major content includes:
(1) Based on the electromagnetic theory, the micro-scale effectiveness of diamagnetic levitation is demonstrated and the magnetomechanical interaction in terms of load-carrying capacity and the restoring in the axial, lateral and inclination directions are evaluated.
(2) The eddy current effect on the performance of diamagnetic bearing is investigated. Due to the good electrical conductivity of some of diamagnetic materials or the intentionally introduced eddy current damper for vibration control, eddy current could be induced in the diamagnetic bearing with viscous force opposing the relative motion between the rotor and the stator. Such damping mechanism is analyzed with a thin sheet model and the image method and compared with that due to aerodynamic effects so as to give an idea of its significance at the micro-scale.
(3) Based on the derived dynamic coefficients, linear vibration characteristics and nonlinear parametric resonance of the rotor-bearing system are studied. Results obtained indicate that there are two major instability problems for diamagnetic bearings.
(4) Due to the malmanufacturing of the bearing, magnetic asymmetry could occur either on the PM part or the diamagnetic part. The impact of such non-ideal working condition on the performance of the bearing is investigated. The rotational loss induced thereby is also studied to show the acceleration characteristics of the bearing.
(5) Basic vibration characteristics of the bearing are assessed experimentally. Compared to other bearing mechanisms for microsystems, diamagnetic approach has the advantage of being completely passive, hereby eliminating the design and operational cost associated with active electromagnetic or electrostatic approaches; and it is more compact in configuration as compared to air bearings, which require connection to the external source of pressurized gas. This thesis represents a first step towards a systematic understanding of a potentialy interesting application of magnetic bearings, and the findings herein would pave the way for further extensive study.
引文
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