【作者】 周健斌；

【导师】 孟光；

【作者基本信息】 上海交通大学 ， 机械设计及理论， 2009， 博士

【摘要】 微机电系统(Microelectromechanical System,简称MEMS)是指集微型传感器、执行器以及信号处理和控制电路、接口电路、通信和电源于一体的微型机电系统。自1987年第一台基于MEMS技术设计、制造的微型电机诞生以来,微机电系统被认为将引导21世纪的一场新的技术革命。由此微型旋转机械,如微型电机、微型涡轮等,作为能量转换以及大幅运动位移的执行器件成为微机电系统研究领域的一个重要分支。微型旋转机械的实现不仅仅是宏观旋转机械的简单的微型化,它具有其自身的特性。由于器件尺寸的减小,尺度效应将给微型旋转机械的设计以及动力学特性带来影响:首先尺度效应使得器件所受的表面力相对体积力增大,从而使得在宏观机械中不考虑的相互作用力,如范德华力、静电作用力、毛细作用力等不再可以忽略。其次,微型旋转机械的工作环境和受力状态不同于宏观旋转机械,制成微型旋转机械的材料也有别于传统旋转机械,其材料特性随着尺度的变化也有很大的不同。微型旋转机械的摩擦、磨损以及润滑问题相比宏观旋转机械而言表现得更加突出。由于尺度的减小,润滑油产生聚合作用而使得微型旋转机械的轴承动力学特性产生很大的不同,甚至由于在微小尺度下液体的粘度增大而使得传统油膜轴承不再适用,因此气体轴承在微型旋转机械中得到广泛的应用。同样,由于尺度的减小以及受当前微加工工艺的限制微型气体轴承相比传统气体轴承具有努森数大,长径比小、隙径比大等特点,传统的针对气体轴承的研究方法以及由此得到的系统特性不再适用。本文针对以上问题进行了研究,主要内容如下:首先概述了MEMS微型旋转机械的发展现状,分析了各种不同形式的微型旋转机械的特点;总结了微型旋转机械的轴承动力润滑形式,重点讨论了微型气体轴承在微型旋转机械中的应用;介绍了MEMS器件中的摩擦、磨损问题,并探讨了由于器件尺寸缩小带来的尺度效应对MEMS器件,特别是微型旋转机械动力学行为特性的影响。在微小尺度下,由于尺度效应的作用,传统机械中忽略不计的一些器件间的相互作用力,比如作用在器件表面或表面间的力,以及由分子间相互作用引起的部件间的相互作用力以及静电力等微观作用力变得不可忽略。这些微观作用力对MEMS器件以及微型旋转机械系统的动力学特性产生影响,甚至决定系统设计的成败。针对微型旋转机械中存在的范德华作用力,建立了其在微型旋转机械系统中的数学表达式,在此基础上建立微观作用力作用下微型转子系统的动力学模型,进而对系统的平衡点特性、频率响应,动态响应等动力学行为进行研究。分析结果表明:在范德华力作用条件下,微型旋转机械的平衡点稳定性随着范德华力相对大小的变化而不同,同时由于范德华力的作用,微型旋转机械系统出现刚度“软化”现象。受尺度效应的影响,在微观条件下微型旋转机械系统中的的摩擦磨损的问题与传统机械存在较大的差异。通过对静电微电机电刷与基板间的接触进行载荷分析,充分考虑尺度效应的影响,针对静电微电机半球形电刷的磨损问题建立了基于Archard磨损定律的数学模型。基于该模型分析了包括毛细作用力、静电吸引力在内的表面力以及电刷的几何参数对微型转子系统的磨损特性的影响。微型气体轴承是微型旋转机械中常用的润滑方式。根据微加工工艺的特点,在微型气体轴承中轴承壁与转子间的最小间隙可达微米甚至更小的量级。在这样的尺度条件下,气膜厚度与气体分子的平均自由程相当,传统气体轴承研究中对工作气体所作的连续流假设不再适用。根据微型气体轴承的工作条件,本文引入了气体分子模型滑移流边界条件,得到可压缩气体非线性修正Reynolds方程,用以描述气膜内的气体压力分布。为兼顾数值计算的精度和效率,根据动压气体轴承压力分布的特点,采用频域配点法,分别以Chebyshev多项式和三角多项式作为轴承轴向和周向的基函数,对上述修正Reynolds方程进行离散化求解。基于离散化修正Reynolds方程,分析了微型气体轴承的静态特性,研究了转子转速、轴承偏心率、长径比以及努森数等参数对微型气体轴承的气膜压力分布、承载能力以及载荷相位角的影响。结果表明:在长径比和转子偏心率较小时,可采用不可压缩短轴承理论进行近似计算;随着转子偏心率的增大,轴承承载能力随着轴承数的增大而非线性增长,载荷偏位角亦随轴承数的增大由π/2逐渐减小,即轴承力方向从与转子位移垂直逐渐变化至沿轴承位移方向;微型气体轴承的载荷参数随着努森的增大呈指数衰减,载荷偏位角呈线性衰减。在工作气体温度较低时,承载能力随温度的升高而增大;当温度高于一定值时,承载能力随温度的升高而降低;随着温度的进一步升高,承载能力受温度的影响逐渐减弱。进一步引入转子受轴承力以及外载荷激励力作用时的动力学方程,与离散瞬态修正Reynolds方程耦合,采用轴心轨迹法(Orbit Method)建立微型气体轴承-转子系统动力学方程,用以描述系统在任意时刻的位移和速度。采用数值积分法求解系统动力学方程,研究各系统参数对微型气体轴承-转子系统的平衡点稳定性、系统受迫响应分岔行为特性、以及动态轴承系数的影响,结果表明:系统在不同转速条件下存在平衡点稳定最小和最大偏心率,分别对应转子涡动不稳定和径向发散不稳定;平衡点的稳定性与轴承长径比以及系统努森数有关。随着轴承长径比的减小,系统稳定区域向低偏心率方向偏移。气体的滑移流边界条件增强了系统的平衡点稳定性。系统的动态轴承系数与系统的扰动频率、轴承数以及努森数有关。随着轴承长径比、努森数、转子转速、转子质量以及转子质量偏心量等参数的改变,系统受迫响应出现同步周期解、倍频解以及拟周期解等丰富的非线性特性。以探索微转子系统振动测试方法,进一步认识微转子系统的动力学特性为目的,分别对采用微型球轴承、转轴直径为2 mm的气动微转子平台和采用干摩擦轴承、转轴直径为1.5 mm的电磁型薄膜微电机的动力学行为进行测试。更多还原

【Abstract】 MEMS, referred to as Microelectromechanical Systems, are functional micro devices based on micro electronics, micro mechanical engineering and material science. Ever since 1987, the first micro electrostatic micro motor based on MEMS technology was fabricated, MEMS technology has been considered to lead a new technical revolution in the 21st century. Among the various MEMS devices, micro rotating machinery, such as micro motor and micro turbine, acting as micro actuators to produce large scale displacement and energy conversion, has also been a new important branch.Micro rotating machinery is not simply the shrunk-sized ordinary rotating devices, but it has distinct characteristics. As the size scales down, the scaling effect largely affects the dynamics in those micro rotating devices, and consequently, affects its design discipline. As a result of the scaling effect, surface forces become relatively large compared with volume forces in small sizes. Hence, the inter-surface forces between the parts of the devices, such as van der Waals force, electrostatic force and Casimir force are not negligible any longer as in the traditional devices. Meanwhile, the working environments and the loading conditions of the micro rotating devices, as well as the materials are also different from their large-scale counterparts. The material properties also vary with its dimensional size in micro scale. The friction, wear and lubrication problems in micro rotating devices become the enabling issues. The polymerization of the lubricants makes the rotor-bearing system so much different in the micro rotating devices so that the oil film bearings become un-available. Consequently, air bearings have been largely used. However, the mathematical model describing the air bearing-rotor system needs to be modified to suit for the micro scale applications. At the same time, as a consequence of the state-of-art of the micro fabrication technologies, the micro gas bearings have such characteristics as small length-to-diameter ratio and large clearance-to-radius ratio. To solve those problems, this thesis carries out efficient studies. The research content and achievement are in details as the followings.A brief introduction on the development of the research in micro rotating machinery is presented in the first chapter. Current realized micro rotating devices based on different disciplines are introduced. The lubrication method used in these devices, especially micro gas journal bearings are discussed. Friction and wear problems in MEMS devices are introduced. The scaling effects to the micro rotating devices are discussed.In the second chapter, the effects of the van der Waals force on the micro-rotor systems are investigated in the perspective of rotordynamics. An expression for van der Waals force acting on the micro-rotor is derived. Dynamical governing equations of the micro-rotor taking into the influences of van der Waals force are presented based on the simplified micro-rotor-bearing model. Equilibrium points of the obtained system and their stabilities are investigated. Numerical simulations show that adhesion occurs once the displacement of the micro-rotor exceeds the stable boundary as a consequence of van der Waals force. Free oscillation and dynamically imbalanced response of the micro-rotor system are investigated using both analytical and numerical methods.In the third chapter, the effect scaling down on the wear process between the bushing and the substrate in a micro motor is investigated. A model to predict the sliding wears between the rotor bushing and the substrate plane in a variable capacitance micro-motor is presented. The model is based on the Archard’s wear law and takes into account the scale effects, including the effects of such surface forces as meniscus force due to humidity and the electrostatic force as a result of the capacitance coupling between the rotor and substrate. Moreover, the scale effects of the material properties, which become scale dependent in micro-scale, on the hemispherical bushing-on-substrate wear process as well as the durability of the bushing are also discussed. Simulation results show that the wear process and the durability of the bushing are largely affected by these effects and it is indicated that sufficient attentions should be taken in the design and fabrication of micro-motors on the scaling effects.In the fourth chapter, static charateristics of the micro gas journal bearing are investigated. Second order slip flow boundary condition of the working gas is emplemented to describe the pressure distribution in the gap of micro gas journal bearing. Static performances, including static pressure distribution, load parameter and phase angle, are investigated.The dynamical behavior of the micro gas journal bearing-rotor system is further investigated in the following chapter. The system is modeled as a rigid rotor supported by bearing forces as a result of gas viscosity and rotational speed. The spectral collection method is employed to discrete the non-linear modified Reynolds equation. A system of non-linear PDEs, which couples the fluid equation and the equations of rotor motion is presented and solved using Runge-Kutta method. The stabitlity of the system equilibrium point is investigated. Based on the orbit method, the dynamical bearing coefficients of the system is studied. Finally, the nonlinear behavior of the system is investigated using the bifurcation diagram of the systems. The bifurcation diagram, rotor center orbits, phase-portraits, frequency spectra and Poincarémaps are utilized to analyze dynamical characteristics of the rotor-bearing system for different operating conditions. The effects of rotational speed and length-to-diameter ratio on the system dynamical behaviors are investigated with both low and high initial eccentricity ratios. The analyses show that the system exhibits complicated behaviors at low eccentricity ratios as a result of self-excited whirl motion. For high eccentricity ratios, the bearing behavior is comprised of synchronous and sub-harmonic motions. A further understanding of the non-linear dynamics of gas journal bearing in MEMS is given by the analysis results.An experiment is carried out to investigate the dynamics of high speed micro rotating systems. The rotor is driven by an commercial dental drill to achieve high speed and its displacement is measured by high-speed, high-accuracy CCD Laser displacement sensors.更多还原