Research On Dynamical Behaviors In Micro Rotor-Bearing Systems

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.