考虑Lomakin效应的微涡轮发动机气体径向轴承动力学特性研究

The microengine provides a promising replacer for the current energy sources with low energy density. Micro gas bearings with high rotational speed (typically 106 rpm) is bottleneck which blocks the development of the microengine. The ultra low length-to diameter ratio (L/D) and axially air supply due to the micro-fabrication limitations, result two special problems for the bearing systems, including the non-fully developed circumferential Couette flow and the Lomakin effect. However, the lubrication model including the above factors has not been developed, and the flow characteristics of the bearing is not described properly. Moreover, the influence of surface roughness on the nonlinear dynamic performance and the whirl stable region of the system have not been studied yet, which becomes obstacle in the design, fabrication and control of the micro gas bearings. In this project, the lubrication model including the non-fully developed circumferential Couette flow and the Lomakin effect and the corresponding dynamic analysis model will be developed in order to gain a deeper appreciation about the steady-state and nonlinear dynamic performance of the system. After that, the effect of surface roughness will be introduce based on fractal geometry theory to study the whirl stable characteristics and nonlinear performance of the micro gas bearing systems. Based on the theoretical research, an integrated in-situ micro gas bearing measurement system will be set up to measure the flow characteristics and the vibration behavior. The key theoretical basis will be provided for the structure design, the establishment of fabrication accuracy and control of the gas bearing for microengine through the study of this project.

微涡轮发动机为能源系统能量密度过低的现状提供了有效解决途径。每分钟百万转以上的微气体轴承是制约微涡轮发动机发展的“瓶颈”。轴向供气及超小宽径比带来的周向Couette流不充分发展性及Lomakin效应是微气体径向轴承所面临的特殊问题，现有润滑模型无法准确描述其流场特性；同时，微尺度下表面粗糙度对轴承系统非线性稳定性裕度的影响规律目前尚不明确，已成为微气体轴承设计加工及稳定控制的障碍。本项目将建立考虑Couette流不充分发展性的润滑力学模型，并采用隐式边界条件以计入Lomakin效应的影响，探讨微气体轴承系统的非线性失稳机理，提出合理的稳定性裕度；基于分形几何理论考察表面粗糙度对轴承系统非线性特性及稳定运转范围的影响规律及机理；搭建微轴承系统动力学测试平台，验证理论模型，探讨微气体轴承在高速运转中的转子振动特性。本研究将为微涡轮发动机的结构设计、加工精度制定及稳定控制提供理论依据。

微涡轮发动机为能源系统能量密度过低的弊端提供了有效解决途径。微气体超高速轴承是制约微涡轮发动机发展的“瓶颈”。轴向供气及超小宽径比带来的周向Couette流不充分发展性及Lomakin效应是微气体径向轴承所面临的特殊问题，现有润滑模型无法准确描述其流场特性。本项目详细分析了Lomakin效应产生的条件、机理及特征，发现轴向供气机制下，微气体径向轴承的入口边界条件是隐式的，这给计算轴承压力分布带来了难处。为了解决这一问题，采用微元体分析法推导了描述气膜压力沿周向和轴向的变化的偏微分方程，并提出了一种求解径向轴承入口压力与气膜压力分布的交叉迭代耦合求解方法，得到了既满足入口压力降条件又满足雷诺方程的轴承气膜压力；分析了入口压力损失所受的影响因素及Lomakin效应对轴承系统的润滑特性的影响规律。项目还分析了Cuette流非充分发展性对Reynold方程推导过程的影响，并结合Fluent流体分析软件的结果对Reynold方程进行修正，得到了同时考虑Lomakin效应及Cuette流非充分发展性的计算模型，研究了Cuette流非充分发展性对轴承系统性能的影响机理及规律。制作了轴承测试样机，搭建了实验平台，进行了有关测试。主要研究结论有：（1）径向轴承的入口压力低于高压气室的压力，且气膜厚度越大、供气压力越高、轴承宽度越小，入口压力损失越明显，对于微气体轴承，入口压力损失不能忽略；（2）Lomakin效应显著提升了轴承的承载力，特别是低速、低偏心率时的承载力，有利于弥补气体径向轴承在低速、低偏心率时承载力不足的缺点；（3）Lomakin效应减小了轴承的偏位角，且使偏位角随偏心率的变化更平缓，从而提高了转子稳定性；（4）Cuette流非充分发展性使气膜中的压力峰值有所降低，从而降低了轴承的承载力，最大可使承载力降低近15%，在偏心率较大、供气压力较小时，影响较为明显。本项目所提出的润滑模型、数值计算方法及研究结论将为微涡轮发动机的结构设计、加工精度制定及稳定控制提供理论依据。