中文摘要：

当硬盘工作时，磁头滑块飞行在高速旋转的磁盘上方，头/盘界面产生了一层只有几个纳米的气膜，该气膜润滑方程为考虑气体稀薄效应的修正Reynolds方程。为了提高磁记录密度，人们正在考虑用离散磁道（Discrete Track Recording，DTR）磁盘取代传统的光滑磁盘。由于这种DTR磁盘表面磁道和沟槽的影响，在数值求解修正Reynolds方程的过程中，就需要足够多的离散网格来分辨出DTR磁盘表面几何形状，从而带来了计算效率问题。基于均匀化理论和修正Reynolds方程的线性流率（Linearized Flow Rate，LFR）模型，该文推导了一个适合分析DTR磁盘气体润滑特性的均匀化Reynolds方程，并采用有限体积法对均匀化Reynolds方程进行了求解和验证。其结果显示：相对于修正Reynolds方程，求解均匀化Reynolds方程只需要很少的离散网格，从而节省了大量的计算时间，大幅提高了计算效率，且两者压力分布、压力中心和承载力的最大相对误差都小于3.5%。

英文摘要：

In an operating hard disk drive the slider is flying over the high speed disk, a few nanometers of gas lubrication film is developed in the head/disk interface, and the gas film lubrication equation is modified by considering the gas rarefied effect. In order to improve the magnetic recording density of hard disk drives, a discrete track recording （DTR） disks are being considered to replace the traditional smooth disk. Owing to the track and grooves on the surface of the DTR disk, a lot of numerical grids are required to discern the surface geometry of the DTR disk, resulting in a low computational efficiency of solving the modified Reynolds equation. In this study, an averaged Reynolds equation suitable for the analysis of gas film lubrication with discrete track recording （DTR） disks was derived based on the homogenization theory and a simplified model of the Reynolds equation with a linearized flow rate （LFR）. The averaged Reynolds equation and the LFR model were solved simultaneously using the finite volume method. With comparing to the modified Reynolds equation, a few discreted numerical grids were required to solve the averaged Reynolds equation, thereby saving a large amount of computational time. The largest relative errors of the pressure distribution, pressure center and bearing capacity of the modified Reynolds equation and the averaged Reynolds equation were less than 3.5%.