硬盘纳米间隙气膜润滑的新模型及其静态特性研究
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摘要
硬盘是当前数据存储的主要途径,并且它的尺寸持续减小、容量逐步增大、成本逐渐降低。随着磁记录密度的不断增加,硬盘中磁头与磁盘间的距离也已经减小到只有几个纳米。在这样小的间隙中,气膜中的气体不能看作严格的连续流体,传统的润滑理论不再适用,必须要考虑气体稀薄效应的影响。
为了准确模拟超薄气膜的压力分布,需要考虑气体稀薄效应及表面粗糙度等对Reynolds方程进行修正。本文基于当前广泛应用的Reynolds方程的FK模型,推出四种模拟超薄气膜润滑的简化新模型：连续FK(Continuous FK, CFK)模型、二阶FK(Second order FK, SOFK)模型、简化FK(Simplified FK, SFK)模型和高精度二阶(Precise second order, PSO)模型。采用最小二乘有限差分(Least square finite difference, LSFD)法分别对四种新模型进行了求解,并将计算结果与FK模型的计算结果进行了对比。数值结果表明,CFK模型是在不影响模拟精度的基础上修正了FK模型分段处具有较大误差的缺陷；SOFK模型和PFK模型与FK模型相比,均在不影响模拟精度的基础上,提高计算效率；PSO与FK模型相比,计算时间短、计算精度高。此外,基于所建立的四种新模型,模拟分析了几种典型二维浮动块的压力分布等气膜静态特性。
基于考虑气体稀薄效应修正Reynolds方程的简化PSO模型,采用LSFD法,求解了引入压力流因子和剪切流因子的量纲一Reynolds方程,并且研究了表面粗糙度对硬盘超低飞高(1-2纳米)气膜静态特性的影响。数值结果表明：粗糙度对超低飞高气膜压力分布和承载力的影响较大,而对压力中心的影响较小；飞行高度越低和／或粗糙度值越大,对压力分布及承载力的影响越明显；在粗糙度值相同的条件下,仅磁头粗糙且取横向粗糙度时,系统压力分布最高,气膜承载力最大；各种情况下,表面粗糙度对压力中心的变化影响不大,说明磁头飞行比较平稳,系统稳定性较好；另外,基于PSO模型研究粗糙度对硬盘气膜静态特性的影响,不仅数值结果精度高,并且具有很高的计算效率。
表面容纳系数(Accommodation coefficient, AC)是影响磁头／磁盘静态特性的重要因素。本文从Poiseuille流比和Couette流比的多项式对数方程出发,推出了
一种模拟硬盘超薄气膜的简化分子气膜润滑(Molecular gas film lubrication, MGL)方程。通过LSFD法对简化的MGL方程进行求解,研究了表面容纳系数对硬盘超低飞高(1nm)气膜静态特性的影响。数值结果表明：对称性分子交互作用时,表面容纳系数对气膜静态特性的影响明显；非对称性分子交互作用时,磁盘表面容纳系数对浮动块气膜静态特性的影响较大,而浮动块表面容纳系数的影响较小。此外,研究了自由分子区域内表面容纳系数对气膜静态特性的影响,结果表明,通过调节浮动块表面的容纳系数,可以在不影响气膜压力分布分布的同时,改变气膜的剪力分布。
Hard disk drives (HDDs) are now the most important means of information storage. They continue to be made smaller in size, higher in capacity, and lower in cost. Recently, the minimum spacing under the slider is within the order of several nanometers, the gas dynamics cannot be described from the continuum transport theory directly, and the convectional lubrication theory developed for gas bearings cannot be applied to these kinds of bearing, and the gaseous rarefaction effects must be taken into account in this case.
To more accurately simulate the pressure distribution of the ultra-thin air bearing film, Reynolds equation must be modified to account for the gas rarefaction effect and surface roughness et al. Started from a widely used FK model of Reynolds equation, four new simplified models, called continuous FK (CFK) model, second order FK (SOFK) model, simplified FK (PFK) model and precise second order (PSO) model, are proposed to simulate the ultra-thin air bearing film in HDDs in this paper. Those new models are solved using a least square finite difference (LSFD) method and the resultant numerical results are compared with those of FK model. Numerical results Shows that CFK model has modified the defects at the junctions of FK model on the basis of higher accuracy in simulating the air bearing film, and SOFK model and PFK model have higher computational efficiency and higher accuracy than those of FK model, and PSO model has less computational time and high accuracy than those of FK model. In addition, pressure distributions of several typical two-dimensional sliders have been simulated based on the four new simplified models.
Generalized non-dimensional Reynolds equation including pressure flow factor and shear flow factor based on PSO model is solved by using LSFD method. Effects of the surface roughness on static characteristics of the air bearing film in HDDs with ultra-low flying heights (1-2 nm) are investigated. Numerical results show that effects of the surface roughness on the pressure distributions and the load carrying capacity are obvious, while effects of the surface roughness on the pressure center are small. Lower flying height and/or greater value of surface roughness will lead to higher influence on the pressure distribution and the load carrying capacity. With the same value of surface roughness, the rough head with transverse roughness leads to the maximum pressure distribution and load carrying capacity of the system. The surface roughness do not have much influence on the pressure center, which indicates that the head/slider has good flying stability. Moreover, based on PSO model to investigate the effects of the surface roughness on static characteristics of air bearing films in HDDs, we can not only obtain good accuracy in numerical results but also achieve very high computational efficiency.
The influence of surface accommodation coefficient (AC) is an important factor to govern the static characteristics of the head/slider. Started from the polynomial logarithm fitting equations of Poisueille flow rate and Couette flow rate, a new simplified molecular gas film lubrication (MGL) equation is proposed to simulate the ultra-thin air bearing film in HDDs. The new simplified MGL equation is solved by using LSFD method. Effects of ACs on the static characteristics of air bearing films in HDDs with ultra-low flying height (1nm) are investigated. Numerical results show that effects of ACs on the static characteristics are obvious for the case of symmetric molecular interaction. effects of ACs at the disk surface on the static characteristics are obvious for the case of non-symmetric molecular interaction, while effects of ACs at the slider surface on the static characteristics are weak. On the other hand, effects of ACs on the static characteristics of air bearing films in the free molecular flow region are investigated. Numerical results show that we can change the distributions of the shear stress while not affect the pressure distributions by adjusting the surface AC.
为了准确模拟超薄气膜的压力分布,需要考虑气体稀薄效应及表面粗糙度等对Reynolds方程进行修正。本文基于当前广泛应用的Reynolds方程的FK模型,推出四种模拟超薄气膜润滑的简化新模型：连续FK(Continuous FK, CFK)模型、二阶FK(Second order FK, SOFK)模型、简化FK(Simplified FK, SFK)模型和高精度二阶(Precise second order, PSO)模型。采用最小二乘有限差分(Least square finite difference, LSFD)法分别对四种新模型进行了求解,并将计算结果与FK模型的计算结果进行了对比。数值结果表明,CFK模型是在不影响模拟精度的基础上修正了FK模型分段处具有较大误差的缺陷；SOFK模型和PFK模型与FK模型相比,均在不影响模拟精度的基础上,提高计算效率；PSO与FK模型相比,计算时间短、计算精度高。此外,基于所建立的四种新模型,模拟分析了几种典型二维浮动块的压力分布等气膜静态特性。
基于考虑气体稀薄效应修正Reynolds方程的简化PSO模型,采用LSFD法,求解了引入压力流因子和剪切流因子的量纲一Reynolds方程,并且研究了表面粗糙度对硬盘超低飞高(1-2纳米)气膜静态特性的影响。数值结果表明：粗糙度对超低飞高气膜压力分布和承载力的影响较大,而对压力中心的影响较小；飞行高度越低和／或粗糙度值越大,对压力分布及承载力的影响越明显；在粗糙度值相同的条件下,仅磁头粗糙且取横向粗糙度时,系统压力分布最高,气膜承载力最大；各种情况下,表面粗糙度对压力中心的变化影响不大,说明磁头飞行比较平稳,系统稳定性较好；另外,基于PSO模型研究粗糙度对硬盘气膜静态特性的影响,不仅数值结果精度高,并且具有很高的计算效率。
表面容纳系数(Accommodation coefficient, AC)是影响磁头／磁盘静态特性的重要因素。本文从Poiseuille流比和Couette流比的多项式对数方程出发,推出了
一种模拟硬盘超薄气膜的简化分子气膜润滑(Molecular gas film lubrication, MGL)方程。通过LSFD法对简化的MGL方程进行求解,研究了表面容纳系数对硬盘超低飞高(1nm)气膜静态特性的影响。数值结果表明：对称性分子交互作用时,表面容纳系数对气膜静态特性的影响明显；非对称性分子交互作用时,磁盘表面容纳系数对浮动块气膜静态特性的影响较大,而浮动块表面容纳系数的影响较小。此外,研究了自由分子区域内表面容纳系数对气膜静态特性的影响,结果表明,通过调节浮动块表面的容纳系数,可以在不影响气膜压力分布分布的同时,改变气膜的剪力分布。
Hard disk drives (HDDs) are now the most important means of information storage. They continue to be made smaller in size, higher in capacity, and lower in cost. Recently, the minimum spacing under the slider is within the order of several nanometers, the gas dynamics cannot be described from the continuum transport theory directly, and the convectional lubrication theory developed for gas bearings cannot be applied to these kinds of bearing, and the gaseous rarefaction effects must be taken into account in this case.
To more accurately simulate the pressure distribution of the ultra-thin air bearing film, Reynolds equation must be modified to account for the gas rarefaction effect and surface roughness et al. Started from a widely used FK model of Reynolds equation, four new simplified models, called continuous FK (CFK) model, second order FK (SOFK) model, simplified FK (PFK) model and precise second order (PSO) model, are proposed to simulate the ultra-thin air bearing film in HDDs in this paper. Those new models are solved using a least square finite difference (LSFD) method and the resultant numerical results are compared with those of FK model. Numerical results Shows that CFK model has modified the defects at the junctions of FK model on the basis of higher accuracy in simulating the air bearing film, and SOFK model and PFK model have higher computational efficiency and higher accuracy than those of FK model, and PSO model has less computational time and high accuracy than those of FK model. In addition, pressure distributions of several typical two-dimensional sliders have been simulated based on the four new simplified models.
Generalized non-dimensional Reynolds equation including pressure flow factor and shear flow factor based on PSO model is solved by using LSFD method. Effects of the surface roughness on static characteristics of the air bearing film in HDDs with ultra-low flying heights (1-2 nm) are investigated. Numerical results show that effects of the surface roughness on the pressure distributions and the load carrying capacity are obvious, while effects of the surface roughness on the pressure center are small. Lower flying height and/or greater value of surface roughness will lead to higher influence on the pressure distribution and the load carrying capacity. With the same value of surface roughness, the rough head with transverse roughness leads to the maximum pressure distribution and load carrying capacity of the system. The surface roughness do not have much influence on the pressure center, which indicates that the head/slider has good flying stability. Moreover, based on PSO model to investigate the effects of the surface roughness on static characteristics of air bearing films in HDDs, we can not only obtain good accuracy in numerical results but also achieve very high computational efficiency.
The influence of surface accommodation coefficient (AC) is an important factor to govern the static characteristics of the head/slider. Started from the polynomial logarithm fitting equations of Poisueille flow rate and Couette flow rate, a new simplified molecular gas film lubrication (MGL) equation is proposed to simulate the ultra-thin air bearing film in HDDs. The new simplified MGL equation is solved by using LSFD method. Effects of ACs on the static characteristics of air bearing films in HDDs with ultra-low flying height (1nm) are investigated. Numerical results show that effects of ACs on the static characteristics are obvious for the case of symmetric molecular interaction. effects of ACs at the disk surface on the static characteristics are obvious for the case of non-symmetric molecular interaction, while effects of ACs at the slider surface on the static characteristics are weak. On the other hand, effects of ACs on the static characteristics of air bearing films in the free molecular flow region are investigated. Numerical results show that we can change the distributions of the shear stress while not affect the pressure distributions by adjusting the surface AC.
引文
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