Whirling, tilting and axial motions of a HDD spindle system due to the manufacturing errors of FDBs

This paper investigates the whirling, tilting and axial motions of a hard disk drive (HDD) spindle system due to manufacturing errors of fluid dynamic bearings (FDBs). HDD spindle whirls around the sleeve with tilting angle due to the centrifugal force of unbalanced mass and the gyroscopic moment of rotating spindle in addition to axial motion. The whirling, tilting and axial motions may be increased by the manufacturing errors of FDBs such as imperfect cylindricity of sleeve bore, or imperfect perpendicularity between shaft and thrust plate. They increase the disk run-out to limit memory capacity and they may result in the instability of the HDD spindle system. This paper proposes the modified Reynolds equations for the coupled journal and thrust FDBs to include the variable film thickness due to the cylindricity of sleeve bore and the perpendicularity between shaft and thrust plate. Finite element method is used to solve the modified Reynolds equation to calculate the pressure distribution. Reaction forces and friction torque are obtained by integrating the pressure and shear stress, respectively. The whirling, tilting and axial motions of the HDD spindle system are determined by solving the equations of a motion of a HDD spindle system in six degrees of freedom with the Runge-Kutta method. It shows that the imperfect cylindricity and perpendicularity increase the whirl radius, axial runout and tilting angle of the HDD spindle system. However, the degradation of dynamic performance due to the imperfect perpendicularity between shaft and thrust plate can be improved by allowing the other manufacturing error of the cylindricity of sleeve bore in such a way to compensate the bad effect of the imperfect perpendicularity.     

Studies on a micro turbine device with both journal- and thrust-air bearings

This paper presents design, fabrication, analysis and test of a silicon-based micro turbine device that is driven by compressed air. To improve the motion stability at high rotational speed, the turbine device employs an enhanced micro air bearing system that includes both journal air bearing and thrust air bearings. The double-sides dynamic thrust air bearings are designed to support the rotor from both its top and bottom sides. The top thrust air bearing employs pump-in spiral groove configuration, and the bottom bearing uses pump-out spiral groove configuration. The dynamic journal air bearing is formed by a plain circular trench with a short journal length (L) and a narrow radial clearance (C). The critical aspect ratio (L/C) over 20:1 is realized through an optimized fabrication process. The micro turbine device has been fabricated, integrated and tested. During the test, the turbine device demonstrated stable operations at a rotational speed of 14,700 rpm.     

A bi-directional rotating fluid bearing system

 Most fluid bearing systems with grooves on the journal/thrust bearing surfaces were designed to rotate in a specified direction and cannot be reversed. This feature of such fluid bearings limits their application range and hence, a bi-directional rotating fluid bearing system is proposed. The results of numerical simulation on the dynamic characteristics of such bearing system are presented and compared with those of one-directional rotating fluid-bearing system. It shows that for the same load capacity and stiffness requirement, the bi-directional rotating fluid bearing system has a higher power consumption than that of the one-directional counterpart. However, the bi- directional rotating fluid bearing system provides the freedom of rotating spindle motor in either direction and widens the application range of fluid bearing spindle motors. Received: 5 July 2001/Accepted: 17 October 2001     

Dynamic characteristics of micro air bearings for microsystems

This paper reports on the dynamic characteristics of micro air bearings that include thrust and journal air bearings for microsystems. The dynamic thrust air bearing employs a spiral groove configuration. Analysis shows that the motion stability and load capacity of a thrust air bearing imposes a contradictive requirement on the groove pattern of the air bearing. The dynamic journal air bearing is realized by using a plain circular trench with a narrow radial clearance of C, and a very small aspect ratio of bearing length versus diameter (L/D). Analysis on the shock tolerance of the journal air bearing shows that the shock tolerance increases with the bearing number, the bearing aspect ratio of L/D and its initial equilibrium eccentricity ratio ε ₀. The optimum values of the bearing parameters are explored and recommended. A prototype of turbine device has been designed based on the recommended bearing configurations and realized via microfabrication.     

Robust design of a HDD spindle system supported by fluid dynamic bearings utilizing the stability analysis of five degrees of freedom of a general rotor-bearing system

This paper proposes a method to improve the robustness of a hard disk drive (HDD) spindle supported by fluid dynamic bearings (FDBs) by utilizing the stability analysis of the five degrees of freedom of a general rotor-bearing system. The Reynolds equations and the perturbed equations of the coupled journal and thrust bearings were solved by FEM to calculate the dynamic coefficients. The paper introduces the radius of gyration to the equations of motion in order to consistently define the stability problem with respect to a single variable, i.e., the mass. The critical mass, which is the threshold between the stability and instability of the HDD spindle, is determined by solving the linear equations of motion. The proposed method was applied to improve the robustness of a HDD spindle supported by FDBs by varying the groove parameters. It shows that the optimized groove design obtained using the proposed method increases both the stability and the modal damping ratio of the half-speed whirl mode. This research also determines the motions of the rotating disk-spindle system by solving its nonlinear equations of motion with the Runge?CKutta method. It shows that the groove design optimized using the proposed method has a small whirl radius in the steady state. It also shows that it has very little displacement due to the shock excitation, and that it quickly recovers to the equilibrium state.     

Complete determination of the dynamic coefficients of coupled journal and thrust bearings considering five degrees of freedom for a general rotor-bearing system

A complete method is presented for calculating the stiffness and damping coefficients of coupled journal and thrust bearings of a general rotor-bearing system considering five degrees of freedom. The Reynolds equations and their perturbation equations were derived by linearization of the bearing reaction with respect to the general five degrees of freedom, i.e., the tilting displacements and angular velocities as well as the translational displacements and velocities. The Reynolds equations and their perturbation equations were transformed into finite element equations by considering the continuity of pressure and flow at the interface between the journal and the thrust bearings. The Reynolds boundary condition was included in the numerical analysis so as to simulate the phenomenon of cavitation. The stiffness and damping coefficients of the proposed method were compared with those found from a numerical differentiation of the loads with respect to the finite displacements and velocities of the bearing center. It was shown that the proposed method may be used to calculate the dynamic coefficients of coupled journal and thrust bearings more accurately and efficiently than the differentiation method. The tilting motion was also been found to play an important role in the determination of force and moment coefficients.     

Dynamic analysis of a HDD spindle system with FDBs due to the bearing width and asymmetric grooves of journal bearing

This paper investigates the dynamic behavior of a HDD spindle system with fluid dynamic bearings (FDBs) by solving the Reynolds equation and the equations of a motion of a HDD spindle system in five degrees of freedom. FEM is used to solve the Reynolds equation in order to calculate the pressure distribution in fluid film. Reaction forces and friction torque are obtained by integrating the pressure and shear stress along the fluid film, respectively. Dynamic behaviors of a HDD spindle system, such as the whirling and the tilting motion, are determined by solving its nonlinear equations of motion with the Runge-Kutta method. This paper also proposes two design methods to improve the dynamic characteristics of a HDD spindle system without increasing friction torque, i.e., optimization of the width of the lower and the upper journal bearings and the journal bearings with asymmetric grooves.     

基于Abaqus的GE17自润滑关节轴承结构分析与改进

针对在GE17自润滑关节轴承轴向静载试验中,轴承内圈轴向位移大于许用值的问题,应用Abaqus建立GE17轴向静力加载模型进行分析,结果表明轴承外圈端面的安装沟槽削弱轴承的轴向刚度。改进GE17轴承结构,减小轴承球径尺寸,增加沟槽内挡边厚度,提高其抗挤压变形能力。试验结果表明,改进后结构在额定载荷下的轴向位移减小10.7%,从而验证仿真结果的准确性和结构改进的有效性,为同类型轴承设计提供参考。     

弹性箔片轴承-盘式永磁电机转子系统轴向冲击响应

轴向磁通永磁(Axial Flux Permanent Magnet,AFPM)电机在给转子输出周向电磁转矩的同时,还作为一种“磁轴承”,与弹性箔片轴承(Gas Foil Bearings,GFBs)并联工作.当GFBs支承的单定子单转子AFPM电机转速发生突变时(如加、减速),叶轮或者透平会产生一个瞬时轴向力.为揭示此轴向冲击对转子系统振动的影响机理,针对采用2个径向GFBs和1个轴向GFB支承的单定子单转子AFPM电机,建立了系统的刚性转子动力学方程,计入了永磁体的轴向吸力、径向回复力以及轴向GFB的推力对转子振动的影响.计算显示：轴向冲击对横向振动的影响非常小,箔片结构刚度的非线性效应会对转子振荡幅值和时间均产生影响,永磁体的负刚度绝对值越大,轴向振幅越大.在设计时,要注意永磁轴承刚度、箔片结构刚度和结构阻尼的合理匹配,以保证转子在轴向冲击下的轴向振荡时间和振幅均不超过允许值.     

Tribological design of a multistep journal bearing

Journal bearings are machine elements with widespread application. The extent of their use, from the automobile engines to gas turbines, gives a significant incentive for improvement of their performance. Various approaches focusing on the journal bearing design have been used in the past in order to reduce power losses and increase load carrying capacity of journal bearings, including artificial texturing, axial and circumferential grooves and bushing specific shapes (e.g. three-lobe bearings). In this paper, the multistep journal bearing is examined. Its performance benefits are quantified. A maximum friction coefficient improvement of 38% is obtained with simultaneous 9.7% improvement of load capacity in comparison to the plain bearing. The specific operating conditions under which these benefits occur are established. The physical mechanism responsible for these improvements is discussed by correlating pressure, shear stress distribution, lubricant thickness and bushing geometry. The ultimate objective of this work is to suggest certain design principles that may adjust the improvement of the desired operating characteristics of the multistep journal bearing. The surface configuration of the bushing is relatively simple and is thus easy to be manufactured.     

Numerical solution of finite modified Reynolds equation for couple stress squeeze film lubrication of porous journal bearings

In this paper, the rheological effect of couple stress fluids on the static and dynamic characteristics of squeeze film lubrication in finite porous journal bearings is studied. The finite modified Reynolds equation is derived from the Stokes constitutive equations for couple stress fluids and is solved numerically by using the finite difference technique. The applied load is considered as a sinusoidal function of time to simulate the bearings operating under cyclic loads. Under a cyclic load, the effect of couple stress is to reduce the velocity of the journal centre and to increase the minimum permissible height of the squeeze film.     

具有轴承不对中的多跨柔性转子系统非线性动力学研究

主要研究了具有不对中轴承支承的柔性多转子耦合系统的动力学建模和非线性动力学行为.首先在短轴承假设、小轴承的不对中量和圆盘不平衡量等几个基本假设条件下,考虑了转子的柔度、不对中轴承的非线性油膜力和圆盘的不平衡等因素后,建立了一个具有轴承不对中的10自由度多跨转子系统非线性动力学模型；最后采用数值方法研究了系统的非线性动力...     

Theoretical analysis of the slip flow effect on gas-lubricated micro spherical spiral groove bearings for machinery gyroscope

The performance of a gas-lubricated micro spherical spiral groove bearing (MSSGB) with slip flow effect is investigated. A modified Reynolds equation incorporated with Barber’s first-order slip flow model is proposed to investigate the flow characteristics of gas in MSSGBs. Parameter transformation and oblique coordinate transformation are applied to eliminate the curve effect on the calculation domain. An improved finite difference method (FDM) based on Green’s formula is used to solve the Reynolds equation. The perturbation method is adopted to determine the dynamic coefficients. The effects of slip flow and bearing parameters, including the groove depths, rotor speeds, and eccentricity ratios, on the bearing characteristics are investigated and discussed. Prediction results show that the slip flow effect on MSSGB performance is significant. Moreover, the groove depth at micro clearance has a crucial influence on bearing performance.     

弹性环挤压油膜阻尼器支撑下的柔性转子系统动力学分析

弹性环挤压油膜阻尼器(Elastic ring squeeze film damper, ERSFD)具有良好的支撑作用和减振效果,但由于其结构和流场耦合行为极为复杂,使得已有的物理模型难以完整表现出ERSFD的力学特性.为了进一步探究ERSFD的力学机理,本文借助有限元仿真平台,采用双向流固耦合的计算方法,剖析弹性环与油膜之间的相互作用,获取ERSFD中油膜压力的分布规律.在此基础上,利用最小二乘法进一步拟合出ERSFD等效刚度、等效阻尼与转子轴颈扰动位移的映射关系,并将其分别引入柔性转子系统动力学模型中.通过数值计算研究了ERSFD支撑下柔性转子系统的振动响应,分别给出了不同转速下转子系统的响应分岔图、轴心轨迹等.同时,通过对比分析,进一步揭示了ERSFD所诱发出的转子系统丰富的非线性动力学行为,有助于对ERSFD轴承支撑特性的理解.     

Stability analysis of a whirling disk-spindle system supported by FDBs with rotating grooves

This paper investigates the stability of a whirling disk-spindle system, supported by coupled journal and thrust bearings with rotating grooves. The stiffness and damping coefficients of the FDBs change periodically with the whirling motion of the disk-spindle system, which makes it difficult to define the stability problem in the inertia coordinate. However, with the introduction of the coordinate system which rotates with the disk-spindle system, the stiffness and damping coefficients are constant, which makes it possible to define the stability problem in the rotating coordinate system. The Reynolds equations and the perturbed equations of the coupled bearings were derived with respect to the rotating coordinate and were solved using FEM to calculate the stiffness and damping coefficients. The critical mass of the rotor-bearing system was determined by solving the linear equations of motion. As a result, the stability increases with an increase in the whirl radius and with a decrease in the rotating speed. It also decreases with an increase in the tilting angle under a small whirl radius while it increases with an increase in the tilting angle under a large whirl radius.     

Stability analysis of a disk-spindle supported by a plain journal bearing and pivot bearing

A hydrodynamic bearing is widely used for hard disk drives, and it is better than a ball bearing in terms of vibration suppression, noise reduction and shock resistance. However, its cost to performance ratio should be further improved. In this study we analyzed the stability of a disk-spindle assembly supported by a hydrodynamic plain journal bearing and a pivot bearing at the bottom of the shaft. As a result, we found that a half-frequency whirl of a vertical spindle caused by the plain journal bearing becomes stable if the gyro factor of the rotor is larger than 0.5. We examined the effects of the bearing design parameters on the stability of the disk-spindle assembly, including the flexibility of the shaft. We also compared the stability of a disk-spindle assembly supported by two plain journal bearings and found that the vertical spindle is always unstable. Thus, the bottom end of the shaft should be supported as a fulcrum.     

冲击载荷作用下滑动轴承油膜压力与应力研究

对动载滑动轴承雷诺方程进行推导,基于有限差分法求解雷诺方程,得到油膜压力分布,并由接触力学分析求得轴承应力。将计算结果与有关研究结论进行对比分析,验证了计算模型的有效性和合理性,并对比分析了阶跃、正弦、孤峰波形冲击作用下滑动轴承油膜压力分布特征。进而对计算方法工程化,研究某舰用齿轮箱滑动轴承在冲击载荷作用下的油膜压力与轴承应力分布,计算结果表明:冲击作用下油膜压力三维分布近似为一连续的抛物面分布,轴承与轴颈接触表层的最大应力逐渐向内表层移动,越靠近接触表面,轴承与轴颈接触表层的最大应力越大,且最大应力产生于最大流体动压力区域。     

不对中联轴器 柔性转子系统非线性动力学行为

主要研究了在滑动轴承支承下转子间具有平行不对中故障的柔性联转子系统非线性动力学行为.首先,在考虑到联轴器的连接刚度后,基于两转子间运动的几何关系和位移约束条件推导了在非线性油膜力作用下平行不对中转子系统的动力学模型,理论分析表明该系统是一个含有时变系数和强非线性特征的11自由度非自治系统.然后采用数值方法重点分析了系统的非线性振动特性,例如,系统的轴心轨迹、频谱相应,Poincaré截面等.结果表明:在较低转速时,转子的涡动轨迹在较小的范围内作同步振荡;随着转速的提高,系统出现倍周期分叉现象,以及准周期、混沌运动等复杂的非线性动力学行为.最后讨论了联轴器的连接刚度对系统运动特性的影响.     

Thin film evaporation effect on heat transport capability in a grooved heat pipe

A theoretical model predicting the heat transfer performance occurring in a grooved heat pipe is developed. The model includes the effects of groove geometry, thin film evaporation, contact angle, and film condensation. The numerical results show that the groove geometry significantly affects the thin film evaporation and condensation. The thin film evaporation plays a key role in the total effective thermal conductivity and determines a limit for the maximum amount of heat transport through the micro regions for a given evaporator geometry. While the contact angle can influence the capillary limitation, it significantly affects the thin film evaporation and the total effective thermal conductivity of a groove heat pipe. In order to verify the theoretical analysis, an experimental investigation on a grooved heat pipe was conducted. The current investigation will result in a better understanding of thin film evaporation and its effect on the maximum heat transport in a grooved heat pipe.     

高性能磁盘机中螺旋槽径向轴承的自由边界

在自密封的螺旋槽径向轴承中,轴承间隙实际上并没有全部充满润滑油,形成了气液界面－自由边界,自由边界不仅会影响轴承的承载力和稳定必 重要的是会影响动密封性,本文开发了求解向承自由边界的数据方法,给出了仿真结果并讨论轴承参数对自由边界的影响,为更精确地计算承载力等特性以及优化设计打下基础。