A parametric study on rocking vibration of rotating disk/spindle systems with hydrodynamic bearings: rotating-shaft design

 The system studied in this paper is a rotating disk/spindle assembly supported by hydrodynamic bearings with a rotating shaft design. Based on an experimentally verified mathematical model [1, 2], this paper presents how various spindle parameters affect critical vibration modes of the system, such as half-speed whirls and (0, 1) unbalanced modes (i.e., rocking modes). The parameters studied include number of disks, hub/shaft interface stiffness, shaft rigidity, thrust bearing location, radial bearing stiffness, radial bearing damping, and radial bearing locations. To simulate operational tests, the numerical study focuses on frequency response functions (FRF) of rotating disk/spindle systems subjected to linear base excitations. Simulation results show that 1-disk configuration has smaller FRF amplitude than the 4-disk configuration. In addition, the amplitude of half-speed whirl is primarily controlled by the radial bearing stiffness. In contrast, the amplitude of (0, 1) unbalanced modes is dominated by hub/shaft interface stiffness. Finally, radial bearing locations significantly affect the amplitude of half-speed whirls and (0, 1) unbalanced modes simultaneously. Received: 16 October 2001/Accepted: 31 December 2001     

轴承预紧力对转子系统静动态特性的影响

轴承预紧力的大小直接影响到滚动轴承-转子系统的静动态特性. 综合考虑离心力和陀螺力矩效应,在Romax软件中建立了5自由度轴承-转子系统动力学模型,分析了预紧力对轴承刚度、工作接触角以及工作寿命的影响,并搭建了轴承 转子系统试验台做验证试验. 在不同轴承预紧力下,分别研究了轴承刚度、工作接触角、工作寿命、静载荷作用下轴承 转子系统的静变形以及动不平衡载荷作用下主轴系统的振动响应等,并在轴承-转子试验台上进行试验验证,得到了轴承预紧力与这些因素的关系曲线. 在此基础上,研究了预紧力对转子系统固有频率的影响,结果表明加大预紧力有助于提高系统的固有频率. 研究结果可为轴承-转子系统的设计与分析提供理论参考.     

Spindle configuration analysis and optimization considering the deformation in robotic machining applications

Robotic machining is an increasing application due to various advantages of robots such as flexibility, maneuverability and competitive cost. For robotic machining, the machining accuracy is the major concern of current researches. And particular attention is paid to the proper modeling of manipulator stiffness properties, the cutting force estimation and the robot posture optimization. However, through our research, the results demonstrate the spindle configuration largely affects the deformation of the robot end-effector (EE). And it may even account for approximately half of the total deformation for machining applications with the force acting perpendicular to the tool. Furthermore, the closer distance between the tool tip and the EE does not mean that the deformation tends to be smaller. Thus, it is reasonable to consider optimizing the spindle configuration based on the optimal robot posture, thereby exhausting advantages of the robot and further reducing machining errors. In this paper, a spindle configuration analysis and optimization method is presented, aiming at confirming the great influence of the spindle configuration on the deformation of the robot EE and minimizing it. First, a deformation model based on the spindle configuration (SC-based deformation model) is presented, which establishes a mapping between the spindle configuration and the deformation of the robot EE. And it confirms the large effect of the spindle configuration on the deformation of the EE. Then, a complementary stiffness evaluation index (CSEI) is proposed. And it adopts matrix norms to evaluate the influence of the spindle configuration on the complementary stiffness matrix in the SC-based deformation model. Using this index, the proposed SC-based deformation model is simplified for the ODG-JLRB20 robot adopted in this paper. Finally, a spindle configuration optimization model is derived to minimize the simplified SC-based deformation model using an iterative procedure. With this model, the optimal spindle configuration with respect to the EE can be obtained for a specific machining trajectory. Experimental results conducted on the ODG-JLRB20 robot demonstrate the correctness and effectiveness of the present method.     

光电转台轻量化几何形状优化研究

对光电转台进行轻量化,首先需要进行几何形状进行优化.筋板如何布置才能使转台的动态刚度达到最优,在设计中一直是一个难点.基于此,通过对转台的连接部件、止推轴承及径向轴承进行有效简化,建立起了光电转台的动力学模型,结合模型.对转台内部的筋板布置形式进行了详尽的研究比较.研究结果表明,要想获得满意的动态刚度,单纯地增加筋板数量并不能达到要求,而应该根据其具体的振动情况来选择合理的筋板布置形式,并且在平行于振型方向的筋板上,开孔时的动刚度效果相对地比未开孔时的动刚度效果要好.     

Dynamic characteristics of a coupled journal and thrust hydrodynamic bearing in a HDD spindle system due to its groove location

 This research numerically analyzes the dynamic characteristics of a coupled journal and thrust hydrodynamic bearing due to its groove location which has the static load due to the weight of a rotor in the axial direction and the dynamic load due to its mass unbalance in the radial direction. The Reynolds equation is transformed to solve a plain member rotating type of journal bearing (PMRJ), a grooved member rotating type of journal bearing (GMRJ), a plain member rotating type of thrust bearing (PMRT), and a grooved member rotating type of thrust bearing (GMRT). FEM is used to solve the Reynolds equations in order to calculate the pressure distribution in a fluid film. Reaction forces and friction torque are obtained by integrating the pressure and shear stress along the fluid film, respectively. Dynamic behaviors, such as whirl radius or axial displacement of a rotor, are determined by solving its nonlinear equations of motion with the Runge–Kutta method. This research shows that the groove location affects the pressure distribution in the fluid film and consequently the dynamic performance of a HDD spindle system. Received: 5 July 2001/Accepted: 17 October 2001     

Active magnetic bearings for machining applications

High-speed machining offers substantial economic benefits due to increased metal cutting productivity. Critical to realizing this technology's promise are the intertwined challenges of spindle dynamic stiffness and cutting process stability. Active magnetic bearings enable greater spindle dynamic stiffness through higher attainable bearing surface speeds, and also provide a means for enhancing cutting process stability. Herein, experimental results from two test rigs are presented illustrating the potential of magnetic bearings for the active suppression of machining chatter. Application challenges and controller design issues are examined in detail.     

基于6DOF模型及动网格的动静压轴承刚度阻尼数值计算

针对传统雷诺方程求解三维油膜流场特性的局限性,提出基于6DOF模型及动网格的动静压轴承刚度阻尼计算方法.以具有典型结构形式的液体动静压轴承为例,通过加载6DOF自定义程序,采用非线性迭代方法计算外载荷作用下轴心轨迹的瞬态变化过程,得到轴颈在外载荷作用下的静平衡位置;通过嵌入UDF宏程序以动网格更新方法实现对轴颈在静平衡位置的扰动,求解Navier-Stokes方程得到轴颈扰动前后位置变化后的瞬态油膜力,利用差分法求得动静压轴承油膜刚度和阻尼,并分析了不同转速下轴承刚度和阻尼的变化规律.     

A novel technique for the fabrication of herringbone grooves in a dynamic thrust bearing combining UV-LIGA with electro-discharge machining

This paper presents a novel technique for the fabrication of herringbone grooves in a dynamic thrust bearing by combining both UV-LIGA (the German words for lithography, electroplating, and molding) and electro-discharge machining (EDM) processes. A negative photoresist is used to fabricate an electroforming mold from which a microelectrode for the EDM process is electroformed. The last step is to employ the microelectrode in the EDM process to fabricate the herringbone grooves in the dynamic thrust bearing. Through the processes of UV-lithography, micro-electroforming and EDM, the accuracy of pattern transfer from the photo mask in UV-lithography to the herringbone grooves on the stainless disk is within 5%. A complex but planar microstructure can be fabricated by this combined technique quickly and accurately.An erratum to this article can be found at     

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.     

Posture optimization methodology of 6R industrial robots for machining using performance evaluation indexes

For industrial robots, the relatively low posture-dependent stiffness deteriorates the absolute accuracy in the robotic machining process. Thus, it is reasonable to consider performing machining in the regions of the robot workspace where the kinematic, static and even dynamic performances are highest, thereby reducing machining errors and exhausting the advantages of the robot. Simultaneously, an optimum initial placement of the workpiece with respect to the robot can be obtained by optimizing the above performances of the robot. In this paper, a robot posture optimization methodology based on robotic performance indexes is presented. First, a deformation evaluation index is proposed to directly illustrate the deformation of the six-revolute (6R) industrial robot (IR) end-effector (EE) when a force is applied on it. Then, the kinematic performance map drawn according to the kinematic performance index is utilized to refine the regions of the robot workspace. Furthermore, main body stiffness index is proposed here to simplify the performance index of the robot stiffness, and its map is used to determine the position of the EE. Finally, the deformation map obtained according to the proposed deformation evaluation index is used to determine the orientation of the EE. Following these steps, the posture of the 6R robot with the best performance can be obtained, and the initial workpiece placement can be consequently determined. Experiments on a Comau Smart5 NJ 220-2.7 robot are conducted. The results demonstrate the feasibility and effectiveness of the present posture optimization methodology.     

Design and construction of an in situ inspection machine for ensuring the dynamic performance of fluid bearings in data storage devices

The objective of the study is to design and construct an in situ inspection machine that would be used to evaluate the dynamic performance of the small-scaled hydrodynamic journal bearings used often for data-storage devices. To this end, novel design ideas of using a high-stiffness air bearing and suspending the test bearing by the specially-designed fixture frame are first proposed, which are accompanied by the special requirements in the manufacturing precisions for various dimensions and geometry characteristics of the components of the experiment system. The capacitor-type sensors, including two custom-mades are next utilized to measure the motions of the spindle and bearing. Finally, a calculating algorithm for deriving performance parameters of the test bearing are proposed, which is intended primarily to estimate rotor stiffness coefficients, load capacity, and eccentricity ratio to determine if the test bearing meet the dynamic performance expected by the original design.     

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     

不同载荷工况下机床主轴预紧力选取的数值分析方法

为研究预紧力对机床主轴的影响,提出在不同载荷工况下机床主轴预紧力选取的数值分析方法.计算得到预紧力与轴承刚度的关系,在轴系结构有限元模型中设置不同预紧力下的轴承刚度值,通过静力学分析求解轴系变形和刚度;计算得到预紧力与轴承发热量的关系,在轴系热分析有限元模型中设置轴承热源,通过传热分析求解主轴温升.计算结果表明,该方法...     

Effects of thrust hydrodynamic bearing stiffness and damping on disk-spindle axial vibration in hard disk drives

This paper aims at investigating the effects of variations in thrust hydrodynamic bearing (HDB) parameters such as axial stiffness and damping coefficients on the axial vibration of disk-spindle systems in hard disk drives. For a parametric study, a closed-form axial frequency response function (FRF) of HDB spindle systems is derived as a function of the axial stiffness and damping coefficients of thrust HDBs. It is known that the axial vibration of the disk-spindle system is composed of two main parts: the vibration of the rigid hub in the axial direction and the disk deflection in the transverse direction. The results from this research clearly show that the vibration amplitudes at low frequency range is dominated by the axial vibration of the hub, and the amplitude of the unbalanced (0,0) mode is dominated by the disk deflection. The parametric study reveals that at low frequency range an increase in the bearing stiffness significantly reduces the hub axial vibration, and hence the axial vibration of the disk-spindle system. Surprisingly, a too much increase in the damping results in a higher amplitude of the unbalanced (0,0) mode. This is because a heavy damping constrains the hub vibration to nearly no motion, resulting in a direct transmission of vibration from the base to disk. To confirm the parametric study, a vibration test was performed on two HDB spindle motors with identical design but different fluid viscosity. The higher viscosity represents the higher axial stiffness and damping in the thrust bearing. The test result indicates that the spindle motor with higher viscosity has a larger unbalanced (0,0) mode amplitude when subjected to an axial base excitation.     

A method to minimize the workpiece deformation using a concept of intelligent fixture

Manufacturing processes are commonly affected by the low stiffness of the components limiting the quality and precision of the final product. Precision is one of the most important issues in the machining process, and the main cause for rejection is the part static deformation and the dynamic vibrations. The static deformation is mainly affected by two factors: deformation due to clamping and process forces, and geometrical distortions due to material removal and residual stress relieving during processing.The deformations caused by the clamping in the fixture are normally associated to existing distortion in the raw workpiece due to previous manufacturing processes and to the clamping forces. These problems lead to uncertainties in the set-up process, hindering the fixture functions, the achievement of a right positioning of the workpiece and the avoidance of deformations due to clamping forces.This paper presents an analysis to identify the causes of the static deformations during clamping and a method to correct the geometrical distortion and deformation of a clamped workpiece by the evaluation of the reaction forces in the selected relevant clamping points. It covers the design and validation of an active clamping unit to minimize the deformation produced by the fixture that could affect the machining process. The developed clamping unit presents an alternative to combine the locator and the clamper in a single component that controls the reaction force and the deformation of the workpiece in the clamping point, and it performs the positioning of that point to minimize the distortion of the workpiece. The clamping unit was verified in laboratory conditions and then tested in an industrial application, evaluating the capabilities related to positioning and reaction force control.     

基于三点法的机床主轴回转误差在线测试技术研究

主轴回转误差是评价机床性能的重要指标,为了提高主轴回转误差的分离精度,在数据采集和处理过程中,提出了两种有效的方法：采用变频率数据采集方法,确保了在不同转速下采集得到的数据的谐波分量相同,使误差分离精度不会因转速的升高而降低；为了消除环境中白噪声对误差分离精度的影响,在同一稳定转速下对主轴轮廓连续采集十个周期的数据,利用集合平均滤波方法消除混合在测试数据中的白噪声。搭建了试验系统,利用提出的方法分离出了机床主轴在不同转速下的回转误差、圆度误差和安装偏心差,验证了方法的有效性。     

用于10-6N~10-5N微力测量的柔性铰链机构设计

在基于静电场原理的微纳力值测量系统中,力值的传递与转化机构起着至关重要的作用。选择平行四边形柔性铰链机构作为其弹性元件,以实现10-6N量级的力值测量。分析了柔性铰链的数学模型,研究了其静态与动态刚度;根据系统要求确定了柔性铰链的目标刚度,并采用有限元方法对其进行优化设计和模态分析;分析了加工精度对铰链刚度的影响。将该铰链用于微力测量系统中,通过实验给出了刚度测试结果和力值测量结果,实验表明,该平行四边形柔性铰链满足微力测量系统对10-6N量级的力值测量要求。     

Prediction method of oil leakage of FDBs using numerical analysis

 Application of a spindle motor using a fluid dynamic bearing (FDB) to hard disk drive (HDD) presents some technical problems. Oil leakage from FDB is one of serious problem that must be solved. In this paper, we discuss a technique used to predict oil leakage from FDB spindle motors based on results of lubrication analysis of FDBs. We conducted oil leakage measurement using FDB spindle motors differing in specifications for FDBs. Then, we analyzed the lubrication in FDBs fitted to the spindle motors used in the measurement. Analysis results were compared with oil leakage measurement results. An analysis result that showed a correlation with the amount of oil leakage was determined as an evaluation item. Use of this evaluation item makes it possible to predict the occurrence of oil leakage with a high accuracy. Received: 5 July 2001/Accepted: 1 November 2001     

Design of flexure hinge mechanism for 10-6 N~10-5 N micro force measurement北大核心CSCD

In a micro-nano force measurement system based on the principle of static electric field, the mechanism used for force transmission and transformation plays a vital role. The parallelogram flexible hinge mechanism is used as elastic element, in order to realize the measurement of force on the scale of 10-6 N. The mathematical model of the flexible hinge is analyzed to study the static and dynamic stiffness. The theory stiffness is determined according to the system requirement. The finite element method is used for the optimization design and modal analysis. The influence to the hinge stiffness of the machining accuracy is analyzed. The stiffness test and force value measurement results are given by experiments. Results show that the parallelogram flexible hinge can be used in the force measurement system on the scale of 10-6 N. ©, 2014, The Editorial Office of Chinese Journal of Sensors and Actuators. All right reserved.     

Prediction of the oil injection time of FDBs in an HDD spindle motor with a tied shaft by utilizing Kirchhoff’s pressure law

We propose a method to predict the oil injection time of fluid dynamic bearings (FDBs) with a tied shaft by applying Kirchhoff’s pressure law. Since the oil is injected by capillary phenomenon, the volume flow rate can be calculated by utilizing Kirchhoff’s pressure law. Then, we calculated the oil injection time of the FDBs with a tied shaft by dividing the volume flow rate by the clearance volumes of the journal bearing, the thrust bearing, and the recirculation channel (RC), respectively. We generated simulation models of the FDBs used in a 2.5″ HDD spindle motor with a tied shaft. The total oil injection times of the FDBs with and without a RC were 0.302 and 0.335 s, respectively. Also, we verified the proposed method by measuring the oil injection time of FDBs with a RC. We applied the proposed method to predict and improve the oil injection time of the FDBs with a tied shaft due to the variation of major parameters affecting the oil injection time.