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.     

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.     

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.     

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.     

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     

Robust shaft design to compensate deformation in the hub press-fitting and disk clamping process of 2.5″ HDDs

We investigated deformation of the outer diameter of a shaft due to the hub press-fitting and disk clamping processes associated with a 2.5″ hard disk drive. We propose a new robust shaft design to minimize the effect of deformation on the outer diameter of the shaft. We numerically show the effect of deformation on the shaft due to the pressure, stiffness, and damping coefficients of fluid dynamic bearings (FDBs), and the critical mass and excitation response of the rotor-bearing system. We also experimentally measured the axial non-repeatable runout and the amplitude at the half speed whirl frequency of FDBs with both conventional and proposed designs. Through these tests we confirm that the proposed design improves the static and dynamic performance of the FDBs and rotor-bearing system.     

Investigation of the electromechanical variables of the spindle motor and the actuator of a HDD due to positioning and free fall

This research investigates the electromechanical variables of a spindle motor and an actuator of an operating hard disk drive (HDD) due to the positioning and the free-fall of a HDD. Magnetic fields of a brushless DC motor and a voice coil motor are determined by the time-stepping finite element equation of the Maxwell equation and the driving circuit equation. The pressure of the fluid dynamic bearings (FDBs) is determined by solving the finite element equation of the Reynolds equation to calculate the reaction force and the friction torque. Dynamic equations of the rotating disk-spindle, actuator, and stationary bodies of a HDD are derived from the Newton–Euler’s equation. The speed control of the rotating disk-spindle and the servo control of the actuator are included to describe the head positioning between the rotating disk and the head. The simulation is performed to investigate the electromechanical variables of the spindle motor and the actuator due to the positioning and the free-fall of a HDD. This research shows that the positioning and the free-fall of a HDD change the electromechanical variables of the spindle motor and the actuator of an operating HDD, and that monitoring their electromechanical variables may identify the positioning and the free-fall of a HDD without using extra sensors.     

Finite element modal analysis of an HDD considering the flexibility of spinning disk–spindle, head–suspension–actuator and supporting structure

This paper presents a finite element method to analyze the free vibration of a flexible HDD (hard disk drive) composed of the spinning disk–spindle system with fluid dynamic bearings (FDBs), the head–suspension–actuator with pivot bearings, and the base plate with complicated geometry. Finite element equations of each component of an HDD are consistently derived with the satisfaction of the geometric compatibility in the internal boundary between each component. The spinning disk, hub and FDBs are modeled by annular sector elements, beam elements and stiffness and damping elements, respectively. It develops a 2-D quadrilateral 4-node shell element with rotational degrees of freedom to model the thin suspension efficiently as well as to satisfy the geometric compatibility between the 3-D tetrahedral element and the 2-D shell element. Base plate, arm, E-block and fantail are modeled by tetrahedral elements. Pivot bearing of an actuator and air bearing between spinning disk and head are modeled by stiffness elements. The restarted Arnoldi iteration method is applied to solve the large asymmetric eigenvalue problem to determine the natural frequencies and mode shapes of the finite element model. Experimental modal testing shows that the proposed method well predicts the vibration characteristics of an HDD. This research also shows that even the vibration motion of the spinning disk corresponding to half-speed whirl and the pure disk mode are transferred to a head–suspension–actuator and base plate through the air bearing and the pivot bearing consecutively. The proposed method can be effectively extended to investigate the forced vibration of an HDD and to design a robust HDD against shock.     

Robust optimal design of the FDBs in a HDD to reduce NRRO and RRO

This research proposes a robust optimal design methodology of the FDBs in a HDD to reduce RRO and NRRO. The critical mass, which determines the dynamic behavior of rotor-bearing system, was selected as an objective function, and the constraint equations were the friction torque of the FDBs, and the stiffness and damping coefficients related with under-damped vibration modes. Ten major design variables of the FDBs were chosen in this optimization problem. The steady-state whirl radius and the shock response at half-speed whirl of the rotating rigid spindle-bearing system were evaluated as RRO and NRRO, respectively. RRO and NRRO of the optimal design were compared with those of conventional one, and it showed that the proposed method could effectively reduce RRO and NRRO.     

Analysis and design of hydrodynamic journal air bearings for high performance HDD spindle

In this paper, we proposed the design concept of NRRO-free non-contact bearings for a high performance hard disk drive (HDD) spindle. We numerically analyzed three types of hydrodynamic journal air bearings [gas dynamic bearing (GDB)], such as a partial herringbone groove, a sinusoidal wave, and a taper-flat type. And we compared their performances in terms of pressure distribution, load capacity, radial stiffness, unbalance response, and stability threshold. For the design examples, we examined the Case 1 with 2.0 m bearing clearance and 10000 rpm, and the Case 2 with 1.0 m clearance and 15000 rpm. As a result of numerical analysis, we found that the taper-flat type was the most promising for high performance HDD spindle compared with the other types. It can have the bearing stiffness of about 3.0 × 10⁶ N/m in Case 1 and of about 2.0 × 10⁷ N/m in Case 2. We also discussed the allowance of parameters for the optimal design of the taper-flat type journal bearing.     

Improvement of dynamic characteristics of a HDD spindle system supported by ball bearing at elevated temperature

This research investigates how the design variables of ball bearing affect the bearing stiffness and the natural frequencies of a hard disk drive (HDD) spindle system at elevated temperature. It shows that any design change that increases the contact angle of ball bearing reduces the variation in the bearing stiffness and the natural frequencies at elevated temperature. This research also proposes a robust HDD spindle motor in which a wave spring maintains a constant preload minimizing the effect of temperature variation. Experimental modal testing shows that the reduction of the natural frequencies at elevated temperature is much less in the proposed HDD spindle system than in the conventional spindle system. The proposed HDD spindle motor can improve the dynamic reliability of a HDD spindle system, which contributes to the high track density of a HDD.     

Behavior of a micron-sized air bubble in operating FDBs using the discrete phase modeling method

This paper investigates the motion of a micron-sized air bubble in the operating fluid dynamic bearings (FDBs) of a spindle motor in a computer hard disk drive. The flow field of FDBs is calculated by solving the Navier–Stokes equation and the continuity equation. The two-phase flow in the air-oil interface is simultaneously solved by using the finite volume method and the volume of fluid (VOF) method. We then analyze the motion of a micron-sized air bubble by applying the discrete phase modeling (DPM) method to the calculated flow field of FDBs. The motion of a micron-sized air bubble determined using the DPM method is verified by comparison with the trajectory of the micron-sized air bubble determined using the VOF method. The trajectories of a micron-sized air bubble with different initial positions in the FDBs are discussed.     

Optimal design of fluid dynamic bearings to develop a robust disk-spindle system in a hard disk drive utilizing modal analysis

This research proposes an optimal design methodology for fluid dynamic bearings (FDBs) in a hard disk drive to improve the dynamic performance of the disk-spindle system. We solved equations of motion for the rigid rotor supported by FDBs with five degrees of freedom. Five modal damping ratios were selected as multi-objective functions. The constraint equations were the friction torque of the FDBs and the stiffness and damping coefficients related to under-damped vibration modes. Ten major design variables of the FDBs were chosen for this optimization problem. The steady-state whirl radius and the shock response at half-speed whirl of the rotating rigid spindle-bearing system were evaluated as RRO and NRRO, respectively. The RRO and NRRO of the optimal design were compared with those of the conventional design. Our results show that the proposed method effectively reduces RRO and NRRO.     

Finite element modal analysis of a rotating disk–spindle system in a HDD with hydrodynamic bearings considering the flexibility of a complicated supporting structure

This paper presents a method to analyze the free vibration of a rotating disk–spindle system in a HDD with hydrodynamic bearings (HDBs) considering the flexibility of a complicated base structure by using finite element method. Finite element equations of each component of a HDD spindle system from the spinning flexible disk to the flexible base plate are consistently derived by satisfying the geometric compatibility in the internal boundary between each component. The rigid link constraints are also imposed at the interface area between the sleeve and hydrodynamic bearings to describe the physical motion at this interface. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem by using the restarted Arnoldi iteration method. The validity of the proposed method is verified by comparing the calculated damped natural frequencies and modes with the experimental results. This research also shows that the supporting structure which includes the stator, housing and base plate plays an important role in determining the natural frequencies and mode shapes of a HDD spindle system     

Transient dynamic analysis of ferro-fluid bearing spindle motor

 With areal recording density of hard disk drives (HDD) historically growing at an average of 60% per year and fast spindle speed to continue to reduce access time, it is becoming increasingly more difficult to maintain the precise positioning required of the GMR heads to read and write data. Any unexpected vibration will cause the data written to a wrong data track. Consequently, the dynamic behaviors of HDD spindle systems and their potential influences on track misregistration are key issues in disk drive design. With rapid advances in the emerging consumer device market, the fluid bearing spindle motors, which have low NRRO, low acoustic noise and high damping, are being developed as next generation spindles. This paper is to study transient dynamic performance of HDD ferro-fluid bearing spindle systems. The FEA based component mode synthesis method is used to reduce the overall spindle system dimensions. The effect of the unbalanced magnetic pulls (UMP) due to two different types of motor configurations (balanced and unbalanced configurations) on the dynamic behaviors of spindle system was investigated. The simulated results show that the motor with balanced configuration provides better spindle dynamic performance due to absence of UMP. The UMP derived from the unbalanced configuration can result in some frequency resonance interactions and adversely affect the HDD servo-tracking system. Received: 5 July 2001/Accepted: 17 October 2001     

Behavior of fluid lubricant and air–oil interface of operating FDBs due to operating condition and seal design

This paper investigated the behavior of fluid lubricant and air–oil interface of operating fluid dynamic bearings (FDBs) by using two-phase flow analysis of air and oil to describe the oil sealing mechanism of operating FDBs. The two-phase flow of fluid lubricant and air was analyzed by using the Navier–Stokes equation and the volume of fluid method of a multi-phase flow. The proposed numerical method was verified by the numerical result of the Reynolds equation and the experimental result of the prior researcher. This research also discussed the effect on the oil leakage of the operating FDBs due to the existence of inward pumping groove, tapering angle and initial position of fluid.     

Lubricant evaluation method for FDBs using TOF-SIMS

 With the increase in recording density and data transfer rate of hard disk drive (HDD), fluid dynamic bearing (FDB) motors have been introduced due to their silence and high rotation accuracy. Although lubricant plays a major role in the development of FDB motors, it is extremely difficult to perform thorough evaluation because the quantity of lubricant used in the motor is as small as several micro liters. This paper describes a lubricant evaluation method for FDBs using the time of flight secondary ion mass spectrometry (TOF-SIMS), which enables simultaneous analyses of elements and organic molecules at PPM levels in an extremely small quantity of sample. By using this method, we found that worn metal elements generated both from spindle and bearings have substantial influences on lubricant degradation. Received: 5 July 2001/Accepted: 1 November 2001     

Vibration predictions and verifications of disk drive spindle system with ball bearings

With areal recording density of hard disk drives (HDD) historically growing at an average of 60% per year, it is becoming increasingly more difficult to maintain the precise positioning required of the ever-smaller GMR heads to read and write data. Any unexpected vibration will cause the data written to a wrong data track, even the vibration amplitude is very small. Consequently, the dynamic behaviors of HDD spindle systems and their potential influence on track misregistration rate must be clearly understood. This paper is to apply an approach based on efficient component mode synthesis (CMS), incorporating multi-body system dynamics technology to predict dynamic characteristics of HDD ball-bearing spindle systems. First, the discrete governing equations of motion for HDD spindle systems, which consist of several flexible and rigid components, are derived through the use of Lagrangian equations. The elastic component modal frequencies and modal shape vectors are then obtained using a finite-element analysis. For ball bearing inherently defects, a mathematical model is used as a time-varying force, resulting in spindle vibrations. The time-varying force and component modal shape vectors are incorporated into the governing equations of the whole spindle systems. An implicit numerical integration method is used to obtain the forced vibration of the HDD spindle system. Finally, the dynamic responses of two typical HDD spindle systems are investigated numerically to predict the significant coupled vibration frequencies, mode shapes and resonance interactions. The results well agree with the solutions predicted by other analytical methods and the experimental results, respectively.     

Friction and wear of spindle motor hydrodynamic bearings for information storage systems during startup and shutdown

This paper investigates the friction and wear characteristics of two typical hydrodynamic bearings for hard disk drive (HDD) spindle motors (SPM), i.e., the herringbone groove and multi-taper bearings, during start-up and shut-down transient operation. The friction characteristics are calculated by a lubricated friction model which is an extension of Kogut and Etsion’s dry friction model (a modified version of the CEB model), while the wear characteristics are qualitatively evaluated in non-dimensional form by the semi-analytical wear model proposed by Holm–Archard. The average flow Reynolds equation and the pressure-compliance relationship of elastic–plastic roughness contact are used together to consider the combined effects of partial lubrication and asperity contact occurring during start-up and shut-down. Then, the friction and wear characteristics of the herringbone groove and multi-taper bearings are calculated and compared under the condition of HDD application.     

Development of a new spindle motor for a hard disk drive

A new spindle motor is developed with a sloped permanent magnet (PM) for a hard disk drive (HDD). In a conventional spindle motor, a pulling plate is installed at the stationary part under the rotating PM to pull down rotating bodies. This axial force is required for stable operation of the spindle motor using a hydrodynamic bearing. However, the pulling plate has considerable iron loss and a negative torque opposing the direction of rotation due to the induced eddy currents. Our proposed model has a sloped PM surface to generate the required axial force as well as torque without the pulling plate. Optimal design is carried out by a response surface methodology, and the new spindle motors are prototyped. The resulting electrical and mechanical performance of the prototyped motors is compared with that of conventional models, showing the possibility of adapting the proposed model for an HDD spindle motor.