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.     

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.     

Effect of an hourglass-shaped sleeve on the performance of the fluid dynamic bearings of a HDD spindle motor

This research investigated the characteristics of fluid dynamic bearings (FDBs) in a HDD spindle motor with an hourglass-shaped sleeve. We demonstrated experimentally that the hourglass-shaped sleeve generated through the ball-sizing process is a major source of large repeatable runout and non-repeatable runout in a HDD spindle system. We also numerically proved the effect of hourglass-shaped sleeves on pressure, friction torque, stiffness and damping coefficients, critical mass, and shock response. Finally, we proposed a robust design for FDBs with hourglass-shaped groove depths to compensate for the decrease in the static and dynamic performance of FDBs with hourglass-shaped sleeves. The proposed hourglass-shaped groove depth improves the performance of FDBs with both straight and hourglass-shaped sleeves.     

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.     

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.     

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.     

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.     

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.     

Development and optimal design of a HDD spindle motor with pulling magnet to reduce electrical loss

A conventional hard disk drive (HDD) spindle motor has a pulling plate to generate the axial magnetic force. However, the pulling plate consumes significant amount of iron loss due to the alternating magnetic field on the pulling plate. We propose the new design of a HDD spindle motor with pulling magnet to generate the pre-load as well as to eliminate the iron loss of the pulling plate. We also develop an optimal design methodology to minimize iron and copper losses from the spindle motor of a computer HDD while maintaining the same level of torque ripple and pulling force. The new design is optimized by the developed optimal design methodology. A metamodel is constructed from the three-dimensional finite element analysis of the magnetic field and the meta-modeling techniques, and the accuracies of the metamodels are discussed. The proposed optimal design problem is solved by the progressive quadratic approximation method. The proposed design reduces the electrical loss of the HDD spindle motor by 30.42?% while maintaining the same level of torque ripple and pulling force.     

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     

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     

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     

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     

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     

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.     

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.     

Improvement of component mode synthesis model for vibration analysis of hard disk drives using attachment modes

I improved the component mode synthesis (CMS) model for free and forced-vibration analyses of hard disk drives using attachment modes. The convergence and the accuracy of the proposed CMS model was improved substantially by applying an attachment mode to a FDB shaft and a pivot shaft in the stationary part model. Different formulations were used for the FDBs and the pivot bearings because of their different damping properties. In the proposed formulation, additional general coordinates corresponding to the attachment modes of the FDB shaft are introduced into the system coordinates; on the other hand, the attachment modes of the pivot shaft moderate the stiffness and damping properties of the pivot bearings. To check the improvement of the convergence and the accuracy, I performed the free and forced-vibration analyses using the previous and proposed CMS models and a full finite element (FE) model. The convergence of the natural frequencies and the frequency response function (FRF) of the disk/spindle system were extremely improved. Moreover, the FRF of the head actuator better matched the full FE model than the previous CMS model when the same number of component modes are used.     

Hinge pivot for disk drive

This paper discusses the findings of a hinge pivot for use in hard disk drives (HDD). The actuator assembly in a HDD is supported by a pivot cartridge and controlled by a servo system to perform seek and track following operations for data recording. The cartridge is composed of a pair of pre-loaded ball bearings. Due to the demand for thin hard disk drives and hence, the need to reduce the height of the actuator assembly, a hinge pivot is proposed to replace the set of bearings. The shaft of the pivot is connected to the sleeve with thin hinges made of ultra-high heat-resistant polyamide film, such as Upilex. Measurement showed that the hinge pivot did not exhibit the nonlinear effects during low frequency actuation, such was inherent for ball bearing pivots. Experiment also showed that at least a million life cycles can be achieved without any performance degradation.