Static and dynamic analyses of the fluid dynamic bearings with a recirculation channel

Abstract

The technique to predict the performance of a rotor-bearing system has been an important topic in maintaining the reliability of various rotating machinery from high-speed turbo machinery to high-precision information storage devices, such as hard disk drives (HDDs). Fluid dynamic bearings (FDBs) have been widely applied to rotating machinery because FDBs support large loads under high-speed operating conditions using the dynamic pressure generated by the pumping and wedge effects of the lubricant. The performance of FDBs is an important factor that determines the overall performance of HDDs since the storage capacity of HDDs depends on the dynamic performance of the rotor-bearing system supported by the FDBs. The recirculation channel (RC) is designed to discharge air bubbles inside the FDBs, which generate non-repeatable runout of HDDs. In this dissertation, the method to predict the static and dynamic characteristics of the FDBs considering an RC was developed by using finite-element and finite-volume analyses.

Firstly, the background of the dissertation is presented and covers the importance of the FDBs and the RC in a HDD disk-spindle system. Previous works on the static and dynamic characteristics of the FDBs are also presented.

Secondly, the finite-element method used to predict the static characteristics of the FDBs with an RC is explicated. A numerical program was developed to simultaneously solve the finite-element equations of Reynolds lubrication for the FDBs and the Hagen–Poiseuille flow for the RC. The proposed method was then validated using experiment and numerical simulation. In the experiment, the tilting, flying, and whirling motions of a rotor of the HDD spindle were measured. In numerical simulations, the static characteristics of the FDBs with an RC calculated from the proposed method were compared with those calculated using computational fluid dynamic software. This dissertation confirms that the proposed method can appropriately predict the performance of the FDBs with an RC.

Thirdly, this dissertation investigated the method to predict the dynamic coefficients of the FDBs with an RC using the discretized perturbation equations of the Reynolds equation and the Hagen–Poiseuille equation. The pure translational stiffness in the axial direction of the FDBs with an RC was evaluated by combining the numerical and experimental results. The dynamic coefficients of the FDBs with an RC were simulated with the variation of the radii of the RC to investigate the influence of the RC on the FDBs using the proposed method. This dissertation confirms that the mathematically perturbed pure axial stiffness of the FDBs with an RC matches well with the physically calculated stiffness.

Finally, this dissertation proposes a numerical procedure to detect the oil leakage of FDBs with a double sealing structure that occurs due to non-operating axial shock using the computational fluid dynamics software. In the experiment, the rigid body motion of a rotor with respect to a stator in FDBs with an RC was investigated using a drop test. After the drop test, oil leakage from the FDBs was observed to verify the simulated results by defining oil leakage in such a way that the oil particles flow in an outward direction and adhere near the outlets. In the simulation, the two-phase flow of air and oil was simulated using the finite-volume method and a volume of fluid method to investigate the unsteady motion and break-up of the air-oil interfaces during and after axial shock. This dissertation confirms that a numerical procedure can predict oil leakage that occurs due to non-operating axial shock.| 회전체-베어링 시스템의 성능을 예측하는 기술은 터보 기계부터 하드 디스크 드라이브 (HDD)와 같은 고정밀 정보 저장장치에 이르기까지 다양한 회전 기계의 신뢰성을 유지하는데 중요한 주제였다. 유체동압베어링은 윤활유의 펌핑 및 쐐기 효과에 의해 생성된 동적 압력을 사용하여 고속에서 큰 하중을 지지하기 때문에 회전 기계에 널리 적용되고 있다. 특히 유체동압베어링은 샤프트와 슬리브 사이의 금속간 접촉을 방지하여 높은 감성과 감쇠를 제공하기 때문에 HDD 스핀들을 지지하는데 주로 적용되어 왔다. HDD의 저장 용량은 유체동압베어링으로 지지되는 회전체-베어링 시스템의 동적 성능에 의존하기 때문에 유체동압베어링의 성능을 정확하게 예측하는 것은 매우 중요하다. 재순환채널은 비반복적인 진동을 발생시키는 유체동압베어링 내부에 잔존하는 기포를 배출하기 위해 적용되었다. 따라서, 재순환채널을 고려한 유체동압베어링의 정 및 동적 특성을 예측할 수 있는 방법 개발은 HDD 스핀들 모터의 성능을 예측하는데 매우 중요하다.

우선, 본 논문에서는 재순환홀이 적용된 유체동압베어링의 정적 특성을 예측할 수 있는 유한요소 해석방법을 제안하였다. Reynolds 방정식과 Hagen-Poiseuille 방정식의 유한요소 방정식을 결합 해석하기 위해서 유한요소 프로그램이 개발되었다. 제안된 방법은 실험 및 수치 해석을 사용하여 각각 검증되었다. 실험에서는 HDD 스핀들 회전자의 틸팅, 훨링 및 부상 높이가 측정되었다. 수치 해석에서는 제안된 유한요소 해석방법으로 계산된 재순환홀이 적용된 유체동압베어링의 정적 특성이 상용 전산 유체역학 프로그램으로 계산된 결과와 비교 검증되었다. 본 논문은 제안된 방법이 재순환홀이 적용된 유체동압베어링의 작동시 정적 특성을 적절하게 예측할 수 있음을 보여준다.

다음으로, 본 논문에서는 Reynolds 방정식과 Hagen-Poiseuille 방정식의 준 평형상태에서의 perturbation 방정식을 유한요소 방정식으로 유도하여 재순환홀이 적용된 유체동압베어링의 동적 특성을 예측할 수 있는 방법을 제안하였다. 제안한 방법을 이용하여 수학적으로 계산된 재순환홀이 적용된 유체동압베어링의 순수 축 방향 병진 강성은 고전적인 강성 정의에 의해서 계산된 순수 축 방향 병진 강성과 비교를 통해 검증되었다. 제안된 방법을 사용하여 재순환홀의 반경 변화에 따라 계산된 유체동압베어링의 강성 및 감쇠 계수가 분석되었다. HDD 스핀들의 회전자에 대한 강체 운동 방정식을 사용하여 축 방향 충격시 재순환홀의 반경 변화에 따른 유체동압베어링의 질량 중심에서의 충격 응답을 분석하였다. 본 논문은 제안된 방법이 재순환홀이 적용된 유체동압베어링의 작동시 동적 특성을 적절하게 예측할 수 있음을 보여준다.

마지막으로, 본 논문에서는 전산 유체역학 프로그램을 사용하여 비작동시의 축 방향 충격에 의한 이중 실 구조를 갖는 유체동압베어링의 유체 누설을 예측하는 해석 방법을 제안하였다. 실험에서는 재순환홀을 갖는 유체동압베어링의 고정자에 대한 회전자의 강체 운동을 HDD의 낙하 시험을 통해 분석하였다. 낙하 시험 후, 유체 오일 입자가 바깥 방향으로 흐르고 공기-오일 계면의 출구 근처에 부착되는 방식으로 유체 누설을 정의하여 축 방향 충격에 의한 유체 누설 해석 결과를 실험으로 관측한 유체 누설 결과와 비교하였다. 수치 해석에서는 축 방향 충격 및 충격 이후 공기-오일 계면의 불안정한 운동 및 파단을 조사하기 위해서 유한체적법 및 VOF 방법을 사용하여 공기-오일의 2상 유동을 해석하였다. 특히 축 방향 충격시 비작동하는 유체동압베어링에 대한 재순환홀의 영향을 분석하였다. 본 논문은 제안한 해석 방법이 비작동시 축 방향 충격에 의한 이중 실 구조를 갖는 유체동압베어링의 유체 누설 및 동적 특성을 예측할 수 있음을 보여준다.; The technique to predict the performance of a rotor-bearing system has been an important topic in maintaining the reliability of various rotating machinery from high-speed turbo machinery to high-precision information storage devices, such as hard disk drives (HDDs). Fluid dynamic bearings (FDBs) have been widely applied to rotating machinery because FDBs support large loads under high-speed operating conditions using the dynamic pressure generated by the pumping and wedge effects of the lubricant. The performance of FDBs is an important factor that determines the overall performance of HDDs since the storage capacity of HDDs depends on the dynamic performance of the rotor-bearing system supported by the FDBs. The recirculation channel (RC) is designed to discharge air bubbles inside the FDBs, which generate non-repeatable runout of HDDs. In this dissertation, the method to predict the static and dynamic characteristics of the FDBs considering an RC was developed by using finite-element and finite-volume analyses.

Firstly, the background of the dissertation is presented and covers the importance of the FDBs and the RC in a HDD disk-spindle system. Previous works on the static and dynamic characteristics of the FDBs are also presented.

Secondly, the finite-element method used to predict the static characteristics of the FDBs with an RC is explicated. A numerical program was developed to simultaneously solve the finite-element equations of Reynolds lubrication for the FDBs and the Hagen–Poiseuille flow for the RC. The proposed method was then validated using experiment and numerical simulation. In the experiment, the tilting, flying, and whirling motions of a rotor of the HDD spindle were measured. In numerical simulations, the static characteristics of the FDBs with an RC calculated from the proposed method were compared with those calculated using computational fluid dynamic software. This dissertation confirms that the proposed method can appropriately predict the performance of the FDBs with an RC.

Thirdly, this dissertation investigated the method to predict the dynamic coefficients of the FDBs with an RC using the discretized perturbation equations of the Reynolds equation and the Hagen–Poiseuille equation. The pure translational stiffness in the axial direction of the FDBs with an RC was evaluated by combining the numerical and experimental results. The dynamic coefficients of the FDBs with an RC were simulated with the variation of the radii of the RC to investigate the influence of the RC on the FDBs using the proposed method. This dissertation confirms that the mathematically perturbed pure axial stiffness of the FDBs with an RC matches well with the physically calculated stiffness.

Finally, this dissertation proposes a numerical procedure to detect the oil leakage of FDBs with a double sealing structure that occurs due to non-operating axial shock using the computational fluid dynamics software. In the experiment, the rigid body motion of a rotor with respect to a stator in FDBs with an RC was investigated using a drop test. After the drop test, oil leakage from the FDBs was observed to verify the simulated results by defining oil leakage in such a way that the oil particles flow in an outward direction and adhere near the outlets. In the simulation, the two-phase flow of air and oil was simulated using the finite-volume method and a volume of fluid method to investigate the unsteady motion and break-up of the air-oil interfaces during and after axial shock. This dissertation confirms that a numerical procedure can predict oil leakage that occurs due to non-operating axial shock.