G. H. Jang*, D. K. Kim *, C. S. Kim**, and H. S. Lee**

1. Improvement of Dynamic Characteristics ofa HDD Spindle System Supported by Ball Bearing Due to Temperature Variation G. H. Jang*, D. K. Kim*, C. S. Kim**, and H. S. Lee** * PREM, Department of Mechanical Engineering, Hanyang University ** Storage Laboratory, Samsung Advanced Institute of Technology

2. Shaft Hub Disk Base Ball Bearing Housing Motivation • To improve the reliability of dynamics of HDD, a robust HDD spindle system at elevated temperature should be developed. Fig. 1 Hard disk drive spindle system Temperature rises Ball bearing characteristics Dynamics of HDD spindle system

3. Objectives • Investigation how design variables of ball bearing changes the bearing stiffness and the natural frequencies of a HDD spindle system at elevated temperature • Development of a robust HDD spindle system at elevated temperature Improvement of the reliability of dynamics of a HDD spindle system

4. Contents • Method of Analysis • Parametric Study of Ball Bearing • Design of a Robust HDD Spindle System • Conclusions

5. 1. Method of Analysis How to investigate the dynamic characteristics of HDD spindle system due to the change of operating temperature

6. 1. Method of Analysis Fig. 2 Analytical model to investigate dynamic characteristics of HDD spindle system due to the change of operating temperature

7. 1. Method of Analysis • Bearing Displacement Due to Temperature Rise (1) (a) Stationary part (b) Rotating part Fig. 3 Finite element model of HDD spindle system for thermal analysis and analysis result Thermal expansion of bearing due to temperature rise

8. Fig. 4 Axial movement of hub due to axial force difference between upper and lower bearings 1. Method of Analysis • Bearing Displacement Due to Temperature Rise (2) Bearing displacement due to temperature rise =Thermal expansion of bearing + Axial movement of hub

9. 1. Method of Analysis • Bearing Characteristics Due to Temperature Rise Inner race Outer race (a) (b) Fig. 5 Bearing race displacement due to temperature rise

10. 1. Method of Analysis • Dynamic Characteristics of HDD Spindle System Due to Temperature Rise Fig. 6 Finite element model of a HDD spindle system Bearing stiffness at elevated temperature Finite element model of HDD spindle system Natural frequencies and mode shapes at elevated temperature

11. 2. Parametric Study of Ball Bearing How does the design variables of ball bearing change the bearing characteristics and the dynamics of HDD spindle system at elevated temperature?

12. 2. Parametric Study of Ball Bearing • Design Variables of Ball Bearing Pd: radial clearance ri: inner race curvature radius ro: outer race curvature radius dB: ball diameter dP: pitch diameter Fig. 7 Structure of a ball bearing Table 1 Major design specification of a ball bearing

13. Fig. 9 Variation of equivalent stiffness of bearing ( :radial, :axial) 2. Parametric Study of Ball Bearing • Bearing Characteristics With Variation of Radial Clearance Fig. 8 Variation of contact angle of bearing • Increase of radial clearance • ⇒ Increase of contact angle at room temperature, 20℃ • ⇒ Reduction of decreasing rate of bearing stiffness due to temperature rise

14. 2. Parametric Study of Ball Bearing Table 2 Variation of natural frequencies of a HDD spindle system due to the change of radial clearance and operating temperature (unit: Hz) • ①②: axial modes by stiffness of base → small frequency shift • ③④⑤: two rocking and one axial modes by bearing stiffness → significant frequency decrease because of decrease of bearing stiffness • Large radial clearance ⇒ Reduction of change of natural frequencies at elevated temperature Reduction of decreasing rate of bearing stiffness at elevated temperature

15. 2. Parametric Study of Ball Bearing • Result of Parametric Study Any design change of bearing to increase contact angle reduces the amount of decrease of bearing deformation, the variation of bearing stiffness and natural frequencies of a HDD spindle system at elevated temperature.

16. 3. Design of a Robust HDD Spindle Motor

17. 3. Design of a Robust HDD Spindle Motor • Spindle Motor with Constant-Pressure Preload Hub Ball bearing Magnet Coil Housing Shaft Wave spring Fig. 10 HDD spindle motor supported by ball bearings with constant-pressure preload • Wave spring between inner race of lower bearing and housing • Upper bearing is glued between shaft and hub Lower bearing is glued at hub⇒Lower bearing can slide along shaft • Constant preload by wave spring⇒Prevent the variation of bearing stiffness and natural frequencies at elevated temperature

18. 3. Design of a Robust HDD Spindle Motor Table 3 Analytical results of natural frequencies due to the change of operating temperature between the conventional and proposed HDD spindle system (unit: Hz) • The variation of natural frequencies at elevated temperature is much smaller in the proposed spindle system than that in the conventional one

19. 3. Design of a Robust HDD Spindle Motor • Prototype of Proposed Spindle Motor Fixing screw Clamp to fix wave spring Wave spring Fig. 11 Prototyped HDD spindle motor supported by ball bearings with constant-pressure preload • Wave spring between inner race of upper bearing and clamp to fix wave spring • Lower bearing is glued between shaft and hub Upper bearing is glued at hub⇒Upper bearing can slide along shaft • Another embodiment of the proposed spindle motor in Fig. 10, which is modified just for the prototype convenience

20. 3. Design of a Robust HDD Spindle Motor Wave spring Clamp to fix wave spring Fig. 12 Actual parts of prototyped HDD spindle motor

21. 3. Design of a Robust HDD Spindle Motor ① ② ③ ④ ⑤ ① ② ③ ④ ⑤ (a) Conventional spindle system (b) Proposed spindle system Fig. 13 Frequency response functions of HDD spindle system measured at 20℃ and 60 ℃

22. 3. Design of a Robust HDD Spindle Motor Table 4 Experimental results of natural frequencies due to the change of operating temperature between the conventional and proposed HDD spindle systems (unit: Hz) • The proposed spindle system has less variation of the natural frequencies corresponding to the vibration modes governed by bearing stiffness (③④⑤) than the conventional one • The variation of natural frequencies of prototype is not as small as that of analytical simulation in Table 3 The wave spring may change its characteristics at elevated temperature

23. 4. Conclusions • Parametric Study of Ball Bearing Any design change of bearing to increase contact angle reduces the amount of decrease of bearing deformation, the variation of bearing stiffness and natural frequencies of a HDD spindle system at elevated temperature. • Design of a Robust HDD Spindle Motor The constant preload by wave spring prevents the variation of bearing stiffness and natural frequencies of the proposed HDD spindle system. The experimental modal testing shows that the proposed HDD spindle system has less variation of natural frequencies than the conventional one.