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Design and characterization of miniature fluid dynamic bearing using novel multi-step elliptical grooves

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This paper investigates the design and characterization of a miniature fluid dynamic bearing using novel multi-step elliptical grooves for small-form-factor data storage applications and miniature fan motors. In contrast to conventional herringbone-grooved cylindrical journal bearings (HGJBs), the proposed journal bearing contains a single set of multi-step elliptical grooves (EGJB). The performance of the proposed multi-step EGJB is characterized numerically using proprietary flow field analysis software. In addition, to reduce the number of optimal full-factorial experimental design tests (323), the Taguchi parameter design methodology is used to find out the optimal design parameters of the multi-step EGJB. Results show that compared to the conventional HGJB presented by the current group in a previous study, the proposed multi-step EGJB improves the load capacity. Consequently, the proposed motor represents another solution for both existing and emerging miniaturized spindle motor applications.

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c :

Clearance (m)

c b :

Centre of bearing

c j :

Centre of journal

d g :

Groove depth (m)

D :

Diameter of journal bearing (m)

e :

Eccentricity (m)

F r :

Radial load (N)

F t :

Tangential load (N)

h :

Film thickness (m)

L :

Length of the journal bearing (m)

L a1, L a2, L a3, L a4, L a5, L a6 :

Length of elliptic in the x-direction (m)

L b1, L b2, L b3, L b4, L b5, L b6 :

Length of elliptic in the y-direction (m)

A :

Length of d to g (m)

L 1 :

Length of a to b (m)

L 2 :

Length of b to c (m)

L 3 :

Length of c to d (m)

L 4 :

Length of d to e (m)

L 5 :

Length of e to f (m)

L 6 :

Length of f to g (m)

N g :

Number of groove

p :

Pressure (Pa)

p cav :

Pressure in cavitation (Pa)

q :

Side leakage (m3/s)

\( \overline{q} \) :

Dimensionless side leakage (2πq/rcLω)

r :

Radius of the journal bearing (m)

t :

Tolerance (m)

W g :

Groove width (m)

W r :

Ridge width (m)

W :

Load (N)

\( \overline{W} \) :

Dimensionless load capacity \( \left( {W/\left( {\mu \omega r^{2} } \right)\left( {c/r} \right)^{2} } \right) \)

Γ :

Groove depth ratio (d g /c)

δ :

Groove width ratio (W g /(W g  + W r ))

ε :

Eccentricity ratio (e/c)

μ :

Coefficient of viscosity (Ns/m2)

Ø :

Circumferential coordinate (rad)

ω :

Angular velocity (rad/s)

ρ :

Fluid density (kg/m3)

η :

Signal-to-noise ratio


  1. Bonneau D, Absi J (1994) Analysis of aerodynamic journal bearings with small number of herringbone grooves by finite element method. J Tribol Trans ASME 116:698–704

  2. Chang-Jian CW (2012) Bifurcation and chaos analysis of the porous squeeze film damper mounted gear-bearing system. Comput Math Appl 64:798–812

  3. Chao PCP, Huang JS (2005) Calculating rotordynamic coefficients of a ferrofluid-lubricated and herringbone-grooved journal bearing via finite difference analysis. Tribol Lett 19:99–109

  4. Chen CY, Yen RH, Chang CC (2011) Spectral element analysis of herringbone-grooved journal bearings with groove–ridge discontinuity. Int J Numer Meth Fluids 66:1116–1131

  5. Chen CY, Liu CS, Li YC, Mou SC (2013) Optimization of miniature hydrodynamic bearing design using the taguchi method. Submitted to P I Mech Eng J J Eng. (revised)

  6. Development of World’s smallest bore hydrodynamic bearing. http://www.ntn.co.jp/english/news/news_files/new_products/news201000012.html. Accessed 4 Aug 2013

  7. Gad AM, Nemat-Alla MM, Khalil AA, Nasr AM (2006) On the optimum groove geometry for herringbone grooved journal bearings. J Tribol Trans ASME 128:585–593

  8. Grantz AL, Rahman MM (2000) Centrifugal capillary seal for use with fluid dynamic bearings. US Patent 6154339

  9. Grantz AL, Kloeppel K, Dunfield J (1999) Oil filling seal for hydrodynamic motor utilizing a movable sealing element. US Patent 5938343

  10. Grimes R, Walsh E, Walsh P (2010) Active cooling of a mobile phone handset. Appl Therm Eng 30:2363–2369

  11. Hashimoto H, Ochiai M, Sunami Y (2012) Robust optimum design of fluid dynamic bearing for hard disk drive spindle motors. J Tribol-Trans ASME 134:041102-1–041102-11

  12. Hijar-Rivera H, Sanchez-Leal J, Valles-Chavez A (2009) Improving a soldering process applying the dual response approach to a Taguchi’s orthogonal array, Int Conf Comput Ind Eng, pp 1174–1178

  13. Hirs GG (1965) The load capacity and stability characteristics of hydrodynamic grooved journal bearings. ASLE Trans 8:296–305

  14. Jang GH, Chang DI (2000) Analysis of a hydrodynamic herringbone grooved journal bearing considering cavitation. J Tribol Trans ASME 122:103–109

  15. Jang GH, Yoon JW (2002) Nonlinear dynamic analysis of a hydrodynamic journal bearing considering the effect of a rotating or stationary herringbone groove. J Tribol Trans ASME 124:297–304

  16. Jang GH, Yoon JW (2003) Stability analysis of a hydrodynamic journal bearing with rotating herringbone grooves. J Tribol Trans ASME 125:291–300

  17. Jung KM, Jang GH (2011) Axial shock-induced motion of the air-oil interface of fluid dynamic bearings of a non-operating hard disk drive. IEEE Trans Magn 47:1911–1917

  18. Kang K, Rhim Y, Sung K (1996) A study of the oil-lubricated herringbone-grooved journal bearing-part 1: numerical analysis. J Tribol Trans ASME 118:906–911

  19. Kawabata N, Ozawa Y, Kamaya S, Miyake Y (1989) Static characteristics of the regular and reversible rotation type herringbone grooved journal bearing. J Tribol Trans ASME 111:484–490

  20. Kim H, Jang G, Ha H (2012) A generalized Reynolds equation and its perturbation equations for fluid dynamic bearings with curved surfaces. Tribol Int 50:6–15

  21. Liu CS, Lin PD (2008) Analysis and validations of fluid dynamic bearing for spindle motors of high-density optical disc players. Jpn J Appl Phys 47:8101–8105

  22. Liu CS, Chuo YC, Lin PH, Tsai MC, Chang YH, Horng JB (2007) Effects of the fluid dynamic bearing design on rotational precision of a spindle motor. IEEE Trans Magn 43:790–792

  23. Liu CS, Lin PD, Tsai MC (2009) A miniature spindle motor with fluid dynamic bearings for portable storage device applications. Microsyst Technol 15:1001–1007

  24. Liu CS, Tsai MC, Yen RH, Lin PD, Chen CY (2010) Design and experimental verification of novel hydrodynamic grooved journal bearing. J Chin Soc Mech Eng 31:137–144

  25. Montgomery DC (1991) Design and analysis of experiments, 3rd edn. Wiley, New York

  26. Nes AS, Braat JJM, Pereira SF (2006) High-density optical data storage. Rep Prog Phys 69:2323–2363

  27. Oelsch J (2005) Hydrodynamic bearing, spindle motor and hard disk drive. US Patent 6948852 B2

  28. Patera AT (1984) A spectral element method for fluid dynamics: laminar flow in a channel expansion. J Comput Phys 54:468–488

  29. Shen IY, Ladd EM, Yang W (2011) Estimating bearing coefficients of fluid-dynamic bearing spindle motors: a theoretical treatment and feasibility study. IEEE Trans Magn 47:1918–1922

  30. Taguchi G (1986) Introduction to quality engineering. Quality Resources, White Plains

  31. Taguchi G (1987) System of experimental design: engineering methods to optimize quality and minimize cost. Quality Resources, White Plains

  32. Taguchi G (1995) Quality engineering (Taguchi methods) for the development of electronic circuit technology. IEEE Trans Reliab 44:225–229

  33. Taguchi G (2001) Taguchi methods in LSI fabrication process, IEEE Int Workshop on Stat Meth, pp 1–6

  34. Vijayaraghavan D, Keith JTG (1989) Development and evaluation of a cavitation algorithm. STLE Tribol Trans 32:225–233

  35. Wang CC, Yao YD, Liang KY, Huang CC, Chang YC (2012) Development of a miniature fan motor. J Appl Phys 111:07E718-1-07E718-3

  36. Wojciechowski E, Phadke MS (2001) Optimizing video compression using robust parameter design. GLOBECOM 4:2634–2639

  37. Yen RH, Chen CY (2010) Enhancement of journal bearings characteristics using novel elliptical grooves. Proc Inst Mech Eng Part J J Eng Tribol 224:259–269

  38. Yen RH, Chen CY (2011) Enhancement of reversible rotation journal bearing performance using elliptical grooves. J Tribol Trans ASME 133:011704-1–011704-9

  39. Zang Y (1996) Shaft seal for hydrodynamic bearing unit. US Patent 5558443

  40. Zang Y, Hatch MR (1995) Analysis of coupled journal and thrust hydrodynamic bearing using finite volume method. ASME AISPS 1:71–79

  41. Zirkelback N, Andrés LS (1998) Finite element analysis of herringbone groove journal bearings: a parametric study. J Tribol Trans ASME 120:234–240

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The author gratefully acknowledges the financial support provided to this study by the National Science Council of Taiwan under Grant No. NSC 101-2221-E-194-065.

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Correspondence to Chien-Sheng Liu.

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Chen, C., Liu, C. & Li, Y. Design and characterization of miniature fluid dynamic bearing using novel multi-step elliptical grooves. Microsyst Technol 21, 91–100 (2015). https://doi.org/10.1007/s00542-013-2023-5

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  • Controllable Factor
  • Load Capacity
  • Taguchi Method
  • Journal Bearing
  • Reynolds Equation