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

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Abstract

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.

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Abbreviations

a c :

ratio of real contact area to nominal contact area

B :

length of bearing, \({\bar{B} = B/2R}\)

d :

distance between mean planes of asperity heights of two contacting rough surfaces

E :

Young’s modulus

E 1, E 2 :

Young’s moduli of journal and bearing

E( ):

expectancy operation

e :

eccentricity of journal

e u :

eccentricity of mass of journal

\({\dot{e}}\) :

velocity of journal

F :

reactive forces, \({\bar{F} = F/{\left( {p_{s} RB/2} \right)}}\)

H :

h/σ

H B :

Brinell hardness

h :

clearance of bearing, \({\bar{h} = h/h_{0}}\)

h 0 :

nominal clearance of bearing

h p :

depth of groove, \({\bar{h}_{p} = h_{p} /h_{0}}\)

h T :

local clearance

I p :

moment of inertia of journal

K :

hardness coefficient

k :

wear coefficient

M :

frictional torque, \({\bar{M}=M/\left(p_{s}R(B/2)^{2}\right)}\)

m :

mass of journal

N g :

number of grooves/tapers

N s :

number of asperities per unit area

P l :

power consumption, \({\bar{P}_{l} = l{\left( {p_{s} R{\left( {B/2} \right)}^{2} \dot{\Theta }_{{Z0}} } \right)}}\)

p c :

contact pressure

p h :

hydrodynamic pressure

p s :

nominal pressure, p s =  0.101MPa

R :

radius of journal

R s :

average radius of asperity summits

T :

driving torque, \({\bar{T} = T/{\left( {p_{s} R{\left( {B/2} \right)}^{2} } \right)} }\)

t :

time, \({\bar{t} = t/t_{\rm c}}\)

t b :

thickness of adsorbed surface film

t c :

time constant, \({t_{\rm c} = 2\pi /\dot{\Theta }_{{Z0}}}\)

V w :

wear volume, \({\bar{V}_{w} = V_{w} /{\left( {h_{0} RB/2} \right)} }\)

W :

applied force, \({\bar{W} = W/{\left( {p_{s} RB/2} \right)} }\)

X :

coordinate axis

Y :

coordinate axis

Y S :

yield strength of material, Y S =  H B /2.8

Z :

coordinate axis, \({\bar{Z} = Z/{\left( {B/2} \right)} }\)

β:

angle of herringbone groove

γ:

positional angle of bearing

γP :

Peklenik number

δ:

height of roughness

δ b :

termination criterion for equilibrium equations

ɛ:

eccentricity ratio, ɛ =  e/h 0

η:

viscosity of lubricant

Θ Z :

rotational angle of journal

\({\dot{\Theta }_{Z}}\) :

angular velocity of journal, \({\bar{\dot{\Theta }}_{Z} = \dot{\Theta }_{Z} t_{\rm c}}\)

\({\dot{\Theta }_{{Z0}}}\) :

nominal angular velocity of journal

\({\dot{\Theta }_{{Z,{\rm startup}},} \dot{\Theta }_{{Z,{\rm shutdown}}} }\) :

termination criteria for startup and shutdown computation

θ:

θ l +  θ p

θ l :

half of land width

θ p :

half of groove width, \({\bar{\theta }_{p} = \theta_{p} /\theta }\)

μ:

friction coefficient

ν:

Poisson’s ratio

ν1, ν2 :

Poisson’s ratios of journal and bearing

σ:

combined standard deviation of rough surfaces

σ s :

combined standard deviation of asperity heights

τc :

shear stress of rough contact

τh :

shear stress of hydrodynamic lubrication

Φ:

angular coordinate

ϕ pΦ, ϕ pZ :

pressure flow factor

ϕ sΦ :

shear flow factor

χ0 :

initial phase angle of journal

ψ:

composite probability density function (PDF) of rough surface

ψ s :

composite PDF of asperity height

ω:

interference, ω =  δ− d

ω M :

critical interference for contact via adsorbed surface film

ω p :

critical interference of elastic deformation, \({\bar{\omega }_{p} = \omega _{p} /\sigma _{s} }\)

c :

adhesion induced by adhesive contact

h :

adsorption induced by contact via adsorbed surface film

X,Y,Z :

along X, Y axis, around Z axis

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Acknowledgments

The authors would like to thank Nidec Corporation for permission to publish these results. The authors are also indebted to Messrs. D. Kikuchi, S. Kitahira and M. Takada for their assistance with the experimental setup and testing.

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Authors and Affiliations

  1. Motor Engineering Research Laboratory, Nidec Corporation, 1-20-13 Osaki, Shinagawa-ku, Tokyo, 141-0032, Japan

    Ming Feng & Takashi Kenjo

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  1. Ming Feng
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  2. Takashi Kenjo
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Correspondence to Ming Feng.

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Feng, M., Kenjo, T. Friction and wear of spindle motor hydrodynamic bearings for information storage systems during startup and shutdown. Microsyst Technol 13, 987–997 (2007). https://doi.org/10.1007/s00542-006-0305-x

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  • DOI: https://doi.org/10.1007/s00542-006-0305-x

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