friction forces in conical intelligent micro-bearings

4-2009
TRIBOLOGIA
259
Krzysztof WIERZCHOLSKI*, Andrzej MISZCZAK**
FRICTION FORCES IN CONICAL INTELLIGENT
MICRO-BEARINGS
SIŁY TARCIA W STOŻKOWYCH INTELIGENTNYCH
MIKROŁOŻYSKACH
Key-words:
micro-bearings, robots, memory
Słowa kluczowe:
mikrołożyska, roboty, pamięć
Summary
In this paper is presented the method of friction force calculations in slide
conical micro-bearings occurring in HDD computer discs. The authors compare they’re own results with the results that were obtained by the G.H. Jang
research team. The considered micro-bearings have intelligent memory features. G.H. Jang attain memory properties through the nano- grooves on the
cylindrical micro-bearing surfaces, which implies the whirling motion and
whirling flows of the lubricant in the bearing gap. In presented paper, the
memory effects are obtained by the conical shapes of the journal and sleeve
and additionally by the grooves with which depths of about 25 nm. Such
*
**
Institute of Mechatronics, Nanotechnology and Vacuum Technique, Technical University Koszalin, PL 75-620 Koszalin, ul. Racławicka 15-17, Poland; e-mail: [email protected]
Akademia Morska w Gdyni; 81-225 Gdynia, ul. Morska 81-87; [email protected]
260
TRIBOLOGIA
4-2009
shapes increase and regulates the proper friction force values and whirling
motion and therefore increase the bearing memory properties.
INTRODUCTION
This paper investigates the dynamic influences of a HDD bearing on the
friction forces occurring during the lubrication process. The mass centre
of HDD micro-bearing is presented in Fig. 1 after Jang and Kim [L. 3].
After Jang, Lee and Kim the mass center of HDD micro-bearing is
usually located above the bearing span center so that it has a conical
whirling motion with tilting angle in which the upper angle has a bigger
radius than the lower part. This can be achieved not only by proper selection of the width of upper and lower journal bearing see Jang [L. 3] but
also after authors knowledge by using the conical shapes of journal bearings Fig. 2. Such conical motion after Jang and conical motion after
Wierzcholski has to be reduced to increase the memory capacity of HDD.
Fig. 1 after Jang [L. 3] and Fig. 2 show the loci of the mass centre,
the upper and the lower journal micro-bearing centers due to the variation
of the width of the upper and lower journal bearing. The total width of
the upper an lower journal bearing centers is 3 mm after Jang and 1 mm
after Wierzcholski, so that the comparison between the models can be
made within similar friction torque.
A
B
C
D
z [m]
× 10-3
Upper journal center
7
6
5
Mass center
4
3
2
x [m] Lower journal center
1
× 10-3 1.2 0.6
0
0
-0.6
-0.6 -1.2
-1.2
0
y [m]
0.6 1.2 × 10-3
Bearing width [mm] (Up-Low); A:1.6-1.8; B:1.8-1.6; C:2.0-1.4; D:2.2-1.2
Fig. 1. Whirling motion of HDD spindle system due to the bearing width of journal bearing after G.H. Jang and C.S. Kim [L. 3]
Rys. 1. Ruch wirujący w układzie wrzecionowym HDD z powodu szerokości czopa
łożyska według G.H. Janga oraz C.S. Kima [L. 3]
4-2009
TRIBOLOGIA
261
b)
c)
d)
e)
f)
a)
Fig. 2. Adhesion in conical micro-bearing, a) conical micro-bearing in HDD spindle system after author, b) micro and nano-roughness, c) adsorption forces,
d) forces caused by the micro-elastic deformations, e) Van-der-Waals electrostatic forces, f) capillary forces: γ , γ1 − angle of cone, sleeve generating
line, Rp – sleeve radius, Rc – journal radius
Rys. 2. Adhezja w mikrołożysku stożkowym; a) mikrołożysko stożkowe w układzie wrzecionowym według autora, b) mikro- i nanochropowatości, c) siły adsorpcji, d) siły
od mikrosprężystych deformacji, e) siły Van-der-Waalsa, f) siły kapilarne;
γ, γ1 − kąt tworzącej stożka i panewki, Rp – promień panewki, Rc – promień czopa
Hence follows that the journal width changes the whirl radius. The
whirl radius of the mass centre and the tilting angle are reduced by 43 and
82% respectively when the width of upper and lower journal bearing
changes from 1.6 and 1.8 mm to 2.2 and 1.2 mm after Jang [L. 3], and by
50 and 89% respectively when the width of upper and lower journal bearing changes from 0.4 and 0.6 mm to 0.7 and 1.0 mm after K. Wierzcholski. Additionally the asymmetric and symmetric grooves on the conical
micro-bearing surface are applied. The depth of the grooves attain about
25 nm. The journal bearing with asymmetric grooves generates the asymmetric pressure distributions which implies the eccentricity of the rotor
[L. 4, 5]. Symmetric grooves on the journal cause concentric motion of a
rotor. Moreover on the cooperating micro-bearing surfaces, apart fro the
hydrodynamic pressure we have adhesion forces between oil particles and
superficial layer particles. Fig. 2 shows adsorption, micro-deformation,
Van-der-Waals and capillary forces in super thin boundary layer in micro-bearing gap.
262
TRIBOLOGIA
4-2009
FRICTION FORCES
This section presents the friction forces calculation in conical microbearing gaps. The influence of the adhesion forces Fadh on the total friction forces FRT can be caused directly by friction forces:
FRT = FR + FRadh
(1a)
or indirectly by pressure and dynamic viscosity changes in following form:
pT = ph + padh , ηT = η + ηadh
(1b)
where we denote: FRadh − friction forces caused only by the adhesion forces, ph − classical hydrodynamic pressure [L. 7, 6], padh − pressure caused
only by the adhesion forces, pT − total pressure, ηT − total dynamic viscosity, η = η(ϕ,yc,xc) − classical liquid dynamic viscosity, ηadh − oil dynamic viscosity caused only by the adhesion forces. The time depended
components FRϕT , FRx c T of friction forces presented in conical coordinates for circumferential and longitudinal directions α1 = ϕ, α3 = xc occurring in micro-bearing conical gaps have the following forms [L. 9]:
 ∂v ϕ 

FRϕT ( t ) = ∫∫  ηT
X c dϕdx c , FRx c T ( t ) =
∂
y
Ωc 
c y =ε
c T
 ∂v x c 

= ∫∫  ηT
X c dϕdx c
∂y c  y = ε
Ωc 
c T
(2)
ε T ( ϕ, x c , t )


y c dy c

∫ ηT (ϕ, y c , x c ) 
∂p T ( t ) 
0
FRϕT ( t ) = ∫∫
 dϕdx c +
ε T (ϕ, x c , t ) − ε T (ϕ, x c , t )
∂
ϕ
dy


Ωc
c

∫ ηT (ϕ, y c , x c ) 
0


(3)




 ω(R + x c cos γ ) 2 
− ∫∫  ε (ϕ, x , t )
 dϕdx c ,
T
c
dy

Ωc 
c

∫ ηT (ϕ, y c , x c ) 
0


4-2009
TRIBOLOGIA
263
ε T ( ϕ, x c , t )



y c dy c


∫ ηT (ϕ, y c , x c ) 
 ∂p T ( t ) 
0
FRx c T ( t ) = R ∫∫ 

ε T (ϕ, x c , t ) − ε T (ϕ, x c , t )
x
∂
c 
dy c

Ωc 


∫
ηT (ϕ, y c , x c ) 
0





(R + x c cos γ )dϕdx c



(4)
Where: yc − gap height direction, Xc ≡ R + xccosγ and 0 ≤ yc ≤ εT, −bc ≤ xc
≤ bc, 0 ≤ ϕ < 2πθ1, 0 ≤ θ1 <1, Ωc(ϕ,xc) − lubrication surface, vϕ, vx − lubricant velocity components in ϕ, xc directions, respectively, γ − angle
between generate line and the cross section plane of the journal,
bc − length of the cone generating line (see Fig. 2), R − radius of the journal.
The value of the total friction forces caused by the adhesion, hydrodynamic pressure and angular velocity of the journal has the form:
FRT = (FRϕT ) 2 + (FRx cT ) 2
(5)
MICRO-BEARING CONICAL GAP HEIGHT WITH GROOVES
If grooves length is situated in xc and ϕ direction then gap height of the
conical micro-bearing has the following form respectively [L. 8]:
k


ε T (ϕ, x c , t ) = ε 1 + λ c ( x c , t ) cos ϕ + ε g1 ∑ (−1) n H η (ϕ − 0,5nϕT ),


n =0
k


ε T (ϕ, x c , t ) = ε 1 + λ c ( x c , t ) cos ϕ + ε g1 ∑ (−1) n H η ( x c − 0,5nx T ), (6)
n =0


264
TRIBOLOGIA
4-2009
for 0 ≤ ϕ < 2π, −bp ≤ x c ≤ bp where λc − eccentricity ratio in conical
micro-bearing, ε − radial clearance in conical micro-bearing, εg1 ≡ εg/ε, εg
− ridge height, Hη − Heavisidea unit function. Symbols ϕT, xc denote periods of grooves sequence about 65 nm in ϕ and xc − directions respectively, k − number of ridges about 1000.
NUMERICAL CALCULATIONS DATA
Numerical calculations of pressure distributions and friction forces are
performed for lower radius of the conical journal from 0.4 to 0.6 mm and
upper radius of conical journal from 0.7 to 1.0 mm. Lubricant viscosity
had value 0.018 Pas. We are taken into account rotating speed 10 000
rpm and radial clearance about 5 micrometer [L. 1, 2].
SKECH OF RESULTS AND MEMORY EFFECTS
• The friction torque due to asymmetric grooves is slightly bigger than
that of symmetric bearing by about 1%.
• The magnitude of the load and the kind of exploitation needs of HDD
micro-bearings are caused the adequate conical whirling motions of
the cylindrical journal. Whirling motion of a HDD system due to the
bearing width of cylindrical micro-bearing journal creates lower and
different upper radius of the journal (see Fig. 1).This fact denotes
memory properties of the micro-bearing which are accommodated to
the proper situations and are giving the carrying capacity and proper
friction forces suitable or adequate to the existing load and exploitation needs. Conical shape of micro-bearing journal provokes and enables better to accommodate the whirling motion of micro-bearing journal than in the case of journal classical cylindrical shape. Hence the
intelligent memory feature for conical journal increases in comparison
to the journal of cylindrical classical shapes.
Acknowledgement
Authors thank for the financial help of Polish Ministerial Grant
3475/B/T02/2009/36 in years 2009-2012.
4-2009
TRIBOLOGIA
265
REFERENCES
1. Bekir Sadik Unlu, Enver Atik: Determination of friction coefficient in journal bearings, Elsevier, Material& Design, 28, 2007, pp. 973–977.
2. Bharat Bhushan: Nano-tribology and nanomechanics of MEMS/NEMS and
BioMEMS, BioNEMS materials and devices. Microelectronic Eng. 84,
2007, pp. 387–412.
3. Jang G.H., Lee S.H., Kim H.W., Kim C.S.: Dynamic analysis of a HDD
spindle system with FDBs due to the bearing width and asymmetric grooves
of journal bearing. Microsystems Technologies, 11, 2005, pp. 499–505.
4. Wierzcholski K., Miszczak A.: Own scientific highlights obtained in the
field of bio and micro-bearings in years 2006-2008. Journal of Kones Powertrain and Transport, Vol. 15, No. 3, Warsaw 2008, pp. 551–554.
5. Wierzcholski K.: Enhancement of memory capacity in hdd micro-bearing
with hyperbolic journals. Journal of Kones Powertrain and Transport,
Vol. 15, No. 3, 2008, pp. 555–560.
6. Wierzcholski K.: Friction forces in microbearing gap with parabolic shapes.
Tribologia, 4 (220), 2008, pp. 195–202.
7. Wierzcholski K.: A new concept of the changes of memory capacity of fluid
dynamics HDD micro-bearings. Tribologia, 4 (220), 2008, pp. 267–274.
8. Wierzcholski K., Miszczak A.: Load Carrying Capacity of Microbearings
with Parabolic Journal. Solid State Phenomena, Trans. Tech. Public.,
Switzerland, Vols. 147–149, 2009, pp. 542–547.
9. Wierzcholski K.: Bio and slide bearings; their lubrication by non-Newtonian
fluids and application in non-conventional systems. Vol. III, Monograph.
Gdańsk University of Tech., 2007.
Recenzent:
Stanisław PYTKO
Streszczenie
Przedmiotem pracy jest wyznaczanie sił tarcia w inteligentnych stożkowych mikrołożyskach HDD z pamięcią, które występują w dyskach komputerowych. Praca niniejsza jest kontynuacją prac autora
i jego współpracowników publikowanych w 2007 roku. Autor porównuje wyniki własne z wynikami uzyskanymi w ostatnich dwóch
latach przez G.H. Janga, który wraz ze swoim zespołem badawczym
uzyskał efekty pamięci występujące w hydrodynamicznych mikro-
266
TRIBOLOGIA
4-2009
łożyskach ślizgowych wyłącznie poprzez nacięcia rowków o głębokości kilkudziesięciu nanometrów na powierzchniach czopów i panewek o kształtach walcowych, przez co uzyskiwane były odpowiednie
przepływy wirowe cieczy smarującej wewnątrz super cienkiej warstewki oleju w szczelinie łożyskowej. Autor zauważył, że niezależnie
od nanorowków zwiększone efekty pamięci można uzyskać poprzez
odpowiednie modelowanie kształtów powierzchni stożkowej czopa
i panewki. Opracowana przez autora teoria smarowania stożkowych
kształtów powierzchni nośnych hydrodynamicznych mikrołożysk
ślizgowych potwierdza wyniki G.H. Janga. Ponadto w pracy wykazano, że efekty inteligentnych mikrołożysk, polegające na zapamiętywaniu określonych obciążeń w warunkach eksploatacji oraz na
odreagowaniu tych obciążeń poprzez wzbudzanie odpowiednich
przepływów wirowych, powodowanych kształtem czopa i panewki,
dodatkowo zwiększają efekty pamięci prezentowane przez dotychczasowych badaczy, a nawet są, zdaniem autora, bardziej skuteczne
aniżeli w przypadkach badań G.H. Janga.