CAPACITY ENHANCEMENT IN HDD CONICAL MICRO-BEARINGS

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1 4-29 R I B O L O G I 25 Krzsztof WIERZCHOLSKI * ndrzej MISZCZK ** CPCIY ENHNCEMEN IN HDD CONICL MICRO-BERINGS ZWIĘKSZENIE NOŚNOŚCI W SOŻKOWYCH MIKROŁOŻYSKCH HDD Ke-words: omputer diss miro-bearings artifiial intelligene Słowa kluzowe: ski komputerowe mikrołożska sztuzna inteligenja Summar his paper presents a method of pressure and arring apait alulation in slide onial miro-bearing ourring in HDD omputer diss. he authors ompare the re own results of pressure and apait distributions with the results that are obtained G.H. Jang. Considered mirobearings have intelligent memor features. G.H. Jang attain memor properties through the nano- grooves on the lindrial miro-bearing surfaes whih implies the whirling motion and whirling flows of the lubriant in the bearing gap. In the presented paper the proper pressures and apait distributions and memor effets the of ourse are obtained b the onial shapes of the journal and sleeve and additionall b the grooves * ** Institute of Mehatronis Nanotehnolog and Vauum ehnique ehnial Universit Koszalin PL Koszalin ul. Raławika 5-7 Poland; krzsztof.wierzholski@wp.pl kademia Morska w Gni; Gnia ul. Morska 8-87; miszzak@am.gnia.pl

2 252 R I B O L O G I 4-29 with depth of about 25 nm. Suh shapes inrease and regulate the pressure and apait distributions and the effet of whirling motion and therefore inrease the bearing memor properties. INRODUCION he presented topi onerns determining the memor and apait enhanement during the slide onial miro-bearing lubriation. Unstea and random flow onditions of the miro-bearing and its sleeve are taken into aount. General analsis of this paper onsiderate the nami behaviour of miro-bearings and makes omparisons with reentl obtained results of other authors [L. 6 7]. he lubriation of onial miro-bearing surfaes is haraterized b various geometries form and artifiial intelligene. he aim of the presented paper is to generalize the reentl alulation methods of the pressure distributions in a thin laer lubriant of slide miro-bearing gaps [L. 5]. oupled journal and thrust hdronami bearing has been reentl used in the preision spindle of a omputer hard disk drive (HDD replaing the onventional ball bearings due to its outstanding low noise and vibration harateristis [L. 3]. In this appliation herringbone grooves have the advantage of self-sealing whih auses the lubriant to be pumped inward and therefore redues side leakage. he also prevent whirl instabilit that is observed in the onial journal bearings at onentri operating onditions. Fig. a b show the onial bearing sstem of a HDD and partiularl a irumferential and longitudinal grooves. Fig.. Conial journal for hdronami HDD miro-bearing (2 rpm after K. Wierzholski: a irumferential and longitudinal grooves on the onial sleeve b irumferential and longitudinal grooves on the onial journal Rs.. Czop stożkowe w hdronamiznh mikrołożskah HDD (2 obr./min wg Wierzholskiego: a rowki obwodowe i wzdłużne na stożkowej panewe b rowki obwodowe i wzdłużne na stożkowm zopie

3 4-29 R I B O L O G I 253 Cooperating surfaes in above devies are limited b the onial surfaes. Random onditions are taking into aount. Miro-bearing has appliation in medial drill bits and hard dis driver HDD spindle medial sstems [L. 5]. he HDD spindle samples have a shaft diameter 3. mm; rotational speed 2 rpm; visosit of 8 P (.8 Pas radial learane 3 mirometers mass 27 g mass moment of inertia.67 kgm 2. he width of upper and lower journal bearing hanges from.6 and.8 mm to 2.2 and.2 mm. he flow analsis of the visoelasti lubriant will be performed b means of the equations of ontinuit and motion [L. 6]. he lubriant flow in bearing gap is generated b rotation of a onial or spherial journal. Bearing sleeve is motionless. he miro-bearing lubriation is haraterized b the nami visosit hanges in thin gap- height diretion. CPCIY DISRIBUIONS IN CONICL MICRO-BERINGS GPS he dimensional pressure funtion p(ϕ t in the onial oordinates (ϕ satisfies the modified Renolds equations ( in the following form: ( = γ ϕ ϕ γ E E(p os R E E(p os R ( ( t E( os R E( E os R s γ ϕ γ ω = ( where ( ( s ϕ ϕ ( s ϕ for = (ϕ ϕ < 2πθ θ < 2b. We denote: γ angle between onial surfae and the ross setion plane of (2

4 254 R I B O L O G I 4-29 the journal b length of the one generating line R radius of the journal t time (see Fig.. If nami visosit is onstant in the gap height diretion then the equation ( tends to the form: X ϕ 3 3 E( E(p X E( E(p = 6 ϕ E( E( = 6ωX 2X ϕ t (3 for = (ϕ X = R osγ where ϕ < 2πθ θ < 2b he equation ( desribes the pressure funtion p(ϕ t in onial miro-bearing if oil visosit hanges in gap height diretion are taken into aount. he equation (3 desribes the pressure funtion p(ϕ t in onial miro-bearing if oil visosit hanges in gap height diretion are negleted. B using the optimal funtion f of probabilit densit distribution of the stohasti gap hanges aused b the roughness the mean value of total film thikness E( and the mean value of pressure funtion E(p are represented b virtue of the epetan operator in the following form [L. 6 7]: E ( = δ f ( δ ( f ( δ dδ σ s for = for = δ δ > where the smbol = denotes the half total range of random variable of thin laer thikness for normal hip joint. he smbol δ denotes dimensionless random part of the gap height. We have δ = o δ and = o where smbol o denotes harateristi value of gap height. he dimensionless value of the standard deviation σ s = was obtained on the basis of alulations for real roughness of miro-bearing surfaes. he arring apaities in onial bearing are alulated from the following formula: (4

5 4-29 R I B O L O G I 255 C on tot (t 2b ϕ = 2b ϕ k k p( ϕ t(r sin ϕ p( ϕ t(r osϕ sin ϕosγdϕd osϕosγdϕd (5 where smbol ϕ k denotes the end oordinate of the film in irumferential diretion and ϕ < 2πθ θ < 2b. Frition oeffiients in onial oordinates are as follows [L. 6]: µ on (t = e F e ϕ Rϕ (on Ctot (t F R (6 where F Rϕ F R denote frition fores in irumferene ϕ and longitudinal diretions and moreover e ϕ e are the unit vetors in onial ϕ and oordinate diretions. NUMERICL CLCULIONS he pressure distributions and apait values in mahine onial slide miro-bearings are determined in the lubriation region Ω whih is defined b the following inequalities: ϕ ϕ k 2b where 2b miro-bearing length. Numerial alulations are performed in Matlab 7.8 Professional Program b virtue of the equation (3 b means of the finite differene method (see Fig. 2. he gap height of the onial miro-bearing and bio-bearing has the following form: = (λ osϕsin γ γ (7 where λ eentriit ratio in onial miro-bearing radial learane of onial miro-bearing or bio-bearing and γ is angle between generate line and horizontal ais.

6 256 R I B O L O G I 4-29 R =. [L. m] L =b /R= ο =.2 [Pas] ω=754 [/s] p o=3.77 [L. MPa] p ma=24.64 [L. MPa] C =32.85 [L. N] C z=5.79 [L. N] ϕ k =3.52 [L. rad] λ Oil film end p ma=3.7 [L. MPa] C =2.43 [L. N] C z=3.6 [L. N] ϕ k =3.559 [L. rad] λ = 6 γ=8 Oil film end p ma=8.3 [L. MPa] C =3.55 [L. N] C z=2.39 [L. N] ϕ k=3.585 [L. rad] λ =.5 γ=8 Oil film end γ=8 Fig. 2. he pressure distributions in onial miro-bearings aused b the rotation in irumferential diretion where onial inlination angle γ = 8 o. Left side presents the view from the film origin right side shows the view from film end Rs. 2. Rozkła iśnienia w stożkowm mikrołożsku wwołane ruhem obrotowm w kierunku obwodowm prz kąie nahleniu γ = 8 o powierzhni boznej z płaszzzną prostopadłą do osi wałka. Rozkła znajdująe się po lewej (prawej stronie rsunku pokazują pozątek (konie rozkładu iśnienia hdronamiznego

7 4-29 R I B O L O G I 257 Fig. 2 shows the numerial pressure values in onial miro-bearing gap for the angle γ = 8 o between onial surfae and the ross setion plane without magneti field influenes and stohasti hanges for: least value of the onial journal R =. m L = b /R = oil nami visosit o =.2 Pas angular veloit ω = 754 s p o = ω o R 2 / 2 p o = 3.77 MPa eentriit values λ =.5; λ =.6; λ =.7. B virtue of the boundar Renolds onditions the angular oordinate of the film end has the values: ϕ k = rad; ϕ k = rad; ϕ k = 3.52 rad. If eentriit ratio inreases from λ =.5 to λ =.7 then the maimum value of hdronami pressure inreases from 8.3 MPa to MPa and total apait in diretion inreases from 3.54 N to N and z diretion inreases from 2.39 N to 5.79 N. CONCLUSIONS If the angle γ between onial surfae and the ross setion plane inreases in onial bio-bearing and miro-bearings then the apait in ross-wise diretion inreases and in longitudinal diretion dereases. We an simulate the inreases of the memor apait of fluid nami HDD miro-bearings not onl b the bearing width and b the herringbone or spiral grooves indiated in papers [L. 6 7] and also b the various shapes of journal bearings. he properties of the hanges of memor apait simulations are funtioning for human bio-bearings with various shapes of bone heads whih are formed during the thousand ears of evolution. REFERENCES. Bharat Bhushan: Nano-tribolog and nanomehanis of MEMS/NEMS and BioMEMS BioNEMS materials and devies. Miroeletroni Engineering pp Jang G.H. Seo C.H. Ho Song Lee: Finite element model analsis of an HDD onsidering the fleibilit of spinning dis-spindle head-suspension-atuator and supporting struture. Mirosstem ehnologies 3 27 pp Jang G.H. Park S.J. Kim C.S. Han J.H.: Investigation of the eletromehanial variables of the spindle motor and the atuator of HDD due to positioning and the free fall. Mirosstem ehnologies 3 27 pp Liu L.X. Spakovszk Z.S.: Effets of Bearing Stiffness nisotrop on Hdrostati Miro gas Journal Bearing Dnami Behavior. J. of Engineering for Gas urbines and Power SME vol pp

8 258 R I B O L O G I Wierzholski K.: Bio and slide bearings; their lubriation b non-newtonian fluids and appliation in non-onventional sstems. Vol. I Seond Edition: Priniples of Human Joint Lubriation. Monograph. Gdańsk Universit of eh Wierzholski K. Miszzak.: Flow on the bio ell surfaes as an element of the miro-bearing tribolog. Journal of Kones Powertrain and ransport 27 vol. 4 No. 2 pp Wierzholski K. Miszzak.: Load Carring Capait of Mirobearings with Paraboli Journal. Solid State Phenomena rans. ehnial Publiations Switzerland Vols pp Reenzent: Stanisław PYKO Streszzenie W niniejszej pra wznaza się rozkła wartośi iśnienia oraz sił nośne w mikrołożskah stożkowh stosowanh w skah komputerowh. Prae z zakresu mikrołożsk ślizgowh publikowane w ostatnih trzeh latah dowodzą że mikro- i nanorowki na powierzhniah zopa i panewki mikrołożsk przzniają się do zwiększenia nośnośi i powodują że łożska mają właśiwośi inteligentne manifestująe się zdolnośią zapamiętwania określonh reakji na konkretne obiążenia w trakie eksploataji. utorz niniejszej pra wkazują że eh pamięi i smulaji nośnośi są powodowane nie tlko nano- i mikrorowkami na powierzhni zopa i panewki ale również rozmaitmi kształtami zopów a w niniejszej pra zopem stożkowm. Opublikowana praa autora w Solid State Phenomena Switzerland (29 dotząa mikrołożsk z zopami paraboliznmi oraz przedstawione w niniejszej pra wniki dotząe łożsk o zopah stożkowh potwierdzają przedstawioną hipotezę. W niniejszej pra autorz przedstawiają równanie tpu Renoldsa wznazająe rozkład iśnienia w szzelinie stożkowego mikrołożska prz uwzględnieniu stohastznie zmiennej wsokośi szzelin łożskowej. Ponadto wznazone został rozkła wartośi iśnienia hdronamiznego oraz wartośi sił nośnej.