Optimization of Air Bearing Slider Design

Transcription

1 Proceedings of TC2005 orld Tribology Congress III Proceedings of TC2005 September 2-6, orld 2005, Tribology shington, Congress D.C., III SA September 2-6, 2005, shington, D.C., SA Optimiztion of Air Bering Slider Design ending ng, Yujun ng, Yunfei Chen Deprtment of Mechnicl Engineering Southest niversity, Nnjing, Chin TC TC ABSTRACT: Hrd disk drives continue to increse the dt storge density. The prmeters of the hed slider flying ttitude must stisfy very strict performnce gols. This pper focuses on the topic of the simulted nneling lgorithm when it is pplied to the problem of slider ir bering design in hrd disk drives. The objective is to minimize the sttic flying height, to keep the pitch ngle within resonble rnge, nd to minimize the roll ngle. The design vribles include recess depth nd geometry configurtion of the slider ir bering surfce. A typicl tri-pd slider ws tken s the physicl model to demonstrte the vlidity of the optiml lgorithm. Results show tht simulted nneling is efficient for the optimiztion of the slider ir bering design. The sttic ir bering chrcteristics were enhnced significntly. 0. Introduction The recent increse in recording density of hrd disk drives demnds extremely low flying heights with uniform pitch nd roll ngles. It is more stringent to void hed crsh with the reduction of the hed/disk gp. Better flying ttitude cn be chieved with proper configurtion of hed slider surfce. The optimiztion of ir bering surfce is of gret interest for the design of hed slider in hrd disk drives. Severl optimiztion lgorithms, such s the genetic lgorithm, the simulted nneling lgorithm, the DIRECT (dividing rectngle) lgorithm nd other methods hve been pplied to the slider ir bering design. O Hr nd Bogy [] used genetic lgorithms nd simulted nneling to chieve the optiml position of the high-pressure rils of trnsverse pressure contour. The objective is to minimize the sum of the vrition of flying height cross the rdius of the disk. Yoon nd Choi [2] presented n optimiztion technique to find n optimum configurtion of the tper-flt slider positioned by rotry ctutor for enhnced sttic ir bering chrcteristics. O Hr [3] designed shped rils slider by mintining flt flying height profile t specified flying height nd roll minimiztion while decresing the sensitivity of the bering to externl lod. ng nd Chen [4] employed complex geometry method to the configurtion optimiztion of two-ril sliders on dynmic chrcteristics. Hong Zhu nd Bogy [5] pplied DIRECT (dividing rectngle) lgorithm to slider ir bering surfce optimiztion. The shortcoming of the bove trditionl optimiztion lgorithm is tht they re esily trpped in locl optiml point. In contrst, genetic lgorithm nd simulted nneling lgorithm, re globl optimiztion lgorithm, which re more widely used in recent yers nd cn produce useful results. In this pper, the simulted nneling (SA) lgorithm is used to design the ir bering surfce of the slider, nd it will be esier to get globl optimized result. The purpose of this study is to get optiml configurtion of hed slider with better flying chrcteristics. Optimiztion results re presented nd discussed. It cn be found from the result tht the SA lgorithm is effective for the slider optimiztion, nd with this optimiztion method we cn get new tri-pd slider with further decresed flying height.. Description of the optimiztion procedure. The simulted nneling lgorithm The simulted nneling is generliztion of Monte Crlo method for exmining the equtions of stte nd frozen sttes of multi-body system. This stochstic globl optimiztion technique cn chieve globl optim in the presence of mny locl optim without the clcultion of Copyright 2005 by ASME

2 grdients to determine serch directions. The method is drwn from the nneling process of solid. In n nneling process, melt, initilly t high temperture nd disordered, is slowly cooled so tht the system is pproximtely towrds thermodynmic equilibrium. As temperture decreses, the system becomes more ordered nd pproches frozen ground stte t the lowest temperture. The process cn be thought of s n dibtic pproch to the lowest energy stte. In this lgorithm, the initil stte energy E nd temperture T of thermodynmic system re supposed first, nd then the Metropolis scheme ws used to clculte the new stte energy t decresed temperture. The temperture continues decremented nd the entire process is repeted until frozen stte is chieved t T0. The Metropolis scheme cn be described s follows: t certin temperture, the initil configurtion is perturbed nd the chnge in energy de is computed. If the energy decresed the new stte is ccepted, otherwise the new stte is ccepted with probbility given by the Boltzmnn fctor exp(-de/t). This process is lso repeted sufficient times to give good smpling sttistics for the current temperture. In n nlogy between the SA lgorithm nd metl nneling process, it cn be found in the SA pproch, the current solution to the combintionl problem is nlogous to the current stte of the thermodynmic system, the objective function to the energy eqution for the thermodynmic system, nd the globl minimum to the ground stte. Hence, the lgorithm is dependent on the nneling schedule, the choice of initil nd finl temperture, the length of Mpkob chin nd how the control prmeter T is reduced s the optimiztion progresses [6][7]..2 ormultion of the optimiztion problem In this pper, tri-pd, which is designed bsed on i s two-ril slider [8], is optimized. The slider is composed of two rils seprted by recess region nd til pd. Ech ril hs flt tper (ig. ). To efficiently increse the dt storge density in hrd disk drives, the flying height of the hed slider should be lower in order to get better signl-to-noise rtio. Also the pitch ngle nd the roll ngle should be in resonble rnge. So in this pper, the objective function is defined s Min H H t rg et () where H is the flying height evluted t given disk rdius nd the Htrget is the trget flying height. The design vribles were the configurtion prmeters of slider surfce nd the recess depth. The prmeters of the slider flying ttitude include flying height h0, pitch ngleα nd roll ngle were lso obtined by n optimiztion pproch. ig. Digrm of the tri-pd slider The flying stte of tri-pd slider is shown in ig., indicting ll forces cting on the slider which consist suspension pre-lod, slider weight nd the ir bering sttic lod. hen the slider flies stedily, the forces nd moments mentioned bove should be in equilibrium. Tht is + 0 X + X X 0 (2) Y+ Y Y 0 where ( p p ) da X x( p p ) da/ Y y( p p ) da/ The non-dimensionl residuls of the force nd moments were defined s + R + X + X X R2 X + X R 2 Y + Y Y Y+ Y So minimize the following objective function Eq. (5), the 2 Copyright 2005 by ASME (3) (4)

3 stedy flying ttitude prmeters cn be cquired. And the constrints of the flying ttitude prmeters re depicted s Eq. (6) R2 R3 R R + (5) h h h α α α β β β The compressible Reynolds eqution is employed here to describe the hydrodynmic lubriction problem between the hed slider nd the disk [9]. And the ukui-kneko model is employed to modify the Poiseuille flow to tke into ccount the rrefction effect. The modified Reynolds eqution for the slider with gs compressibility nd rrefction effects is written in the non-dimensionl form s QPH ˆ X P ΛxPH X P + QPH Λ PH PH Y Y T 3 ˆ 3 y σ [ ] where P is the non-dimensionl pressure, H is the non-dimensionl film thickness, X nd Y re non-dimension coordinte vribles of the slider long length nd width direction, ˆQ is the Poiseuille flow fctor for the ukui-kneko model, T is non-dimension time, x nd y re the bering numbers in the x nd y directions, σ is the squeeze number. The implicit control volume scheme is used to discretize the generlized Reynolds eqution. Then Eq. (7) cn be trnsformed to set of liner lgebric eqution, which cn be solved using the lternte itertive lgorithm. ig.2 shows the pressure distribution over the slider surfce. ith the pressure P, the sttic ir bering lod cn be clculted through Eq. (3). (6) (7).3 Numericl procedure There re minly two prts in our optimiztion process. The principl prt is optimiztion lgorithm, nd the other is flying chrcteristics solver including sttic nlysis. The initil configurtion prmeters of the slider were given rndomly nd flying ttitude prmeters were clculted by the solver. Then new shpe of the slider ws generted in the optimiztion prt nd new flying prmeters were got gin. Ech step the cost function ws evluted nd nlyzed. The process ws repeted till the objective function ws relized. The overll procedure for solving the optimiztion problem is illustrted in ig.3. ig.3 lowchrt of the optimum design of the slider The optimiztion prt genertes new shpe of the slider using X X + + α( β β ) (8) i i where Xi nd Xi+ re the design vrible vlues of strting point nd tril point respectively, α is rndom vrible tht tkes on vlues between 0 nd, nd re the upper nd lower limits of the design vribles. et i nd i+ be the cost function vlues of strting point Xi nd tril point Xi+, respectively. The Metropolis cceptnce rule is described s follow i+ i Pi ( i+ ) i+ i exp( ) i+ > i T (9) where T is the nneling temperture. ig.2 The slider pressure distribution 2. Results nd discussions The design prmeters of the prototype slider used in this pper re showed in Tble. 3 Copyright 2005 by ASME

4 Tble. Initil vlues of design prmeters Dimension of slider Initil vlues Slider length X (mm) 0.5 Slider width Y (mm) 0.4 Tper length HX (mm) 0.05 Tper height Ht ( ) Ril length RX (mm) 0.5 Ril width RY (mm) Til pd length TX(mm) 0.05 Til pd width T(mm) 0.08 Til pd width2 T2(mm) 0.2 roove depth ( ) 3 The originl flying prmeters re showed in Tble 2. Tble.2 Initil vlues of the flying ttitude prmeters lying ttitude prmeters Initil vlues lying height (nm) Pitch ngle ( rd) Roll ngle ( rd) Strting with this design, optimiztion of the slider configurtion ws crried out to chieve the desired flying height. 2. Two-dimensionl problem The rils were chosen s the design res to evlute the efficiency of the optimiztion procedure. The design spce ws limited in given domin s the design constrins. Results show tht the flying height decresed mrkedly, the roll ngle reduced, nd the pitch ngle hd resonble vlue. Tble.3 indictes tht the reducing of the slider width cn decrese the slider flying height. Tble.3 contour optimiztion result of the ril Air bering design Optimized vlues RX (mm) 0.97 RY (mm) lying height (nm) Pitch ngle ( rd) Roll ngle ( rd) Six-dimensionl problem The dimension of the slider surfce nd the recess depth were tken s design vribles to compre with the two-dimensionl problem. The optimized results re showed in Tble 4. e got the very uniform flying height of nm, the pitch ngle rd nd the roll ngle rd, respectively. Tble 4 indictes tht design the ril, til nd recess depth rtionlly cn fll the slider mrkedly. The results in Tble 3 nd 4 show tht the numericl procedure with the SA pproch is effective. Tble.4 contour optimiztion of the slider Air Bering Design Optimized vlues HX(mm) RX (mm) RY(mm) T (mm) T2 (mm) roove depth ( ) lying height (nm) Pitch ngle ( rd) Roll ngle ( rd) Conclusion This pper proposed n optimiztion strtegy for the shpe design of hed slider in hrd disk drives. Our optimiztion objective is to reduce the slider flying height, long with proper pitch ngle nd roll ngle. Simulted nneling lgorithm is employed here to ccomplish the numericl procedure. Modified Reynolds eqution is used to solve the ultr-thin film gs lubriction with the ukui-kneko model. Results show tht simulted nneling lgorithm is efficient to produce the optimized ir bering slider surfce with improved flying performnce. The flying height is lowered significntly with uniform pitch nd roll. It cn be concluded tht the pproch is lso effective for the optimiztion design of other typicl sliders. REERENCE. Mtthew. A. O Hr, Dvid. B. Bogy, 995, Robust design optimiztion techniques for ultr-low flying sliders, IEEE Trnsctions on Mgnetics, 3(995), Sng-Joon Yoon, Dong-Hoon Choi, 995, Design optimiztion of the tper-flt slider positioned by rotry ctutor, ASME Journl of Tribology, 7(995), Mtthew. A. O Hr, Yong Hu, Dvid. B. Bogy, 996, 4 Copyright 2005 by ASME

5 Effects of slider sensitivity optimiztion, IEEE Trnsctions on Mgnetics, 32(996), ng Yujun, Chen Yunfei, Yue Zheng, Yn Jingping, 2002, Configurtion Optimiztion of Two-Ril Sliders on Dynmic Chrcteristic, Journl of Southest niversity, 8(2002), Hong Zhu, Dvid B. Bogy, 2002, DIRECT lgorithm nd its ppliction to slider ir-bering surfce optimiztion, IEEE Trnsctions on Mgnetics, 38(2002), Kng lishng, Xie yun, You shiyong, uo zhuhu, Simulted Anneling Algorithm, Publishing House of Science, ISBN ng-ong i, Cheng-I eng, Chi-Chun Hwng, 996, Roughness effects on the dynmic coefficients of ultr-thin gs film in mgnetic recording, ASME Journl of Tribology, 8(996), Yong hu, Dvid B. Bogy, 998, Solution of the Rrefied s ubriction Eqution sing n Additive Correction Bsed Multigrid Control Volume Method, ASME Journl of Tribology, 20(998), Copyright 2005 by ASME