SISOM 007 and Homagial Session of the Commission of Acoustics, ucharest 9-31 May TRIOLOGICAL EHAVIOR OF THRUST EARING USING STRUCTURED SURFACES PART 1 THEORETICAL ACKGROUND Gabriel-Arin MIHALCEA *, Octavian GRIGORE * * S.C. I.C.T.M. S.A. ucharest, email: aringabriel@yahoo.com, gmihalcea@ictcm.ro The need to reduce friction and the amount of wear on machine element comonents involved in sliding contact is ever resent. The efficiency, reliability, and durability of such comonents deend on the friction that occurs at the sliding contact interface. The effects of the film lubricant fluid film thickness and surface roughness have a decisive role on the lubrication rocess. The first textured surfaces where obtained by lateau-honing. The first art of the aer resents the use of structured surfaces to imrove tribological roerties of the thrust bearings. The accent will be set on theoretical background of friction rocesses and friction arameters. Keywords: structured surfaces, loading caacity, thrust bearing characteristics. 1. INTRODUCTION There is always the desire to increase the load caacity or the ower density of the machine elements, which of course will lead to higher severity of the surface interaction. oth the need to reduce friction and the desire to increase load caacity require effective lubrication strategy for sliding surfaces. Surface lubrication involves many asects hysical and chemical roerties of the surface material and the lubricant. The classical theory of hydrodynamic lubrication yields linear, Couette velocity distribution with zero ressure gradients between smooth arallel surfaces under steady-state sliding. The hydrodynamic film results instable and it will collase under any external force acting normal to the surfaces. A stable fluid film with sufficient load-carrying caacity in arallel sliding surfaces can be obtained with macro or micro surface structure of different tyes. That means waviness and rotruding micro-aserities or textured surfaces obtained by different technological rocesses. Recently exeriments roved a doubling load carrying caacity for the surface structured design. Of course, due to the arallel sliding the erformance of these kind of bearings is oorer than more sohisticated taered or steed bearings. Models of a structured arallel-thrust bearing are resented and the effect of structure surfaces on load-carrying caacity is analyzed.. COMPUTATION MODELS The aer [1] resents an analytical model of a arallel thrust bearing which is shown in Figure 1. A lane disk (D) is rotating relative to a number of identical stationary ads (P). Each ad roerly textured, develos the same hydrodynamic force. It is sufficient to determine the hydrodynamic ressure distribution over a single ad in order to evaluate the load carrying caacity of the comlete arallel thrust bearing. It was used a simlified model of a single ad in the form of a rectangular arallel slider, as reresented in Figure. The dimles are characterized by the followers geometrical and functional arameters, [1,]: regularly distributed over a ortion, 0 α 1, of the slider width, in the sliding direction, x, and over the full slider length, L, as shown in Figure. α = reresents the textured ortion of the slider;
179 Tribological behavior of thrust bearing using structured surfaces. Part 1 Theoretical background each dimle is modeled by a sherical segment deth h and and is located in the center of an imaginary rectangular cell of sides r 1 r, as is resented in Figure ; δ = h0 r ; dimensionless clearance: ( ) asect ratio of the imaginary dimle cell: k = r r1 ; the dimensionless arameter k = r r1 characterizes the cell shae and the area density of dimles is given by S = π r 4 k r. ( ) 1 The two-dimensional, steady-state form of the Reynolds equation for an incomressible Newtonian fluid in a laminar flow, [1,]: 3 3 h h + h = 6μ U (1) x x z z x will be reduced to a dimensionless form by using the defined arameters: x z h 1 3μU x = ;z = ;h = ; = 1 ; Λ = r r h0 Λ (), a r a where: a = the ambient ressure, h0 = the bearing clearance, Λ = the dimensionless bearing number. The result of these oeration becomes: 3 3 1 h h + h = (3), x x z z δ x where the dimensionless clearance, defined as: h 0 δ = (4). r ased on the assumtion of sherical dimles the dimensionless film thickness at a secific oint of the textured surfaces given by, [1,]: h = 1 + l h 1 + 8hδ l 1 4δ r ( ) h 1 x + z l l 8hδ for x + z 1 (5a) and l l > h = 1 for x + z 1 (5b), L A axis of rotation D rotating disk P bearing ad W axial load Figure 1 The rincile of arallel thrust baering r 1 z r h 0 Figure a Model of laser structured slider r r 1 r Figure b Cross section of a arallel artialy structured slider U x h where x l, zl are local dimensionless coordinates with their origin of a single dimle cell, given by: xl zl x l = ; zl = (6) r r L L The boundary conditions are, [1,]: ( 0; z) = ( ; z) = x; = x; = 0 (7) These boundary conditions should be comleted by the conditions at the boundaries of ossible cavitations regions associated with each individual dimle. The ressure in the cavitations zones will be considered zero. The resented analytical model is valid for all values of slider length L, and width. However if the slider
Gabriel-Arin MIHALCEA, Octavian GRIGORE 180 is long enough in the z direction (normal to the sliding velocity), with a ratio L > 4, the end effects in this direction can be neglected, the ressure distribution in z direction became eriodical with a eriod equal to the imaginary cell size, r. ecause of this eriodicity, it is sufficient to consider a single column of dimles along the x axis, as resented in Figure 3. because of the symmetry of the dimles column about the x axis the ressure distribution will be symmetric about this axis too. For the comlete ressure distribution it is sufficient to consider only a half of the dimles column with z varying from 0 to r. The eriodicity, symmetry and continuity of the ressure distribution yields to: ( x;0) = ( x; r ) = 0 (8) y z Figure 3 Single dimles column of an infinitly long slider and its boundary conditions Figure 4 Tyical distibution of local resure for artial and full structured slider The Reynolds equation (3) accorded with the boundary considerations was solved for a infinite or a finite long slider, in the aer [1] by a finite differences method using non-uniform grid over the imaginary dimle cell with a denser mesh within the dimle area (about five times denser then outside dimles). Discretization of the Reynolds equation, using finite differences, comes to a set of linear algebraic equations for the nodal values of the ressure. These equations were solved using the successive over-relaxation Gauss-Seidel iterative method. The dimensionless load carrying caacity yields from numerically integration of the dimensionless ressure over the slider area, symmetry and continuity of the ressure distribution yields to: W = L dz dx (9a) for the finite long slider and W = dz 0 0 r 0 0 L L dx (9b) for infinitely long slider, Wh0 6δ where W is: W = (10a) or W = W (10b). μ UL L 3. THEORETICAL RESULTS Parametric analysis was erformed to investigate the effect of various dimensionless arameters of the roblem on the load carrying caacity of arallel sliders. The arameters are: dimensionless dimled ortion of the slider: 0 α 1; dimle asect ratio: 0 < ε 0, 5; dimensionless clearance: 0,0 δ 0, 5 ; cell asect ratio: 0,4 k 1; density of the dimles: 0 S 0, 8; slider length over width ratio: 0 L ; < dimensionless slider width: 5 00. Parameters selection, [1,3]: From a large number of numerical simulations it was found that the cell asect ratio, k, has an adverse effect on load caacity if larger then 1, so the analysis was restricted to k 1. In this range it was found
181 Tribological behavior of thrust bearing using structured surfaces. Part 1 Theoretical background that k has a negligible effect on the load carrying caacity. It was selected a tyical value for the asect ratio, k = 1. It was found too, that increasing the arameter above the value of = 50 has a negligible effect on W and it was selected this value of = 50 for comutation. The investigation of δ showed a very little effect on the dimensionless load carrying caacity. It was found that some arameters affects the load carrying caacity; these are: o L that characterizes the slider geometry; o α, h, S which characterizes the surface structuring. Two different effects of the dimles were found corresonding to the cases of artial structuring, α <1, and full structuring α = 1, [1,3],, [1,5]: In the case of artial structuring no otimum for the dimles density,, was observed; in this case the load caacity inverses with increasing area density of the dimles; this would be exected since the limiting case =1 corresonds to the ste slider, which is the otimum known geometry for a slider S bearing. In the case of full structuring there is an otimum value for the area density of the dimles: = 0.13. The results in Figure 4 that shows tyical distributions of the local ressure along the centre line of a single column of dimles for two cases of artial ( α = 0.6) and full ( α = 1) structuring. The results of tests shown in Figure 4 rare obtained for: infinitely long slider having a dimensionless width = 5; dimensionless dimle deth h =1.3 ; area density of dimles S = 0. 5,, [1]. It is shown that each dimle strongly affects the neighboring dimles, there is a collective dimles effect. This collective effect results in a ste-like ressure distribution over the structured ortion of the slider. The dimles in the full structured case do not interact, there is a single dimle effect resulting in a eriodic distribution with local cavitations zones. The otimum area density for maximum ressure and load caacity was S = 0.13 and the maximum local ressure is = 75. S S 4. RESULTS AND DISCUSSION FOR INFINITELY LONG SLIDER A tyical case of an infinitely long slider was selected in aer [1] to demonstrate the effect of the various imortant structure arameters on the load carrying caacity. Figure 5 resents the effect of the structured ortion, α, at different values of dimensionless dimle deth, h. A dimle area density S = 0. 5, which is high enough to roduce substantial load carrying caacity and I also racticable technologically to avoid dimles overlaing, was selected for this case. Figure 5 shows zero load carrying caacity for α = 0 as would be exected with a non structured arallel slider. At α = 1, full structured slider, a certain load carrying caacity Figure 5 The effect of the structured ortion α on the dimensionless load carrying caacity of an infinitely
Gabriel-Arin MIHALCEA, Octavian GRIGORE 18 exists, due to the individual dimle effect, but it is quite low. Figure 5, [1,4] reveals an interesting case of otimum at α =0. 6 and h =1.3 that maximizes the load carrying caacity. As can be seen this maximum in the load carrying caacity is an order of magnitude higher than the load carrying caacity for α =1. So for infinitely long sliders it is referable to use collective dimle effect as the individual one. Figure 6, [1,4] resents the effect of on the load carrying caacity at various be seen an otimum for S values. As can, that is almost indeendent of, does exist in the range 0.5 h. This otimum is close to h =1. 3, however, it is very weak, so that in range of values 1 h the load carrying caacity at a given S is nearly constant. Figure 7, [1,4] shows that the load carrying caacity is nearly roortional to the area density of the dimles, S. In fact the maximum of load carrying caacity is obtained with the maximum area density. It can be concluded that at α =0.6 the structured infinitely long slider behaves in the same manner as a ste slider. Using Figure 7, for h =1. 5, an emirical relation for the best load carrying caacity of an infinitely long structured slider can be found in the form: W = 0. 16S (11). Equation (11) is valid in the range 0.5 α 0. 65, dimensionless dimle deth 1 h, and dimle density 0.4 S 0.8. h S h Figure 6 The effect of dimensionless dimle deth h on the dimensionless load carrying caacity of an infinitely long arallel slider with otimum value ortion α = 0,6 and various densities S Figure 7 The effect of dimle area density S on the dimensionless load carrying caacity of an infinitely long arallel slider with otimum value ortion α = 0,6, and various dimensionless dimle deth h 5. RESULTS AND DISCUSSION FOR FINITE SLIDER It was investigated a wide range of L ratio for the case of finite slider. An otimum value of h =1.5was found for the load carrying caacity. This otimum, as in the case of infinitely long slider, is weak and, in the range of 1 h 1.5 the load carrying caacity is almost constant. Another interesting finding is that, contrary to the long slider case, for L 0. 5 it is better to structure the full width ( α = 1) of the slider rather than just a ortion of it ( α <1). Figure 8 The effect slider asect ratio L/ on the otimum value of structured ortion α ot for maximum load carrying caacity of finite arallel sliders
183 Tribological behavior of thrust bearing using structured surfaces. Part 1 Theoretical background S In this case otimum dimle density is = 0.13 and the individual dimle effect with local cavitations is dominant. As the ratio L increases above 0.5 the otimum value of α dros sharly, and at about L =1. 5 it retains the otimum value of about 0.6 that is tyical of long sliders. Figure 8, [1,5] resents the relation between otimum α values and the ratio L, for h =1. 5 and = 0.13. The S area density which is otimum for L < 0.5 was maintained as a common basis for comarison throughout the L range although it is not the best for L < 0. 5. The differences are relatively small. As can be seen fro Figure 9, [1,5] reducing the ratio L has a ronounced effect on the load caacity. Here again S = 0. 13 was selected as a common basis for comarison to allow inclusion of the full structured slider with α = 1. Figure 9 shows Figure 9 The effects of the structured ortion α and slider imortant reduction of the load carrying caacity of asect ratio L/ on the dimensionless load carrying caacity of finite arallel sliders the load carrying caacity with diminishing L ratio over the whole range of α. The reduction is more ronounced for α between 0.5 and 0. 6. The reason for the load caacity reduction is the increase of side leakage in short sliders, which revents build u of high hydrodynamic ressure and suresses the collective effect of the artial structured slider. As can be seen from Figure 9 the individual effect in the case of full structured slider, when α =1 is almost unaffected by the leakage and the sliders with substantially different L values have very similar load caacities. 6. CONCLUSIONS It was demonstrated the otential of load carrying caacity of bearings with structured surfaces. A model of structured arallel slider was develoed and the effects of surface structure on the load carrying caacity was analyzed, [1]. There a two hysical mechanisms for generating hydrodynamic ressure in arallel thrust bearing,[1, 3]: Dimle individual effect corresonding to the full with structuring ( α = 1) and it is not useful for develoing a large load carrying caacity exected from a hydrodynamic thrust bearing. It can be beneficial in a very short slider contacts (mechanical seals). The otimum dimles density was found to be S = 0. 13. Dimle collective effect which corresonds to the artial with structuring ( α < 1) and is generates substantial load carrying caacity, aroaching that of otimum conventional thrust bearings. The effect is useful in finite and long slide bearings with L 0. 5. The otimum value is α = 0. 6 and the maximum load carrying caacity is W = 0. 16S and the maximum dimle density is desired in this case. REFERENCES FOR PART 1 1. RIZMER, V., KLINGERMAN, Y., ETSION, I., A laser surface textured arallel thrust bearing, Tribology Trasaction, 46, 3, 397-403, 003.. WAKUDA M., YAMAUCHI Y., KANZAKI S., YASUDA Y., Effect of surface texturing on friction reduction between ceramic and steel materials under lubricated sliding contact, Wear, 54, Elsevier Science S.A, 003.
Gabriel-Arin MIHALCEA, Octavian GRIGORE 184 3. MARIAN, V., Lubrication of the textured surfaces, Deart. of Machine Elements and Tribology, University POLITEHNICA of ucharest, 006. 4. MIHALCEA, G.A., Procese de frecare ungere uzare şi bazele de calcul ale lagărelor axiale cu frecare fluidă, Referat Ştiinţific, Universitatea POLITEHNICA din ucureşti, Facultatea de Inginerie Mecanică, Catedra de Organe de maşini şi Tribologie, mai 1989. 5. MIHALCEA, G.A., Surafeţe structurate, caracterizare şi alicaţii, Referat la Doctorat, Academia Română, Institutul de Mecanica Solidelor, ucureşti, august 005.