Analysis of Static and Dynamic Load on Hydrostatic Bearing with Variable Viscosity and Pressure

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1 Indian Journal of Science and Tecnology Supplementary Article Analysis of Static and Dynamic Load on Hydrostatic Bearing wit Variable Viscosity and Pressure V. Srinivasan* Professor, Scool of Mecanical Engineering, Barat University, Cennai-7; Abstract Hydrostatic bearing finds wide application in macine tools wit various tecnologies because of teir ig stiffness and damping caracteristic. Te environmental conditions, suc as low and/or ig temperatures, dust and dirt, moisture and unusual mounting conditions, can also affect a bearing s performance adversely. Terefore, bot mecanical and environmental factors may affect te coice of a bearing and its performance. For ig speed applications it is necessary to ave design data including te effect of rotational lubricant inertia.te objective of te study is to design a ydrostatic bearing wit following properties suc as ig stiffness, damping caracteristic and lubrication inertia. In te present study Reynolds equation is used and boundary conditions are canged for various parameters suc as temperature distribution, viscosity variation and radial load. Te simulated results were analyzed in detail and found tat increasing te viscosity of ydrostatic trust bearing under specific conditions wen bot surfaces are rotated, te wear and tear are minimized and life time as been increased. Tis will be of great use in ig speed applications. Keywords: Hydrostatic Bearing, Viscosity, Pressure, Temperature, Reynolds Equation, Lubricant. 1. Introduction It is customary in te teory of lubrication to assume tat te influence of te inertia terms in te equations of motion are negligible compared wit te effect of te viscous term. Wen te lubricant gap and te flow rate are small, te pressure falls logaritmically in a radial direction towards te edge of te bearing, as indicated by te exact solution of te Navier Stokes equations. Studies ignoring te inertia terms and assuming negligible transverse velocity components as been reported [1]. Wen te lubricant gap and flow rate are large, te viscosity variation is governed mainly by te inertia terms in te equations of motion and positive pressure gradients are encountered at te smaller radii and negative pressure gradients furter out towards te edge of te bearing. Solutions for te condition of large lubricant gap and flow rate for stationary parallel discs are well known. Te radial inertia of te lubricant can create a significant cange in te viscosity variation, particularly wen air is used as te lubricant, resulting in a loss in te load capacity of te bearing [2]. In te practical applications of externally pressurized trust bearings, it is usual for one of te bearing surfaces to rotate. As te speed of rotation increases, te centripetal inertia term become dominant relative to te viscous term reducing te overall viscosity variation. Researcers ave investigated tis particular case, deriving expressions for te viscosity variation for plane and stepped bearings [, 4]. Te same was revealed by oter wonders tat te importance of bot te radial and te rotational inertia terms in te equations of motion as recently increased due to extreme bearing operating conditions [5]. Hydrostatic trust bearings caracteristics: Hig loadcarrying capacity, zero wear of bearing surfaces, low friction *Corresponding autor: V. Srinivasan (srinivasan_v9669@yaoo.co.in)

2 4778 Analysis of Static and Dynamic Load on Hydrostatic Bearing wit Variable Viscosity and Pressure Temperature Figure 1. Pad tickness (load and bearing). at low or zero speeds, large fluid film stiffness and damping, as sown in Figure 1 reduced vibrations and good positional accuracy [6]. Different bearing configurations were considered and it was reported tat te addition of te stem enabled tis bearing to support radial loads [2]. Analytically studied te performance of circular trust pad ydrostatic bearing of various recess sapes, i.e., triangular, square, rectangular etc. Tey compared results wit te solutions obtained by an electrical analog tecnique. Owing to rapid tecnological advancements in manufacturing tecniques, super eavy constant flow ydrostatic trust bearing aving sector recess can be used widely in te many industrial eavy applications. In order to provide reasonable data for design, lubrication, termal deformation and force deformation computation for ydrostatic trust bearing in te eavy equipment, it is important to compute viscosity variation, temperature distribution and oil flow rate of te super eavy constant flow ydrostatic trust bearing aving sector recess [7]. Flat-land trust bearings are te simplest and least expensive to make. Tey andle ligt loads for simple positioning of rotors in electric motors, appliances, cranksafts, and oter macinery. Flat-land bearings carry 10 to 20% te load of oter trust-bearing types. Previous studies reveal tat flat parallel surfaces do not directly build oil-film pressure troug pumping action [8] as sown in Figure 2. Tey depend instead on termal expansion of bot te oil film and bearing surface to generate an oil-supporting wedge. Self-acting ydro dynamically lubricated slider bearings ave, owever, certain important disadvantages: 1. If te design speed is low, it may not be possible to generate sufficient ydrodynamic pressure. 50 Figure Freqency PTD pad 0.5mm PTD pad 1.0mm PTD pad 1.5mm Frequency wit tickness of pad. 2. Fluid film lubrication may break down during starting, direction canging, and stopping.. In a journal bearing te saft runs eccentrically and te bearing location varies wit load, tus implying low stiffness. In ydrostatic also called externally pressurized lubricated bearings te bearing surfaces are separated by a fluid film maintained by a pressure source outside te bearing [9]. Hydrostatic bearings avoid disadvantages 1 and 2 and reduce te variation of bearing location wit load mentioned in disadvantage. Te caracteristics of ydrostatically lubricated bearings are: 1. Extremely low friction 2. Extremely ig load-carrying capacity at low speeds. Hig positional accuracy in ig-speed, ligt-load applications 4. A lubrication system more complicated tan tat for self-acting bearings. Terefore, ydrostatically lubricated bearings are used wen te requirements are extreme as in large telescopes and radar tracking units, were extremely eavy loads and extremely low speeds are used, or in macine tools and gyroscopes, were extremely ig speeds, ligt loads, and gas lubricants are used. Fluid bearings use a tin layer of liquid or gas fluid between te bearing faces, typically sealed around or under Vol 6 (6S) June 201 Indian Journal of Science and Tecnology Print ISSN: Online ISSN:

3 V. Srinivasan 4779 te rotating saft. Tere are two principal ways of getting te fluid into te bearing: In fluid static, ydrostatic and many gas or air bearings, te fluid is pumped in troug an orifice or troug a porous material. In fluid-dynamic bearings, te bearing rotation sucks te fluid on to te inner surface of te bearing, forming a lubricating wedge under or around te saft. Hydrodynamic bearings rely on bearing motion to suck fluid into te bearing and may ave ig friction and sort life at speeds lower tan design or during starts and stops. An external pump or secondary bearing may be used for startup and sutdown to prevent damage to te ydrodynamic bearing [10]. A secondary bearing may ave ig friction and sort operating life, but good overall service life if bearing starts and stops are infrequent. Te tin films can be tougt to ave pressure and viscous forces acting on tem. Because tere is a difference in velocity tere will be a difference in te surface traction vectors [11]. Because of mass conservation we can also assume an increase in pressure, making te body forces different. Fluid bearings can be relatively ceap compared to oter bearings wit a similar load rating. Te bearing can be as simple as two smoot surfaces wit seals to keep in te working fluid [12]. In contrast, a conventional rolling-element bearing may require many ig-precision rollers wit complicated sapes. Hydrostatic and many gas bearings do ave te complication and expense of external pumps. 2. Objectives To analyse te viscosity variation of te lubricant used for te ydrostatic trust bearing. To analyse te load carrying capacity of te lubricant used for te ydrostatic trust bearing. To analyse te static and dynamic caracteristic of various film tickness in ydrostatic trust bearing. To analyse te temperature variation of te lubricant used for te ydrostatic trust bearing. design. Te pressure pads in ydrostatic bearings carry te load capacity. Most ydrostatic systems (trust or journal bearings) use several evenly spaced pads so nonsymmetrical load distributions can be andled. To estimate performance, pads can be treated separately. Pressure is maintained in te recess by fluid pumped troug a flow restrictor. Te pressure lifts te rotor until flow out of te recess and over te land equals flow in. A constant gap is maintained for a given recess pressure and bearing load. Te gap establises te volume of fluid pumped troug te bearing. An alternative design is to connect a fluid displacement pump (gear or vane type) directly to eac pocket witout flow restriction. Pressurizing pump power can be estimated from te product of pad pressure and total flow troug te pads. For an estimate of lubricant flow rate, a gap (or film tickness) is assumed -- typical values are to in. Design of flow restrictors influences bearing stiffness, pumping power, supply pressure, and lubricant flow. A flow restrictor is necessary to provide a pressure drop between te supply manifold and te pad recesses to ensure pressure requirements in any given pad never exceed supply pressure. A bearing wit restrictors is called a compensated bearing. Action of te restrictors is suc tat if te trust load is centered, pressure in all te pads is equal and lower tan pump pressure. If te load is off center, te gap decreases somewat on te loaded side and flow from te pad also decreases. Tis results in an increase in loaded-pad pressure and a decrease in pad pressure on te opposite side. Te runner automatically seeks a nearly level attitude. Te boundary conditions for slip flow at te surface of a gas bearing can be written as.. Researc Analysis Modeling Te researc deals wit te designing of a complex ydrostatic bearing of self-acting type satisfying te requiring Figure. Bearing surface contact. Vol 6 (6S) June 201 Indian Journal of Science and Tecnology Print ISSN: Online ISSN:

4 4780 Analysis of Static and Dynamic Load on Hydrostatic Bearing wit Variable Viscosity and Pressure u slip 2 f u = s f l z were f is te reflection coefficient, l is te mean free pat and s is a numerical constant. Because s and f are close to unity it can be assumed tat s( 2 f)/ f is unity. As te molecular mean free pat l depends upon fluid viscosity, pressure and temperature it can be approximated by te relation. 16 1/ 2 l = ( RT ) 52 ( p) 1 / (2) 2 p were R is te gas constant, T te temperature of te gas, te viscosity of te gas and p its pressure. Te effect of slip is also important on te flow beaviour of liquids especially wen te bearing surface is very smoot and is operating at iger surface temperatures as sown in Figure were te viscosity of te base oil decreases near te surface. Tis effect as been studied for liquids. Te slip velocity at te will can be written as u slip wall (1) 1 u = b z () were b is te coefficient of sliding friction at te wall and is te liquid viscosity..1 Reynolds Equation Te pysical configuration of fluid flow between two curved surfaces is sown in Figure 1. Te basic equations of motion and te equation of continuity for a Newtonian fluid considering te variation of fluid properties bot across and along te film tickness can be written as wall Du p u u r = rx Dt x + 2 x x y 2 u x x w z + u + u u + w y x y z z x D r u p u u = ry Dt y + 2 y y x 2 u y y w z (4) + w + u u + u z y z x x y Dw p w u r = rz Dt z + 2 z z x (5) 2 w z z u y + u + w w + u (6) x z x y y z + ( ru) + ( ru) + ( rw) = 0 6(a) t x y z Wit te usual assumptions of lubrication teory equations. can be simplified to p = u x z z (7) p = u y z z (8) were p = p (x, y) is te film pressure. Equation represents a generalized form of Reynolds equation for compressible fluid film lubrication considering slip velocities at te bearing surfaces. Te two sets of functions F and G depend upon te variation of fluid properties bot along and across te film and on te slip conditions at te surfaces wic is sown in Figure 4. Te viscosity of te lubricant can vary across te film tickness wic is sown in Figure 5 and may be different near te bearing surfaces owing to te reaction of additives Figure 4. Temperature due to Oil Film Pressure Rotational Speed(rmp) Temperature distribution curve. Vol 6 (6S) June 201 Indian Journal of Science and Tecnology Print ISSN: Online ISSN:

5 V. Srinivasan 4781 f ilm t ic k n e s s Viscosity variation across te film crank angle Liquid ydrostatic trust bearing working principle is tat lubricating oil wic is compulsively injected into oil cavity forms bearing capacity of ydrostatic bearing troug trottling action of te gap between resistive oil edges and te rotary table, lifts bearing spindle, and bears external loads. Te working principle of ydrostatic bearing wit quantitative oil supply is sown as Figure 1. Lubricating oil enters into oil cavity from pump along inlet and flows out along te radial sallow recess and resistive oil edges of external ring as sown in Figure 1. Flow mobility of te fluid between HIP round rail and rotating worktable must meet mass conservation, momentum conservation and energy conservation. Figure 5. viscosities. Temperature distribution curve wit various and surfactants wit te surfaces. Te most general form of Reynolds equation to study suc a situation is given by te equation + ( ru) + ( ru) + ( rw) = 0 t x y z Considering a reasonable case were te density and viscosity of te lubricant near te bearing surfaces may be different from tat of te central region gives te viscosity canges. Te pressure boundary condition necessary for te solution of eqn.(8) in general are not satisfactorily known and ence a one dimensional analysis is carried out in Reynold equation 7(a) to study qualitatively te effect of pseudo plasticity on piston ring lubrication. In order to increase rotational speed and bearing capacity of a constant flow ydrostatic trust bearing, a teoretical study concerning lubrication performance of a super eavy constant flow ydrostatic trust bearing aving sector recess is described. Te Computational Fluid Dynamics and te Finite Volume Metod ave been used to compute te lubrication caracteristics of a super eavy constant flow ydrostatic trust bearing, suc as recess pressure, recess temperature and oil flow rate. Tis study teoretically analyzes te influence of workbenc rotational speed on te bearing lubrication performance according to computational fluid dynamics and lubricating teory. It as revealed its viscosity variation law, temperature distribution law and oil flow rate..2 Mass Conservation Equation Te law of mass conservation is te basic law wic meets any mobile system. Mass conservation equation is: r + ( ru) + ( ru) + ( r w) = 0 t x y z were r is density (kg/m); t is time (s); u,u and w are in te x, y and z direction component of speed vector u. Flow capacity is kg/s, external pressure is 0.1 Mpa, te worktable rotational speed of 2.5 rpm, 8 rpm, 10 rpm, 12.5 rpm, 16 rpm, 20 rpm, 25 rpm, 1.5 rpm and 40 rpm, te tree-dimensional pressure fields, temperature fields and flow fields. Te recess and obviously overlapping in te oil cavities, te flow state is from laminar flow to turbulent flow. 4. Findings Tis researc after using te modified Reynolds equations assuming tat tere is a relation between te viscosity and film tickness determines te flow, te load, and te pumping power loss for bearing. Te simulation model as establised tat tere is a relationsip between ydrostatic trust bearing performance and various film tickness in recess pad. Te simulation model as also proved tat tere is decrease in te viscosity variation due to increasing te viscosity of ydrostatic trust bearing under te condition wen one bearing surface is rotated. Te simulation model noting but Reynold equation + ( ru) + ( ru) + ( rw) = 0 t x y z Vol 6 (6S) June 201 Indian Journal of Science and Tecnology Print ISSN: Online ISSN:

6 4782 Analysis of Static and Dynamic Load on Hydrostatic Bearing wit Variable Viscosity and Pressure as also proved tat tere is decrease in te viscosity variation or temperature due to increasing te viscosity of ydrostatic trust bearing under te condition wen bot bearing surface is rotated. Te ydrostatic trust bearings to reduce te numbers of parts and size, and to eliminate expensive mineral lubricant storage and pumping, tus furter satisfying stringent environmental constraints. Despite te many advantages offered by ydrostatic bearings, rotor dynamic instabilities due to ydrodynamic (sear flow) and fluid compressibility effects are issues of primary concern for ig speed operation wit large pressure differentials. Laboratory measurements of load, leakage, orque, and identification of rotor dynamic force coefficients aided to bencmark are compared wit simulation model tecnique. Te agreement also been tested. 5. Conclusion Te lubrication caracteristics of a super eavy constant flow ydrostatic trust bearing, suc as recess pressure, recess temperature and oil flow state are computed according to te Computational Fluid Dynamics and te Finite Volume Metod. Tis study teoretically analyzes te influence of workbenc rotating velocity on te viscosity variation law, temperature distribution law and oil flow state. Te following conclusions are made based on te numerical calculations done by iterative metod for te two-dimensional oil film pressure field state of a super eavy constant flow ydrostatic trust bearing by te usage of te fluid dynamics, lubricating teory and te Finite Volume Metod. Te results sow tat oil cavity pressure is almost invariant by increasing of workbenc rotating velocity, oil cavity temperature is increasing gradually by increasing of workbenc rotating velocity. Eac type of bearing as unique geometric and manufactured features tat influence te amount of friction tat occurs during operation. Tis, combined wit factors discussed previously about ow an application can influence eat generation, underscores te fact tat a power transmission system is a complex assembly tat interacts wit its surrounding environment. 6. References 1. Cattopadyay A K, Majumdar B C (1984). Steady state solution of finite ydrostatic porous oil journal bearing wit tangential velocity slip, Tribology International, vol 17(6), Prabu T J, and Ganesan N (1999). Effects of tilt on te caracteristics of multirecess ydrostatic trust bearing under conditions of no rotation, Wear, vol 92(2), Osman T A, Safar Z S et al. (2006). Experimental assessment of ydrostatic trust bearing performance Original Researc Article, Tribology International, vol 29(), Spur G, and Patzwald R (1998). Lubrication of ydrodynamic journal bearings wit magnetic fluids Production Engineering, vol 5(1), Yacout A W, Ismaeel A S et al. (2007). Te combined effects of te centripetal inertia and te surface rougness on te ydrostatic trust sperical bearing performance, Tribology International, vol 40(), Andrés L S, and Cilds D (2007). Angled injection ydrostatic bearings, analysis and comparison to test results, Journal of Tribology, vol 119(1), Stansfield F M (1970). Hydrostatic bearings for macine tools, Te Macinery Publising Co, van Beek A, and Lepic L (2007). Te combined effects of te centripetal inertia and te surface rougness on te ydrostatic trust sperical bearing performance, Tribology International, vol 40(), Kurtin K, Cilds D et al. (199). Experimental versus teoretical caracteristics of a ig-speed ybrid (combination Hydrostatic and Hydrodynamic) bearing, Journal of Tribology, vol 115(1), Andrés L S (1998). Bulk flow analysis of ybrid trust bearings for process fluid applications, Journal of Tribology, vol 122(1), Civens D R, and Civens D E (1999). Impact of ydrostatic bearings on te design and performance of telescopes, SPIE Proceedings, Acquisition, Tracking, and Pointing XIII, 12, vol Andrés L S (2006). A ybrid radial bearing wit improved rotor dynamic stability, 1st International Conference in Rotor dynamics of Macinery, ISCORMA1, Paper Vol 6 (6S) June 201 Indian Journal of Science and Tecnology Print ISSN: Online ISSN:

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