Hydrostatic Journal Bearing

1. INTRODUCTION Market demands of new machine tools, oriented towards productivity improvements, can be satisfied by innovative designs capable of working simultaneously at higher speed and power ranges. A typical currently available toplevel spindle can provide 40 kW at 40–50 k rpm, but some manufacturing sectors ask for100 k rpm spindles capable of working at the same (or higher) power. At such high speeds even the most performing ball bearings are not suitable for their limitations due to noise and vibrations phenomena, wear of balls and cage, frequent uneconomical maintenance interventions (and consequent long lay-offs from production),local structural deformations induced by temperature rising due to high friction levels. Even conventional hydrostatic bearings do not allow the reaching of such high performances mainly because of the effects of temperature rising, resulting from energy dissipations generated by fluid viscosity.

2. TYPES OF BEARING 2.1 ROLLING CONTACT BEARING A rolling contact bearing consist of four parts – inner and outer races, a rolling element like ball, roller or needle and a cage which hold the rolling elements together and spaces them evenly around the periphery. Depending upon the type of rolling element, bearing are classified as ball bearing, cylindrical roller bearing, taper roller bearing and needle bearing. Depending upon the direction of the load, the bearing are classified as roller bearing and thrust bearing. There is however, no clear distinction between this two groups. Certain types of radial bearing also take thrust load and some type of the thrust bearing also take radial load. Rolling contact bearing having a low starting friction as comparing to the sliding contact bearing so it is also called antifriction bearing. But it is also more noisy , and low resistance to shock loading

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2.2 HYDRODYNAMIC BEARING In a hydrodynamic lubricated bearing there is a thick film between the journal and the bearing. A little consideration will show that when the bearing is supplied with sufficient lubricant, a pressure is buildup in clearance space when journal is rotating about its axis that eceentric with the bearing axis. So the load can be supported by this pressure without any actual contact between the journal and bearing. Load carrying ability of this bearing arise simply because of a viscous fluid resist being pushed around. 2.3 HYDROSTATIC BEARING Hydrostatics bearing is defined as a system of lubrication in which the load supporting fluid film, separating the two surface, is created by an external source, like pump, supplying sufficient fluid under the pressure. Since the lubricant is supply the under pressure, this type of bearing called externally pressurized bearing. In this type of bearing as the pump start high pressure fluid is admitted in the clearance space, forcing the surface of bearing and journal to separate out compared to the hydrostatic bearing , hydrodynamic bearing are in simple construction, easy to maintain and lower initial as well as maintenance cost. Hydrostatic bearing is costly it offer the advantage : (1) High load carrying capacity even low speed, (2) No starting friction and, (3) No rubbing action at any operating speed or load. This types of bearing are used on the vertical turbo-generators, centrifuges and ball mills 2.4 FLOATING BEARING In the full-floating journal bearing we located a floating sleeve between the journal and bearing surface. the floating sleeve can be operated for a wide range speed for a given shaft . In high speed element like turbines and compressor sometime we getting overheating of the journal bearing which is also encounter in high speed operation. So for this we increasing the clearance but increasing of clearance get into decreasing load carrying capacity. But the full-floating journal bearing means increasing oil flow without increasing clearance. A floating sleeve provides the two channels through which the oil may flow. (2)

Fig:1 Difference between conventional bearing and full-floating bearing 2.5 SQUEEZE FILM JOURNAL BEARING There is a certain case, the bearings are oscillate or rotate so slowly squeeze film bearing gives a satisfactory result. If load is uniform or varying in magnitude while acting in constant direction, this becomes a thin film or possibly a zero film problem. But if load reverse its direction, the squeeze film may developed sufficient capacity to carry the dynamic load without between the journal and bearing. such bearing are known as the squeeze film journal bearing.

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3. THE COAXIAL FLOATING SLEEVE A feasible approach to high-speed / high-power machine tool consists in placing free sleeve between the shaft and the housing, thus splitting the total relative speed in two contributions Comparative tests on different coaxial ball bearing configurations have proven this solution being not practicable because, depending on tested layout, either of the two coaxial bearings is not driven into rotation. It follows that the speed ratio between the two ball bearings has to be forced and controlled by external pneumatic/mechanical devices. On the contrary, the proposed coaxial hydrostatic configuration keeps all the advantages of an hydrostatic bearing: contactless capability, no wear phenomena, no maintenance required, the viscosity of the lifting fluid being the only source of friction. Moreover, if properly dimensioned, this bearing configuration allows to divide the total relative velocity into two almost identical contributions, whose ratio is self-controlled by the balance of the viscous torques acting on the internal and external cylindrical surfaces of the sleeve. This way, through the simplification of the technical difficulties related to high speed design, the target of 100 krpm can be achieved with the current available know how. The insertion of the sleeve allows saving up to half of the friction power generated by the same bearing without the bush. This happens because of the quadratic relationship existing between the friction power in an hydrostatic clearance and relative speed of its two opposite sliding surfaces; thus, once given the shaft speed, the reduction of friction power is maximum when the speed of the floating sleeve becomes half the one of the shaft. Of course, under the same conditions, friction powers decrease when increasing the clearance height; nevertheless this height cannot become too high as this solution would also increase the flow

rate, and consequently the pumping power.

Friction cannot be further decreased by reducing the viscosity of the fluid, as the current limit of the best industrial oils is about 4–5 cSt. Damping performances are also improved, while stiffness characteristics are expected to be reduced. This last shortcoming can be overcome by introducing automatic bipartition valves on the feeding line of the pads of the external bearing, in order to provide infinite stiffness on the external clearance: this way the total stiff-ness is the same as the one of a single-clearance hydrostatic bearing. Anyway the realized test bench was (4)

not provided with such devices, as in a real spindle the main stiffness problems originates from the deformability of both shaft and cantilever tool head; eccentricities

of the

bearings are negligible if compared to the for ementioned deformations. Disadvantages and costs coming from the need of a feeding system (pumps, filters, tanks, etc.) are expected to be widely compensated by economical advantages of higher production rates, by avoiding to interrupt production for maintenance, and new market opportunities due to high speed capability. Previous experimental activities on a pneumostatic test bench proved the floatingsleeve bearing to be capable of splitting the global relative speed gap into two contributions of comparable sizes. These tests also pointed out that an accurate definition of the clearance heights is essential for having the bearing working properly, that is obtaining the desired speed ratio between the sleeve and the shaft. Therefore, when the rotating speed increases up to some 100 krpm, the deformability of the rotating components has to be accounted for, as elastic radial expansions modify the nominal heights of the clearances by becoming comparable with the heights themselves An incorrect design of the clearances or the neglecting of centrifugal deformations may prevent from reaching the requested performances. The purpose of this paper is to provide hydrostatic designers with a new bearing configuration suitable for very high speed spindles, describing a method enabling them to correctly predict the behaviour and the performances of the bearing with the best engineering precision: this requires accounting for the radial expansions of the sleeve.

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4. THE RIGID MODEL The geometry of the hydrostatic bearing is sketched in Fig. 2: geometry of the pads on the shaft and on the external housing is shown in Fig. 3. The model is based on the following hypothesis: (a) the viscosity of the lifting fluid does not depend on temperature, (b) fluid viscosity has a constant value inside each of the two clearances, (c) there is no slip of the fluid at the walls, (d) the lifting fluid is uncompressible; corrections on this hypothesis are required when using air or gas (e) laminar flow: velocity profile across the clearances is linear and shear stressis constant,

FIG 2. scheme of the bearing with floating element

FIG 3. CAD model of prototype bearing. (6)

(f) local effects of curvature on fluid flows are neglected as the gap height is negligiblewith respect to its radius, (g) all eccentricities e are zero, so hydrodynamic phenomena are ignored. In order to write the expression for the rotating speed ω

2

of the floating sleeve, the

viscous torques T1 and T2 acting on the opposite surface of the floating element are forced to be equal, once the system is working in steady conditions. Torques can be expressed by intergrating the viscous shear stress τ over the whole bearingfriction areas S: S = NP.Af = NP.(AP –3/4AR) being NP the number of pads of the bearing, Af the pad friction area, AP the area of a single pad and AR the recess area T = 1

∫

S1

R .τ .dS, 1 1

T = 2

∫

S2

R .τ .dS, 2 2

According to hypothesis (e), considering the expression of viscous shear stress , and then writing the relative tangential velocity υ as ∆ ω .R, the shear stress becomes: τ = ( υ µ) / h = (µ∆ ω .R)/h So the expressions of the viscous torques can be rewritten as follows: T1= (µ1 (R1)2 S1 (ω 1 - ω 2))/h1 T2= (µ2 ( R2)2 S2 ω 2)/h2 Now, imposing T1 = T2, the angular speed ratio ω 1/ω 2 can be written as a function of the ratios of viscosities and clearance heights: (ω 1 / ω 2) = 1 + [(µ2 / µ1) (Af2 /Af1) (h1/h2) (R1/R2)2] Since the shaft speed is the independent parameter, speed ratio is expressed as Ω = ω 2/ω 1. The ratio of pad number NP2/NP1 does not appear in Eq. (5) as the described prototype has the same number of pads on both the shaft and the external bearing.

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5. EXPERIMENTAL RESULT A prototype of a hydrostatic spindle has been built in order to test the performances of hydrostatic bearings with floating coaxial bush. The shaft is supported by two bearings, each of them having a 30 mm diameter and provided with 4 pads. The diameters of the external bearings are 39 mm and they also have 4 pads each. The height of the inner clearance h1 between the shaft and the coaxial sleeve ( Fig. 2 ) is 17 µ m h2 is 32 µ m. The working fluid is a 5 cSt oil, provided at a pressure of 5.5 MPa (4.2 MPa inside the pads of the external bearing) and the prototype has been tested up to a shaft speed of 50,000 rpm

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6. THE DEFORMABLE BEARING When working at high speed ranges, the centrifugal forces acting on the rotating components produce radial expansions that cannot be neglected, as they are comparable to the clearance heights. FEM mapped models of shaft (Fig. 4), coaxial sleeve (Fig. 5) and external housing have been developed in order to account for these phenomena. Applied loads include centrifugal forces and pressure distributions on pads and sills. Radial expansions have been computed for different rotating speeds, obtaining ∆ R–ω diagrams that have been then converted into parabolic polynomials, to be used as inputs on a MatLab program. In fact, given a ω 1 shaft speed, the calculation of the speed ratio Ω is not a linear problem since ω 2 depends on the clearance heights, whose actual values are influenced by ω 2 through radial expansions:

Fig.4.Mapped mesh of shaft

Fig.5. Mapped mesh of the co-axial full-floating bush. (9)

The unlinear problem is solved by using a step integration method that simulates the actual spindle starting process (Fig. 6). Given ω 1(t) and ω 2(t) in a generic time-step (t), radial expansions dh(t) are determined by using polynomial expressions from FEM analysis. Using the previous eq(4) ω 1(t) and ω 2(t), the angular speed ω 1 at the next time step (t + ∆ t) ω 2(t + ∆ t)= ω 2(t) + [(T1(t)-T2(t)) ∆ t]/J ω 1(t + ∆ t) is an input paramrter ,according to the scheduled ramp-shaped starting

Fig.6. Shaft ramp-shaped starting:comparison of rigid and flexible coaxial bush

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7. RESULT AND ANALYSIS Theoretical results and experimental data are compared in Fig. 7. All the numerical curves are shifted from the experimental line. This difference originates from indeterminateness on the actual values of the most relevant quantities

heights and

viscosities. In fact, due to constructive allowances on bearing diameters, actual clearance heights may result different from their nominal values: dashed lines identify a region where hi are consistent with the imposed design tolerances. Therefore machining process of functional components requires a very high limit of accuracy, for even minimal changes in bearing diameters can produce appreciable consequences on the desired spindle performances. Moreover fluid viscosity is affected by temperature, as oil warms up when flowing across the sills: for instance, supposing 1 cSt difference between µ 1 and µ 2, this causes Ω (spindle idle condition) to fall down from some 0.4 to 0.33. Values of ω resulting from the rigid model are constant all over the working speed range. Once the deformability of the bearing is accounted for, the speed ratio ω decreases as shaft speed increases, someway similar to experimental data. A formulation concerning the relationship between shaft speed and fluid viscosity is currently being evaluated since it might improve the fitting of the theoretical curve to the experimental one. A further deviation from experimental results is caused by eccentricities. Hypothesis (g) assumed a zero eccentricity condition but, on the real spindle, this assumption never comes true, as the axis of the shaft and the ones of the bush and the housing are never aligned. As a consequence, clearance heights are no longer constant: they become a function of the angular coordinate, h = h(θ ). This condition generates hydrodynamic phenomena, which are not included in the developed model and whose effects become more relevant as rotating speed increase

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Fig.7. comparision of numerical result and experimental data.

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8. FUTURE DEVELOPMENT AND CONCLUSION Current efforts are directed towards the solution of the main shortcomings. The first issue concerns the indeterminateness of h and µ . Therefore a further full-floating hydrostatic prototype is being designed: it will be extensively provided with advanced sensor devices for the acquisition of all the interesting physical parameters (P,T,ω , e, etc.) on both internal and external bearings. From a theoretical point of view, the mathematical model of the floating bearing will be improved by embedding a µ (T,∆ ω ) relationship and developing a method capable of accounting for eccentricity effects. In machine tools working at high-speed/high-power ranges the proposed hydrostatic journal bearing with coaxial full-floating sleeve represents a valid option to replace advanced ball bearings, as its only disadvantage consists in very careful finishing and close tolerances required on the mating surfaces. Of course, the floating sleeve is worth to be used only if its rotating speed becomes nearly half the one of the shaft (Ω ≈ 0.5); in order to fit this requirement the designer must carefully fix the clearance heights and then evaluate the centrifugal deformations occurring on the sleeve. Results from the proposed method has shown a good accordance with available experimental data.

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