Special Lubrication Problems for Bearings Running at High Speed

Keywords: radial bearings, high speeds bearings, thickness of lubricant film 1 Introduction In the case of the bearings, the accidental contact pressure reaches high values (1000 - 3000) MPa, therefore, it is important to utilize lubrication systems dependent on factors such as: load, springiness of the interlocking gear’s materials, variation of the lubricant’s viscosity with pressure, peripheral speed and geometry [1]. Experimental tests referring to the running of bearings at high speeds were conducted on a stand which was designed and developed by the author. The stand is equipped with complex equipment for registering temperatures, friction moments, speeds and lubricant film thickness. Fig.1 The stand for testing bearings at high speed (I). In Fig. 1 and Fig. 2 the stand for testing bearings at high speeds is presented. It is made up of a testing head, intermediate broach, driving unit, lubrication installation, loading system, electrical installation and frame. Fig.2. The stand for testing bearings at high speed (II). The test head includes a front and a rear broach between which is a housing enclosing a hydrostatic bearing supported elastic, within which the testing bearing is mounted. The hydrostatic bearing is designed to ensure an evenly distributed lubricant film, which has the role of ensuring minimum friction torque of bearing measurement. The test bearing is mounted on the shaft and in the housing through interchangeable bushings. 2 Theoretical aspects In the case of the point contact, solving the Reynolds equation becomes difficult because of the lateral leaks that cannot be ignored. So, in this case, the starting point is the Reynolds equation for the bidirectional leak: (1) and (2) where v_x and v_y represent the medium peripheral speeds on the rolling Ox direction and on the lateral Oy direction, according to Fig. 3. The contact between the two bodies (1) and (4) may be equated with a contact between a plane and an equivalent revolving body which has the equivalent curve shaped Rx and Ry beams in the contact point, where: , (3) In the case when two bodies are elastically distorted under the action of the normal load Q, the vertical distance between 2 points situated on the distorted surfaces is identical with the similar distance between the equivalent body and the plane. This is shown in Fig.4, where: Fig.3. The geometry of the Hertzian rolling point contact. This is shown in Fig.4, where: (4) Fig.4. The thickness of the separation film between an equivalent ellipsoid and a flat surface. In (4), h₀ is the thickness of the lubricant film in the central area, s(x,y) represents the space between the two bodies or clearance, and w(x,y) is the elastic distortion [2]. The clearance s(x,y) is given by the formula: (5) The elastic distortion, in the case of perfectly elastic, homogenous and isotropic bodies, is given by the relation: (6) In (6), p(ξ,δ) represents the pressure under a point (ξ,δ) from the contact area. Changes in the viscosity and the lubricant’s density have to be taken into consideration as a consequence of the high pressures from the contact area. Thus, Barus’s relation for viscosity can be applied, where: (7) Dowson’s formula for the variation of the lubricant’s density with the pressure can be used: (8) Solving (1) is very difficult, but as a consequence of experimental determinations, the presence of a central plate was emphasized, where h ₀ is the thickness of the film of a horseshoe-shaped notch, situated in the exit area of the contact. [3] The practical importance presents h_min (the minimum thickness of the lubricant) and h₀ (the central thickness). Essentially, these depend on U, the speed parameter, and w the loading parameter (Fig. 5). Fig. 5 Entry-Exit The shape of the profile in an EHD point contact. Using the principle of the resistive method and considering the contacts between balls and bearing races, as a consequence of their separation through the lubricant film realizing electrical resistances when the flow passes from one level to another, the electrical resistance of a contact varies exponentially with the thickness of the film: (9) where proportionality factor K, depends on the pressure, temperature, lubricant type, contact’s dimension, rigor, etc. The resistive method allows qualitative, comparative measurement, of the lubrication system with diverse lubrication mediums. If it is considered a cylindrical roller bearing and the equivalent electrical scheme, it can be written that the global resistance of the bearing is: (10) where R_c,e and R_c,i represent the electrical resistances at the level of interior and exterior contacts and “2” is the number of balls. The use of the capacitive method means using a low voltage radio frequency flow applied to the frames between which the lubricant film is located. The lubricant film functions as a dielectric and the films thickness has to be determined. The method requires that while testing, the dielectric constant of the oil should not vary. The method is also practicable because, when the thickness of the film is small, the measured capacity is higher and therefore, the measurement’s precision is correct. The difficulty was caused by the frequency of the piercing of the film by the contacts of low resistance, among the surfaces’ asperities or conductive particles [4]. 3 Experimental aspects By reducing the thickness of the film due to the thermal effects and the lubricant in the bearing, more kinds of lubrication regimes can be developed, in conformity with the λ parameter. From Fig. 6, the result is that the complete regime EHD is obtained only for λ ≥ 3. In Fig. 6, λ represents the film parameter that is selected in the calculation according to the lubrication regime. Fig. 7 shows points of interest, in terms of lubrication, in a radial ball bearing. In the contacts between the balls and rolling elements, EHD lubrication regimes are achieved due to the loads and their reduced conformities, with film thicknesses of h_min, (≈ 1μm) [5]. Fig. 6. Thickness versus parameter film. Fig. 7. Points of interest regarding the lubrication in a radial ball bearing. The cages' rate of wear in seats needs to be verified, insuring that the outside surface of the cage can not be in contact with the collar of the bearing ring. Also, deposits from the cage material on the contact surfaces of the rolling units and rings must not be present [6]. Fig. 8 The typical wear forms that develop on the cage. Typical wear forms which develop on the cage are presented in Fig. 8. There are pronounced wear prints observed on the cages’ guiding shoulders (A surfaces) as well as in the ball seats (B surfaces). By testing carried out on a TALYROND device, circumferential non-uniform wear was exhibited; wear was manifested only on certain sections. As a result of the impurities in the oil through wear products, an exaggerated increase of temperatures in the bearing was obtained, parallel to the increase in the friction moment. If considerable wear prints are observed in Fig. 8, in Fig. 9 and Fig. 10 these wear prints are greatly attenuated, denoting a positive running speed, and also retrieved by the depressed moment of friction. Fig. 9 The typical wear forms which develop on the cage. Fig.10 The typical wear forms which develop on the cage. With the help of an attachment designed by the author, a series of diagrams were traced to determine the correlation between the total film thickness at the level of balls - ball races contacts and the electric capacity. Fig. 11 presents such a correlation, observing that in the domain of high thickness, the method can be used with good results while in the case of a small film thickness there is the risk of electic penetration of the film [7]. Due to the radial loadings, in (10) only the resistances from the loaded balls (balls 1 and 2) occur, in the case of other contacts the electrical resistance is ∞. Due to the small thicknesses of the lubricant film (