Rolling Element Bearing Contact Geometry Analysis

Rolling element bearings are subjected to a variety of loads during the operation of machinery. Raceway contact geometries should be designed and analyzed in a manner which accurately models internal contact stress distributions for these different load cycle conditions. To properly determine contact stresses, analyses should determine the orientation of rolling elements relative to the raceways through consideration of load, bearing alignment and bearing internal geometry. Since design loads are not always well defined and machinery upgrades may increase loads, contact geometry designs should have sufficient flexibility to handle conditions differing from the initial design loads. An analytical procedure with examples is discussed.     

A Simplified Model to Study EHL Film Collapse During Rapid Halting Motion

A theoretical model for describing the EHL film thickness during rapid deceleration is presented. The theory is based on the pioneer work of Ertel (1939) and Grubin (1949), who gave the first analytical solution for the elastohydrodynamic lubrication of a line contact under stationary operating conditions. An extension is made here for rapid halting motion. The proposed model is well adapted when the halting period is small in comparison to the transit time (i.e. 2b/u, ratio between the contact width and the rolling speed). This work completes the model of Glovnea and Spikes (2001b), appropriate for slow halting motion but which suffers from experimental fitting, and the model of Chang (2000) that is more suitable for speed or load oscillations at a wavelength close to the transit time.

This behavior implies that stop-start, reciprocating or rapidly halting machine components may be able to maintain a separating film for longer than would be expected based on steady-state EHL theory. An application to a ball bearing arrangement in a space mechanism is finally made in order to assess the model capabilities.     

The Performance of Heavily Loaded Oscillating Roller Bearings from 300 F to 600 F

Over 1000 roller bearings have been evaluated at elevated temperatures as oscillating bearings and load-life characteristics determined through statistical analysis of failure data. Operating temperatures of 300 F, 450 F, and 600 F were investigated. Bearing materials investigated included AISI 52100 steel, M-2 tool steel and 440-C stainless steel. Grease lubrication was used. The bearing load range included 250,000 psi to 500,000 psi maximum Hertz stress. AISI 52100 steel proved satisfactory for temperatures to 450 F. Tool steel (M-2) and 440 C stainless steel proved satisfactory for temperatures to 600 F. Although failure modes were predominantly by plastic deformation, wear and oxidation, failure distribution frequencies fit the Weibull distribution commonly used in bearing fatigue studies. Data scatter was less than that expected for continuously rotating ball bearings.     

The Design of Externally Pressurized Gas Lubricated Bearings by the Method of Bearing Equivalence

This paper presents the theoretical development and experimental verification of a simplified technique for the design of externally pressurized gas lubricated bearings. The general procedure is to establish an equivalent rectangular bearing which is the performance replica of an arbitrary gas bearing configuration. The resulting equivalent bearing has the same load support, clearance, area, source pressure, entrance losses, and mass flow as the arbitrary bearing which is analyzed. In accomplishing this end, the general rectangular bearing is analyzed, a consistent criterion of equivalence is defined, and theoretical analyses are compared to experimental data.     

圆柱滚子轴承滚动体修形技术的研究

分析了传统的滚动体修形的特点，提出了新的修形方法，根据新方法获得了新的修形曲线。有限元分析表明，新的修形曲线与对数曲线一样，可以避免滚于两端的边界应力集中。用新的修形方法还可以对滚于进行非对称修形，从而克服了对称修形无法避免的由偏载产生的“偏载效应”。     

A Method to Calculate Frictional Effects in Oil-Lubricated Ball Bearings

Friction and heat generation in oil-lubricated ball bearings is mainly the result of sliding in the ball-raceway contacts and agitation of the lubricant in the free space between the balls, cage. and bearing rings. Endurance of a ball bearing is highly dependent on the thicknesses of the oil films which serve to separate the balls from the raceways in a well-lubricated bearing. The film thicknesses, in turn, are dependent upon the lubricant's viscous properties. These are functions of bearing temperatures and are determined by the balance between the rates of frictional heat generation and heat dissipation. Therefore, in the design of a ball bearing application such as the high speed rotor and low speed rotor support bearings in an aircraft gas turbine, it is important to be able to predict the bearing frictional heat generation rates with reasonable accuracy. This paper presents a method to perform the required calculations considering hearing loading and speeds, realistic lubricant rheological properties, and a relatively simple heat transfer system between the hearing rings, halls. And lubricant. The results of the analysis are shown to compare favorably with experimental data.     

The Effects of Lubricant Rheology on the Performance of Journal Bearings

Experiments have been carried out on a relatively simple journal bearing rig to test the theory that extra load-carrying capacity is generated the elasticity of viscoelastic lubricants. Model lubricants were used. The viscoelastic lubricants were solutions of high-molecular-weight polyisobutene in low-molecular-weight polyisobutene while the inelastic lubricant was low-molecular-weight polyisobutene.

The extra load-carrying capacity has been established. An analysis of the detailed results strongly indicates that the extra benefit of elasticity is much greater than that predicted by existing theory.     

Thermally-Induced Failures in Railroad Tapered Roller Bearings

An Association of American Railroads (AAR) class F (6 1/2 × 12) tapered-roller bearing assembly is modeled, using finite elements, to examine thermally-induced failures observed in the laboratory when the bearing is operating at relatively high speeds. It is hypothesized that this failure is caused by an unstable thermal expansion/internal bearing load feedback process. Sequentially-coupled, transient thermal and static structural models are used to obtain the thermal-mechanical transient time response as a function of speed, seal type, and lubricant starvation at the rib contact. The model assumes no external loads and zero initial preload (zero end-play). Therefore, the loads developed in the bearing are thermally-induced and self-equilibrated. Two train speeds, viz. 80 and 100 mph, are considered. Simulation results indicate that at axle rotational speeds equivalent to a train speed of 100 mph, a combination of grease starvation and heat flux from the contact seals cause high rib temperature and subsequent unstable load growth which will lead to failure. At rotational speeds equivalent to train speeds of 80 mph or for bearing assemblies that utilize special design seals, the rib temperature is relatively low and no operational instabilities were observed for the model used.     

Torque Variations in Instrument Ball Bearings

Disturbances in the torques and motions in angular contact instrument ball bearing pairs are described and analyzed. Among others, a motion of the ball retainer, analogous to dry friction whirl, is attributed to frictional coupling between balls and retainer, and an interaction between bearings, resulting in several low frequency perturbations, is explained in terms of ball errors. Experimental confirmation is obtained.     

Crack Propagation of Rolling Contact Fatigue in Ball Bearing Steel Due to Tensile Strain

Crack propagations or failure modes in rolling element bearings, which had been difficult to explain via conventional crack propagation mechanisms such as the orthogonal shear stress mechanism, were discussed from the viewpoint of a tensile strain mechanism. Contact stresses are compressive in three axes, whose values differ from each other; then strain can be tensile in one of these directions, acting at a right angle to the direction of maximum compressive stress. A crack is considered to propagate by this tensile strain. When contact stress is small, a crack produced by some cause can propagate by this elastic tensile strain. When contact stress is large, residual tensile strain is produced by plastic deformation, which can also influence the crack propagation. Several failure modes of rolling element bearings, which had been difficult to explain, were explained by tensile strain.     

Non-Linear Transient Stability Analysis of a Rigid Rotor Supported on Hydrodynamic Journal Bearings with Rough Surfaces

Non-linear transient stability analysis has been performed to study the sub-synchronous whirl stability of a rigid rotor supported on two symmetric hydrodynamic bearings with rough surfaces subjected to a unidirectional constant load. A Reynolds type equation for finite hydrodynamic bearings, with different models of rough surfaces, has been solved using the stochastic finite element method. The trajectories of the journal center have been obtained by solving the equations of motion of the journal center by the fourth-order Runge-Kutta method. Results show an increase in the stability with transverse roughness and a decrease in the stability with isotropic roughness. A small improvement in stability is obtained with longitudinal roughness.     

A Noise Analysis of Cylindrical Roller Bearings Operating Under Zero External Load

The purpose of this article is to numerically investigate one source of acoustic noise in roller bearings, that which results from the motion of the rollers in the bearing under zero external load. For the sake of simplification, it was assumed that the cylindrical roller bearings are infinitely long. Furthermore, the effects of the following on the noise of the bearing were also examined: the radial clearance of the bearing, the viscosity of the lubricant, and the number of rollers. The results of the study show that the fundamental frequency of the noise components of the cylindrical roller bearing corresponds to the multiplication of the number of rollers and the whirling frequency of the roller center. The acoustical frequency spectra of the cylindrical roller bearing are pure tone spectra, containing the fundamental frequency of the roller bearing and its superharmonics. The factors that decrease the sound pressure level of a cylindrical roller bearing include low lubricant viscosity, high radial clearance, and a reduced number of rollers. The results and discussions of the present article could aid in the design of low-noise cylindrical roller bearings.     

Calculated Performance of Non-Newtonian Lubricants in Finite Width Journal Bearings

A numerical procedure has been developed for the calculation of the performance of non-Newtonian, polymer-thickened lubricants in finite width journal bearings. Such oils were found to act as if they had averaged “anisotropic viscosities,” i.e., different viscosities in the circumferential and side leakage directions, even though the viscosity was taken to have one definite value, a function of the resultant shear stress, at each point in the oil film. Overall, polymer oils carried less load at a given eccentricity, gave less friction and a flatter pressure distribution than mineral oils of the same low shear viscosities. By analogy with the previously calculated infinite width case, which gave similar results, it is expected that the flatter viscosity temperature slope of the polymer oils will compensate for their apparent viscosity decrease. The program has also been adapted to “natural” boundary conditions, which improve upon the delineation of the cavitation region on the inlet side of the bearing.     

高速客车轴箱轴承的偏载分析及轴承滚子非对称修形

通过对铁路高速客车轴箱轴承在偏载下滚动体与内外圈的接触应力和位移等所进行的有效元分析，提出了滚子非对称修形新概念。有限元分析结果表明，由于轴向载荷的影响，滚动体与内外圈的接触应力和位移等沿滚动体轴线的分布发生偏移，传统的对称修形虽然可以避免滚动体两端的边界应力集中，但无法克服“偏载效应”。为了同时避免所谓的“边缘效应”和克服“偏载效应”，必须根据偏载下滚动体与内外圈的接触应力或位移的偏移分布规律对滚子进行相应的非对称母线修形，从而使非对称修形滚子轴承有更高的可靠性和使用寿命。     

Specific Film Thickness—A Closer Examination of the Effects of EHL Film Thickness and Surface Roughness on Bearing Fatigue

Analysis of literature bearing-fatigue life results shows that fatigue life is not a simple function of the widely accepted specific film thickness, λ, which is the ratio of the EHL film thickness h to composite surface roughness [sgrave]. Instead, the influence of film thickness on bearing life increases with increasing surface roughness; at about 0.20 micrometer (8 microinch) composite roughness life increases with the square root of h while at about 0.46 micrometer (18 microinches) life increases with h squared.

The negative effect of surface roughness on bearing life appears to be relatively independent of film thickness. This suggests that surface roughness affects fatigue life by some mechanism in addition to the degree of interaction of asperities through an intervening EHL film. Additional test results are needed to confirm this point.     

A Fatigue Life Comparison of Two-Row Tapered Roller Bearings and Spherical Roller Bearings

Tests were run to compare the fatigue life of two-row tapered roller bearings to that of spherical roller bearings. Both bearing types had an outer diameter of 110 mm with the spherical roller bearing having a 22 percent larger dynamic radial load rating than the tapered roller bearings. All tests were run at 165 percent of the respective two-row dynamic radial load ratings. The results show that both the indirect mounting (double cup or outer ring) and the direct mounting (double cone or inner ring) tapered roller bearings gave significantly better fatigue lives than the spherical roller bearings. These results appear to contradict the present ISO 281 standard which assigns a 1.15 b_m rating factor to spherical roller bearings compared to a b_m rating factor of 1.10 for that of tapered roller bearings.     

Analysis of Double-Row Tapered Roller Bearings,Part II – Results: Prediction of Fatigue Life and Heat Dissipation

The model developed to predict the performance of double-row tapered roller bearings (DRTRB) and described in the first part of the paper is now exemplified. For a given example results on the internal load distribution, bearing fatigue life and hear generation are presented and discussed for various operating conditions including the mounting preload. It is revealed that some sliding occurs at the contact between the rollers and the cone that contributes significantly to the total power dissipated within the bearing. It is also shown that an optimum axial compression (or mounting preload) may be found in terms of fatigue life and heat dissipated. As the main conclusion the initial compression between bearing rows was found to play a major role upon the bearing behavior and therefore should be considered carefully for each application.     

A Critique of Rolling Contact Fatigue Criteria for Bearing Rings with Hoop Stresses

Tensile residual and interference fit stresses not treated in classical bearing formulations are known to reduce bearing rolling contact fatigue (RCF) life. Recent modifications of such theory to account for these stresses have simply included them in the computation of a single yield stress type criterion—either maximum shear or equivalent stress. An alternative modification is proposed and demonstrated for fatigue crack initiation that recognizes the primary influence of the maximum range of shear stress but includes the effect of normal stress on the critical planes, as in other successful bulk fatigue criteria for multiaxial nonproportional stress cycle fatigue.     

Evaluation of Ion-Sputtered Molybdenum Disulfide Bearings for Spacecraft Gimbals

High-density, sputtered molybdenum disulfide films (MoS₂) were investigated as lubricants for the next generation of spacecraft gimbal bearings where low torque signatures and long life are required. Low friction in a vacuum environment, virtually no out-gassing, insensitivity to low temperature, and radiation resistance of these lubricant films are valued in such applications. One hundred and twenty five thousand hours of accumulated bearing lest time were obtained on 24 pairs of flight-quality bearings ion-sputtered with three types of advanced MoS₂ films. Life tests were conducted in a vacuum over a simulated duty cycle for a space pay bad gimbal. Optimum retainer and ball material composition were investigated. Comparisons were made with test bearings lubricated with liquid space lubricants.

Self-lubricating PTFE retainers were required for long life, i.e., > 40 million gimbal cycles. Bearings with polyimide retainers, silicon nitride ceramic balls, or steel balls sputtered with MoS₂ film suffered early torque failure, irrespective of the type of race-sputtered MoS₂ film. Failure generally resulted from excess film or retainer debris deposited in the ball track which tended to jam the bearing. Both grease lubricated and the better MoS₂ film lubricated bearings produced long lives, although the torque with liquid lubricants was lower and less irregular.     

Power Loss Predictions in High-Speed Rolling Element Bearings Using Thermal Networks

In high-speed rolling element bearings (REB), the lubricant is used to separate the mating surfaces but also to cool down the parts while the system is in operation. In the context of optimizing oil circuits, a clear understanding of the lubricant cooling mechanisms is therefore required in order to reach a compromise between a good cooling capacity and the constraints on mass, size, and power. In this article, a model is presented that makes it possible to predict temperature distributions in high-speed thrust ball bearings. It is found that the prediction or measurement of global power loss cannot discriminate between several combinations of traction and drag forces. On the other hand, the predicted temperature distributions appear as very sensitive to the relative importance given to hydrodynamic rolling tractions or drag losses. Based on these findings, a methodology is suggested in order to define the most realistic power loss models to be used in high-speed REB simulations.