Pradeep K. Gupta

Frictional instabilities in ball bearings

Computer modeling techniques are used to investigate instabilities in the motions of ball and cage in a ball bearing. As the friction at ball/race and ball/cage contacts increases, the cage mass center whirl orbit changes from circular to polygonal and then to a rather erratic shape under excessive friction. The corresponding variations in whirl velocities also increase to represent bearing squeal. It is shown that cage instabilities are directly dependent on the ball/race traction slope, under low slip velocities, and the friction coefficient at the cage interfaces. Under steep traction slopes, the variation in traction at higher slip rates is also significant in high-speed bearings. In particular, it is found that a negative traction slope, in the high-slip region, may produce appreciable ball skid which promotes excessive interaction in the cage pockets and, perhaps, the most damaging instability of the cage, where the mechanical interactions progressively increase to indicate significant potentials fo...

Modeling of Instabilities Induced by Cage Clearances in Ball Bearings

Generalized dynamic motion of balls and cage in a ball bearing are simulated by solving the differential equations of motion under prescribed operating conditions and bearing geometry. The general cage motion is parametrically evaluated as a function of clearances both in the ball pockets and at the guide lands. The design significance of the modeling approach is demonstrated by the prediction of critical clearances which trigger certain instabilities in the cage motion. In more practical terms, the correlation between cage clearances and instability defines a wear life for the bearing under the prescribed operating conditions. Presented at the 45th Annual Meeting in Denver, Colorado May 7–10, 1990

Current Status of and Future Innovations in Rolling Bearing Modeling

Current state-of-the-art in modeling the performance of rolling bearings is reviewed in terms of fundamental analytical formulations and the development of computer codes for performance simulations. Some of the basic equations, which constitute the foundation of the various types of models, are reviewed before presenting a schematic approach for the development of rolling bearing models. Some of the key developments over the last several decades that have led to the current status of rolling bearing modeling are presented. Though some of the models are restricted to the developing organizations, and their use is only available in terms of application support, others have been packaged in the form of commercially available software products. These models provide immediate practical implementation of several tribological disciplines in their most up-to-date and advanced form. With the advancements in high-speed computing technologies, solutions to the most sophisticated analytical formulations have become possible. However, the parallel advancement in rotating machinery systems has continued to challenge the state-of-the-art of rolling bearing modeling and in order to meet the future requirements, further developments in certain areas are required. Such requirements include improvements in lubricant behavior, development of lubricant and material property databases, more advanced thermal management and modeling of bearing interactions, more sophisticated models to estimate energy dissipated in lubricant churning and drag, and implementation of modern object-oriented computing languages for better support of modeling software products on the current and anticipated future computer systems.

On the Dynamics of a Tapered Roller Bearing

The general motion of a roller and the cage in a tapered roller bearing is modeled as a function of frictional behavior in the bearing and cage clearances. Roller skew is shown to increase with increasing friction. At relatively high friction and low cage pocket and guide land clearances, the roller tends to pivot in the cage pocket such that it is in steady contact on one side of the pocket while the contact is cyclic on the other side with the roller skew frequency equal to its angular velocity. Such a pivoting motion promotes a high-frequency whirl of the cage which is clearly seen both in the whirl orbit and the whirl velocity solutions. As the friction in the bearing reduces such a high-frequency whirl is completely eliminated. When the cage clearances are somewhat larger, nominal cage whirl, with an almost circular orbit and with whirl velocity equal to cage angular velocity, is produced at higher values of friction. Again the whirl gradually subsides as the friction in the bearing is reduced. The results demonstrate significance of the computer modeling approach to optimizing bearing design under prescribed frictional behavior and operating environment.

On the frictional instabilities in a cylindrical roller bearing

Computer simulations of a high-speed cylindrical roller bearing, as obtained by the computer code ADORE, are used to correlate bearing performance to the frictional behavior at the roller/race and cage contacts. It is shown that an optimum traction-slip relation at the roller/race contacts may be determined to produce minimum race wear and heat generation in the bearing. Unlike the well defined circular cage mass center whirl orbits commonly seen in ball bearings, no significant cage whirl was found in a lightly loaded cylindrical roller bearing over the range of frictional parameters considered. Presented at the 44th Annual Meeting in Atlanta, Georgia May 1–4, 1989

Some Dynamic Effects in High-Speed Solid-Lubricated Ball Bearings

Dynamic performance simulations of a high-load, high-speed ball bearing for turbine-engine applications are considered using the available Dynamics of Rolling Element Bearings (DREB) computer program. It is shown that the key element in the bearing design is the traction behavior at the ball/race interface for the prescribed materials. With a given traction model, the geometry of the bearing may be designed to ensure acceptable ball/cage collision forces and to ensure the general stability of the cage. Presented as an American Society of Lubrication Engineers paper at the ASLE/ASME Lubrication Conference in New Orleans, Louisiana, October 5–7, 1981

Modeling of Wear in a Solid-Lubricated Ball Bearing

Computer modeling of wear in a solid-lubricated ball bearing for high-speed turbine applications is considered in terms of local interactions and the overall dynamics of the bearing elements. With prescribed coefficients of wear at the various interfaces between the interacting bearing elements, the computer model ADORE is used to obtain the time-averaged wear rates for the balls, races, and the cage as a function of the operating conditions typical of a gas turbine application. The model presents analytical estimates of wear in the ball pockets and at the guide lands of the cage, and it provides some guidance for optimizing cage design in solid-lubricated ball bearings. Presented at the 41st Annual Meeting in Toronto, Ontario, Canada May 12–15, 1986

Modeling of Instabilities Induced by Cage Clearances in Cylindrical Roller Bearings

The generalized cage motion is parametrically evaluated as a function of clearances both in the cage pockets and at the cage-to-race guide lands. Definite correlations between certain cage instabilities and the operating clearances provide practical guidance for optimization of cage clearances for a given performance specification

Traction coefficients for some solid lubricants for rolling bearing dynamics modeling

For specific use in rolling bearing dynamics computer codes, available experimental traction data on some solid lubricants is correlated to a simple algebraic equation defining traction as a function of slip or slide-to-roll ratio. The coefficients of the model are computed by regression analysis of available experimental data and are tabulated for immediate practical use. Presented as a Society of Tribologists and Lubrication Engineers Paper at the STLE/ASME Tribology Conference in Orlando, Florida, October 11–13, 1999

Comparison of Models for Ball Bearing Dynamic Capacity and Life

Generalized formulations for dynamic capacity and life of ball bearings, based on the models introduced by Lundberg and Palmgren and Zaretsky, have been developed and implemented in the bearing dynamics computer code ADORE. Unlike the original Lundberg-Palmgren dynamic capacity equation, where the elastic properties are part of the life constant, the generalized formulations permit variation of elastic properties of the interacting materials. The newly updated Lundberg-Palmgren model allows prediction of life as a function of elastic properties. For elastic properties similar to those of AISI 52100 bearing steel, both the original and updated Lundberg-Palmgren models provide identical results. A comparison between the Lundberg-Palmgren and the Zaretsky models shows that at relatively light loads the Zaretsky model predicts a much higher life than the Lundberg-Palmgren model. As the load increases, the Zaretsky model provides a much faster drop-off in life. This is because the Zaretsky model is much more sensitive to load than the Lundberg-Palmgren model. The generalized implementation, where all model parameters can be varied, provides an effective tool for future model validation and enhancement in bearing life prediction capabilities.