Determination of ball bearing dynamic stiffness

The dynamic radial stiffness characteristics of rolling element bearings are currently determined by analytical methods that have not been experimentally verified. These bearing data are vital to rotating machinery design integrity because accurate critical speeds and rotor stability predictions are highly dependent on the bearing stiffness. A tester was designed capable of controlling the bearing axial preload, speed, and rotor unbalance. The rotor and support structures were constructed to permit critical speeds that are predominantly determined by a 57 mm test bearing. A curve of calculated critical speed versus stiffness was used to determine the actual bearing stiffness from the empirical data. The results of extensive testing are used to verify analytical predictions, increase confidence in existing bearing computer programs, and to serve as a data base for efforts to correct these programs

Application of the finite-element method for determining the stiffness of rolling bearings

The paper presents the results of numerical tests performed with use of the FEM method, the aim of which was determining the stiffness of the outer raceway - rolling element - inner raceway system of bearing 6307. The characterization obtained has been compared with a characterization determined with analytical methods and in the next stage, it will be used to determine the total stiffness of the bearing, variable in working time. Correct modelling of bearing stiffness is one of important conditions for obtaining correct results of simulation calculations. Obtained results will allow the determination of possibilities of limiting vibroactivity of toothed gears, commonly used in transport

NASA helicopter transmission system technology program

The purpose of the NASA Helicopter Transmission System Technology Program is to improve specific mechanical components and the technology for combining these into advanced drive systems to make helicopters more viable and cost competitive for commerical applications. The history, goals, and elements of the program are discussed

Vibration transmission through rolling element bearings in geared rotor system, part 1

A mathematical model is proposed to examine the vibration transmission through rolling element bearings in geared rotor systems. Current bearing models, based on either ideal boundary conditions for the shaft or purely translational stiffness element description, cannot explain how the vibratory motion may be transmitted from the rotating shaft to the casing. This study clarifies this issue qualitatively and quantitatively by developing a comprehensive bearing stiffness matrix of dimension 6 model for the precision rolling element bearings from basic principles. The proposed bearing formulation is extended to analyze the overall geared rotor system dynamics including casing and mounts. The bearing stiffness matrix is included in discrete system models using lumped parameter and/or dynamic finite element techniques. Eigensolution and forced harmonic response due to rotating mass unbalance or kinematic transmission error excitation for a number of examples are computed

Bearings: Technology and needs

A brief status report on bearing technology and present and near-term future problems that warrant research support is presented. For rolling element bearings a material with improved fracture toughness, life data in the low Lambda region, a comprehensive failure theory verified by life data and incorporated into dynamic analyses, and an improved corrosion resistant alloy are perceived as important needs. For hydrodynamic bearings better definition of cavitation boundaries and pressure distributions for squeeze film dampers, and geometry optimization for minimum power loss in turbulent film bearings are needed. For gas film bearings, foil bearing geometries that form more nearly optimum film shapes for maximum load capacity, and more effective surface protective coatings for high temperature operation are needed

Spur-Gear-System Efficiency at Part and Full Load

A simple method for predicting the part- and full-load power loss of a steel spur gearset of arbitrary geometry supported by ball bearings is described. The analysis algebraically accounts for losses due to gear sliding, rolling traction, and windage in addition to support-ball-bearing losses. The analysis compares favorably with test data. A theoretical comparison of the component losses indicates that losses due to gear rolling traction, windage, and support bearings are significant and should be included along with gear sliding loss in a calculation of gear-system power loss

A review of physics-based models in prognostics: application to gears and bearings of rotating machinery

Health condition monitoring for rotating machinery has been developed for many years due to its potential to reduce the cost of the maintenance operations and increase availability. Covering aspects include sensors, signal processing, health assessment and decision-making. This article focuses on prognostics based on physics-based models. While the majority of the research in health condition monitoring focuses on data-driven techniques, physics-based techniques are particularly important if accuracy is a critical factor and testing is restricted. Moreover, the benefits of both approaches can be combined when data-driven and physics-based techniques are integrated. This article reviews the concept of physics-based models for prognostics. An overview of common failure modes of rotating machinery is provided along with the most relevant degradation mechanisms. The models available to represent these degradation mechanisms and their application for prognostics are discussed. Models that have not been applied to health condition monitoring, for example, wear due to metal–metal contact in hydrodynamic bearings, are also included due to its potential for health condition monitoring. The main contribution of this article is the identification of potential physics-based models for prognostics in rotating machinery

The practical impact of elastohydrodynamic lubrication

The use of elastohydrodynamics in the analysis of rolling element bearings is discussed. Relationships for minimum film thickness and tractive force were incorporated into computer codes and used for bearing performance prediction. The lambda parameter (ratio of film thickness to composite surface roughness) was shown to be important in predicting bearing life and failure mode. Results indicate that at values of lambda below 3 failure modes other than the classic subsurface initiated fatigue can occur

Dynamics of a split torque helicopter transmission

A high reduction ratio split torque gear train has been proposed as an alternative to a planetary configuration for the final stage of a helicopter transmission. A split torque design allows a high ratio of power-to-weight for the transmission. The design studied in this work includes a pivoting beam that acts to balance thrust loads produced by the helical gear meshes in each of two parallel power paths. When the thrust loads are balanced, the torque is split evenly. A mathematical model was developed to study the dynamics of the system. The effects of time varying gear mesh stiffness, static transmission errors, and flexible bearing supports are included in the model. The model was demonstrated with a test case. Results show that although the gearbox has a symmetric configuration, the simulated dynamic behavior of the first and second compound gears are not the same. Also, results show that shaft location and mesh stiffness tuning are significant design parameters that influence the motions of the system

Propagation of surface initiated rolling contact fatigue cracks in bearing Steel

Surface initiated rolling contact fatigue, leading to a surface failure known as pitting, is a life limiting failure mode in many modern machine elements, particularly rolling element bearings. Most research on rolling contact fatigue considers total life to pitting. Instead, this work studies the growth of rolling contact fatigue cracks before they develop into surface pits in an attempt to better understand crack propagation mechanisms. A triple-contact disc machine was used to perform pitting experiments on bearing steel samples under closely controlled contact conditions in mixed lubrication regime. Crack growth across the specimen surface is monitored and crack propagation rates extracted. The morphology of the generated cracks is observed by preparing sections of cracked specimens at the end of the test. It was found that crack initiation occurred very early in total life, which was attributed to high asperity stresses due to mixed lubrication regime. Total life to pitting was dominated by crack propagation. Results provide direct evidence of two distinct stages of crack growth in rolling contact fatigue: stage 1, within which cracks grow at a slow and relatively steady rate, consumed most of the total life; and stage 2, reached at a critical crack length, within which the propagation rate rapidly increases. Contact pressure and crack size were shown to be the main parameters controlling the propagation rate. Results show that crack propagation under rolling contact fatigue follows similar trends to those known to occur in classical fatigue. A log-log plot of measured crack growth rates against the product of maximum contact pressure and the square root of crack length, a parameter describing the applied stress intensity, produces a straight line for stage 2 propagation. This provides the first evidence that growth of hereby-identified stage 2 rolling contact fatigue cracks can be described by a Paris-type power law, where the rate of crack growth across the surface is proportional to the contact pressure raised to a power of approximately 7.5