Thermal Evaluation of a Dry Nonrotating Thin Section Contact Bearing

1996 ◽  
Vol 118 (4) ◽  
pp. 610-614 ◽  
Author(s):  
E. W. Spence ◽  
D. A. Kaminski
Keyword(s):  
Thermal Resistance ◽  
Axial Load ◽  
Ball Bearing ◽  
Elastic Stress ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Difference Model ◽  
Angular Contact Ball Bearing ◽  
Outer Race ◽  
Hertzian Contact Theory

The thermal resistance of an angular contact ball bearing as a function of the radial and axial load is investigated numerically. An elastic stress analysis, based on Hertzian contact theory, provides circumferentially-varying contact areas for input to the thermal model. A finite difference model of the combined conductive, convective and radiative transport from the inner to outer race is used to calculate the overall thermal resistance of the bearing.

A New Method to Analyze Three-Dimensional Non-Repetitive Run-Out (3D-NRRO) of Angular Contact Ball Bearings

2011 ◽  
Author(s):  
Zhaohui Yang ◽  
Jun Hong ◽  
Jinhua Zhang ◽  
Micheal Yu Wang ◽  
Baotong Li
Keyword(s):  
Three Dimensional ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Ball Bearings ◽  
Angular Contact Ball Bearing ◽  
Geometrical Errors ◽  
Ultra Precision ◽  
The Relationship ◽  
Hertzian Contact Theory

As ultra-precision index of high-precision ball bearings, the value of three-dimensional non-repetitive run-out (3D-NRRO) directly influences the rotation accuracy in complex mechanical system. Reducing 3D-NRRO contributes to improve the quality of manufacturing in machining tools. This paper develops five-freedom model to analyze the 3D-NRRO of an angular contact ball bearing caused by geometrical errors of the rings raceways and the balls. In the model, the variation of contact angle caused by centrifugal force of balls is taken into consideration, and the geometrical errors of rings raceway and balls are described by Fourier series. Meanwhile, based on Hertzian contact theory and the solution method of dimensional chains, the 3D-NRRO analytical program has been developed, the value of 3D-NRRO analysis is shown. From the results, the relationship between the 3D-NRRO and the geometrical errors of rings raceway and balls are analyzed quantitatively. Findings of this paper provide theoretical supports to reduce or control the 3D-NRRO by optimizing manufacturing process of bearing components.

scholarly journals Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

2021 ◽  
Vol 11 (2) ◽  
pp. 787
Author(s):  
Bartłomiej Ambrożkiewicz ◽  
Grzegorz Litak ◽  
Anthimos Georgiadis ◽  
Nicolas Meier ◽  
Alexander Gassner
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Hertzian Contact ◽  
Two Degrees Of Freedom ◽  
Wide Range ◽  
Shape Errors ◽  
Nonlinear Features ◽  
Fourier Transform Phase ◽  
Hertzian Contact Theory

Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.

Approximate Analytical Model for Hertzian Elliptical Wheel/Rail or Wheel/Crossing Contact Problems

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
F. D. Fischer ◽  
M. Wiest
Keyword(s):  
Contact Pressure ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Technical Accuracy ◽  
Elliptical Contact ◽  
Current Approximation ◽  
Analytical Expressions ◽  
Maximum Contact ◽  
Hertzian Contact Theory

The Hertzian contact theory is approximated according to a concept by Tanaka (2001, “A New Calculation Method of Hertz Elliptical Contact Pressure,” ASME J. Tribol., 123, pp. 887–889) yielding simple analytical expressions for the elliptical semi-axes, the maximum contact pressure, the mutual approach and the contact spring constant. Several configurations are compared using the exact Hertz theory and the current approximation. The results agree within technical accuracy.

Simulation of Traction Drive Ratio Changes

2000 ◽  
Author(s):  
Z. Zou ◽  
Y. Zhang ◽  
X. Zhang ◽  
W. Tobler
Keyword(s):  
Hertzian Contact ◽  
Contact Theory ◽  
Hydrodynamic Theory ◽  
Traction Drive ◽  
Input And Output ◽  
Piston Displacement ◽  
Simulation Results ◽  
Traction Drives ◽  
Stability And Accuracy ◽  
Hertzian Contact Theory

Abstract In the simulation model presented in this paper, the kinematic characteristics of traction drives are formulated using classical Hertzian contact theory and elasto-hydrodynamic theory. The roller swing motion is governed by an equation derived based on Newton’s Second Law and is coupled to the side slip, torque input and output, as well as ratio variations. A control strategy with feedbacks for both the roller swing and the piston displacement is applied for ratio control based on stability and responsiveness considerations. The model has been implemented systematically in Matlab/Simulink environment. The effectiveness of the ratio control system in terms of stability and accuracy is illustrated by the simulation results included in this paper.

Difference between the ideal and combined spherical joints and its effects on parallel manipulators

2019 ◽  
Vol 234 (5) ◽  
pp. 1112-1129
Author(s):  
Shuai Fan ◽  
Shouwen Fan
Keyword(s):  
Machine Tools ◽  
Parallel Manipulators ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Contact Deformation ◽  
Spherical Joint ◽  
Universal Joint ◽  
Deformation Models ◽  
Hertzian Contact Theory ◽  
The Ideal

When using parallel manipulators as machine tools, the spherical joint has been widely used and replaced by a combination of a universal joint and a rotating unit, but the introduced differences and effects have not been studied in detail. In this paper, an approach to establish the mathematical models of the ideal and combined spherical joints is presented, and the differences between the two spherical joints are given from the perspective of constraints, workspace, clearance, and contact deformation. First, the non-interference workspace of a class universal joint is investigated by using a simple and clear projection method, where the constraint domain and workspace of two spherical joints are proposed. Next, the approximate clearance models of these two spherical joints are analyzed, and the corresponding contact deformation models are also given based on the Hertzian Contact theory. Finally, a 1PU + 3UPS parallel manipulator is used to verify the discrepant effects of two spherical joints on parallel manipulators. If the combined spherical joint is used, the results indicate that the improvement in the workspace is significant, but the drop in stiffness is also evident. Thus, this paper provides a theoretical basis for researchers to use combined spherical joints.

A Systematic Model for the Analysis of Contact, Side Slip and Traction of Toroidal Drives

1999 ◽  
Vol 122 (4) ◽  
pp. 523-528 ◽  
Author(s):  
Y. Zhang ◽  
X. Zhang ◽  
W. Tobler
Keyword(s):  
Traction Force ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Kinematic Parameters ◽  
Traction Drive ◽  
Continuously Variable Transmissions ◽  
Toroidal Traction ◽  
Hertzian Contact Theory ◽  
Slip Force ◽  
Ratio Range

This paper presents a systematic model for the design and analysis of toroidal traction drive continuously variable transmissions (CVT). The contacts between the input disk, the roller and the output disk of the traction drive are formulated using the classical Hertzian contact theory. The traction force and side slip force occurring in CVT operation are modelled based on the elasto-hydrodynammic theory and are correlated to the traction drive geometric and kinematic parameters. The model allows for the quantitative analysis of traction drive operation under various torque inputs and over the desired ratio range. [S1050-0472(00)01004-7]

Extension of Hertzian Theory for Bodies With a Single Coating

2003 ◽  
Author(s):  
Shuangbiao Liu ◽  
Qian Wang
Keyword(s):  
Numerical Solutions ◽  
Layered Materials ◽  
Sufficient Accuracy ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Numerical Analyses ◽  
Convenient Tool ◽  
Homogeneous Materials ◽  
Hertzian Contact Theory ◽  
Single Coating

The Hertzian theory is a convenient tool for analyzing counterformal bodies in mechanical contacts. However, it is limited to homogeneous materials. This paper reports the results from recent research that extends the Hertzian contact theory to layered materials. Numerical analyses are conducted to evaluate the accuracy of the formulas of the extended Hertzian theory, and the comparison with numerical solutions indicates that the formulas have sufficient accuracy.

Reinvestigation into railway wheel-track interaction and suspension damage

2020 ◽  
pp. 095440972093202
Author(s):  
Renfan Luo ◽  
David Vincent
Keyword(s):  
High Speed ◽  
Sensitivity Study ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Fe Model ◽  
Fe Modelling ◽  
Wheel Flat ◽  
The Impact ◽  
Hertzian Contact Theory ◽  
Wheel Track

Without considering either velocity or acceleration effects, the current conventional method presented in literature applies the vertical deflection of a wheel centre caused by a flat defect to the Hertzian contact theory. This method has been numerically and theoretically proved to be inappropriate and can incorrectly predict a higher wheel-rail impact force for a low speed than a high speed. Therefore, under a hypothesis of no wheel bouncing and sliding, two new methods, the velocity-based and the acceleration-based have been proposed. The former method takes the wheel centre deflection change in each computational increment from the Hertzian contact theory while the latter applies the wheel centre acceleration caused by the flat in revolutions to the wheel as a force in dynamic simulation, which interprets the speed effects on impacts precisely. A sensitivity study proves that the velocity-based method is unreliable as opposed to the acceleration-based method. A beam/rigid FE model has also been developed to inspect the wheel-track interaction by performing dynamic analysis in the time domain. It has been found out that the impact responses predicted by the FE analysis and the velocity method are similar and the FE results heavily depend on the compute increment, which implies the FE modelling in ABAQUS may be unreliable for this issue with current applied increments. Finally, the results calculated using the acceleration method have been employed to study the suspension/damper torsional stress caused by a wheel flat. This indicates that a wheel flat may lead to potential fatigue damage if without proper maintenance management.

Impact of Flexible Bent Beam Using Component Mode Techniques

1999 ◽  
Author(s):  
Cristian I. Diaconescu ◽  
Dan B. Marghitu
Keyword(s):  
Power Series ◽  
Elastic Beam ◽  
Point Of View ◽  
Component Mode Synthesis ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Rigid Surface ◽  
Plastic Indentation ◽  
The Impact ◽  
Hertzian Contact Theory

Abstract The Component Mode Synthesis technique is applied to the impact of a flexible curved bar. The mode functions are selected such that the method can be made computationally as simple as possible, without compromising accuracy. From this point of view, a simple power series is selected. Both transversal and axial elastic deflection are considered. To describe the impact between the elastic beam and the rigid surface the classical Hertzian contact theory and elastio-plastic indentation theory are used.

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