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.

Frictional Analysis of MoS2 Coated Ball Bearings: A Three-Dimensional Finite Element Analysis

1997 ◽  
Vol 119 (4) ◽  
pp. 754-763 ◽  
Author(s):  
M. R. Lovell ◽  
M. M. Khonsari ◽  
R. D. Marangoni
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Experimental Tests ◽  
Element Model ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Element Analysis ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Hertzian Contact Theory

A brief review of finite element contact and friction theory is presented for low-speed bearing operations. A three-dimensional finite element model is developed to realistically characterize the friction experienced by a coated ball bearing element. The finite elements results, which are obtained for various normal loads and ball materials, are verified using Hertzian contact theory and previous experimental tests performed by the authors. From the results, general trends for the frictional behavior of coated bearing surfaces are established and implications to the field of controls, as applied to precision positioning and tracking instruments are discussed.

A New High-Precision Bearing Measuring System for Non-Repetitive Run-Out (NRRO)

2012 ◽  
Author(s):  
Zhaohui Yang ◽  
Jun Hong ◽  
Jinhua Zhang ◽  
Michael Yu Wang ◽  
Jian Liu
Keyword(s):  
High Precision ◽  
Axial Direction ◽  
Measuring System ◽  
Air Bearing ◽  
Angular Contact Ball Bearing ◽  
Displacement Sensors ◽  
Geometrical Errors ◽  
Ultra Precision ◽  
Spindle Vibration

As ultra-precision index of high-precision ball bearings, the value of non-repetitive run-out (NRRO) directly influences the rotation accuracy in complex mechanical system. Reducing NRRO contributes to improve the quality of manufacturing in machining tools. This paper developed a new high-precision bearing measuring system to analyze the NRRO of an angular contact ball bearing caused by geometrical errors of bearings’ parts. The characteristic of measuring system as follows: (1) The air-bearing spindle that is drive by servomotor is used to support the test bearing to ensure the system accuracy and continuously variable; (2) The air-bearing of flat is used to load of non-contact on the test bearing along axial direction for simulation conditions of bearings; (3) The multi-capacitive displacement sensors are used to measure run-out of the air-bearing spindle vibration of the radial direction, then the run-out is separated as system error; (4) The NRRO of axial and radial directions caused by geometrical errors of the rings raceways and the balls could be analyzed.

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.

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.

scholarly journals The three-dimensional lattice as an architectural space

2018 ◽  
Vol 212 ◽  
pp. 04005
Author(s):  
Andrey Bolshakov
Keyword(s):  
Three Dimensional ◽  
Human Movement ◽  
Theoretical Understanding ◽  
Architectural Space ◽  
Spatial Lattice ◽  
Spatial Grids ◽  
Relationship Of ◽  
The Relationship ◽  
Main Material

Space is the main material with which the architect works. The space organized by the means of architecture is an art environment for the life of society. With many aspects of the organization of space, which are studied in the literature, the problem of their assembly and integration remains unsolved. The paper proposes a method of assembling spatial representations in architecture-the correlation of the spatial lattice and the factors of its form-formation, considered in the system, i.e. together. The approach is that in a broad overview of the world architecture, both in its theory and in practice, from historical to modern, examples of modification of spatial grids under the influence of one or a group of dominant factors are revealed. As a result, provisions on the relationship of the geometry of spatial grids with the following factors have been revealed: publicity and privacy; architectonics, the influence of the lattice on the differentiation of the streams of human movement; the architecture’s ability to carry a message; navigation properties, evaluation of connectivity and centrality of places in the spatial lattice; evaluation of the quality of the composition through the identification of ways of order and randomness in the elements of the spatial lattice. The results of the work can be used both for theoretical understanding of the architectural space in the study and design of architecture, and in architectural education.

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.

scholarly journals Dynamic Model of Planetary Roller Screw Mechanism with Considering Torsional Degree of Freedom

2020 ◽  
Vol 306 ◽  
pp. 01003
Author(s):  
Linping Wu ◽  
Shangjun Ma ◽  
Qi Wan ◽  
Geng Liu
Keyword(s):  
Dynamic Model ◽  
Mechanical Design ◽  
Relative Displacement ◽  
Hertzian Contact ◽  
Torsional Stiffness ◽  
Roller Screw ◽  
Mode Characteristics ◽  
Screw Mechanism ◽  
The Relationship ◽  
Hertzian Contact Theory

To predict accurately the dynamics performance of planetary roller screw mechanism, it is necessary to establish its streamline and engineering-compliant dynamic model, which is the basis of mechanical design and precision control of the system. In this paper, the relative displacement between roller and ring gear along the line of action is deduced and the relationship between nature frequencies and the number of rollers is discussed. Considering the torsional stiffness of all components and the thread mesh stiffness based on the Hertzian contact theory, the purely torsional model for planetary roller screw mechanism is presented to reveal the natural frequencies and vibration mode characteristics of the system. The results show that the natural properties of undamped system in planetary roller screw mechanism are mainly reflected by two typical vibration modes: rotational mode and roller mode.

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