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]

Kinematic Analysis and Modeling of Traction Drive CVT

1999 ◽  
Author(s):  
X. Zhang ◽  
W. Tobler ◽  
Y. Zhang
Keyword(s):  
Traction Force ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Hydrodynamic Theory ◽  
Kinematic Parameters ◽  
Traction Drive ◽  
Continuously Variable Transmissions ◽  
Toroidal Traction ◽  
Hertzian Contact Theory ◽  
Slip Force

Abstract 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 classical Hertzian contact theory. The traction force and side slip force occurring in CVT operation are modeled based on elasto-hydrodynamic theory and are correlated to the traction drive geometric and kinematic parameters. The model allows for the quantitative analysis of traction drive operation under specified torque inputs and over the desired ratio range.

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.

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.

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.

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.

Stress Analysis of a Touchdown Bearing Having an Artificial Crack

2017 ◽  
Author(s):  
Neda Neisi ◽  
Eerik Sikanen ◽  
Janne E. Heikkinen ◽  
Jussi Sopanen
Keyword(s):  
Stress Intensity ◽  
High Speed ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Frictional Contacts ◽  
Dynamic Friction Coefficient ◽  
Surface Failure ◽  
Propagation Analysis ◽  
Hertzian Contact Theory

The active magnetic bearings (AMBs) are often the preferred bearing solution in high speed rotating machines. Even though AMBs have numerous advantages in comparison to normal bearings they are sensitive to the power shutdowns. In the absence of electromagnetic field, the rotor collides with touchdown bearing. The high contact forces occurring between the rotor and touchdown bearing might lead to a contact surface failure in the touchdown bearings. In this study, the simulation model has been used to study the stresses of the touchdown bearing with an artificial crack. Flexibility of the rotor is modelled using the finite element method and frictional contacts are defined between the rotor and touchdown bearing. Hertzian contact theory is used to model all internal contacts in the ball bearing type touchdown bearings. This makes it possible to obtain the Hertzian contact stresses in each ball of the touchdown bearing and evaluate the stress intensity factors for a crack propagation analysis. The results show that increase in the dynamic friction coefficient between the rotor and bearing as well as increase in the air gap leads to a higher maximum Hertzian stress. As a result of the higher contact stress the stress intensity factor will increase.

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.

Sign in / Sign up

Export Citation Format

Share Document