Solution of the Contact Zone Orientation for Normal Elliptical Hertzian Contact

2011 ◽  
Vol 78 (3) ◽  
Author(s):  
Philip P. Garland ◽  
Robert J. Rogers
Keyword(s):  
Analytical Solution ◽  
Contact Zone ◽  
Hertzian Contact ◽  
Stress Distributions ◽  
Friction Forces ◽  
Elastic Bodies ◽  
Closed Form Analytical Solution ◽  
Elliptical Boundary ◽  
Contact Parameters ◽  
Contact Ellipse

Many mechanical designs have parts that come into, or lose, contact with each other. When elastic bodies with second order surface geometries come into contact, the contact patch is expected to be approximately flat and to have an elliptical boundary. Classic Hertzian contact mechanics can be used to model such contacts, but since there is no closed-form analytical solution to predict the major and minor axes of the contact zone ellipse, approximate numerical methods have been developed, some of which are very accurate. Predictions of the mutual approach of the bodies and the contact pressure distribution can then be made. Although the shape of the contact ellipse has been modeled and solved for, to date there has been no solution for the orientation of the contact ellipse with respect to either of the contacting bodies. The contact ellipse orientation is needed in order to model the shear stress distributions that occur when sticking friction forces are developed and separate contact zones of sticking and slipping are expected. Using the results of a numerical solution for the conventional contact parameters, this paper presents an analytical solution of the orientation of the contact ellipse, which is shown to depend only on the curvatures and the relative orientation of the contacting bodies. In order to validate the analytical solution, the results are compared with those from ABAQUS™ finite element simulations for cases of identical bodies and bodies with dissimilar curvatures. The predictions of the contact ellipse orientation angles and the major and minor semi-axes agree very well for all cases considered.

scholarly journals REFINING THE CALCULATION OF THE CAR TRACTION POWER

2019 ◽  
Vol 16 (5) ◽  
pp. 572-579 ◽  
Author(s):  
E. A. Maksimov ◽  
E. P. Chelyabinsk
Keyword(s):  
Elastic Modulus ◽  
Comparative Analysis ◽  
Contact Zone ◽  
Traditional Method ◽  
Traditional Methods ◽  
Friction Forces ◽  
Refined Equation ◽  
Refined Calculation ◽  
Traction Power ◽  
Tangential Friction

Introduction. Traction power of the car is used to determine its traction-speed properties. The purpose of the paper is the calculation refinement of the car traction power.Materials and methods. The authors used the methodology of the refined calculation of the car traction power.Results. The authors carried out the comparative analysis of the refined and traditional methods for calculating traction power. As a result, the authors obtained the refined equation for calculating the traction power, taking into account the elastic modulus, the width of the contact track, the free radius of the wheel, the deflection of the tire and the tangential friction forces in the contact zone. The largest discrepancy between the curve of the vehicle’s traction power calculated by the updated methodology and the curve of the vehicle’s traction power calculated by the traditional method was 26.8%.Discussion and conclusions. The results of the research are useful to specialists of automobile and transport enterprises and masters of universities to compare the traction and speed properties of the various car types.

Analysis of Motion of the Impact-Dry-Friction Pair of Bodies and its Application to the Investigation of the Impact Dampers Dynamics

1999 ◽  
Author(s):  
František Peterka
Keyword(s):  
Analytical Solution ◽  
Numerical Simulations ◽  
Mechanical System ◽  
Relative Motion ◽  
Dry Friction ◽  
Friction Pair ◽  
Strong Nonlinearity ◽  
Friction Forces ◽  
The Impact ◽  
Analysis Of Motion

Abstract The motion with impacts and dry friction forces appears in some mechanical systems as mechanisms with clearances, (e.g., in gearings, pins, slots, guides, valve gears etc.), impact dampers, relays, forming and mailing machines, power pics etc. Such mechanisms include one or more pairs of impacting bodies, which introduce the strong nonlinearity into the system motion. The motion of the general pair of bodies with the both-sides impacts and dry friction forces is assumed (Fig.1). It can be the part of a more complex chain of masses in the mechanical system. Dead zones in the relative motion of bodies can be caused by assumed nonlinearities. The mathematical conditions controlling the numerical simulations or analytical solution of the motion are introduced. The application of this method is explained by the study of the influence of dry friction force on amplitude-frequency characteristics of four types of dynamical and impact dampers with optimised parameters.

Dynamic Interaction of Two Independent SDOF Oscillators Supported by a Flexible Foundation Embedded in a Half-Space: Closed-Form Analytical Solution for Incident Plane SH-Waves

2021 ◽  
pp. 1-24
Author(s):  
Liguo Jin ◽  
Liting Du ◽  
Haiyan Wang
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Half Space ◽  
Strong Interaction ◽  
Rigid Foundation ◽  
Structural Stiffness ◽  
Sh Waves ◽  
Closed Form Analytical Solution ◽  
Flexible Foundation ◽  
Plane Sh Waves

This paper presents a closed-form analytical solution for the dynamic response of two independent SDOF oscillators standing on one flexible foundation embedded in an elastic half-space and excited by plane SH waves. The solution is obtained by the wave function expansion method and is verified by comparison with the results of the special cases of a rigid foundation and the published research result of a flexible foundation. The model is utilized to investigate how the foundation stiffness influences the system response. The results show that there will be a significant interaction between the two independent structures on one flexible foundation and the intensity of the interaction is mainly dependent on foundation stiffness and structural stiffness. For a system with more flexible foundation, strong interaction will exist between the two structures; larger structural stiffness will also lead to a strong interaction between the two structures. When the structural mass and the structural stiffness are all larger, the flexible foundation cannot be treated as a rigid foundation even if the foundation stiffness is many times larger than that of soil. This model may be useful to get insight into the effects of foundation flexibility on the interaction of two independent structures standing on one flexible foundation.

scholarly journals Determination of Wheel-Rail Contact Characteristics by Creating a Special Program for Calculation

2014 ◽  
Vol 10 (3) ◽  
pp. 48-59 ◽  
Author(s):  
Ioan Sebeşan ◽  
Yahia Zakaria
Keyword(s):  
Normal Stress ◽  
Contact Zone ◽  
Experimental Results ◽  
Programming Environment ◽  
Special Program ◽  
Friction Coefficients ◽  
Future Developments ◽  
Working Quality ◽  
Contact Ellipse

Abstract The authors in this paper describe the steps of creating a special program in GUI tool in Matlab. The program is designed to calculate the main properties of wheel-rail contact zone, such as: contact ellipse dimensions, normal stress and friction coefficients. All the relevant equations, which were introduced by different researchers, are firstly presented and modified to be applicable to the programming environment, and then the program was built. In the end, the program working quality is discussed and some expected future developments on this program are suggested. The proposed program can make the comparison between theoretical and experimental results, when they are available, easier and faster.

Sliding Contact Between Dissimilar Elastic Bodies

1988 ◽  
Vol 110 (4) ◽  
pp. 592-596 ◽  
Author(s):  
A. Sackfield ◽  
D. A. Hills
Keyword(s):  
Elastic Constants ◽  
Carrying Capacity ◽  
Sliding Contact ◽  
Hertzian Contact ◽  
Load Carrying Capacity ◽  
Two Dimensional ◽  
Careful Choice ◽  
Elastic Bodies ◽  
Load Carrying ◽  
Two Bodies

An analysis is presented of the stresses induced by sliding between two bodies having different elastic constants. It is assumed that the bodies are plane (i.e., two dimensional), are symmetrical with respect to a line perpendicular to the plane of contact, and are smooth and continuous. It is shown that a careful choice of profile leads to a better load carrying capacity than for a Hertzian contact, but that the severity of the stresses induced is greater than for uncoupled sliding, i.e., where the bodies have similar elastic constants.

An Improved Analytical Model for Deflections of a Circular Multi-Layer Piezoelectric Actuator

2005 ◽  
Author(s):  
Mandar Deshpande ◽  
Laxman Saggere
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Piezoelectric Actuator ◽  
Plate Theory ◽  
Analytical Models ◽  
Sensors And Actuators ◽  
Closed Form Solutions ◽  
Design And Optimization ◽  
Closed Form Analytical Solution ◽  
Model Correlation

Models for simple closed-form analytical solutions for accurately predicting static deflections of circular thin-film piezoelectric microactuators are very useful in design and optimization of a variety of MEMS sensors and actuators utilizing piezoelectric actuators. While closed-form solutions treating actuators with simple geometries such as cantilevers and beams are available, simple analytical models treating circular bending-type actuators commonly used in MEMS applications are generally lacking. This paper presents a closed-form analytical solution for accurately estimating the deflections and the volume displacements of a circular multi-layer piezoelectric actuator under combined voltage and pressure loading. The model for the analytical solution presented in this paper, which is based on classical laminated plate theory, allows for inclusion of multiple layers and non-uniform diameters of various layers in the actuator including bonding and electrode layers, unlike other models previously reported in the literature. The analytical solution presented is validated experimentally as well as through a finite element solution and excellent experiment-model correlation within 1% variation is demonstrated. General guidelines for optimization of circular piezoelectric actuator are also discussed. The utility of the model for design optimization of a multi-layered piezoelectric actuator is demonstrated through a numerical example wherein the dimensions of a test actuator are optimized to improve the displaced volume by three-fold under combined voltage and resisting pressure loads.

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