scholarly journals Improved Pressure Distribution in Elliptic Elastic Contacts between High-Order Surfaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Marilena Glovnea ◽  
Sergiu Spinu ◽  
Emanuel Diaconescu
Keyword(s):  
Pressure Distribution ◽  
Contact Area ◽  
Recurrence Relations ◽  
High Order ◽  
Central Pressure ◽  
Contact Center ◽  
Eighth Order ◽  
Uniform Current ◽  
Derivatives Of ◽  
Contact Parameters

The improvement of mechanical contacts or microcontacts seeks a nearly uniform current density over most of contact area. When microtopography is homogeneous, this aim is achieved if nominal shape of contacting surfaces yields a nearly uniform central pressure which decreases monotonously to zero in contour points. These authors derived recently this shape for circular contacts by employing high-order surfaces. This paper extends this result to elliptical contacts. Some results are used to this end, derived for elliptical elastic contacts between high-order surfaces. As homogeneous high order surfaces lead to a highly nonuniform pressure distribution, central pressure is flattened by making the first derivatives of pressure vanish in contact center. Then, the contacts between fourth, sixth, and eighth, order surfaces are analyzed and recurrence relations for pressure distribution and contact parameters are proposed.

Flat Central Pressure in Circular Elastic Contacts Between High Order Surfaces

2005 ◽  
Author(s):  
Emanuel Diaconescu ◽  
Marilena Glovnea
Keyword(s):  
Pressure Distribution ◽  
Electrical Contacts ◽  
High Order ◽  
Sixth Order ◽  
Central Pressure ◽  
Thrust Bearings ◽  
Revolution Surfaces ◽  
Bounding Surfaces

High order revolution surfaces are often used in electrical contacts/micro-contacts or in miniature thrust bearings. This paper advances general contact formulae for these bounding surfaces. In a particular case, these relations yield known Hertz pressure distribution and contact elements. Then, the contacts between fourth and sixth order surfaces are analyzed.

Elliptical Contact Area Between Elastic Bodies Bounded by High Order Surfaces

2005 ◽  
Author(s):  
Emanuel N. Diaconescu
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Fourth Order ◽  
Contact Area ◽  
High Order ◽  
Normal Displacement ◽  
Hertz Theory ◽  
Elastic Bodies ◽  
Surface Normal ◽  
Elliptical Contact

Hertz theory fails when contacting surfaces are expressed by a sum of even polynomials of higher powers than two. An alternative analytical solution implies the knowledge of contact area. In the case of elliptical domains, there are some published proposals for the correlation between pressure distribution and surface normal displacement. This paper identifies the class of high order surfaces which lead to elliptical contact domains and solves a contact between fourth order surfaces.

scholarly journals Ball Convergence of an Efficient Eighth Order Iterative Method Under Weak Conditions

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 260 ◽  
Author(s):  
Janak Sharma ◽  
Ioannis Argyros ◽  
Sunil Kumar
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Higher Order ◽  
High Order ◽  
Convergence Order ◽  
Eighth Order ◽  
First Derivative ◽  
Ball Convergence ◽  
Derivatives Of

The convergence order of numerous iterative methods is obtained using derivatives of a higher order, although these derivatives are not involved in the methods. Therefore, these methods cannot be used to solve equations with functions that do not have such high-order derivatives, since their convergence is not guaranteed. The convergence in this paper is shown, relying only on the first derivative. That is how we expand the applicability of some popular methods.

A General Solution for Optimized Circular Contacts

2004 ◽  
Author(s):  
Marilena Glovnea ◽  
Emanuel Diaconescu
Keyword(s):  
General Solution ◽  
Pressure Distribution ◽  
Edge Effects ◽  
Contact Area ◽  
Front Surface ◽  
Electrical Contacts ◽  
Machine Design ◽  
Central Pressure ◽  
Uniform Pressure ◽  
Optimum Pressure

Many classical applications in machine design and recent ones in the field of electrical contacts or micro-contacts involve surface circular contacts which show important edge effects. To optimize these contacts, a uniform pressure distribution must be generated over an important part of contact area. This requires a specifically profiled front surface. Previously, these authors proposed a solution based on an optimum pressure distribution. This leads numerically to a punch profile which is approximated by a polynomial. The pressure generating this polynomial profile is found and compared to initial proposal. Recent investigations establish a correspondence between a polynomial punch surface and generated pressure. Starting from this correspondence, a new general approach is offered. The same optimum pressure as previously is accepted. Its profile is approximated by a function advanced in the paper. This function yields directly an even polynomial punch profile. Formulae for central pressure and normal approach are derived.

Measurement and Visualization of the Contact Pressure Distribution of Rubber Disks and Tires

1995 ◽  
Vol 23 (4) ◽  
pp. 238-255 ◽  
Author(s):  
E. H. Sakai
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Contact Area ◽  
Light Absorption ◽  
Lateral Force ◽  
Contact Pressure Distribution ◽  
High Definition ◽  
The Road ◽  
Close Relationship ◽  
Processing Techniques

Abstract The contact conditions of a tire with the road surface have a close relationship to various properties of the tire and are among the most important characteristics in evaluating the performance of the tire. In this research, a new measurement device was developed that allows the contact stress distribution to be quantified and visualized. The measuring principle of this device is that the light absorption at the interface between an optical prism and an evenly ground or worn rubber surface is a function of contact pressure. The light absorption can be measured at a number of points on the surface to obtain the pressure distribution. Using this device, the contact pressure distribution of a rubber disk loaded against a plate was measured. It was found that the pressure distribution was not flat but varied greatly depending upon the height and diameter of the rubber disk. The variation can be explained by a “spring” effect, a “liquid” effect, and an “edge” effect of the rubber disk. Next, the measurement and image processing techniques were applied to a loaded tire. A very high definition image was obtained that displayed the true contact area, the shape of the area, and the pressure distribution from which irregular wear was easily detected. Finally, the deformation of the contact area and changes in the pressure distribution in the tread rubber block were measured when a lateral force was applied to the loaded tire.

A method for tire wet grip performance evaluation based on grounding characteristics

2021 ◽  
pp. 095440702110158
Author(s):  
Chen Liang ◽  
Maoqing Shan ◽  
Guolin Wang ◽  
Daqian Zhu ◽  
Xingpeng Chen
Keyword(s):  
Pressure Distribution ◽  
Contact Area ◽  
Central Area ◽  
Principal Component ◽  
Area Ratio ◽  
Width Ratio ◽  
Characteristic Parameters ◽  
Radial Tire ◽  
Optical Test ◽  
Wet Grip

The wet grip performance of tire is one of the important performances affecting vehicle safety. The steering, acceleration, and braking of the vehicle are directly affected by the grounding characteristics between the radial tire and the ground. In order to study the influence of grounding characteristics of the tire on wet grip performance, ten 205/55R16 tires produced by different manufacturers were selected and tested. The grounding characteristics of the tires were tested using an optical test rig for tire grounding pressure distribution, considering inflation pressure distribution, load and wheel alignment. The tire-road contact area was subdivided into five parts, and 69 parameters were used to describe the grounding characteristics. A software was proposed to process the test results automatically, and 69 grounding characteristic parameters of each tire were obtained. Correlation analysis on tire wet grip performance and grounding characteristics was used for selecting the principal parameters. Finally, eight grounding characteristic parameters related to tire wet grip performance was obtained. Among them are five grounding characteristic parameters (central area rectangle ratio, central area width, internal shoulder length-to-width ratio, external and internal shoulder contact area ratio, external and internal shoulder impression area ratio) which have high correlation to tire wet grip performance, and three grounding characteristic parameters (external shoulder width, external shoulder length-to-width ratio, external and internal shoulder width ratio) which have low correlation to the wet grip performance of the tire. The principal component analysis method was used to analyze the highly correlated grounding characteristic parameters, and the regression equation for evaluating tire wet grip performance was fitted. The comparison of experimental and fitted values show that the errors are within 4%. The result demonstrates that, the method for evaluating wet grip performance of the radial tire through tire-road grounding characteristics was achieved.

scholarly journals New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
W. M. Abd-Elhameed
Keyword(s):  
Galerkin Method ◽  
Boundary Value Problems ◽  
Chebyshev Polynomials ◽  
Hypergeometric Functions ◽  
Jacobi Polynomials ◽  
Boundary Value ◽  
High Order ◽  
Sixth Order ◽  
Special Cases ◽  
Derivatives Of

This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Chebyshev polynomials are deduced as special cases. Some new reduction formulae for summing some terminating hypergeometric functions of unit argument are also deduced. As an application, and with the aid of the new introduced derivatives formulae, an algorithm for solving special sixth-order boundary value problems are implemented with the aid of applying Galerkin method. A numerical example is presented hoping to ascertain the validity and the applicability of the proposed algorithms.

scholarly journals On accurate high-order numerical derivatives computations for quantum chemistry purposes

2018 ◽  
Keyword(s):  
Quantum Chemistry ◽  
Finite Field ◽  
Numerical Differentiation ◽  
Field Method ◽  
High Order ◽  
Parameter Choice ◽  
Derivatives Of ◽  
Finite Field Method ◽  
Account Electron

Various molecular parameters in quantum chemistry could be computed as derivatives of energy over different arguments. Unfortunately, it is quite complicated to obtain analytical expression for characteristics that are of interest in the framework of methods that account electron correlation. Especially it relates to the coupled cluster (CC) theory. In such cases, numerical differentiation comes to rescue. This approach, like any other numerical method has empirical parameters and restrictions that require investigation. Current work is called to clarify the details of Finite-Field method usage for high-order derivatives calculation in CC approaches. General approach to the parameter choice and corresponding recommendations about numerical steadiness verification are proposed. As an example of Finite-Field approach implementation characterization of optical properties of fullerene passing process through the aperture of carbon nanotorus is given.

Sign in / Sign up

Export Citation Format

Share Document