A Semianalytical Solution for Normal Contacts Involving a Thin Elastic Layer

2008 ◽  
Author(s):  
E. N. Diaconescu ◽  
M. L. Glovnea
Keyword(s):  
Numerical Methods ◽  
Analytical Solution ◽  
Pressure Distribution ◽  
Layer Thickness ◽  
Contact Area ◽  
Elastic Layer ◽  
Constant Thickness ◽  
Elastic Bodies ◽  
Thin Elastic Layer

Many technical assemblies can be modelled by a constant thickness elastic layer pressed between two elastic bodies. These models are solved up to date either by numerical methods or analytically, when the outer bodies are rigid cylinders. This paper advances a semi-analytical solution for the case the outer bodies are identical elastic paraboloids. It is shown that contact area is elliptical having semi-axes dependent on layer thickness and the pressure distribution is half-ellipsoidal.

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.

The Numerical Methods in Geometric Construction Mapping

2011 ◽  
Vol 490 ◽  
pp. 312-322
Author(s):  
Henryk G. Sabiniak ◽  
Robert Cichowicz
Keyword(s):  
Numerical Methods ◽  
Pressure Distribution ◽  
Constant Thickness ◽  
Contact Lines ◽  
The Finite Element Method ◽  
Geometrical Modelling ◽  
Theory Of Plates ◽  
Worm Gears ◽  
Short Time ◽  
Physical Phenomena

A dynamic development of numerical methods enables even so complicated geometrical modelling as modelling of hypoidal teeth, and in particular of worm teeth. Building on the basis of the finite element method of this type of geometrical mathematical model enables observing and analysing physical phenomena taking place in the teeth, e.g. changes of pressure distribution along the contact lines depending on the phase of meshing for particular cooperating pairs of teeth. Due to limited technical possibilities and mathematical apparatus such analyses were carried out only on the basis of the theory of plates with constant thickness. An unquestionable advantage of such numerical modelling is a short time needed to obtain final results, which enables profound analysis of the transmitted load. The knowledge of course of pressure distribution along the contact lines of particular pairs of intermeshing teeth in worm gears already in the design phase enables taking into consideration in adequate correction or even modification of the working surface of teeth, with the aim to equalise the distribution of pressure.

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 Application of hybrid asymptotic methods and modern software for mathematical models developing for nonlinear dynamics of structures with variables in time parameters

2021 ◽  
pp. 66-70
Author(s):  
S. Homeniuk ◽  
S. Grebenyuk ◽  
D. Gristchak
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Methods ◽  
Nonlinear Systems ◽  
Analytical Solution ◽  
Mathematical Models ◽  
Nonlinear Dynamic ◽  
Numerical Solutions ◽  
Hybrid Approach ◽  
Time Dependent ◽  
Forced Oscillations

The relevance. The aerospace domain requires studies of mathematical models of nonlinear dynamic structures with time-varying parameters. The aim of the work. To obtain an approximate analytical solution of nonlinear forced oscillations of the designed models with time-dependent parameters. The research methods. A hybrid approach based on perturbation methods, phase integrals, Galorkin orthogonalization criterion is used to obtain solutions. Results. Nonlocal investigation of nonlinear systems behavior is done using results of analytical and numerical methods and developed software. Despite the existence of sufficiently powerful numerical software systems, qualitative analysis of nonlinear systems with variable parameters requires improved mathematical models based on effective analytical, including approximate, solutions, which using numerical methods allow to provide a reliable analysis of the studied structures at the stage designing. An approximate solution in analytical form is obtained with constant coefficients that depend on the initial conditions. Conclusions. The approximate analytical results and direct numerical solutions of the basic equation were compared which showed a sufficient correlation of the obtained analytical solution. The proposed algorithm and program for visualization of a nonlinear dynamic process could be implemented in nonlinear dynamics problems of systems with time-dependent parameters.

Layer-Thickness Dependence of Hardness and Local Bucking Behavior in Electrodeposited Ni-Co-Cu/Cu Multilayered Films

2021 ◽  
Vol 1016 ◽  
pp. 170-176
Author(s):  
Yoshihisa Kaneko ◽  
Tomohiro Kubomae ◽  
Naofumi Kawakami ◽  
Hiroyuki Hagiwara ◽  
Makoto Uchida
Keyword(s):  
Layer Thickness ◽  
Local Buckling ◽  
Constant Thickness ◽  
Cross Sectional ◽  
Multilayered Films ◽  
Buckling Behavior ◽  
Vertical Thickness ◽  
Annealed Copper ◽  
Hardness Values ◽  
Compressive Tests

The effect of layer thickness on hardness and buckling behavior was investigated on Ni-Co-Cu/Cu multilayered films. The Ni-Co-Cu/Cu multilayered films were grown on annealed copper substrates by electrodeposition. We fabricated the multilayered films with various layer thicknesses ranging from 10 nm to 1000 nm. First, dependence of Vickers hardness on the Cu layer thickness was investigated. When the Ni-Co-Cu layer had the constant thickness of 75 nm and the Cu layer thickness was smaller than 75 nm, the hardness increased rapidly with decreasing Cu layer thickness. Subsequently, compressive tests were conducted on the multilayered films having the component layers ranging from100 nm to 1000 nm, where the hardness values did not change rapidly with layer thickness. The copper substrates coated with the multilayered films were compressed until 20% strain. From SEM surface observations after the compressive tests, formations of band-like structures having a certain thickness were recognized. Cross-sectional observation revealed that some band-like structures were formed as a result of local buckling of the multilayered film. The vertical thickness of the bank-like structures increased linearly with increasing component layer thickness.

scholarly journals Analytical Solution of System of Volterra Integral Equations Using OHAM

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Muhammad Akbar ◽  
Rashid Nawaz ◽  
Sumbal Ahsan ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Numerical Methods ◽  
Analytical Solution ◽  
Integral Equations ◽  
Function Method ◽  
Auxiliary Function ◽  
Volterra Integral Equations ◽  
Large Parameter ◽  
Reliable Technique ◽  
Present Technique ◽  
Optimal Homotopy Asymptotic Method

In this work, a reliable technique is used for the solution of a system of Volterra integral equations (VIEs), called optimal homotopy asymptotic method (OHAM). The proposed technique is successfully applied for the solution of different problems, and comparison is made with the relaxed Monto Carlo method (RMCM) and hat basis function method (HBFM). The comparisons show that the present technique is more suitable and reliable for the solution of a system of VIEs. The presented technique uses auxiliary function containing auxiliary constants, which control the convergence. Moreover, OHAM does not require discretization like other numerical methods and is also free from small or large parameter.

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