• Tribology and Lubricants
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• v.31 no.4
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• pp.177-182
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• 2015

Tapered roller bearings are widely used in equipment where high combined thrust and radial loads are experienced. A certain amount of tilting between the tapered rollers and the races always occurs because of bending moment load conditions and shaft deflection. It is now well understood that a coherent elastohydrodynamic lubrication (EHL) film separates the rollers and races. In spite of extensive study on EHL problems for over half a century, relatively few studies have focused on the finite line contacts problem. This study presents a complete numerical analysis of the effects of roller tilting on the EHL characteristics in a tapered roller bearing. We systematically analyze this highly nonlinear problem using finite differences with fully non-uniform grids and the Newton-Raphson method. Detailed EHL pressure distributions and film shapes are presented under moderate loads and material parameters. A very small roller tilting significantly affects the pressure distributions and film shapes near both ends of the roller. Moreover, the effect of tilting on the EHL characteristics at the small end is much greater than that at the large end. Therefore, in designing optimum profiles for tapered roller bearings, the profile radius should be larger at the small end.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.50 no.9
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• pp.431-437
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• 2001

Since the eddy current problem usually depends on the geometry of the moving conductive sheet and the shape of the pole projection area, there is no general method to find out its analytical solution. The analysis of the eddy current in a rotating disk is performed in the case of time-invariant field to find its analytical solution. As a method to solve the eddy current problem, the concept of the Coulomb charge and image method are proposed with the consideration of the boundary condition. Firstly, the line charge is obtained from the volume charge generated in the rotating disk and Coulomb's law is applied. Secondly, the finite disk radius is considered by introducing an imaginary eddy current to satisfy the boundary condition that the radial component of the eddy current is zero at the edge of the relating disk. Thirdly, the braking torque is calculated by applying Lorentz force law. Finally, the computed braking torque is compared with the measured one As a result, it can be said that the proposed model presents fairly accurate results in a low angular velocity range although a large error is observed as the angular velocity of the disk increases.

• Structural Engineering and Mechanics
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• v.38 no.3
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• pp.361-384
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• 2011

Earlier studies on hollow-circular rubber bearings, all of which are conducted for steel-reinforced bearings, indicate that the hole presence not only decreases the compression modulus of the bearing but also increases the maximum shear strain developing in the bearing due to compression, both of which are basic design parameters also for fiber-reinforced rubber bearings. This paper presents analytical solutions to the compression problem of hollow-circular fiber-reinforced rubber bearings. The problem is handled using the most-recent formulation of the "pressure method". The analytical solutions are, then, used to investigate the effects of reinforcement flexibility and hole presence on bearing's compression modulus and maximum shear strain in the bearing in view of four key parameters: (i) reinforcement extensibility, (ii) hole size, (iii) bearing's shape factor and (iv) rubber compressibility. It is shown that the compression stiffness of a hollow-circular fiber-reinforced bearing may decrease considerably as reinforcement flexibility and/or hole size increases particularly if the shape factor of the bearing is high and rubber compressibility is not negligible. Numerical studies also show that the existence of even a very small hole can increase the maximum shear strain in the bearing significantly, which has to be considered in the design of such annular bearings.

• Geomechanics and Engineering
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• v.18 no.3
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• pp.225-234
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• 2019

A numerical stepwise approach for cavity expansion problem in strain-softening rock or soil mass is investigated, which is compatible with Mohr-Coulomb and generalized Hoek-Brown failure criteria. Based on finite difference method, plastic region is divided into a finite number of concentric rings whose thicknesses are determined internally to satisfy the equilibrium and compatibility equations, the material parameters of the rock or soil mass are assumed to be the same in each ring. For the strain-softening behavior, the strength parameters are assumed to be a linear function of deviatoric plastic strain (${\gamma}p^*$) for each ring. Increments of stress and strain for each ring are calculated with the finite difference method. Assumptions of large-strain for soil mass and small-strain for rock mass are adopted, respectively. A new numerical stepwise approach for limited pressure and plastic radius are obtained. Comparisons are conducted to validate the correctness of the proposed approach with Vesic's solution (1972). The results show that the perfectly elasto-plastic model may underestimate the displacement and stresses in cavity expansion than strain-softening coefficient considered. The results of limit expansion pressure based on the generalised H-B failure criterion are less than those obtained based on the M-C failure criterion.

• Structural Engineering and Mechanics
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• v.90 no.4
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• pp.357-370
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• 2024

Due to the fact that the mechanism of the effects of temperature and initial geometric imperfection on low-velocity impact problem of axially moving plates is not yet clear, the present paper is to fill the gap. In the present paper, the nonlinear dynamic behavior of axially moving imperfect graphene platelet reinforced metal foams (GPLRMF) plates subjected to lowvelocity impact in thermal environment is analyzed. The equivalent physical parameters of GPLRMF plates are estimated based on the Halpin-Tsai equation and the mixing rule. Combining Kirchhoff plate theory and the modified nonlinear Hertz contact theory, the nonlinear governing equations of GPLRMF plates are derived. Under the condition of simply supported boundary, the nonlinear control equation is discretized with the help of Gallekin method. The correctness of the proposed model is verified by comparison with the existing results. Finally, the time history curves of contact force and transverse center displacement are obtained by using the fourth order Runge-Kutta method. Through detailed parameter research, the effects of graphene platelet (GPL) distribution mode, foam distribution mode, GPL weight fraction, foam coefficient, axial moving speed, prestressing force, temperature changes, damping coefficient, initial geometric defect, radius and initial velocity of the impactor on the nonlinear impact problem are explored. The results indicate that temperature changes and initial geometric imperfections have significant impacts.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.6
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• pp.1001-1004
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• 1987

In this study mathematical properties of variational solution and solution of the boundary integral equation of the linear elasticity problem are studied. It is first reviewed that a variational solution for the three-dimensional linear elasticity problem exists in the Sobolev space [ $H^{1}$(.OMEGA.)]$^{3}$ and, then, it is shown that a unique solution of the boundary integral equation is identical to the variational solution in [ $H^{1}$(.OMEGA.)]$^{3}$. To represent the boundary integral equation, the Green's formula in the Sobolev space is utilized on the solution domain excluding a ball, with small radius .rho., centered at the point where the point load is applied. By letting .rho. tend to zero, it is shown that, for the linear elasticity problem, boundary integral equation is valid for the variational solution. From this fact, one can obtain a numerical approximatiion of the variational solution by the boundary element method even when the classical solution does not exist.exist.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.14 no.1
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• pp.8-18
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• 2002

In this paper, wave energy absorption of OWC(oscillating water column) device is analyzed. The analytic model consists of a partially immersed circular vertical cylinder open at its end and an air turbine connected with the air chamber. The boundary value problem is decomposed into scattering problem related to scattering by an incident wave in the absence of a pressure variation and radiation problem describing the flow due to an oscillating pressure in the absence of an incident wave. By invoking the continuity of an air flow inside the chamber, the oscillating pressure in a chamber is derived. With oscillating pressure, the mean power absorbed by OWC device and the capture width are obtained. In numerical calculation, the induced volume flux across the internal free surface of the chamber in the scattering and radiation problem and the maximum capture width are compared with various design parameters such as radius and submergence depth of chamber and wave conditions. The maximum capture width obtained by choosing the optimal value of turbine constant occurs at the first resonant mode (Helmholtz mode) among the natural frequencies of a circular cylinder chamber.

• Advances in nano research
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• v.15 no.3
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• pp.215-224
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• 2023

Nonlinearity plays an important role in control systems and the application of design. For this reason, in addition to linear vibrations, nonlinear vibrations of the stepped nanobeam are also discussed in this manuscript. This study investigated the vibrations of stepped nanobeams according to Eringen's nonlocal elasticity theory. Eringen's nonlocal elasticity theory was used to capture the nanoscale effect. The nanoscale stepped Euler Bernoulli beam is considered. The equations of motion representing the motion of the beam are found by Hamilton's principle. The equations were subjected to nondimensionalization to make them independent of the dimensions and physical structure of the material. The equations of motion were found using the multi-time scale method, which is one of the approximate solution methods, perturbation methods. The first section of the series obtained from the perturbation solution represents a linear problem. The linear problem's natural frequencies are found for the simple-simple boundary condition. The second-order part of the perturbation solution is the nonlinear terms and is used as corrections to the linear problem. The system's amplitude and phase modulation equations are found in the results part of the problem. Nonlinear frequency-amplitude, and external frequency-amplitude relationships are discussed. The location of the step, the radius ratios of the steps, and the changes of the small-scale parameter of the theory were investigated and their effects on nonlinear vibrations under simple-simple boundary conditions were observed by making comparisons. The results are presented via tables and graphs. The current beam model can assist in designing and fabricating integrated such as nano-sensors and nano-actuators.

• Tribology and Lubricants
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• v.6 no.1
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• pp.99-107
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• 1990

Most of machines and structures contain the elements which contact each other directly. When these elements subjected to vibration or repeated load, local relative movement occurs between the elements in contact which results in, a kind of wear. In order to know the factors which govern fretting, we have to analyze the phenomenon of microslip which causes fretting by using a general and efficient method from a viewpoint of contact mechanics. Based on the results of analysis, it is necessary to propose the way of minizing fretting which is one of the most significant surface failure. In this report, a general and efficient algorithm is applied to analyze the contact problem of the bolted joint, which is one of the typical elements damaged by fretting, with ratios of plate thickness, the ratios of Young's moduli, the ratios of the plate thickness to bolt radius varied. Finally, the ways of minizing fretting for the boked joint are suggested.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.175-178
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• 1997

This study was carried out to obtain an analytical expression for the specifications of the Stewart Platform that minimize the maximum force acting on the hydraulic cylinder. The position and orientation of the platform were calculated by means of the inverse kinematic analysis. The maximum force to be exerted on a cylinder was calculated using the Newton's second law for the case when the platform is moved along a horizontal axis with 0.6 g, the maximum translational acceleration possible. This paper suggests a mathematical model to minimize the maximum actuating force using radius and angle ratios as design variables. Finally, a fuzzy set for the minimum actuating force is proposed for this dynamic optimal design problem.