• International Journal of Railway
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• v.6 no.4
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• pp.148-154
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• 2013

This article has tried to review the maximum contact stresses in the contact area of the wheel and rail as a result of lateral movement of the wheel on rail by taking advantage from Hertz theory. Since wheel movement on rail is accompanied by lateral movement due to wheel profile conisity, so the contact point of wheel and rail is not constant and the contact stresses are therefore changeable in every single moment. Since the shape of rail profile and rail inclination, wheel diameter and the mechanical properties of the wheel and rail are effective on the stresses of contact area, these parameters have been studied by applying Hertz theory. This article aims to calculate the contact stresses in different parts on the wheel surface by using Hertz theory.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.816-821
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• 2005

The cycloid reducer has very high efficiency, high ratios, high stiffness and small size, in comparison with a conventional gear mechanism, which makes it an attractive candidate for limited space and precision application such as industrial robot. There are several publications on analysis and design of the cycloid reducer, however, it was assumed that the contact stiffness of pin rollers and cycloid disk is constant regardless of their contact geometry. Moreover, the torsional stiffness of the cycloid reducer couldn't be calculated due to the assumption. In this paper, we present a new procedure of calculating torsional stiffness of the cycloid reducer using Hertz contact theory. First, conventional force analysis of the cycloid reducer is briefly reviewed. Then, iterative numerical calculation procedure of the contact stiffness is proposed based on the Hertz contact theory where the contact stiffness depends on the contact force. In addition, total torsional stiffness of the cycloid reducer is estimated considering its rolling element bearing stiffness. The torsional stiffness of the cycloid reducer is dominated by the rolling element bearing stiffness since the contact stiffness of the cycloid disk is too large.

• Journal of Industrial Technology
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• v.28 no.A
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• pp.81-88
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• 2008

Generally, Hertz theory is used to analyze the contact problem of two bodies. It is simple derivation of solution in the contact part. And calculation time is short Moreover, it can mean well that many wear occurs relatively. However, material property becomes plastic deformation when large perpendicular pressure acts on a small contact surface product. In this case, Hertz theory is inapplicable. Therefore this thesis carried the finite element analysis in consideration of material elasticitystrain and the shape of the geometric from contact point. And it compared with Hertz theory that change of the contact surface and contact pressure.

• Proceedings of the Korean Nuclear Society Conference
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• 1999.05a
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• pp.75-75
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• 1999

• Proceedings of the KSR Conference
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• 2005.05a
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• pp.409-414
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• 2005

It is difficult to apply the Hertz theory to the wheel-rail contact problem which has the complicated geometric form and plastic deformation. Therefore, we perform the elastic-plastic FE analysis and compare the results with those of Hertz theory. Kalker's simplified theory of rolling contact is used to discretize the contact patches and calculate local traction and slip. The wear volumes are calculated using Archard wear equation.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.9
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• pp.1615-1626
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• 1992

In this study, vibrations and resulting acoustic radiations from an elastic beam impacted by a steel ball were studied theoretically and experimentally. First the transverse vibrations of free-free elastic beams are analysed with modal analysis technique. The impact forces are modeled with the Hertz's theory and the contanct duration is compared with the measured values. Also the calculated beam vibrations are verified with the experimental results. Then the acoustic radiations due to the beam vibration are studied numberically and experimentally. The acousticpressure is calculated assuming the beam has an elliptical cross-section. The predicted acoustic pressure is compared with the measured value. It was found that both the predicted beamvibrations using the Hertz's theory and the estimated acoustic pressure under the assumption of an elliptical cross- section are in very good agreements with the measured values.

• Proceedings of the KSME Conference
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• 2005.11a
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• pp.219.1-219.1
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• 2005

• Journal of KSNVE
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• v.8 no.1
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• pp.132-138
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• 1998

The dynamic response of symmetric cross-ply and angle-ply composite laminated plates under impact loads is investigated using a higher order shear deformation theory. A modified Hertz law is used to predict the impact loads and a four node finite element is used to model the plate. By using a higer order shear deformation theory, the out-of-plane shear stresses, which can be a crucial factor in the failure of composite plates, are determined with significant accuracy. This is accomplished by using a stress recovery technique using the in-plane stresses. The results compared with previous investigations showed good agreement. It can be seen that this method of analyzing impact problems is more efficient than current three dimensional methods in terms of time and expense.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.838-843
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• 2008

Since thickness deformation and lateral deflection often occurs during the collision of flexible bodies, they should be considered simultaneously in the impact analysis. The thickness deformation, however, cannot be considered in beam/shell theory since the thickness is assumed to be constant in the theory. So, solid elements are employed to estimate the thickness deformation. However, the CPU time increases significantly if solid elements are employed. In the present study, a modeling method for the impact analysis of a flexible body employing Hertzian contact theory is presented. The efficiency and the accuracy of the modeling method are discussed with some numerical examples.

• Structural Engineering and Mechanics
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• v.25 no.1
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• pp.1-20
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• 2007

Dynamic behaviors of the contact surface between ball and raceway in a guideway mechanism vary with the applied loads and hence affect the mechanical responses of machine tools. The study aims to investigate the nonlinear characteristics of dynamic behaviors at the rolling contact interface in linear guideway mechanisms. Firstly, analytical method was introduced to understand the contact behaviors based on Hertz contact theory in a point-to-point way. Then, the finite element approach with a three-dimensional surface-to-surface contact model and appropriate contact stiffness was developed to study the dynamic characteristics of such linear guideways. Finally, experiments with modal test were conducted to verify the significance of both the analytical and the numerical results. Results told that the finite element approach may provide significant predictions. The study results also concluded that the current nonlinear models based on Hertz's contact theory may accurately describe the contact characteristic of a linear guideway mechanism. In the modal analysis, it was told that the natural frequencies vary a little with different loading conditions; however, the mode shapes are changed obviously with the magnitude of applied loads. Therefore, the stiffness of contact interface needs to be properly adjusted during simulation which may affect the dynamic characteristics of the machine tools.